Statistical analysis

Litter decomposition

Source code and data found at https://github.com/maRce10/litter_decomposition_EFFEX

Purpose

• Evaluate role of nutrient availability on litter decomposition

 

cols <- viridis(10, alpha = 0.7)
fill_color <- viridis(10)[7]

# brms models
chains <- 4
iters <- 40000
prior <- c(prior(normal(0, 10), "b"), prior(normal(0, 50), "Intercept"),
    prior(student_t(3, 0, 20), "sd"))

# set ggplot2 them
ggplot2::theme_set(theme_classic(base_size = 20))


# standard error
se <- function(x) sd(x)/sqrt(length(x))

1 Site characteristics

soil <- read.csv("./data/raw/soils_effex.csv")

preds <- names(soil)[7:17]

soil$pool.n <- factor(soil$pool.n)

levels(soil$pool.n) <- c("no.n", "n")

for (i in preds) {
    form <- as.formula(paste(i, "~ pool.n + pool.p"))
    print(i)

    mod <- brm(form, data = soil, chains = chains, family = gaussian(),
        iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
        cores = chains, prior = c(prior(normal(0, 10), "b"), prior(normal(0,
            50), "Intercept")), file = paste0("./data/processed/",
            i, "_pooled_model"), file_refit = "on_change")
}

preds <- names(soil)[7:17]

for (i in preds) {
    extended_summary(read.file = paste0("./data/processed/", i, "_pooled_model.rds"),
        gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
        remove.intercepts = TRUE)
}

1.1 ph.h2o_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	ph.h2o ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	57373.74	48309	1664004957

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.084	-0.006	0.175	1	59038.57	48309.0
pool.pp	0.104	0.015	0.194	1	57373.74	48318.2

1.2 resin.p_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	resin.p ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 30.9)	40000	4	1	20000	0 (0%)	0	57961.13	52214.16	1531674567

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	1.930	-12.400	16.063	1	64784.65	53121.93
pool.pp	16.442	0.626	31.023	1	57961.13	52214.16

1.3 resin.p.no.outlier_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	resin.p.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 27)	40000	4	1	20000	0 (0%)	0	44847.3	46327.93	2096696539

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.203	-13.264	13.647	1	59378.99	52345.57
pool.pp	21.152	5.045	35.404	1	44847.30	46327.93

1.4 tc.g.kg.18_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	tc.g.kg.18 ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 4.5)	40000	4	1	20000	0 (0%)	0	63121.58	49927.59	1374186359

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-2.342	-6.678	2.002	1	63521.49	49927.59
pool.pp	0.285	-4.121	4.627	1	63121.58	50046.02

1.5 tn.g.kg.18_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	tn.g.kg.18 ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	58531.45	46374.4	772312416

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.150	-0.565	0.267	1	59926.93	49974.06
pool.pp	0.026	-0.392	0.440	1	58531.45	46374.40

1.6 tp.g.kg.18_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	tp.g.kg.18 ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 565.6)	40000	4	1	20000	0 (0%)	0	68442.12	53031.23	532966702

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.003	-19.623	19.494	1	68442.12	53031.23
pool.pp	0.045	-19.340	19.697	1	69481.22	54683.43

1.7 tp.g.kg.18.no.outlier_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	tp.g.kg.18.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 478.9)	40000	4	1	20000	0 (0%)	0	69342.37	53547.36	1716433649

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.075	-19.547	19.574	1	69342.37	53547.36
pool.pp	0.078	-19.538	19.763	1	70066.34	56200.05

1.8 CN_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	CN ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	55930.11	48759.38	675162061

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.157	-0.633	0.318	1	55930.11	48759.38
pool.pp	-0.015	-0.488	0.459	1	58599.54	50110.82

1.9 CP.no.outlier_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	CP.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 10.7)	40000	4	1	20000	0 (0%)	0	62823.22	49458.11	257447415

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-2.136	-9.002	4.745	1	62823.22	49552.82
pool.pp	-5.966	-12.841	1.029	1	63184.44	49458.11

1.10 NP.no.outlier_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	NP.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	59651.87	47775.52	2143149156

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.175	-0.861	0.508	1	62165.12	50442.73
pool.pp	-0.593	-1.292	0.105	1	59651.87	47775.52

1.11 litter.mg.C.ha.yr_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	litter.mg.C.ha.yr ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	56795.19	48364.42	308107221

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.420	-0.936	1.779	1	56795.19	49532.70
pool.pp	0.235	-1.112	1.568	1	57467.82	48364.42

1.12 Microbial CNP

soil_master <- read.csv("./data/raw/strimastersoils.csv")

2 Nutrient change

2.1 Nitrogen

Content

nutr <- read.csv("./data/raw/litter-nutrients-mas.csv")

nutr$plot.f <- as.factor(nutr$plot)

nutr$days.sc <- scale(nutr$days)

nutr$litter.n.content.prop.initial <- nutr$litter.n.content.perc.initial/100

nutr$litter.n.content.prop.initial <- ifelse(nutr$litter.n.content.prop.initial >=
    1, 0.99999, nutr$litter.n.content.prop.initial)

# remove plot 9
sub.nutr <- nutr[nutr$plot != 9, ]

agg_n <- aggregate(litter.n.content.perc.initial ~ colecta + treat +
    days, nutr, mean)

agg_n$sd <- aggregate(litter.n.content.perc.initial ~ colecta + treat +
    days, nutr, sd)$litter.n.content.perc.initial

agg_n$se <- aggregate(litter.n.content.perc.initial ~ colecta + treat +
    days, nutr, se)$litter.n.content.perc.initial

agg_n$treat <- factor(agg_n$treat, levels = c("C", "N", "P", "NP"))

pd <- position_dodge(15)

ggplot(agg_n, aes(x = days, y = litter.n.content.perc.initial, color = treat)) +
    geom_point(size = 2, position = pd) + geom_errorbar(aes(ymax = litter.n.content.perc.initial +
    se, ymin = litter.n.content.perc.initial - se), width = 0, position = pd) +
    geom_line(size = 1.2, position = pd) + scale_color_viridis_d(alpha = 0.5) +
    labs(x = "Time (days)", y = "Litter N content (% initial)", color = "Treatment") +
    scale_x_continuous(breaks = unique(agg_n$days), labels = unique(agg_n$days)) +
    theme(legend.position = c(0.9, 0.8))

ggsave("./output/Litter_N_content.tiff", dpi = 300)

Download image

fit.n <- brm(litter.n.content.prop.initial ~ treat * days.sc + (1 |
    plot.f), data = nutr, chains = chains, cores = chains, family = Beta(link = "logit"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    prior = prior, file = "./data/processed/litter.n.content.rem_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/litter.n.content.rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.2 litter.n.content.rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	litter.n.content.prop.initial ~ treat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	16887.3	31642.83	1667653932

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
treatN	-1.627	-3.063	-0.482	1	16887.30	31642.83
treatNP	-0.013	-1.119	1.095	1	26557.10	35114.04
treatP	-0.021	-1.138	1.085	1	27450.49	35309.69
days.sc	-0.583	-0.919	-0.276	1	31261.91	40822.98
treatN:days.sc	-0.394	-0.836	0.058	1	37286.64	47352.96
treatNP:days.sc	0.039	-0.375	0.459	1	39912.37	49646.56
treatP:days.sc	0.042	-0.375	0.464	1	38791.04	49342.65

Concentration

agg_conc_n <- aggregate(perc.n ~ colecta + treat + days, nutr, mean)

agg_conc_n$sd <- aggregate(perc.n ~ colecta + treat + days, nutr,
    sd)$perc.n

agg_conc_n$se <- aggregate(perc.n ~ colecta + treat + days, nutr,
    se)$perc.n

agg_conc_n$treat <- factor(agg_conc_n$treat, levels = c("C", "N",
    "P", "NP"))

pd <- position_dodge(15)

ggplot(agg_conc_n, aes(x = days, y = perc.n, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = perc.n + se, ymin = perc.n -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5) + labs(x = "Time (days)", y = "Litter N concentration (%)",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_conc_n$days),
    labels = unique(agg_conc_n$days)) + theme(legend.position = c(0.3,
    0.8))

ggsave("./output/Litter_N_concentration.tiff", dpi = 300)

Download image

nutr$prop.n <- nutr$perc.n/100

fit.perc.n <- brm(prop.n ~ treat * days.sc + (1 | plot.f), data = nutr,
    chains = chains, core = chains, family = Beta(link = "logit"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    prior = prior, file = "./data/processed/litter.n.perc_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/litter.n.perc_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.3 litter.n.perc_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.n ~ treat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	36167.17	48007.43	129583210

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
treatN	-0.093	-0.228	0.040	1	60646.74	58903.66
treatNP	-0.049	-0.182	0.082	1	59674.00	59089.37
treatP	-0.023	-0.154	0.109	1	58600.92	57777.26
days.sc	0.134	0.045	0.222	1	36167.17	48007.43
treatN:days.sc	-0.076	-0.197	0.045	1	46890.95	55436.18
treatNP:days.sc	-0.031	-0.154	0.092	1	46425.46	55967.33
treatP:days.sc	-0.012	-0.134	0.111	1	46558.85	57029.65

Proportion N

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")

sub.nutr$prop.n <- sub.nutr$perc.n/100

sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")

fit_np_treat_by_rem_leave <- brm(prop.n ~ pool.n * days.sc + pool.p *
    days.sc + (1 | plot), data = sub.nutr, chains = chains, iter = iters,
    family = Beta(link = "logit"), control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/n_perc_by_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/n_perc_by_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.4 n_perc_by_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.n ~ pool.n * days.sc + pool.p * days.sc + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	77764.23	59163.96	915417491

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.070	-0.028	0.167	1	101379.00	59163.96
days.sc	0.069	-0.006	0.143	1	77764.23	60522.39
pool.pp	0.022	-0.077	0.120	1	102860.49	59576.53
pool.nn:days.sc	0.051	-0.039	0.141	1	99083.06	61667.86
days.sc:pool.pp	0.022	-0.066	0.112	1	95117.85	59856.35

Content N

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")

sub.nutr$prop.n <- sub.nutr$perc.n/100

sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")



fit_np_treat_by_rem_leave <- brm(litter.n.content.prop.initial ~ pool.n *
    days.sc + pool.p * days.sc + (1 | plot), data = sub.nutr, chains = chains,
    family = Beta(link = "logit"), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/n_content_by_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/n_content_by_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.5 n_content_by_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	litter.n.content.prop.initial ~ pool.n * days.sc + pool.p * days.sc + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	16821.19	27214.59	1616033078

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.748	0.036	1.690	1	18161.65	28858.56
days.sc	-0.869	-1.146	-0.598	1	49509.94	53142.84
pool.pp	0.763	0.045	1.724	1	16821.19	27214.59
pool.nn:days.sc	0.130	-0.203	0.457	1	52482.79	53569.79
days.sc:pool.pp	0.201	-0.130	0.526	1	48625.91	54786.25

2.6 Phosphorus

Content

nutr$litter.p.content.prop.initial <- nutr$litter.p.content.perc.initial/100

# excluding plot 9
agg_p <- aggregate(litter.p.content.perc.initial ~ colecta + treat +
    days, sub.nutr, mean)

agg_p$sd <- aggregate(litter.p.content.perc.initial ~ colecta + treat +
    days, sub.nutr, sd)$litter.p.content.perc.initial

agg_p$se <- aggregate(litter.p.content.perc.initial ~ colecta + treat +
    days, sub.nutr, se)$litter.p.content.perc.initial


agg_p$treat <- factor(agg_p$treat, levels = c("C", "N", "P", "NP"))


pd <- position_dodge(15)

ggplot(agg_p, aes(x = days, y = litter.p.content.perc.initial, color = treat)) +
    geom_point(size = 2, position = pd) + geom_errorbar(aes(ymax = litter.p.content.perc.initial +
    se, ymin = litter.p.content.perc.initial - se), width = 0, position = pd) +
    geom_line(size = 1.2, position = pd) + scale_color_viridis_d(alpha = 0.5) +
    labs(x = "Time (days)", y = "Litter P content (% initial)", color = "Treatment") +
    scale_x_continuous(breaks = unique(agg_p$days), labels = unique(agg_p$days)) +
    theme(legend.position = c(0.9, 0.8))

ggsave("./output/Litter_P_content.tiff", dpi = 300)

Download image

fit.p <- brm(litter.p.content.prop.initial ~ treat * days.sc + (1 |
    plot.f), data = nutr[nutr$litter.p.content.prop.initial < 1, ],
    chains = chains, prior = prior, cores = chains, iter = iters,
    family = Beta(link = "logit"), control = list(adapt_delta = 0.99,
        max_treedepth = 15), file = "./data/processed/litter.p.content.rem_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/litter.p.content.rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.7 litter.p.content.rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	litter.p.content.prop.initial ~ treat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	31950.41	37831.69	915208762

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
treatN	-0.430	-1.067	0.189	1	33103.34	40082.39
treatNP	0.006	-0.623	0.619	1	31950.41	38576.21
treatP	0.405	-0.212	1.059	1	32589.88	37831.69
days.sc	-0.625	-0.915	-0.353	1	35031.81	44577.87
treatN:days.sc	-0.053	-0.448	0.344	1	43834.54	52654.69
treatNP:days.sc	0.131	-0.241	0.505	1	41935.57	51406.50
treatP:days.sc	-0.009	-0.409	0.388	1	44888.81	53895.67

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")

sub.nutr$prop.n <- sub.nutr$perc.n/100


sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")

sub.nutr$litter.p.content.prop.initial <- sub.nutr$litter.p.content.perc.initial/100

fit.p <- brm(litter.p.content.prop.initial ~ pool.n * days.sc + pool.p *
    days.sc + (1 | plot.f), data = sub.nutr[sub.nutr$litter.p.content.prop.initial <
    1, ], family = Beta(link = "logit"), chains = chains, prior = prior,
    cores = chains, iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), file = "./data/processed/litter.p.content.perc.initial_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/litter.p.content.perc.initial_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.8 litter.p.content.perc.initial_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	litter.p.content.prop.initial ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	42824.2	43352.43	43891969

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.286	-0.048	0.626	1	44160.93	45169.46
days.sc	-0.611	-0.835	-0.392	1	48922.56	55655.18
pool.pp	0.309	-0.029	0.644	1	42824.20	43352.43
pool.nn:days.sc	-0.089	-0.351	0.171	1	63850.90	60149.59
days.sc:pool.pp	0.066	-0.193	0.324	1	60491.19	56399.36

Concentration

agg_conc_p <- aggregate(perc.p ~ colecta + treat + days, sub.nutr,
    mean)

agg_conc_p$sd <- aggregate(perc.p ~ colecta + treat + days, sub.nutr,
    sd)$perc.p

agg_conc_p$se <- aggregate(perc.p ~ colecta + treat + days, sub.nutr,
    se)$perc.p

agg_conc_p$treat <- factor(agg_conc_p$treat, levels = c("C", "N",
    "P", "NP"))

pd <- position_dodge(15)

ggplot(agg_conc_p, aes(x = days, y = perc.p, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = perc.p + se, ymin = perc.p -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5) + labs(x = "Time (days)", y = "Litter P concentration (%)",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_conc_p$days),
    labels = unique(agg_conc_p$days)) + theme(legend.position = c(0.9,
    0.8))

ggsave("./output/Litter_P_concentration.tiff", dpi = 300)

Download image

# convert to proportions to use beta distribution
sub.nutr$prop.p <- sub.nutr$perc.p/100

fit.perc.p <- brm(prop.p ~ treat * days.sc + (1 | plot.f), data = sub.nutr,
    chains = chains, cores = chains, family = Beta(), iter = iters,
    control = list(adapt_delta = 0.99, max_treedepth = 15), prior = prior,
    file = "./data/processed/litter.p.perc_model", file_refit = "on_change")

extended_summary(read.file = "./data/processed/litter.p.perc_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.9 litter.p.perc_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.p ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	49287.17	57423.14	838385675

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.079	-0.283	0.436	1	80454.38	61093.74
days.sc	-0.033	-0.325	0.254	1	49287.17	57423.14
pool.pp	0.109	-0.250	0.466	1	79902.64	61281.60
pool.nn:days.sc	-0.004	-0.343	0.332	1	64208.70	60773.47
days.sc:pool.pp	0.037	-0.299	0.374	1	63313.29	61284.53

Pooled P

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")

sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")


fit.perc.p <- brm(prop.p ~ pool.n * days.sc + pool.p * days.sc + (1 |
    plot.f), data = sub.nutr, chains = chains, cores = chains, family = Beta(),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    prior = prior, file = "./data/processed/litter.p.perc_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/litter.p.perc_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.10 litter.p.perc_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.p ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	49287.17	57423.14	838385675

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	0.079	-0.283	0.436	1	80454.38	61093.74
days.sc	-0.033	-0.325	0.254	1	49287.17	57423.14
pool.pp	0.109	-0.250	0.466	1	79902.64	61281.60
pool.nn:days.sc	-0.004	-0.343	0.332	1	64208.70	60773.47
days.sc:pool.pp	0.037	-0.299	0.374	1	63313.29	61284.53

Takeaways

• Litter P content is significantly lower in plus N treatment plots than in control plot, after accounting for variation explained by time

 

2.11 Remaining litter

Download image

Download image

fit <- brm(prop.litter.rem ~ trat * days.sc + (1 | plot.f), data = dat,
    chains = chains, family = Beta(), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/prop.litter.rem_model",
    file_refit = "on_change")

# dat$days.fc <- as.numeric(as.factor(dat$days)) # monotonic
# effect of time fit_mo <- brm(prop.litter.rem ~ trat *
# mo(days.fc) + (1 | plot.f), data = dat, chains = chains,
# family = Beta(), iter = iters, control =
# list(adapt_delta=0.99, max_treedepth=15), cores = chains,
# prior = prior, file =
# './data/processed/prop.litter.rem_model_monotonic', file_refit
# = 'on_change')

extended_summary(read.file = "./data/processed/prop.litter.rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.12 prop.litter.rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.wood.rem ~ trat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	20000	4	1	10000	0 (0%)	0	16872.71	23764.8	1828689869

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
tratN	0.118	-0.128	0.366	1	25420.93	24370.70
tratNP	0.254	0.012	0.496	1	24798.43	26473.85
tratP	0.197	-0.045	0.438	1	25725.64	25244.62
days.sc	-0.910	-1.094	-0.737	1	16872.71	23764.80
tratN:days.sc	-0.006	-0.244	0.234	1	20661.18	27810.64
tratNP:days.sc	0.097	-0.140	0.333	1	20685.17	28019.73
tratP:days.sc	0.175	-0.058	0.412	1	20811.62	27760.94

dat$pool.n <- factor(dat$pool.n)

levels(dat$pool.n) <- c("no.n", "n")

fit <- brm(prop.litter.rem ~ pool.n * days.sc + pool.p * days.sc +
    (1 | plot.f), data = dat, chains = chains, family = Beta(), iter = iters,
    control = list(adapt_delta = 0.99, max_treedepth = 15), cores = chains,
    prior = prior, file = "./data/processed/prop.litter.rem_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/prop.litter.rem_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.13 prop.litter.rem_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.litter.rem ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	62101.61	57460.4	1782064894

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.005	-0.116	0.106	1	83216.49	57460.40
days.sc	-0.705	-0.800	-0.612	1	62101.61	58956.00
pool.pp	0.073	-0.038	0.183	1	87071.32	57939.41
pool.nn:days.sc	-0.007	-0.114	0.099	1	80137.61	61149.43
days.sc:pool.pp	0.107	0.000	0.215	1	77120.40	59967.96

2.14 Remaining wood

Download image

 

dat$prop.wood.rem <- dat$perc.wood.rem/100

fit2 <- brm(prop.wood.rem ~ trat * days.sc + (1 | plot.f), data = dat,
    chains = chains, family = Beta(), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/prop.wood.rem_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/prop.wood.rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.15 prop.wood.rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.wood.rem ~ trat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	35031.72	46489.04	759730670

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
tratN	0.119	-0.129	0.368	1	52775.14	54547.99
tratNP	0.254	0.008	0.498	1	52405.88	54272.89
tratP	0.197	-0.047	0.442	1	52616.14	52551.39
days.sc	-0.912	-1.096	-0.736	1	35031.72	46489.04
tratN:days.sc	-0.005	-0.246	0.237	1	44660.38	56089.04
tratNP:days.sc	0.099	-0.136	0.334	1	42945.91	55080.66
tratP:days.sc	0.177	-0.057	0.414	1	42878.43	53367.71

dat$prop.wood.rem <- dat$perc.wood.rem/100

dat$pool.n <- factor(dat$pool.n)

levels(dat$pool.n) <- c("no.n", "n")

fit2 <- brm(prop.wood.rem ~ pool.n * days.sc + pool.p * days.sc +
    (1 | plot.f), data = dat, chains = chains, family = Beta(), iter = iters,
    control = list(adapt_delta = 0.99, max_treedepth = 15), cores = chains,
    prior = prior, file = "./data/processed/prop.wood.rem_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/prop.wood.rem_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

2.16 prop.wood.rem_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.wood.rem ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	74032.63	54748.32	28695825

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.085	-0.254	0.084	1	85986.97	57764.11
days.sc	-0.933	-1.078	-0.791	1	74032.63	59306.25
pool.pp	0.165	-0.004	0.332	1	84792.55	54748.32
pool.nn:days.sc	0.047	-0.112	0.206	1	96922.82	63045.91
days.sc:pool.pp	0.137	-0.025	0.299	1	89845.98	62564.19

3 K

3.1 Litter

Correlation between Silvia’s and Andrea’s K

k_vals <- read.csv("./data/raw/k-values-corr.csv")

k_vals$k.sil.wood <- abs(k_vals$k.sil.wood)

cor(k_vals$k.av.litt, k_vals$k.sil.litt)

[1] 0.9327804

cor(k_vals$k.av.wood, k_vals$k.sil.wood)

[1] 0.9623055

Comparing all treatments vs control

agg_kvals <- aggregate(k.sil.litt ~ Treatment, k_vals, mean)
agg_kvals$se <- aggregate(k.sil.litt ~ Treatment, k_vals, se)$k.sil.litt
agg_kvals$sd <- aggregate(k.sil.litt ~ Treatment, k_vals, sd)$k.sil.litt
agg_kvals$n <- aggregate(k.sil.litt ~ Treatment, k_vals, length)$k.sil.litt
agg_kvals$treat <- factor(agg_kvals$Treatment, levels = c("C", "N", "P", "NP"))
agg_kvals$n.labels <- paste("n =", agg_kvals$n) 

# composed box plot
ggplot(k_vals, aes(x = Treatment, y = k.sil.litt)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the right
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
   labs(y = "Decomposition constant (k)") +
  # ylim(c(-0.39, 0.145)) +
  geom_text(data = agg_kvals, aes(y = rep(0.4, nrow(agg_kvals)), x = Treatment, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1)) +
    scale_x_discrete(labels=c("C" = "Control", "N" = "+N",
                              "NP" = "+NP", "P" = "+P"))

ggsave("./output/litter_decomposition_k_by_treatment.tiff", dpi = 300)

Download image

fit_k.litter <- brm(k.sil.litt ~ Treatment + (1 | quadrat), data = k_vals,
    chains = chains, family = gaussian(), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/k_litter_model",
    file_refit = "on_change")

extended_summary(gsub.pattern = "b_treatment|b_", gsub.replacement = "",
    highlight = TRUE, remove.intercepts = TRUE, read.file = "./data/processed/k_litter_model.rds")

3.2 k_litter_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.litt ~ Treatment + (1 | quadrat)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	8 (1e-04%)	0	48188.3	53957.43	1990407839

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
TreatmentN	0.237	-0.182	0.650	1	48188.30	53957.43
TreatmentNP	-0.157	-0.575	0.259	1	49353.64	54230.69
TreatmentP	-0.008	-0.424	0.409	1	48264.71	54663.36

pooled N and P

k_vals$pool.p <- ifelse(k_vals$Treatment %in% c("P", "NP"), "p", "no.p")
k_vals$pool.n <- ifelse(k_vals$Treatment %in% c("N", "NP"), "n", "no.n")

k_vals$pool.n <- factor(k_vals$pool.n)

levels(k_vals$pool.n) <- c("no.n", "n")

fit_k.litter <- brm(k.sil.litt ~ pool.p + pool.n + (1 | quadrat),
    data = k_vals, chains = chains, family = Gamma(link = "log"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/k_litter_pooled_model",
    file_refit = "on_change")

extended_summary(gsub.pattern = "b_treatment|b_", gsub.replacement = "",
    highlight = TRUE, remove.intercepts = TRUE, read.file = "./data/processed/k_litter_pooled_model.rds")

3.3 k_litter_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.litt ~ pool.p + pool.n + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	33 (0.00041%)	0	72277.17	53247.81	913293624

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.pp	-0.129	-0.319	0.061	1	73014.04	53247.81
pool.nn	-0.023	-0.212	0.166	1	72277.17	54264.67

Phosphorus vs no-phosphorus

fit_k.litter.p.np <- brm(k.sil.litt ~ p.treat + (1 | quadrat), data = k_vals,
    chains = chains, family = Gamma(link = "log"), iter = iters, ,
    control = list(adapt_delta = 0.99, max_treedepth = 15), cores = chains,
    prior = prior, file = "./data/processed/k_litter_p_nop_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/k_litter_p_nop_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

3.4 k_litter_p_nop_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.litt ~ p.treat + (1 | quadrat)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	22 (0.00028%)	0	67015.63	50456.69	803160143

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
p.treatwith.p	-0.202	-0.498	0.092	1	67015.63	50456.69

agg_kvals <- aggregate(k.sil.litt ~ p.treat, k_vals, mean)
agg_kvals$se <- aggregate(k.sil.litt ~ p.treat, k_vals, se)$k.sil.litt
agg_kvals$sd <- aggregate(k.sil.litt ~ p.treat, k_vals, sd)$k.sil.litt
agg_kvals$p.treat <- factor(agg_kvals$p.treat, labels = c("No P", "P"))
agg_kvals$n <- aggregate(k.sil.litt ~ p.treat, k_vals, length)$k.sil.litt
agg_kvals$n.labels <- paste("n =", agg_kvals$n) 
k_vals$p.treat <- factor(k_vals$p.treat, labels = c("No P", "P"))

# composed box plot
rn_p_litter <- ggplot(k_vals, aes(x = p.treat, y = k.sil.litt)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
  labs(y = "Decomposition constant (k)", x = "P treatment") +
  geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = p.treat, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))  +
    scale_x_discrete(labels=c("No P" = "No P", "P" = "+P"))

rn_p_litter

ggsave("./output/litter_phosphorus_decomposition_k.tiff", dpi = 300)

Nitrogen vs no-nitrogen

fit_k.litter.n.nn <- brm(k.sil.litt ~ n.treat + (1 | quadrat), data = k_vals,
    chains = chains, family = Gamma(link = "log"), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/k_litter_n_no_n_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/k_litter_n_no_n_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

3.5 k_litter_n_no_n_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.litt ~ n.treat + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	15 (0.00019%)	0	72242.88	53236.64	1667737665

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
n.treatwith.n	0.031	-0.162	0.223	1	72242.88	53236.64

agg_kvals <- aggregate(k.sil.litt ~ n.treat, k_vals, mean)
agg_kvals$se <- aggregate(k.sil.litt ~ n.treat, k_vals, se)$k.sil.litt
agg_kvals$sd <- aggregate(k.sil.litt ~ n.treat, k_vals, sd)$k.sil.litt
agg_kvals$n.treat <- factor(agg_kvals$n.treat, labels = c("No N", "N"))
agg_kvals$n <- aggregate(k.sil.litt ~ n.treat, k_vals, length)$k.sil.litt
agg_kvals$n.labels <- paste("n =", agg_kvals$n) 
k_vals$n.treat <- factor(k_vals$n.treat, labels = c("No N", "N"))

# composed box plot
rn_n_litter <- ggplot(k_vals, aes(x = n.treat, y = k.sil.litt)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
  labs(y = "Decomposition constant (k)", x = "P treatment") +
  geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = n.treat, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))  +
    scale_x_discrete(labels=c("No P" = "No P", "P" = "+P"))

rn_n_litter

ggsave("./output/litter_nitrogen_decomposition_k.tiff", dpi = 300)

3.6 Wood

Comparing all treatments vs control

agg_kvals <- aggregate(k.sil.wood ~ Treatment, k_vals, mean)
agg_kvals$se <- aggregate(k.sil.wood ~ Treatment, k_vals, se)$k.sil.wood
agg_kvals$sd <- aggregate(k.sil.wood ~ Treatment, k_vals, sd)$k.sil.wood
agg_kvals$n <- aggregate(k.sil.wood ~ Treatment, k_vals, length)$k.sil.wood
agg_kvals$treat <- factor(agg_kvals$Treatment, levels = c("C", "N", "P", "NP"))
agg_kvals$n.labels <- paste("n =", agg_kvals$n) 

# composed box plot
ggplot(k_vals, aes(x = Treatment, y = k.sil.wood)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
   labs(y = "Decomposition constant (k)") +
  # ylim(c(-0.39, 0.145)) +
  geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = Treatment, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1)) +
    scale_x_discrete(labels=c("C" = "Control", "N" = "+N",
                              "NP" = "+NP", "P" = "+P"))

ggsave("./output/wood_decomposition_k_by_treatment.tiff", dpi = 300)

Download image

fit_k.wood.p.treat <- brm(k.sil.wood ~ Treatment + (1 | quadrat),
    data = k_vals, chains = chains, family = Gamma(link = "log"),
    iter = iters * 2, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/k_wood_treatment_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/k_wood_treatment_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

3.7 k_wood_treatment_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.wood ~ Treatment + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	80000	4	1	40000	65 (0.00041%)	0	98166.04	105611.9	855747887

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
TreatmentN	0.012	-0.346	0.371	1	100934.75	107608.8
TreatmentNP	-0.251	-0.608	0.106	1	99322.53	108781.5
TreatmentP	-0.234	-0.594	0.125	1	98166.04	105611.9

pooled N and P

k_vals$pool.p <- ifelse(k_vals$Treatment %in% c("P", "NP"), "p", "no.p")
k_vals$pool.n <- ifelse(k_vals$Treatment %in% c("N", "NP"), "n", "no.n")

k_vals$pool.n <- factor(k_vals$pool.n)

levels(k_vals$pool.n) <- c("no.n", "n")

fit_k.wood.p.pooled <- brm(k.sil.wood ~ pool.p + pool.n + (1 | quadrat),
    data = k_vals, chains = chains, family = Gamma(link = "log"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/k_wood_pooled_model",
    file_refit = "on_change")

extended_summary(gsub.pattern = "b_treatment|b_", gsub.replacement = "",
    highlight = TRUE, remove.intercepts = TRUE, read.file = "./data/processed/k_wood_pooled_model.rds")

3.8 k_wood_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	sil.k.wood ~ pool.p + pool.n + (1 | quadrat)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	19 (0.00024%)	0	72247.85	53648.68	977910876

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.pp	-0.497	-0.901	-0.093	1	73065.71	53648.68
pool.nn	-0.006	-0.406	0.396	1	72247.85	54566.47

## Phosphorus vs no-phosphorus

agg_kvals <- aggregate(k.sil.wood ~ p.treat, k_vals, mean)
agg_kvals$se <- aggregate(k.sil.wood ~ p.treat, k_vals, se)$k.sil.wood
agg_kvals$sd <- aggregate(k.sil.wood ~ p.treat, k_vals, sd)$k.sil.wood


agg_kvals$p.treat <- factor(agg_kvals$p.treat, labels = c("No P", "P"))
agg_kvals$n <- aggregate(k.sil.wood ~ p.treat, k_vals, length)$k.sil.wood
agg_kvals$n.labels <- paste("n =", agg_kvals$n) 


k_vals$p.treat <- factor(k_vals$p.treat, labels = c("No P", "P"))


# composed box plot
rn_p_wood <- ggplot(k_vals, aes(x = p.treat, y = k.sil.wood)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
  labs(y = "Decomposition constant (k)", x = "P treatment") +
  geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = p.treat, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))  +
    scale_x_discrete(labels=c("No P" = "No P", "P" = "+P"))

rn_p_wood

ggsave("./output/phosphorus_decomposition_k.tiff", dpi = 300)

Download image

fit_k.wood.p.no.p <- brm(k.sil.wood ~ p.treat + (1 | quadrat), data = k_vals,
    chains = chains, family = Gamma(link = "log"), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/k_wood_p_no_p_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/k_wood_p_no_p_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

3.9 k_wood_p_no_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.wood ~ p.treat + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	10 (0.00012%)	0	64734.01	54706.61	1645430139

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
p.treatwith.p	-0.248	-0.5	0.001	1	64734.01	54706.61

3.10 Nitrogen vs no-nitrogen

agg_kvals <- aggregate(k.sil.wood ~ n.treat, k_vals, mean)
agg_kvals$se <- aggregate(k.sil.wood ~ n.treat, k_vals, se)$k.sil.wood
agg_kvals$sd <- aggregate(k.sil.wood ~ n.treat, k_vals, sd)$k.sil.wood
agg_kvals$n.treat <- factor(agg_kvals$n.treat, labels = c("No N", "N"))
agg_kvals$n <- aggregate(k.sil.wood ~ n.treat, k_vals, length)$k.sil.wood
agg_kvals$n.labels <- paste("n =", agg_kvals$n) 
k_vals$n.treat <- factor(k_vals$n.treat, labels = c("No N", "N"))

# composed box plot
rn_n_wood <- ggplot(k_vals, aes(x = n.treat, y = k.sil.wood)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
  labs(y = "Decomposition constant (k)", x = "P treatment") +
  geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = n.treat, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))  +
    scale_x_discrete(labels=c("No P" = "No P", "P" = "+P"))

rn_n_wood

ggsave("./output/nitrogen_decomposition_k.tiff", dpi = 300)

Download image

fit_k.wood.n.no.n <- brm(k.sil.wood ~ n.treat + (1 | quadrat), data = k_vals,
    chains = chains, family = Gamma(link = "log"), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/k_wood_n_no_n_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/k_wood_n_no_n_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

3.11 k_wood_n_no_n_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	k.sil.wood ~ n.treat + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	17 (0.00021%)	0	65193.64	55407.67	1393075606

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
n.treatwith.n	0	-0.255	0.254	1	65193.64	55407.67

4 Nutrient content by remaining litter mass

4.1 Nitrogen

nutr$prom.hoja.reman.sc <- scale(nutr$prom.hoja.reman)

ggplot(data = nutr, aes(x = prom.hoja.reman, y = perc.n, color = treat)) +
    geom_point() + labs(x = "Remaining litter mass (% initial)", y = "Litter N concentration (%)",
    color = "Treatment") + scale_color_viridis_d(alpha = 0.5) + geom_smooth(method = "lm",
    se = FALSE) + scale_x_reverse()

ggsave("./output/nitrogen_by_litter_mass.tiff", dpi = 300)

Download image

nutr$prop.n <- nutr$perc.n/100
fit_pern_by_rem_leave <- brm(prop.n ~ prom.hoja.reman.sc * treat +
    (1 | plot), data = nutr, chains = chains, family = Beta(link = "logit"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/n_per_by_leave_rem_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/n_per_by_leave_rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

4.2 n_per_by_leave_rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.n ~ prom.hoja.reman.sc * treat + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	46098.2	54930.62	1419862621

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
prom.hoja.reman.sc	-0.097	-0.188	-0.008	1	46098.20	54930.62
treatN	-0.092	-0.232	0.044	1	66658.88	59069.86
treatNP	-0.036	-0.170	0.100	1	66868.65	58149.07
treatP	-0.016	-0.150	0.119	1	66587.62	59170.26
prom.hoja.reman.sc:treatN	0.033	-0.091	0.156	1	56656.88	59418.75
prom.hoja.reman.sc:treatNP	-0.047	-0.186	0.090	1	61314.28	61993.63
prom.hoja.reman.sc:treatP	-0.009	-0.138	0.119	1	58600.17	61521.39

fit_pern_by_rem_leave <- brm(prop.n ~ prom.hoja.reman.sc * treat +
    (1 | plot), data = nutr, chains = chains, family = Beta(link = "logit"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/n_per_by_leave_rem_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/n_per_by_leave_rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

4.3 n_per_by_leave_rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.n ~ prom.hoja.reman.sc * treat + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	46098.2	54930.62	1419862621

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
prom.hoja.reman.sc	-0.097	-0.188	-0.008	1	46098.20	54930.62
treatN	-0.092	-0.232	0.044	1	66658.88	59069.86
treatNP	-0.036	-0.170	0.100	1	66868.65	58149.07
treatP	-0.016	-0.150	0.119	1	66587.62	59170.26
prom.hoja.reman.sc:treatN	0.033	-0.091	0.156	1	56656.88	59418.75
prom.hoja.reman.sc:treatNP	-0.047	-0.186	0.090	1	61314.28	61993.63
prom.hoja.reman.sc:treatP	-0.009	-0.138	0.119	1	58600.17	61521.39

4.4 Phosphorus

ggplot(data = sub.nutr, aes(x = prom.hoja.reman, y = perc.p, color = treat)) +
    geom_point() + labs(x = "Remaining litter mass (% initial)", y = "Litter P concentration (%)",
    color = "Treatment") + scale_color_viridis_d(alpha = 0.5) + geom_smooth(method = "lm",
    se = FALSE) + scale_x_reverse()

ggsave("./output/phosphorus_by_litter_mass.tiff", dpi = 300)

Download image

sub.nutr$prom.hoja.reman.sc <- scale(sub.nutr$prom.hoja.reman)

sub.nutr$prop.p <- sub.nutr$perc.p/100

fit_perp_by_rem_leave <- brm(prop.p ~ prom.hoja.reman.sc * treat +
    (1 | plot), data = sub.nutr, chains = chains, family = Beta(link = "logit"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/p_per_by_leave_rem_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/p_per_by_leave_rem_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

4.5 p_per_by_leave_rem_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	prop.p ~ prom.hoja.reman.sc * treat + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	45911.09	48188.43	168759349

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
prom.hoja.reman.sc	0.031	-0.302	0.340	1	45911.09	48188.43
treatN	-0.101	-0.594	0.388	1	66767.28	59107.27
treatNP	0.028	-0.448	0.506	1	64658.84	58565.19
treatP	0.073	-0.441	0.580	1	65754.39	59305.79
prom.hoja.reman.sc:treatN	0.017	-0.439	0.469	1	55504.55	56147.13
prom.hoja.reman.sc:treatNP	-0.048	-0.520	0.418	1	55914.18	58512.29
prom.hoja.reman.sc:treatP	-0.035	-0.507	0.432	1	56621.27	56984.24

Takeaways

• Nitrogen percentage, but no Phosphorus percentage, increases along with remaining litter mass

 

5 Nutrient ratios

5.1 C:N

# excluding plot 9
agg_cn <- aggregate(cn.mol.kg ~ colecta + treat + days, nutr, mean)

agg_cn$sd <- aggregate(cn.mol.kg ~ colecta + treat + days, nutr, sd)$cn.mol.kg

agg_cn$se <- aggregate(cn.mol.kg ~ colecta + treat + days, nutr, se)$cn.mol.kg


agg_cn$treat <- factor(agg_cn$treat, levels = c("C", "N", "P", "NP"))

pd <- position_dodge(15)

ggplot(agg_cn, aes(x = days, y = cn.mol.kg, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = cn.mol.kg + se, ymin = cn.mol.kg -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5) + labs(x = "Time (days)", y = "Litter C:N ratio",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_cn$days),
    labels = unique(agg_cn$days)) + theme(legend.position = c(0.9,
    0.8))

ggsave("./output/cn_ratio_through_time.tiff", dpi = 300)

Download image

fit.cn <- brm(cn.mol.kg ~ treat * days.sc + (1 | plot.f), data = nutr,
    chains = chains, family = Gamma(link = "log"), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/cn_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/cn_model.rds", gsub.pattern = "b_treatment|b_",
    gsub.replacement = "", highlight = TRUE, remove.intercepts = TRUE)

5.2 cn_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cn.mol.kg ~ treat * days.sc + (1 | plot.f)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	35587.38	44645.52	1143833718

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
treatN	0.009	-0.099	0.111	1	45969.23	44645.52
treatNP	-0.007	-0.110	0.097	1	46816.05	48244.92
treatP	-0.009	-0.113	0.094	1	47348.16	50561.75
days.sc	-0.180	-0.244	-0.118	1	35587.38	47992.48
treatN:days.sc	0.039	-0.046	0.124	1	45580.65	56260.34
treatNP:days.sc	0.014	-0.072	0.101	1	45607.95	54630.70
treatP:days.sc	-0.001	-0.087	0.085	1	45397.25	54204.90

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")

sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")

fit.cn <- brm(cn.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 |
    plot.f), data = sub.nutr, chains = chains, family = gaussian(),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/cn_pooled_model2",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/cn_pooled_model2.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

5.3 cn_pooled_model2

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cn.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	70922.09	57566.19	161678448

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.326	-1.549	0.896	1	87506.75	57566.19
days.sc	-2.386	-3.289	-1.488	1	70922.09	61664.32
pool.pp	-0.524	-1.732	0.689	1	88220.05	58006.12
pool.nn:days.sc	-0.670	-1.751	0.414	1	90006.00	61094.47
days.sc:pool.pp	-0.234	-1.305	0.844	1	88619.19	62452.26

5.4 N:P

# excluding plot 9
agg_np <- aggregate(np.mol.kg ~ colecta + treat + days, sub.nutr,
    mean)

agg_np$sd <- aggregate(np.mol.kg ~ colecta + treat + days, sub.nutr,
    sd)$np.mol.kg

agg_np$se <- aggregate(np.mol.kg ~ colecta + treat + days, sub.nutr,
    se)$np.mol.kg


agg_np$treat <- factor(agg_np$treat, levels = c("C", "N", "P", "NP"))


pd <- position_dodge(15)

ggplot(agg_np, aes(x = days, y = np.mol.kg, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = np.mol.kg + se, ymin = np.mol.kg -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5) + labs(x = "Time (days)", y = "Litter N:P ratio",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_np$days),
    labels = unique(agg_np$days)) + theme(legend.position = c(0.2,
    0.8))

ggsave("./output/np_ratio_through_time.tiff", dpi = 300)

Download image

fit.np <- brm(np.mol.kg ~ treat * days.sc + (1 | plot.f), data = sub.nutr,
    chains = chains, family = gaussian(), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/np_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/np_model.rds", gsub.pattern = "b_treatment|b_",
    gsub.replacement = "", highlight = TRUE, remove.intercepts = TRUE)

5.5 np_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	np.mol.kg ~ treat * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 5.3)	40000	4	1	20000	0 (0%)	0	41007.87	48820.84	579910719

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
treatN	1.201	-3.053	5.508	1	49715.47	51006.06
treatNP	-2.417	-6.618	1.863	1	49894.96	49578.50
treatP	-3.147	-7.700	1.476	1	50348.36	48820.84
days.sc	4.426	1.783	7.053	1	41007.87	52509.45
treatN:days.sc	-1.790	-5.413	1.821	1	50394.31	57568.65
treatNP:days.sc	-1.805	-5.442	1.804	1	49985.13	56081.79
treatP:days.sc	-1.430	-5.270	2.454	1	53311.35	55156.44

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")


sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")

fit.cn <- brm(np.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 |
    plot.f), data = sub.nutr, chains = chains, family = gaussian(),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/np_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/np_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

5.6 np_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	np.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 5.3)	40000	4	1	20000	0 (0%)	0	61509.67	53836.89	676130983

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.940	-4.035	2.178	1	71063.98	56909.25
days.sc	2.948	0.741	5.145	1	61509.67	57679.84
pool.pp	-3.434	-6.491	-0.307	1	73981.72	53836.89
pool.nn:days.sc	1.212	-1.451	3.853	1	80364.56	62229.69
days.sc:pool.pp	-0.717	-3.343	1.917	1	76934.24	60342.60

5.7 C:P

# excluding plot 9
agg_cp <- aggregate(cp.mol.kg ~ colecta + treat + days, sub.nutr,
    mean)

agg_cp$sd <- aggregate(cp.mol.kg ~ colecta + treat + days, sub.nutr,
    sd)$cp.mol.kg

agg_cp$se <- aggregate(cp.mol.kg ~ colecta + treat + days, sub.nutr,
    se)$cp.mol.kg

agg_cp$treat <- factor(agg_cp$treat, levels = c("C", "N", "P", "NP"))


pd <- position_dodge(15)

ggplot(agg_cp, aes(x = days, y = cp.mol.kg, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = cp.mol.kg + se, ymin = cp.mol.kg -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5) + labs(x = "Time (days)", y = "Litter C:P ratio",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_cp$days),
    labels = unique(agg_cp$days)) + theme(legend.position = c(0.9,
    0.8))

ggsave("./output/cp_ratio_through_time.tiff", dpi = 300)

Download image

fit.cp <- brm(cp.mol.kg ~ treat * days.sc + (1 | plot.f), data = sub.nutr,
    chains = chains, family = gaussian(), iter = iters, cores = chains,
    prior = prior, file = "./data/processed/cp_model", file_refit = "on_change")

extended_summary(read.file = "./data/processed/cp_model.rds", gsub.pattern = "b_treatment|b_",
    gsub.replacement = "", highlight = TRUE, remove.intercepts = TRUE)

5.8 cp_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cp.mol.kg ~ treat * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 106.3)	40000	4	1	20000	0 (0%)	0	62183.29	54476.32	1789568456

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
treatN	0.327	-19.220	19.986	1	62606.85	55520.65
treatNP	-0.296	-19.879	19.113	1	63093.42	55249.52
treatP	-0.277	-19.860	19.448	1	63377.19	55433.86
days.sc	-6.126	-21.105	9.108	1	62183.29	54476.32
treatN:days.sc	0.369	-17.654	18.204	1	66553.98	58235.32
treatNP:days.sc	-4.798	-22.854	13.180	1	66003.03	57751.21
treatP:days.sc	-2.664	-20.834	15.494	1	64783.90	56574.64

sub.nutr$pool.p <- ifelse(sub.nutr$treat %in% c("P", "NP"), "p", "no.p")
sub.nutr$pool.n <- ifelse(sub.nutr$treat %in% c("N", "NP"), "n", "no.n")


sub.nutr$pool.n <- factor(sub.nutr$pool.n)

levels(sub.nutr$pool.n) <- c("no.n", "n")

fit.cn <- brm(cp.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 |
    plot.f), data = sub.nutr, chains = chains, family = gaussian(),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/cp_pooled_model",
    file_refit = "on_change")

extended_summary(read.file = "./data/processed/cp_pooled_model.rds",
    gsub.pattern = "b_treatment|b_", gsub.replacement = "", highlight = TRUE,
    remove.intercepts = TRUE)

5.9 cp_pooled_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cp.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 106.3)	40000	4	1	20000	0 (0%)	0	49279.16	51752.89	1583776905

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
pool.nn	-0.106	-19.546	19.468	1	49530.50	51841.82
days.sc	-5.325	-20.757	10.232	1	49279.16	51752.89
pool.pp	-0.526	-20.030	19.001	1	50219.39	53109.33
pool.nn:days.sc	-0.987	-18.409	16.520	1	52068.26	52702.46
days.sc:pool.pp	-6.579	-23.831	10.864	1	50389.63	52780.69

---

6 Combined plots

6.1 Remaining mass

agg_rem_w$substrate <- "Wood"
agg_rem$substrate <- "Litter"

names(agg_rem) <- names(agg_rem_w) <- c("colecta", "trat", "days",
    "perc.rem", "sd", "se", "substrate")

agg_rem_pooled <- rbind(agg_rem, agg_rem_w)

ggplot(agg_rem_pooled, aes(x = days, y = perc.rem, color = trat)) +
    geom_point(size = 2, position = pd) + geom_errorbar(aes(ymax = perc.rem +
    se, ymin = perc.rem - se), width = 0, position = pd) + geom_line(size = 1.2,
    position = pd) + scale_color_viridis_d(alpha = 0.5, labels = c("Control",
    "+N", "+P", "+NP")) + labs(x = "Time (days)", y = "Remaining mass (%)",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_rem_pooled$days),
    labels = unique(agg_rem_pooled$days)) + facet_wrap(~substrate,
    nrow = 2)

ggsave("./output/remaining_mass_combined.tiff", dpi = 300)

Download image

6.2 Litter content

agg_p$nutrient <- "P"
agg_n$nutrient <- "N"

names(agg_n) <- names(agg_p) <- c("colecta", "treat", "days", "perc",
    "sd", "se", "nutrient")

agg_np2 <- rbind(agg_n, agg_p)

ggplot(agg_np2, aes(x = days, y = perc, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = perc + se, ymin = perc -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5, labels = c("Control", "+N",
        "+P", "+NP")) + labs(x = "Time (days)", y = "Litter nutrient content (% initial)",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_p$days),
    labels = unique(agg_p$days)) + facet_wrap(~nutrient, nrow = 2)

ggsave("./output/litter_content_combined.tiff", dpi = 300)

Download image

6.3 Concentration

agg_conc_p$nutrient <- "P"
agg_conc_n$nutrient <- "N"

names(agg_conc_n) <- names(agg_conc_p) <- c("colecta", "treat", "days",
    "perc", "sd", "se", "nutrient")

agg_conc_np <- rbind(agg_conc_n, agg_conc_p)

ggplot(agg_conc_np, aes(x = days, y = perc, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = perc + se, ymin = perc -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5, labels = c("Control", "+N",
        "+P", "+NP")) + labs(x = "Time (days)", y = "Litter nutrient concentration (%)",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_conc_p$days),
    labels = unique(agg_conc_p$days)) + facet_wrap(~nutrient, nrow = 2,
    scales = "free_y")

ggsave("./output/concentration_combined.tiff", dpi = 300)

Download image

6.4 Nutrient ratios

agg_cn$nutrients <- "C:N"
agg_cp$nutrients <- "C:P"
agg_np$nutrients <- "N:P"

names(agg_cn) <- names(agg_cp) <- names(agg_np) <- c("colecta", "treat",
    "days", "mol.kg", "sd", "se", "nutrients")

agg_ratios <- rbind(agg_cn[, names(agg_cn)], agg_cp[, names(agg_cn)],
    agg_np[, names(agg_cn)])

ggplot(agg_ratios, aes(x = days, y = mol.kg, color = treat)) + geom_point(size = 2,
    position = pd) + geom_errorbar(aes(ymax = mol.kg + se, ymin = mol.kg -
    se), width = 0, position = pd) + geom_line(size = 1.2, position = pd) +
    scale_color_viridis_d(alpha = 0.5, labels = c("Control", "+N",
        "+P", "+NP")) + labs(x = "Time (days)", y = "Litter nutrient ratios",
    color = "Treatment") + scale_x_continuous(breaks = unique(agg_ratios$days),
    labels = unique(agg_ratios$days)) + facet_wrap(~nutrients, nrow = 3,
    scales = "free_y")

ggsave("./output/nutrient_ratios_combined.tiff", dpi = 300, width = 10,
    height = 12)

Download image

6.5 Decomposition constant

rn_n_wood_dat <- rn_n_wood$data[, c("n.treat", "k.sil.wood")]
rn_n_litter_dat <- rn_n_litter$data[, c("n.treat", "k.sil.litt")]
rn_p_wood_dat <- rn_p_wood$data[, c("p.treat", "k.sil.wood")]
rn_p_litter_dat <- rn_p_litter$data[, c("p.treat", "k.sil.litt")]

names(rn_p_wood_dat) <- names(rn_n_wood_dat)  <- names(rn_p_litter_dat) <- names(rn_n_litter_dat) <- c("treatment", "k")
rn_p_wood_dat$substrate <- rn_n_wood_dat$substrate <- "wood"
rn_p_litter_dat$substrate <- rn_n_litter_dat$substrate <- "litter"

rn_n_wood_dat$nutrient <- rn_n_litter_dat$nutrient <- "N"
rn_p_litter_dat$nutrient <- rn_p_wood_dat$nutrient <- "P"

rn_k_dat <- rbind(rn_n_wood_dat, rn_p_wood_dat, rn_n_litter_dat, rn_p_litter_dat)                             
                             
# composed box plot
ggplot(rn_k_dat, aes(x = treatment, y = k)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
  labs(y = "Decomposition constant (k)", x = "P treatment") +
  # geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = n.treat, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))  +
    scale_x_discrete(labels=c("No P" = "No P", "P" = "+P")) +
    facet_grid(~ substrate)

ggsave("./output/decomposition_k_combined_v1.tiff", dpi = 300, width = 10, height = 12)

Download image

# composed box plot
ggplot(rn_k_dat, aes(x = treatment, y = k)) +
## add half-violin from {ggdist} package
  ggdist::stat_halfeye(
    fill = fill_color,
    alpha = 0.5,
    ## custom bandwidth
    adjust = .5,
    ## adjust height
    width = .6,
    .width = 0,
    ## move geom to the cright
    justification = -.2,
    point_colour = NA
  ) +
  geom_boxplot(fill = fill_color,
    width = .15,
    ## remove outliers
    outlier.shape = NA ## `outlier.shape = NA` works as well
  ) +
  ## add justified jitter from the {gghalves} package
  gghalves::geom_half_point(
    color = fill_color,
    ## draw jitter on the left
    side = "l",
    ## control range of jitter
    range_scale = .4,
    ## add some transparency
    alpha = .5,
    transformation = ggplot2::position_jitter(height = 0)

  ) +
  labs(y = "Decomposition constant (k)", x = "P treatment") +
  # geom_text(data = agg_kvals, aes(y = rep(-0.387, nrow(agg_kvals)), x = n.treat, label = n.labels), nudge_x = 0, size = 6) +
     theme_classic(base_size = 18) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))  +
    scale_x_discrete(labels=c("No P" = "No P", "P" = "+P")) +
    facet_grid(substrate ~ nutrient, scales = "free_x")

ggsave("./output/decomposition_k_combined_v12.tiff", dpi = 300, width = 10, height = 12)

Download image

7 Carbon inputs/outputs

7.1 Litter

7.1.1 N

# read data
c_input_litter <- read.csv("./data/raw/annual_litter_C_input.csv")

# same with ggplot2
ggplot(c_input_litter, aes(x = n.pooled, y = cr.total)) + geom_boxplot() +
    labs(y = "Carbon input (Mg C ha-1 yr-1)", x = "N treatment") +
    theme_classic(base_size = 18) + scale_x_discrete(labels = c(no.n = "-N",
    with.n = "+N"))

# mod1 <- lm(cr.total ~ n.pooled, data =
# c_input_litter[complete.cases(c_input_litter), ])

prior <- c(prior(normal(0, 10), "b"), prior(normal(0, 50), "Intercept"))


litter_input_n <- brm(cr.total ~ n.pooled, data = c_input_litter[complete.cases(c_input_litter),
    c("cr.total", "n.pooled")], chains = chains, family = gaussian(),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/litter_input_n_model",
    file_refit = "on_change")

extended_summary(fit = litter_input_n, highlight = TRUE, remove.intercepts = TRUE)

7.2 litter_input_n

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cr.total ~ n.pooled	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	47439.53	41816.38	26169603

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_n.pooledwith.n	0.071	-0.337	0.487	1	47439.53	41816.38

7.2.1 P

ggplot(c_input_litter, aes(x = p.pooled, y = cr.total)) + geom_boxplot() +
    labs(y = "Carbon input (Mg C ha-1 yr-1)", x = "P treatment") +
    theme_classic(base_size = 18) + scale_x_discrete(labels = c(no.p = "-P",
    with.p = "+P"))

litter_input_p <- brm(cr.total ~ p.pooled, data = c_input_litter[complete.cases(c_input_litter),
    c("cr.total", "p.pooled")], chains = chains, family = gaussian(),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/litter_input_p_model",
    file_refit = "on_change")

extended_summary(fit = litter_input_p, highlight = TRUE, remove.intercepts = TRUE)

7.3 litter_input_p

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cr.total ~ p.pooled	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	48518.02	42903.88	603178782

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_p.pooledwith.p	-0.096	-0.51	0.319	1	48518.02	42903.88

7.4 CO2 output

7.4.1 N

c_avg_co2 <- read.csv("./data/raw/co2_plot_averages.csv")

ggplot(c_avg_co2, aes(x = pool.n, y = annual.flux)) + geom_boxplot() +
    labs(y = "Carbon output (Mg C ha-1 yr-1)", x = "N treatment") +
    theme_classic(base_size = 18)

prior <- c(prior(normal(0, 10), "b"), prior(normal(0, 50), "Intercept"))

co2_output_n <- brm(annual.flux ~ pool.n, data = c_avg_co2[complete.cases(c_avg_co2),
    ], chains = chains, family = gaussian(), iter = iters, control = list(adapt_delta = 0.99,
    max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/co2_output_n_model",
    file_refit = "on_change")

extended_summary(fit = co2_output_n, highlight = TRUE, remove.intercepts = TRUE)

7.5 co2_output_n

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	annual.flux ~ pool.n	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	50024.09	42637.79	306100029

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_pool.nPN	1.081	-1.215	3.366	1	50024.09	42637.79

7.5.1 P

ggplot(c_avg_co2, aes(x = pool.p, y = annual.flux)) + geom_boxplot() +
    labs(y = "Carbon output (Mg C ha-1 yr-1)", x = "P treatment") +
    theme_classic(base_size = 18)

co2_output_p <- brm(annual.flux ~ pool.p, data = c_avg_co2[complete.cases(c_avg_co2),
    ], chains = chains, family = gaussian(), iter = iters, control = list(adapt_delta = 0.99,
    max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/co2_output_p_model",
    file_refit = "on_change")

extended_summary(fit = co2_output_p, highlight = TRUE, remove.intercepts = TRUE)

7.6 co2_output_p

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	annual.flux ~ pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	51625.97	44811.71	1833764711

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_pool.pPP	0.57	-1.764	2.906	1	51625.97	44811.71

8 Microbial biomass

8.1 N

soil_mic <- read.csv("./data/raw/strimastersoils.csv")

# names(soil_mic)


soil_mic$BS <- soil_mic$BS/100
soil_mic$Al.sat <- soil_mic$Al.sat/100

variables <- c("mic.c", "mic.n", "mic.p", "mic.cn", "mic.cp", "mic.np",
    "AG", "BG", "XYL", "CEL", "NAG", "LAP", "MUP", "BIS", "S", "BG.NAG",
    "BG.MUP", "NAG.MUP", "BG.S", "NAG.S", "MUP.S", "ph.h2o", "ph.cacl2",
    "tc.g.kg.18", "tn.g.kg.18", "tp.g.kg.18", "CN", "CP", "NP", "k2so4.C",
    "nitrate.2017", "resin.p", "ox.Al", "ox.Fe", "Al", "Ca", "Fe",
    "K", "Mg", "Mn", "Na", "TEB", "ECEC", "BS", "Al.sat")


variables[!variables %in% names(soil_mic)]

character(0)

for (i in variables) {
    soil_mic$var <- soil_mic[, i]
    gg <- ggplot(soil_mic, aes(x = treat.pool.n, y = var)) + geom_boxplot() +
        geom_jitter() + labs(y = i, x = "N treatment") + theme_classic(base_size = 18)

    print(gg)
}

soil_mic$var <- NULL

prior <- c(prior(normal(0, 10), "b"), prior(normal(0, 50), "Intercept"))

for (i in variables) {
    soil_mic$var <- soil_mic[, i]

    fam <- Gamma(link = "log")

    if (i %in% c("BS", "Al.sat"))
        fam <- Beta(link = "logit") else if (any(soil_mic$var < 0))
        soil_mic$var <- soil_mic$var + min(abs(soil_mic$var)) + 1e-04

    co2_output_n <- brm(var ~ treat.pool.n, data = soil_mic, chains = chains,
        family = fam, iter = iters, control = list(adapt_delta = 0.99,
            max_treedepth = 15), cores = chains, prior = prior, file = paste("./data/processed/soil_",
            i, "_model", sep = ""), file_refit = "on_change")
}

for (i in variables) {
    mod <- paste("./data/processed/soil_", i, "_model.rds", sep = "")

    # print(paste('###', i))

    # print('<br>')

    extended_summary(read.file = mod, highlight = TRUE, remove.intercepts = TRUE)
}

8.2 soil_mic.c_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50056.97	44399.96	1048612606

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.015	-0.135	0.163	1	50056.97	44399.96

8.3 soil_mic.n_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	55194.14	44394.02	620083842

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.008	-0.141	0.159	1	55194.14	44394.02

8.4 soil_mic.p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50554.16	44978.2	1705825401

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.137	-0.706	0.425	1	50554.16	44978.2

8.5 soil_mic.cn_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53675.73	43286.97	945490801

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.005	-0.06	0.071	1	53675.73	43286.97

8.6 soil_mic.cp_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48766.3	43533.35	758109104

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.118	-0.677	0.429	1	48766.3	43533.35

8.7 soil_mic.np_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50611.52	43737.19	623667626

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.152	-0.724	0.415	1	50611.52	43737.19

8.8 soil_AG_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50390.32	41933.96	413707254

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.683	-0.227	1.562	1	50390.32	41933.96

8.9 soil_BG_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51303.8	44547.72	1423846020

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0	-0.318	0.313	1	51303.8	44547.72

8.10 soil_XYL_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51580.4	43697.72	250356946

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.201	-0.424	0.019	1	51580.4	43697.72

8.11 soil_CEL_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	54480.45	45568.53	1495070855

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.271	-0.539	-0.004	1	54480.45	45568.53

8.12 soil_NAG_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52309.59	45689.58	157324855

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.059	-0.5	0.38	1	52309.59	45689.58

8.13 soil_LAP_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50427.18	43807.01	61789085

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.061	-0.123	0.241	1	50427.18	43807.01

8.14 soil_MUP_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48769.08	42562.98	1487964286

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.025	-0.212	0.16	1	48769.08	42562.98

8.15 soil_BIS_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53007.32	43862.13	1854109569

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.027	-0.16	0.213	1	53007.32	43862.13

8.16 soil_S_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53001.26	44602.74	1300695161

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.442	0.184	0.699	1	53001.26	44602.74

8.17 soil_BG.NAG_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52333.81	44087.55	1640455467

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.066	-0.29	0.418	1	52333.81	44087.55

8.18 soil_BG.MUP_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	54354.84	43218.54	451859965

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.007	-0.257	0.27	1	54354.84	43218.54

8.19 soil_NAG.MUP_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	49937.27	43895.43	479400828

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.039	-0.371	0.291	1	49937.27	43895.43

8.20 soil_BG.S_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53770.81	45621.45	1321964644

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.505	-0.783	-0.23	1	53770.81	45621.45

8.21 soil_NAG.S_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53435.49	44457.67	1482520037

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.57	-0.899	-0.243	1	53435.49	44457.67

8.22 soil_MUP.S_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50998.96	44714.77	1502704492

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.478	-0.648	-0.31	1	50998.96	44714.77

8.23 soil_ph.h2o_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51867.18	45151.44	795850558

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.018	-0.019	0.054	1	51867.18	45151.44

8.24 soil_ph.cacl2_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51815.37	45301.38	1401049143

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.02	-0.012	0.051	1	51815.37	45301.38

8.25 soil_tc.g.kg.18_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52230.53	45318.31	7447136

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.053	-0.153	0.044	1	52230.53	45318.31

8.26 soil_tn.g.kg.18_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52556.95	45569.59	1146528163

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.038	-0.138	0.062	1	52556.95	45569.59

8.27 soil_tp.g.kg.18_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	49894.08	45025.61	1168252258

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.065	-0.193	0.319	1	49894.08	45025.61

8.28 soil_CN_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51520.78	45357.64	1322327565

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.013	-0.061	0.035	1	51520.78	45357.64

8.29 soil_CP_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48680.27	41289.78	101726671

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.104	-0.374	0.163	1	48680.27	41289.78

8.30 soil_NP_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48846.28	43402.47	1270710134

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.088	-0.365	0.186	1	48846.28	43402.47

8.31 soil_k2so4.C_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53927.69	45763.14	1070220198

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.051	-0.142	0.041	1	53927.69	45763.14

8.32 soil_nitrate.2017_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50337.29	43223.91	359163032

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.195	-0.487	0.096	1	50337.29	43223.91

8.33 soil_resin.p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48893.93	41454.89	876971613

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.069	-1.056	1.159	1	48893.93	41454.89

8.34 soil_ox.Al_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	49141.2	42952.56	1320258032

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.06	-0.082	0.201	1	49141.2	42952.56

8.35 soil_ox.Fe_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53613.61	43687.69	836977121

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.055	-0.155	0.262	1	53613.61	43687.69

8.36 soil_Al_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53687.01	45391.43	1520224625

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.084	-0.228	0.058	1	53687.01	45391.43

8.37 soil_Ca_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50876.02	43350.54	2049339314

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.092	-0.418	0.6	1	50876.02	43350.54

8.38 soil_Fe_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	47853.59	43033.11	648824471

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.182	-0.609	0.239	1	47853.59	43033.11

8.39 soil_K_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53940.4	45930.04	945628376

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.056	-0.152	0.264	1	53940.4	45930.04

8.40 soil_Mg_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51519.4	43660.18	1413138599

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.215	-0.059	0.488	1	51519.4	43660.18

8.41 soil_Mn_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52450.84	46752.57	1222938933

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.327	-0.724	0.068	1	52450.84	46752.57

8.42 soil_Na_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48319.6	42886.46	504747857

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.012	-0.858	0.809	1	48319.6	42886.46

8.43 soil_TEB_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50297.83	43834.86	221157550

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.11	-0.239	0.46	1	50297.83	43834.86

8.44 soil_ECEC_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	55238.75	43657.61	1318796507

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.028	-0.164	0.107	1	55238.75	43657.61

8.45 soil_BS_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52846.25	44558.75	842999925

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	0.204	-0.171	0.58	1	52846.25	44558.75

8.46 soil_Al.sat_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.n	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52103.51	43553.15	28613706

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.nno.n	-0.169	-0.54	0.204	1	52103.51	43553.15

8.47 P

for (i in variables) {
    soil_mic$var <- soil_mic[, i]
    gg <- ggplot(soil_mic, aes(x = treat.pool.p, y = var)) + geom_boxplot() +
        geom_jitter() + labs(y = i, x = "N treatment") + theme_classic(base_size = 18)

    print(gg)
}

soil_mic$var <- NULL

prior <- c(prior(normal(0, 10), "b"), prior(normal(0, 50), "Intercept"))

for (i in variables) {
    soil_mic$var <- soil_mic[, i]

    fam <- Gamma(link = "log")

    if (i %in% c("BS", "Al.sat"))
        fam <- Beta(link = "logit") else soil_mic$var <- soil_mic$var + min(abs(soil_mic$var)) + 1e-04

    co2_output_n <- brm(var ~ treat.pool.p, data = soil_mic, chains = chains,
        family = fam, iter = iters, control = list(adapt_delta = 0.99,
            max_treedepth = 15), cores = chains, prior = prior, file = paste("./data/processed/soil_",
            i, "_p_model", sep = ""), file_refit = "on_change")
}

for (i in variables) {

    # print(paste('###', i)) print('<br>')

    mod <- paste("./data/processed/soil_", i, "_p_model.rds", sep = "")

    extended_summary(read.file = mod, highlight = TRUE, remove.intercepts = TRUE)
}

8.48 soil_mic.c_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52815.96	44643.1	1410388778

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.008	-0.082	0.097	1	52815.96	44643.1

8.49 soil_mic.n_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52794.68	46822.58	2133030045

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.022	-0.065	0.11	1	52794.68	46822.58

8.50 soil_mic.p_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	47771.71	42911.08	569771158

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.536	0.114	0.953	1	47771.71	42911.08

8.51 soil_mic.cn_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52339.14	44798.78	1824816502

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.012	-0.054	0.03	1	52339.14	44798.78

8.52 soil_mic.cp_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50338.83	44815.98	504408909

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.17	-0.597	0.249	1	50338.83	44815.98

8.53 soil_mic.np_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52444.94	44483.51	1166263785

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.129	-0.576	0.315	1	52444.94	44483.51

8.54 soil_AG_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50973.55	44146.78	1888031748

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.27	-0.606	1.132	1	50973.55	44146.78

8.55 soil_BG_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52216.02	44513.83	2015288702

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.163	-0.355	0.027	1	52216.02	44513.83

8.56 soil_XYL_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51926.47	45063.27	1016965150

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.032	-0.186	0.122	1	51926.47	45063.27

8.57 soil_CEL_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53118.19	43648.91	129713067

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.051	-0.145	0.246	1	53118.19	43648.91

8.58 soil_NAG_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53297.85	43143.25	559935875

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.065	-0.392	0.259	1	53297.85	43143.25

8.59 soil_LAP_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53290.02	45022.28	1471666862

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.013	-0.124	0.097	1	53290.02	45022.28

8.60 soil_MUP_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51326.73	41936.9	253537481

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.05	-0.161	0.062	1	51326.73	41936.9

8.61 soil_BIS_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52035.94	45117.31	1298056656

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.074	-0.184	0.036	1	52035.94	45117.31

8.62 soil_S_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51264.29	43462.54	422033495

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.026	-0.242	0.187	1	51264.29	43462.54

8.63 soil_BG.NAG_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50065.21	43618.49	1820284231

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.109	-0.346	0.128	1	50065.21	43618.49

8.64 soil_BG.MUP_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51616.77	42053.02	208349016

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.097	-0.266	0.07	1	51616.77	42053.02

8.65 soil_NAG.MUP_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53679.24	46089.57	256697027

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.003	-0.222	0.227	1	53679.24	46089.57

8.66 soil_BG.S_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52979.52	43800.39	458011613

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.099	-0.332	0.134	1	52979.52	43800.39

8.67 soil_NAG.S_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51050.87	43038.25	1115811220

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.006	-0.29	0.275	1	51050.87	43038.25

8.68 soil_MUP.S_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51580.23	43167.48	424644961

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.036	-0.211	0.14	1	51580.23	43167.48

8.69 soil_ph.h2o_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51867.32	46079.65	449266213

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.012	-0.019	0.042	1	51867.32	46079.65

8.70 soil_ph.cacl2_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51764.06	43692.87	808782001

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.003	-0.027	0.032	1	51764.06	43692.87

8.71 soil_tc.g.kg.18_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53329.79	44767.88	557080911

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.006	-0.054	0.066	1	53329.79	44767.88

8.72 soil_tn.g.kg.18_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51130.27	44575.58	909676702

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.005	-0.056	0.066	1	51130.27	44575.58

8.73 soil_tp.g.kg.18_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	55070.58	44592.65	1517616170

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.112	-0.042	0.265	1	55070.58	44592.65

8.74 soil_CN_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	53154.82	41924.48	980893121

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0	-0.035	0.035	1	53154.82	41924.48

8.75 soil_CP_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	49077.93	43640.13	1877978843

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.112	-0.279	0.055	1	49077.93	43640.13

8.76 soil_NP_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	49230.4	42944.99	481022454

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.114	-0.286	0.059	1	49230.4	42944.99

8.77 soil_k2so4.C_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	49114.65	43826.35	578047706

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.002	-0.056	0.06	1	49114.65	43826.35

8.78 soil_nitrate.2017_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	54872.61	44939.65	1019934469

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.149	-0.358	0.056	1	54872.61	44939.65

8.79 soil_resin.p_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50658.03	41551.49	2007192121

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	1.464	0.607	2.299	1	50658.03	41551.49

8.80 soil_ox.Al_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	55632.56	45127.43	1682132424

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.006	-0.079	0.092	1	55632.56	45127.43

8.81 soil_ox.Fe_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51232.56	44039.44	443025579

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.029	-0.1	0.158	1	51232.56	44039.44

8.82 soil_Al_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50111.19	42882.31	955637997

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.052	-0.14	0.037	1	50111.19	42882.31

8.83 soil_Ca_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52371.71	45637.49	2096082951

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.568	0.282	0.856	1	52371.71	45637.49

8.84 soil_Fe_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51719.29	44508.7	1213893636

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.074	-0.22	0.367	1	51719.29	44508.7

8.85 soil_K_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51844.09	43639.53	678770394

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.029	-0.103	0.16	1	51844.09	43639.53

8.86 soil_Mg_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52095.78	45142.31	1794541253

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.033	-0.156	0.223	1	52095.78	45142.31

8.87 soil_Mn_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	51929.86	44205.72	1123578253

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.067	-0.247	0.378	1	51929.86	44205.72

8.88 soil_Na_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	47703.16	41307.24	2114117209

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.11	-0.947	0.724	1	47703.16	41307.24

8.89 soil_TEB_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50372.42	46346.36	95652643

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.304	0.112	0.496	1	50372.42	46346.36

8.90 soil_ECEC_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	48552.37	44552.81	580602680

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.044	-0.033	0.122	1	48552.37	44552.81

8.91 soil_BS_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	52387.68	43695.21	1042335918

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	0.558	0.255	0.859	1	52387.68	43695.21

8.92 soil_Al.sat_p_model

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	var ~ treat.pool.p	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	54009.19	47074.01	656346342

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_treat.pool.pp	-0.53	-0.825	-0.236	1	54009.19	47074.01

8.93 BIS by Nitrate rate

soil_mic$Nrat <- soil_mic$nitrate.2017/soil_mic$resin.p

ggplot(soil_mic, aes(x = Nrat, y = BIS)) + geom_point() + geom_smooth(method = "lm") +
    theme_classic(base_size = 18)

BIS_Nitrate_mod <- brm(BIS ~ Nrat, data = soil_mic, chains = chains,
    family = Gamma(link = "log"), iter = iters, control = list(adapt_delta = 0.99,
        max_treedepth = 15), cores = chains, prior = prior, file = "./data/processed/soil_BIS_by_Nitrate_rate_model",
    file_refit = "on_change")

extended_summary(fit = BIS_Nitrate_mod, highlight = TRUE, remove.intercepts = TRUE)

8.94 BIS_Nitrate_mod

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	BIS ~ Nrat	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	50530.8	42963.66	1164919495

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_Nrat	0.017	0	0.035	1	50530.8	42963.66

9 CO2 data

9.1 All sampling events

co2mean <- read.csv("./data/raw/CO2_dat_mean.csv")

co2mean$date4 <- as.Date(co2mean$date4)
co2mean$day <- co2mean$date4 - min(co2mean$date4)

exp_flux_pool_mod <- brm(exp.flux ~ pool.n * day + (1 | id.plot/collar.generic),
    data = co2mean, chains = chains, family = student(), iter = iters,
    control = list(adapt_delta = 0.99, max_treedepth = 15), cores = chains,
    prior = prior, file = "./data/processed/exp_flux_pool_n_model",
    file_refit = "on_change")

Running /usr/lib/R/bin/R CMD SHLIB foo.c using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’ gcc -I”/usr/share/R/include” -DNDEBUG -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/Rcpp/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/unsupported” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/BH/include” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/src/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppParallel/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/rstan/include” -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include ‘/home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/stan/math/prim/fun/Eigen.hpp’ -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -fpic -g -O2 -ffile-prefix-map=/build/r-base-BPEaBJ/r-base-4.5.0=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wno-format-security -c foo.c -o foo.o In file included from /home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/Eigen/Core:19, from /home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/Eigen/Dense:1, from /home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22, from : /home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: cmath: No such file or directory 679 | #include | ^~~~~~~ compilation terminated. make: *** [/usr/lib/R/etc/Makeconf:202: foo.o] Error 1

extended_summary(fit = exp_flux_pool_mod, highlight = TRUE, remove.intercepts = TRUE)

9.2 exp_flux_pool_mod

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	exp.flux ~ pool.n * day + (1 | id.plot/collar.generic)	student (identity)	b-normal(0, 10) Intercept-normal(0, 50) nu-gamma(2, 0.1) sd-student_t(3, 0, 2.5) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	33000.07	43714.7	1386974416

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_pool.nnoN	-0.839	-1.519	-0.165	1	33000.07	43714.70
b_day	-0.009	-0.012	-0.006	1	87398.98	60692.18
b_pool.nnoN:day	0.006	0.002	0.009	1	90354.29	61147.64

exp_flux_pool_p_mod <- brm(exp.flux ~ pool.p * day + (1 | id.plot/collar.generic),
    data = co2mean, chains = chains, family = student(), iter = iters,
    control = list(adapt_delta = 0.99, max_treedepth = 15), cores = chains,
    prior = prior, file = "./data/processed/exp_flux_pool_p_model",
    file_refit = "on_change")

Running /usr/lib/R/bin/R CMD SHLIB foo.c using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’ gcc -I”/usr/share/R/include” -DNDEBUG -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/Rcpp/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/unsupported” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/BH/include” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/src/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppParallel/include/” -I”/home/m/R/x86_64-pc-linux-gnu-library/4.5/rstan/include” -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include ‘/home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/stan/math/prim/fun/Eigen.hpp’ -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -fpic -g -O2 -ffile-prefix-map=/build/r-base-BPEaBJ/r-base-4.5.0=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wno-format-security -c foo.c -o foo.o In file included from /home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/Eigen/Core:19, from /home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/Eigen/Dense:1, from /home/m/R/x86_64-pc-linux-gnu-library/4.5/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22, from : /home/m/R/x86_64-pc-linux-gnu-library/4.5/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: cmath: No such file or directory 679 | #include | ^~~~~~~ compilation terminated. make: *** [/usr/lib/R/etc/Makeconf:202: foo.o] Error 1

extended_summary(fit = exp_flux_pool_p_mod, highlight = TRUE, remove.intercepts = TRUE)

9.3 exp_flux_pool_p_mod

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	exp.flux ~ pool.p * day + (1 | id.plot/collar.generic)	student (identity)	b-normal(0, 10) Intercept-normal(0, 50) nu-gamma(2, 0.1) sd-student_t(3, 0, 2.5) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	36045.7	47450.92	1801513762

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_pool.pP	0.176	-0.536	0.899	1	36045.70	47450.92
b_day	-0.006	-0.008	-0.003	1	99278.34	61672.84
b_pool.pP:day	0.001	-0.002	0.005	1	94342.06	59599.81

9.4 Only first and last sampling events

co2mean <- read.csv("./data/raw/CO2_dat_mean.csv")

co2mean$date4 <- as.Date(co2mean$date4)
co2mean$day <- co2mean$date4 - min(co2mean$date4)

sub_co2mean <- co2mean[co2mean$day %in% c(0, max(co2mean$day)), ]

sub_co2mean$day_f <- ifelse(sub_co2mean$day == 0, "first", "last")

exp_flux_pool_fl_mod <- brm(exp.flux ~ pool.n * day_f + (1 | id.plot/collar.generic),
    data = sub_co2mean, chains = chains, family = Gamma(link = "log"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/exp_flux_pool_n_first_last_model",
    file_refit = "on_change")

extended_summary(fit = exp_flux_pool_fl_mod, highlight = TRUE, remove.intercepts = TRUE)

9.5 exp_flux_pool_fl_mod

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	exp.flux ~ pool.n * day_f + (1 | id.plot/collar.generic)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 2.5) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	41481.73	52368.68	793319142

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_pool.nnoN	-0.083	-0.241	0.074	1	41481.73	52368.68
b_day_flast	-0.184	-0.285	-0.084	1	66962.94	61807.41
b_pool.nnoN:day_flast	0.067	-0.069	0.201	1	64565.91	61471.79

exp_flux_pool_p_fl_mod <- brm(exp.flux ~ pool.p * day_f + (1 | id.plot/collar.generic),
    data = sub_co2mean, chains = chains, family = Gamma(link = "log"),
    iter = iters, control = list(adapt_delta = 0.99, max_treedepth = 15),
    cores = chains, prior = prior, file = "./data/processed/exp_flux_pool_p_first_last_model",
    file_refit = "on_change")

extended_summary(fit = exp_flux_pool_p_fl_mod, highlight = TRUE, remove.intercepts = TRUE)

9.6 exp_flux_pool_p_fl_mod

	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	exp.flux ~ pool.p * day_f + (1 | id.plot/collar.generic)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 2.5) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	35314.55	47345.04	1209038702

	Estimate	l-95% CI	u-95% CI	Rhat	Bulk_ESS	Tail_ESS
b_pool.pP	0.017	-0.142	0.175	1	35314.55	47345.04
b_day_flast	-0.154	-0.254	-0.054	1	57512.82	57924.25
b_pool.pP:day_flast	0.011	-0.125	0.147	1	54256.51	55731.36

10 Combined model diagnostics

check_rds_fits(path = "./data/processed", html = TRUE)

	fit	formula	family	priors	iterations	chains	thinning	warmup	diverg_transitions	rhats > 1.05	min_bulk_ESS	min_tail_ESS	seed
1	cn_model.rds	cn.mol.kg ~ treat * days.sc + (1 | plot.f)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	21056	29398	1143833718
2	CN_pooled_model.rds	CN ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	30321	38267	675162061
3	cn_pooled_model2.rds	cn.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	25964	38212	161678448
4	co2_output_n_model.rds	annual.flux ~ pool.n	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	29286	36219	306100029
5	co2_output_p_model.rds	annual.flux ~ pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	29399	38777	1833764711
6	cp_model.rds	cp.mol.kg ~ treat * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 106.3)	40000	4	1	20000	0 (0%)	0	7445	6323	1789568456
7	cp_pooled_model.rds	cp.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 106.3)	40000	4	1	20000	0 (0%)	0	7246	7047	1583776905
8	CP.no.outlier_pooled_model.rds	CP.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 10.7)	40000	4	1	20000	0 (0%)	0	29778	39107	257447415
9	exp_flux_pool_n_first_last_model.rds	exp.flux ~ pool.n * day_f + (1 | id.plot/collar.generic)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 2.5) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	10294	24738	793319142
10	exp_flux_pool_n_model.rds	exp.flux ~ pool.n * day + (1 | id.plot/collar.generic)	student (identity)	b-normal(0, 10) Intercept-normal(0, 50) nu-gamma(2, 0.1) sd-student_t(3, 0, 2.5) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	6660	18983	1386974416
11	exp_flux_pool_p_first_last_model.rds	exp.flux ~ pool.p * day_f + (1 | id.plot/collar.generic)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 2.5) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	8835	19530	1209038702
12	exp_flux_pool_p_model.rds	exp.flux ~ pool.p * day + (1 | id.plot/collar.generic)	student (identity)	b-normal(0, 10) Intercept-normal(0, 50) nu-gamma(2, 0.1) sd-student_t(3, 0, 2.5) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	6727	19294	1801513762
13	k_litter_model.rds	k.sil.litt ~ Treatment + (1 | quadrat)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	8 (1e-04%)	0	20484	26650	1990407839
14	k_litter_n_no_n_model.rds	k.sil.litt ~ n.treat + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	15 (0.0001875%)	0	20084	20797	1667737665
15	k_litter_p_nop_model.rds	k.sil.litt ~ p.treat + (1 | quadrat)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	22 (0.000275%)	0	19481	19365	803160143
16	k_litter_pooled_model.rds	k.sil.litt ~ pool.p + pool.n + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	33 (0.0004125%)	0	15776	12192	913293624
17	k_wood_n_no_n_model.rds	k.sil.wood ~ n.treat + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	17 (0.0002125%)	0	18256	21244	1393075606
18	k_wood_p_no_p_model.rds	k.sil.wood ~ p.treat + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	40000	4	1	20000	10 (0.000125%)	0	20314	25040	1645430139
19	k_wood_pooled_model.rds	sil.k.wood ~ pool.p + pool.n + (1 | quadrat)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	19 (0.0002375%)	0	18913	27175	977910876
20	k_wood_treatment_model.rds	k.sil.wood ~ Treatment + (1 | quadrat)	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) shape-gamma(0.01, 0.01)	80000	4	1	40000	65 (0.00040625%)	0	37556	25286	855747887
21	litter_input_n_model.rds	cr.total ~ n.pooled	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	27933	34717	26169603
22	litter_input_p_model.rds	cr.total ~ p.pooled	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	27654	36152	603178782
23	litter.mg.C.ha.yr_pooled_model.rds	litter.mg.C.ha.yr ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	29444	38067	308107221
24	litter.n.content.rem_model.rds	litter.n.content.prop.initial ~ treat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	11049	24371	1667653932
25	litter.n.perc_model.rds	prop.n ~ treat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	27802	36645	129583210
26	litter.p.content.perc.initial_pooled_model.rds	litter.p.content.prop.initial ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	15873	21732	43891969
27	litter.p.content.rem_model.rds	litter.p.content.prop.initial ~ treat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	13259	17304	915208762
28	litter.p.perc_model.rds	prop.p ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	34825	36680	838385675
29	n_content_by_pooled_model.rds	litter.n.content.prop.initial ~ pool.n * days.sc + pool.p * days.sc + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	11468	21590	1616033078
30	n_per_by_leave_rem_model.rds	prop.n ~ prom.hoja.reman.sc * treat + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	27747	36872	1419862621
31	n_perc_by_pooled_model.rds	prop.n ~ pool.n * days.sc + pool.p * days.sc + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	28534	41884	915417491
32	np_model.rds	np.mol.kg ~ treat * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 5.3)	40000	4	1	20000	0 (0%)	0	21703	35240	579910719
33	np_pooled_model.rds	np.mol.kg ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sd-student_t(3, 0, 20) sigma-student_t(3, 0, 5.3)	40000	4	1	20000	0 (0%)	0	21942	32981	676130983
34	NP.no.outlier_pooled_model.rds	NP.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	27893	35607	2143149156
35	p_per_by_leave_rem_model.rds	prop.p ~ prom.hoja.reman.sc * treat + (1 | plot)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	32890	39496	168759349
36	ph.h2o_pooled_model.rds	ph.h2o ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	28904	39052	1664004957
37	prop.litter.rem_model.rds	prop.wood.rem ~ trat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	20000	4	1	10000	0 (0%)	0	11934	17029	1828689869
38	prop.litter.rem_pooled_model.rds	prop.litter.rem ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	27021	36431	1782064894
39	prop.wood.rem_model.rds	prop.wood.rem ~ trat * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	24920	35876	759730670
40	prop.wood.rem_pooled_model.rds	prop.wood.rem ~ pool.n * days.sc + pool.p * days.sc + (1 | plot.f)	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01) sd-student_t(3, 0, 20)	40000	4	1	20000	0 (0%)	0	25312	36334	28695825
41	resin.p_pooled_model.rds	resin.p ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 30.9)	40000	4	1	20000	0 (0%)	0	33460	45980	1531674567
42	resin.p.no.outlier_pooled_model.rds	resin.p.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 27)	40000	4	1	20000	0 (0%)	0	31940	41129	2096696539
43	soil_AG_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29525	36818	413707254
44	soil_AG_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30025	37761	1888031748
45	soil_Al_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29808	36724	1520224625
46	soil_Al_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28622	37554	955637997
47	soil_Al.sat_model.rds	var ~ treat.pool.n	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29441	38080	28613706
48	soil_Al.sat_p_model.rds	var ~ treat.pool.p	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30409	38045	656346342
49	soil_BG_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29120	38568	1423846020
50	soil_BG_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29711	37361	2015288702
51	soil_BG.MUP_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29376	38290	451859965
52	soil_BG.MUP_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28854	35992	208349016
53	soil_BG.NAG_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29385	37766	1640455467
54	soil_BG.NAG_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28726	38258	1820284231
55	soil_BG.S_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30480	37610	1321964644
56	soil_BG.S_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29644	38046	458011613
57	soil_BIS_by_Nitrate_rate_model.rds	BIS ~ Nrat	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29949	38069	1164919495
58	soil_BIS_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28874	37133	1854109569
59	soil_BIS_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29223	35552	1298056656
60	soil_BS_model.rds	var ~ treat.pool.n	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29932	38924	842999925
61	soil_BS_p_model.rds	var ~ treat.pool.p	beta (logit)	b-normal(0, 10) Intercept-normal(0, 50) phi-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30266	37000	1042335918
62	soil_Ca_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30666	37929	2049339314
63	soil_Ca_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28802	38600	2096082951
64	soil_CEL_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30598	36053	1495070855
65	soil_CEL_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28419	35678	129713067
66	soil_CN_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28714	37750	1322327565
67	soil_CN_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28666	37146	980893121
68	soil_CP_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28973	36489	101726671
69	soil_CP_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29487	37362	1877978843
70	soil_ECEC_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29857	35530	1318796507
71	soil_ECEC_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29688	37011	580602680
72	soil_Fe_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29182	37215	648824471
73	soil_Fe_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28815	35498	1213893636
74	soil_K_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29740	36260	945628376
75	soil_K_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28739	37225	678770394
76	soil_k2so4.C_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29316	37526	1070220198
77	soil_k2so4.C_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28919	37492	578047706
78	soil_LAP_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29020	36260	61789085
79	soil_LAP_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29211	37723	1471666862
80	soil_Mg_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28430	35458	1413138599
81	soil_Mg_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30189	38131	1794541253
82	soil_mic.c_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29726	38442	1048612606
83	soil_mic.c_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29534	38510	1410388778
84	soil_mic.cn_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30052	37425	945490801
85	soil_mic.cn_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29105	37961	1824816502
86	soil_mic.cp_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29327	38116	758109104
87	soil_mic.cp_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30850	38635	504408909
88	soil_mic.n_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29159	38617	620083842
89	soil_mic.n_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29908	37760	2133030045
90	soil_mic.np_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30291	38743	623667626
91	soil_mic.np_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29826	36889	1166263785
92	soil_mic.p_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30210	37203	1705825401
93	soil_mic.p_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29978	39417	569771158
94	soil_Mn_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	31016	39420	1222938933
95	soil_Mn_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29933	38473	1123578253
96	soil_MUP_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30075	36456	1487964286
97	soil_MUP_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28785	36889	253537481
98	soil_MUP.S_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30129	37840	1502704492
99	soil_MUP.S_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28168	36530	424644961
100	soil_Na_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30455	36192	504747857
101	soil_Na_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	31007	38133	2114117209
102	soil_NAG_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29040	38968	157324855
103	soil_NAG_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29542	36999	559935875
104	soil_NAG.MUP_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30190	36686	479400828
105	soil_NAG.MUP_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29694	36241	256697027
106	soil_NAG.S_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29222	37742	1482520037
107	soil_NAG.S_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28629	37036	1115811220
108	soil_nitrate.2017_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28974	38876	359163032
109	soil_nitrate.2017_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29368	37214	1019934469
110	soil_NP_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29165	38048	1270710134
111	soil_NP_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28070	34311	481022454
112	soil_ox.Al_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28666	38300	1320258032
113	soil_ox.Al_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29299	37531	1682132424
114	soil_ox.Fe_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29963	37742	836977121
115	soil_ox.Fe_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29540	37662	443025579
116	soil_ph.cacl2_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30031	36457	1401049143
117	soil_ph.cacl2_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28997	36056	808782001
118	soil_ph.h2o_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30325	38491	795850558
119	soil_ph.h2o_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30466	37967	449266213
120	soil_resin.p_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29537	36683	876971613
121	soil_resin.p_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29233	36521	2007192121
122	soil_S_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29649	37015	1300695161
123	soil_S_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29255	37268	422033495
124	soil_tc.g.kg.18_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29106	37710	7447136
125	soil_tc.g.kg.18_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30219	36218	557080911
126	soil_TEB_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30012	36939	221157550
127	soil_TEB_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28848	37219	95652643
128	soil_tn.g.kg.18_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29156	37302	1146528163
129	soil_tn.g.kg.18_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29028	37188	909676702
130	soil_tp.g.kg.18_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	28718	37097	1168252258
131	soil_tp.g.kg.18_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29052	38229	1517616170
132	soil_XYL_model.rds	var ~ treat.pool.n	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	29679	36636	250356946
133	soil_XYL_p_model.rds	var ~ treat.pool.p	gamma (log)	b-normal(0, 10) Intercept-normal(0, 50) shape-gamma(0.01, 0.01)	40000	4	1	20000	0 (0%)	0	30590	37416	1016965150
134	tc.g.kg.18_pooled_model.rds	tc.g.kg.18 ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 4.5)	40000	4	1	20000	0 (0%)	0	31016	39122	1374186359
135	tn.g.kg.18_pooled_model.rds	tn.g.kg.18 ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 2.5)	40000	4	1	20000	0 (0%)	0	29686	37369	772312416
136	tp.g.kg.18_pooled_model.rds	tp.g.kg.18 ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 565.6)	40000	4	1	20000	0 (0%)	0	35762	46463	532966702
137	tp.g.kg.18.no.outlier_pooled_model.rds	tp.g.kg.18.no.outlier ~ pool.n + pool.p	gaussian (identity)	b-normal(0, 10) Intercept-normal(0, 50) sigma-student_t(3, 0, 478.9)	40000	4	1	20000	0 (0%)	0	36458	47868	1716433649

 

Session information

R version 4.5.0 (2025-04-11)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.5 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.10.0 
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0  LAPACK version 3.10.0

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=es_CR.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=es_CR.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=es_CR.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=es_CR.UTF-8 LC_IDENTIFICATION=C       

time zone: America/Costa_Rica
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] brmsish_1.0.0     ggdist_3.3.3      brms_2.22.0       Rcpp_1.1.0       
 [5] viridis_0.6.5     viridisLite_0.4.2 ggridges_0.5.6    posterior_1.6.1  
 [9] ggrepel_0.9.6     cowplot_1.1.3     tidybayes_3.0.7   ggplot2_3.5.2    
[13] readxl_1.4.5      knitr_1.50        kableExtra_1.4.0 

loaded via a namespace (and not attached):
 [1] pbapply_1.7-4        gridExtra_2.3        formatR_1.14        
 [4] remotes_2.5.0        inline_0.3.21        sandwich_3.1-1      
 [7] rlang_1.1.6          magrittr_2.0.3       multcomp_1.4-28     
[10] matrixStats_1.5.0    compiler_4.5.0       mgcv_1.9-3          
[13] loo_2.8.0            systemfonts_1.2.3    callr_3.7.6         
[16] vctrs_0.6.5          reshape2_1.4.4       stringr_1.5.1       
[19] pkgconfig_2.0.3      arrayhelpers_1.1-0   crayon_1.5.3        
[22] fastmap_1.2.0        backports_1.5.0      labeling_0.4.3      
[25] rmarkdown_2.29       ps_1.9.1             ragg_1.4.0          
[28] purrr_1.0.4          xfun_0.52            jsonlite_2.0.0      
[31] gghalves_0.1.4       parallel_4.5.0       R6_2.6.1            
[34] stringi_1.8.7        RColorBrewer_1.1-3   StanHeaders_2.32.10 
[37] cellranger_1.1.0     estimability_1.5.1   rstan_2.32.7        
[40] zoo_1.8-14           bayesplot_1.12.0     Matrix_1.7-3        
[43] splines_4.5.0        tidyselect_1.2.1     rstudioapi_0.17.1   
[46] abind_1.4-8          yaml_2.3.10          codetools_0.2-20    
[49] processx_3.8.6       curl_6.4.0           pkgbuild_1.4.8      
[52] lattice_0.22-7       tibble_3.3.0         plyr_1.8.9          
[55] withr_3.0.2          bridgesampling_1.1-2 coda_0.19-4.1       
[58] evaluate_1.0.3       survival_3.8-3       sketchy_1.0.5       
[61] RcppParallel_5.1.10  xml2_1.3.8           pillar_1.11.0       
[64] tensorA_0.36.2.1     packrat_0.9.2        checkmate_2.3.2     
[67] stats4_4.5.0         distributional_0.5.0 generics_0.1.4      
[70] rstantools_2.4.0     scales_1.4.0         xtable_1.8-4        
[73] glue_1.8.0           emmeans_1.11.1       tools_4.5.0         
[76] xaringanExtra_0.8.0  mvtnorm_1.3-3        grid_4.5.0          
[79] tidyr_1.3.1          ape_5.8-1            QuickJSR_1.7.0      
[82] nlme_3.1-168         cli_3.6.5            textshaping_1.0.1   
[85] svUnit_1.0.6         svglite_2.1.3        Brobdingnag_1.2-9   
[88] dplyr_1.1.4          V8_6.0.4             gtable_0.3.6        
[91] digest_0.6.37        TH.data_1.1-3        htmlwidgets_1.6.4   
[94] farver_2.1.2         htmltools_0.5.8.1    lifecycle_1.0.4     
[97] MASS_7.3-65