make_excretion()
load('../data/data_excretion.Rda')
kable(head(data_exc))
ID date time1 vial1 vol1 time2 vial2 vol2 length SRP_before SRP_after NH4_before NH4_after time_elapsed Notes P_exc N_exc treatment population
HQ.LOL.1 12/9 8:46 95 22.0 9:07 104 20 19.93 0.00 0.04 2.10 3.20 0:21 all lengths from pre-experiment sheet 0.04 1.10 HQ LL
HQ.LOL.2 12/9 8:47 96 21.5 9:08 102 20 18.60 0.07 -0.04 2.15 2.20 0:21 -0.11 0.05 HQ LL
HQ.LOL.3 12/9 8:49 97 22.5 9:10 91 20 18.30 0.04 0.11 2.05 2.09 0:21 0.07 0.04 HQ LL
HQ.LOL.4 12/9 8:51 98 19.5 9:12 87 20 18.10 0.03 0.06 2.17 2.21 0:21 0.03 0.04 HQ LL
HQ.LOL.5 12/9 8:53 105 22.0 9:14 93 20 19.66 -0.23 -0.17 0.61 0.68 0:21 0.06 0.07 HQ LL
HQ.LOL.6 12/9 8:55 100 21.0 9:16 89 20 18.84 -0.31 -0.21 0.23 0.31 0:21 0.10 0.08 HQ LL

We will initially only use measurements over zero, because they need to be logged.

data_exc <- data_exc %>%
  filter(N_exc > 0, P_exc > 0)


ggplot(data_exc, aes(y = N_exc, x = length, col = treatment, group = population)) +
  geom_point() +
  facet_grid( ~ population) +
  scale_x_log10() + scale_y_log10() +
  labs(y = expression(paste('N excretion (', mu, 'ug/min)')), 
       x = 'Standard length (mm)') +
  theme_bw()

ggplot(data_exc, aes(y = P_exc, x = length, col = treatment, group = population)) +
  geom_point() +
  facet_grid( ~ population) +
  scale_x_log10() + scale_y_log10() +
  labs(y = expression(paste('N excretion (', mu, 'ug/min)')), 
       x = 'Standard length (mm)') +
  theme_bw()

Data Analyses

In order to test for differences in excretion rates we fit two linear models (one for N and one for P). Because excretion rate and fish size scale alometrically, we log-transformed excretion rates when including them as response variables, and included the logarithm of fish length as a covariate. We included population, food treatment, and their interaction, as explanatory factors.

model_N <- lm(log(N_exc) ~ log(length) + treatment * population, data = data_exc)

knitr::kable(summary(model_N)$coefficients)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.129439 9.1297608 -0.4523052 0.6549495
log(length) 1.023238 3.1747477 0.3223054 0.7499012
treatmentLQ -1.096752 0.4895752 -2.2402116 0.0342066
populationLL -1.741545 0.5575805 -3.1233958 0.0044804
treatmentLQ:populationLL 2.534747 0.7570780 3.3480665 0.0025792 
model_P <- lm(log(P_exc) ~ log(length) + treatment * population, data = data_exc)

knitr::kable(summary(model_P)$coefficients)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.4011766 9.7394008 0.8625969 0.3965587
log(length) -3.7479962 3.3867415 -1.1066673 0.2789732
treatmentLQ 0.2243500 0.5222666 0.4295699 0.6711883
populationLL -0.1655622 0.5948129 -0.2783434 0.7830380
treatmentLQ:populationLL 0.2296339 0.8076319 0.2843298 0.7784994