Hybrids First Flower GLMM
John Powers
Jan 18, 2018
Modified from hybridseeds.Rmd (April 2017)
Guides
- Bolker et al. 2009. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology & Evolution.
- Bolker. GLMM FAQ
- Bolker et al. 2011. GLMMs in action: gene-by-environment interaction in total fruit production of wild populations of Arabidopsis thaliana. Part 1, Part 2
- Bolker. In: Ecological Statistics: Contemporary Theory and Application
- Bolker et al. 2013. Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS
- Bolker et al. 2012. Owls example: a zero-inflated, generalized linear mixed model for count data
- other examples from Non-Linear Model Working Group
- A Practical Guide to Mixed Models in R
- Schielzeth and Nakagawa 2012. Nested by design: model fitting and interpretation in a mixed model era. Methods in Ecology and Evolution.
- Stroup. Rethinking the Analysis of Non-Normal Data in Plant and Soil Science
- Elston et al. 2001. Analysis of aggregation, a worked example: Numbers of ticks on red grouse chicks
- Annika Nelson. Ant GLMM Example
- R package pscl vignette: Regression Models for Count Data in R
Purpose
Identify reproductive barriers between two sympatric moth-pollinated plant species, Schiedea kaalae and S. hookeri by fitting a generalized linear mixed model (GLMM).
In the experimental design, the following crosstypes were made:
- within species, between population (may show outbreeding depression or heterosis)
- within species, within populations (may show inbreeding depression)
- hybrids between species (indicates species barrier from pollination to seed production)
In this analysis the response variable is the date of first flower (if the plant flowered and was scored) of each cross. Other barriers (hybrid survival, flowering) could be analyzed in a similar framework, with appropriate changes to the underlying distribution.
Fixed effects:
- crosstype - hybrids, within population, between populations
- species - species of the maternal plant that produced the Inflo Biofirstflower
Potential random effects:
- mompop - maternal plant population
- mompid - maternal plant, specified by its population and ID
- dadpop - paternal plant population
Data Import
ff <- read.table("firstflower6.csv", header=T, sep="\t")
ff$firstflower.date[ff$firstflower.date==""] <- NA
ff$firstflower.date[ff$use.firstflower!="yes"] <- NA
ff <- ff[!is.na(ff$firstflower.date),]
ff$firstflower.date <- as.Date(ff$firstflower.date)
ff <- ff[ff$crossid!=107,] ##FIND OUT WHAT CROSS THIS IS
ff$alive[ff$use.alive.flowered!="yes"] <- NA
ff <- ff[!is.na(ff$alive),]
crosses <- read.table("hybrids.csv", header=T, sep="\t", colClasses=c(mompop="factor", dadpop="factor"))
crosscol <- c("green","blue","orange","red")
#treat populations as factors
ff$mompop <- crosses$mompop[match(ff$crossid, crosses$crossid)]
ff$momid <- crosses$momid[match(ff$crossid, crosses$crossid)]
ff$species <- crosses$momsp[match(ff$crossid, crosses$crossid)]
ff$dadpop <- crosses$dadpop[match(ff$crossid, crosses$crossid)]
ff$dadid <- crosses$dadid[match(ff$crossid, crosses$crossid)]
ff$dadsp <- crosses$dadsp[match(ff$crossid, crosses$crossid)]
ff$crosstype <- crosses$crosstype[match(ff$crossid, crosses$crossid)]
ff$cross <- crosses$cross[match(ff$crossid, crosses$crossid)]
#rename crosstype codes
ff$crosstype <- factor(ff$crosstype, levels=c("between", "within", "hybrid"))
#made "between" the first reference level to facilitate comparison between outcrossing populations and hybridizing species
ff$mompop <- sapply(ff$mompop, mapvalues, from = c("794","866","899","879","892","904","3587"), to = c("WK","WK","WK","879WKG","892WKG","904WPG","3587WP"))
ff$dadpop <- sapply(ff$dadpop, mapvalues, from = c("794","866","899","879","892","904","3587"), to = c("WK","WK","WK","879WKG","892WKG","904WPG","3587WP"))
#define interactions
ff <- within(ff, sxc <- interaction(species,crosstype))
ff <- within(ff, sxcxm <- interaction(species,crosstype,mompop,momid))
ff <- within(ff, mompid <- as.factor(paste(mompop,momid,sep=".")))
ff <- within(ff, dadpid <- as.factor(paste(dadpop,dadid,sep=".")))
ff <- within(ff, smompop <- as.factor(paste(species,mompop,sep="")))
ff$firstflower <- as.integer(round(difftime(ff$firstflower.date, "2016-03-10")))
#check final structure
str(ff) 'data.frame': 1084 obs. of 39 variables:
$ index : int 1 2 4 12 13 15 17 24 25 26 ...
$ crossid : int 1 1 1 1 1 1 1 2 2 2 ...
$ plantid : Factor w/ 32 levels "0","1","10","11",..: 2 15 27 5 7 9 11 2 15 26 ...
$ crossid.plantid : Factor w/ 1618 levels "100-1","100-2",..: 98 154 220 104 107 113 123 650 718 752 ...
$ death.date : Factor w/ 133 levels "","100-2: 5/19/16",..: 1 1 1 1 1 1 1 1 1 1 ...
$ firstflower.day : Factor w/ 70 levels "","10/11","10/13",..: 3 23 26 43 36 21 22 56 40 27 ...
$ firstflower.date : Date, format: "2016-10-13" "2016-11-27" ...
$ use.alive.flowered : Factor w/ 3 levels "?","no","yes": 3 3 3 3 3 3 3 3 3 3 ...
$ alive : Factor w/ 3 levels "?","no","yes": 3 3 3 3 3 3 3 3 3 3 ...
$ use.firstflower : Factor w/ 4 levels "missed","never flowered",..: 4 4 4 4 4 4 4 4 4 4 ...
$ flowered : Factor w/ 3 levels "?","no","yes": 3 3 3 3 3 3 3 3 3 3 ...
$ saved.1 : Factor w/ 2 levels "no","yes": 1 1 1 1 2 1 1 1 1 1 ...
$ saved.2 : Factor w/ 2 levels "no","yes": 1 1 1 1 2 2 1 1 1 1 ...
$ sampled.VOC : Factor w/ 2 levels "no","yes": 1 1 1 1 2 2 1 1 1 1 ...
$ biomass.inflo : Factor w/ 2 levels "no","yes": 2 2 2 2 1 1 2 1 2 2 ...
$ biomass.firstinflo : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 1 ...
$ use.fib : Factor w/ 4 levels "double","#N/A",..: 4 4 4 4 4 4 4 4 1 2 ...
$ delay : Factor w/ 35 levels "","0","1","10",..: 25 30 30 14 27 18 30 25 23 35 ...
$ firstinflo.collect.date: Factor w/ 70 levels "2016-07-12","2016-07-21",..: 46 63 55 17 7 60 62 15 10 70 ...
$ firstinflo.weigh.date : Factor w/ 48 levels "2017-07-26","2017-07-27",..: 17 20 20 9 20 1 20 7 46 48 ...
$ firstinflo.biomass.mg : Factor w/ 1093 levels "100","100.1",..: 508 629 461 266 65 666 790 1 4 1093 ...
$ comments.fib : Factor w/ 31 levels "","10/13/17?",..: 1 1 1 1 1 1 1 1 10 24 ...
$ biomass.veg : logi NA NA NA NA NA NA ...
$ comments.SS : Factor w/ 44 levels "","?","\"1 terminlal infl\"",..: 1 1 1 1 1 1 1 1 1 1 ...
$ comments.JP.SGW : Factor w/ 78 levels "","105-9: 7/12/16 spray",..: 1 1 1 1 1 1 1 1 1 1 ...
$ mompop : Factor w/ 5 levels "3587WP","WK",..: 3 3 3 3 3 3 3 3 3 3 ...
$ momid : Factor w/ 17 levels "1","10","10-1",..: 7 7 7 7 7 7 7 7 7 7 ...
$ species : Factor w/ 2 levels "hook","kaal": 1 1 1 1 1 1 1 1 1 1 ...
$ dadpop : Factor w/ 5 levels "3587WP","WK",..: 3 3 3 3 3 3 3 3 3 3 ...
$ dadid : Factor w/ 23 levels "1","10","10-1",..: 19 19 19 19 19 19 19 3 3 3 ...
$ dadsp : Factor w/ 2 levels "hook","kaal": 1 1 1 1 1 1 1 1 1 1 ...
$ crosstype : Factor w/ 3 levels "between","within",..: 2 2 2 2 2 2 2 2 2 2 ...
$ cross : Factor w/ 4 levels "HH","HK","KH",..: 1 1 1 1 1 1 1 1 1 1 ...
$ sxc : Factor w/ 6 levels "hook.between",..: 3 3 3 3 3 3 3 3 3 3 ...
$ sxcxm : Factor w/ 510 levels "hook.between.3587WP.1",..: 195 195 195 195 195 195 195 195 195 195 ...
$ mompid : Factor w/ 23 levels "3587WP.10","3587WP.14",..: 8 8 8 8 8 8 8 8 8 8 ...
$ dadpid : Factor w/ 24 levels "3587WP.10","3587WP.14",..: 9 9 9 9 9 9 9 7 7 7 ...
$ smompop : Factor w/ 5 levels "hook879WKG","hookWK",..: 1 1 1 1 1 1 1 1 1 1 ...
$ firstflower : int 217 262 241 159 138 257 260 152 144 243 ...Data Inspection
Replication
The sample sizes are unbalanced at all levels, including maternal population:
reptab <- with(ff, table(smompop,crosstype))
mosaic(reptab, pop=F)
labeling_cells(text = reptab, margin = 0)(reptab)
Replication is low for some within-population crosses. The replication is even lower for each maternal plant, so we need to be wary of estimates when subsetting at this level:
with(ff, kable(table(mompid,crosstype)))| between | within | hybrid | |
|---|---|---|---|
| 3587WP.10 | 0 | 1 | 0 |
| 3587WP.14 | 15 | 0 | 6 |
| 3587WP.15 | 5 | 3 | 0 |
| 3587WP.7 | 19 | 14 | 12 |
| 3587WP.A | 5 | 1 | 0 |
| 3587WP.C | 16 | 1 | 0 |
| 879WKG.10-1 | 42 | 5 | 28 |
| 879WKG.2-2 | 31 | 34 | 89 |
| 879WKG.G-2 | 14 | 9 | 26 |
| 879WKG.H-2 | 0 | 0 | 4 |
| 879WKG.N-5 | 7 | 7 | 17 |
| 892WKG.1 | 24 | 5 | 7 |
| 892WKG.10 | 1 | 0 | 0 |
| 892WKG.2 | 2 | 0 | 0 |
| 892WKG.3 | 3 | 1 | 2 |
| 892WKG.4 | 1 | 0 | 0 |
| 892WKG.5 | 13 | 7 | 5 |
| 904WPG.2 | 15 | 9 | 15 |
| 904WPG.3 | 22 | 30 | 2 |
| 904WPG.5 | 75 | 33 | 19 |
| WK.2 | 137 | 19 | 105 |
| WK.2E- 1 | 6 | 0 | 27 |
| WK.4 | 54 | 8 | 26 |
Overall data distribution
To identify the best-fitting distribution, we make quantile-quantile plots of the raw data against various distributions. The more points within the confidence interval envelopes, the better the fit. Later, we present quantile-quantile plots of the model residuals to assess model fit.
#QQ plots against various distributions
set.seed(1)
par(mfrow=c(1,3))
normal <- fitdistr(log(ff$firstflower+1), "normal")
qqp(log(ff$firstflower+1), "norm", main="Normal")
lognormal <- fitdistr(ff$firstflower+1, "lognormal")
qqp(ff$firstflower+1, "lnorm", main="Log Normal")
#pois <- fitdistr(ff$firstflower+1, "Poisson")
#qqp(ff$firstflower, "pois", pois$estimate, main="Poisson")
#nbinom <- fitdistr(ff$firstflower+1, "Negative Binomial")
#qqp(ff$firstflower+1, "nbinom", size = nbinom$estimate[[1]], mu=nbinom$estimate[[2]], main="Negative Binomial")
gamma <- fitdistr(ff$firstflower+1, "gamma")
qqp(ff$firstflower+1, "gamma", shape = gamma$estimate[[1]], rate = gamma$estimate[[2]], main="Gamma")
distributions by fixed factors
ggplot(ff,aes(x=firstflower,fill=species)) +
geom_histogram(data=subset(ff,species == "hook"), aes(y=-..density..),binwidth=10)+
geom_histogram(data=subset(ff,species == "kaal"), aes(y= ..density..),binwidth=10)+
coord_flip() + facet_grid(~crosstype) + labs(y="Histogram", x="Days to Flower")
distributions by random factors
ggplot(aes(y=firstflower, x=mompid, color=crosstype), data=ff) + geom_count(alpha=0.8) + coord_flip() + labs(x="Maternal plant", y="Days to Flower")
Fixed effects
Effects and interactions in these plots are simply given by the mean, which may be unduly influenced by high values.
intplot <- ggplot(ff,aes(x=crosstype,y=firstflower))+
geom_count(aes(size = ..prop.., group=sxc),alpha=0.5)+
stat_summary(aes(x=as.numeric(crosstype)),fun.y=mean,geom="line")+ facet_grid(~species)
intplot + aes(group=species, color=species)
Random effects
Maternal population
intplot + aes(group=mompop, color=mompop)
Maternal plant
intplot + aes(group=mompid, color=mompop)
Paternal population
intplot + aes(group=dadpop, color=dadpop)
Paternal plant
intplot + aes(group=dadpid, color=dadpop)
Run models on subsets
Run many generalized linear models on subsets of the data defined by crosstype | mompid to see if effects estimates are consistent within maternal plants.
Most maternal plant subsets agree, but some are problematic outliers. These plants can be picked out visually from the random effects interaction plot above, the estimated parameters of each subset model, and the QQ plot of the estimated parameters:
#had to get rid of species or mompid since mompid is nested inside species. dadpop also works
glm.lis <- lmList(log(firstflower)~crosstype|mompid,data=ff, family="gaussian")
plot.lmList(glm.lis,scale=list(x=list(relation="free"))) Loading required package: reshape
Attaching package: 'reshape' The following objects are masked from 'package:plyr':
rename, round_any The following object is masked from 'package:Matrix':
expand Using grp as id variables
qqmath.lmList(glm.lis)# Using as id variables
Models
We constructed the following models with the package glmmADMB. They all have the same fixed effects, species x crosstype, and response variable, log10(firstflower)
- X = standard GL(M)M
| distribution, Random Effects: | None | Maternal plant | Maternal population |
|---|---|---|---|
| normal (norm) | X | X | X |
#Normal (Gaussian) distribution, identity link
sc.norm <- lm(firstflower~species*crosstype, data=ff)
sc.mix.mompid <- lmer(firstflower~species*crosstype + (1|mompid), data=ff)
sc.mix.mompop <- lmer(firstflower~species*crosstype + (1|mompop), data=ff)
sc.mix.momdadpid <- lmer(firstflower~species*crosstype + (1|mompid) + (1|dadpid), data=ff)
sc.mix.momdadpop <- lmer(firstflower~species*crosstype + (1|mompop) + (1|dadpop), data=ff)Model comparison
AIC
We will use the Aikake Information Criterion to pick the model the best fits the data, penalized by the number of parameters. Differences of 2 units are significant.
sc.names <- c("sc.norm","sc.mix.mompid","sc.mix.mompop","sc.mix.momdadpid","sc.mix.momdadpop")
sc.list <- sapply(sc.names, get, USE.NAMES=T)
sc.AIC <- ICtab(sc.list,mnames=sc.names,type="AIC", base=T, delta=F) # for AICc, nobs=nobs(sc.list[[1]])
class(sc.AIC)<-"data.frame"
all.names <- c(sc.names)
all.list <- sapply(all.names, get, USE.NAMES=T)
all.AIC <- dfun(rbind(sc.AIC))
all.AIC <- all.AIC[order(all.AIC$dAIC),]
kable(all.AIC, format.arg=list(digits=3))| dAIC | df | |
|---|---|---|
| sc.mix.momdadpid | 0.00 | 9 |
| sc.mix.momdadpop | 4.79 | 9 |
| sc.mix.mompop | 9.87 | 8 |
| sc.mix.mompid | 10.10 | 8 |
| sc.norm | 38.01 | 7 |
The best-fiting model is a mixed model with the following components:
- response: firstflower
- fixed effects: species, crosstype, species x crosstype
- random effect: mompid dadpid
Overdispersion
Looking at the normal, fixed effects model, we see that the residuals are not normal:
shapiro.test(sc.norm$residuals)#raw residuals!
Shapiro-Wilk normality test
data: sc.norm$residuals
W = 0.92377, p-value < 2.2e-16Coefficients
The coefficients estimated for each model agree qualitatively.
sc <- sapply(sc.names, get, USE.NAMES=T)
coefplot2(sc, legend.x="topright",legend=T,legend.args=list(cex=0.8, xpd=T, inset=c(-0.1,0)), col.pts=sample(gg_color_hue(length(sc.names))), spacing=0.05, lwd.2=2, lwd.1=4, intercept=F)
Inference
We chose the model with nearly the best (lowest) AIC, to carry out inference tests and parameter estimation.
Description
mod <- sc.mix.momdadpid
print(mod) Linear mixed model fit by REML ['lmerMod']
Formula: firstflower ~ species * crosstype + (1 | mompid) + (1 | dadpid)
Data: ff
REML criterion at convergence: 10125.27
Random effects:
Groups Name Std.Dev.
dadpid (Intercept) 4.811
mompid (Intercept) 3.616
Residual 25.816
Number of obs: 1084, groups: dadpid, 24; mompid, 23
Fixed Effects:
(Intercept) specieskaal
168.119 15.772
crosstypewithin crosstypehybrid
6.467 18.236
specieskaal:crosstypewithin specieskaal:crosstypehybrid
-16.480 -10.611Test significance of random effects
Using a likelihood ratio test, with a null hypothesis of zero variance, the random effect (maternal plant) is significant for both model parts:
anova(sc.norm, sc.mix.mompid) #double this p-value. or simulate null by permuting data.Test significance of interaction
By dropping it from the model and performing a likelihood-ratio test, we see that the species x crosstype interaction is significant for the count model but not the binary model:
sxc.chisq <- drop1(mod, test="Chisq") #load from file
dfun(sxc.chisq) Single term deletions
Model:
firstflower ~ species * crosstype + (1 | mompid) + (1 | dadpid)
Df dAIC LRT Pr(Chi)
<none> 0.0000
species:crosstype 2 9.1181 13.118 0.001417 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model summary
The model estimated the following parameters, with individual parameter significance determined by the Wald z-test, and fixed effect significance determined by analysis of deviance Wald test.
summary(mod) Linear mixed model fit by REML ['lmerMod']
Formula: firstflower ~ species * crosstype + (1 | mompid) + (1 | dadpid)
Data: ff
REML criterion at convergence: 10125.3
Scaled residuals:
Min 1Q Median 3Q Max
-1.9387 -0.6797 -0.1938 0.4445 3.9211
Random effects:
Groups Name Variance Std.Dev.
dadpid (Intercept) 23.14 4.811
mompid (Intercept) 13.08 3.616
Residual 666.49 25.816
Number of obs: 1084, groups: dadpid, 24; mompid, 23
Fixed effects:
Estimate Std. Error t value
(Intercept) 168.119 2.870 58.58
specieskaal 15.772 3.897 4.05
crosstypewithin 6.467 3.389 1.91
crosstypehybrid 18.236 3.229 5.65
specieskaal:crosstypewithin -16.480 4.743 -3.47
specieskaal:crosstypehybrid -10.611 6.368 -1.67
Correlation of Fixed Effects:
(Intr) spcskl crsstypw crsstyph spcskl:crsstypw
specieskaal -0.738
crsstypwthn -0.303 0.223
crsstyphybr -0.657 0.654 0.269
spcskl:crsstypw 0.220 -0.330 -0.718 -0.196
spcskl:crsstyph 0.510 -0.675 -0.138 -0.765 0.206Anova(mod, type=3) Analysis of Deviance Table (Type III Wald chisquare tests)
Response: firstflower
Chisq Df Pr(>Chisq)
(Intercept) 3431.199 1 < 2.2e-16 ***
species 16.382 1 5.176e-05 ***
crosstype 32.055 2 1.095e-07 ***
species:crosstype 13.017 2 0.001491 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Predicted random effects
These are box and QQ (to check normality) plots of the estimated random effect of each maternal plant.
predre <- setNames(data.frame(RE=ranef(mod)$mompid,SD=ranef(mod, sd=T)$`1`),c("RE","SD"))
ggplot(predre, aes(x = rownames(predre),y=RE)) +
geom_point(size = 2) + coord_flip()+
geom_errorbar(aes(ymin = RE-SD, ymax = RE+SD)) + labs(x="Maternal plants", y="Predicted random effects")
#Count
reStack <- ldply(ranef(mod))
print( qqmath( ~`(Intercept)`|.id, data=reStack, scales=list(relation="free"),
prepanel = prepanel.qqmathline,
panel = function(x, ...) {
panel.qqmathline(x, ...)
panel.qqmath(x, ...)
},
layout=c(1,1)))Least square means
The least square means procedure can generate predictor estimates of each type, and give their significance groupings with a post-hoc Tukey test. S. hookeri-produced hybrids produce less Inflo Biofirstflower than either crosses between or within S. hookeri populations. The other differences are not significant, but remember that the fixed effect of hybrid (vs. between) was significant (model summary).
#Count
rg <- ref.grid(sc.mix.momdadpid) Loading required namespace: lmerTest#summary(rg)
sxc.lsm <- lsmeans(rg, ~ crosstype*species)
plot(sxc.lsm)
options(digits=4)
cld.mod <- cld(sxc.lsm, Letters=letters) #tukey letterings
cld.mod$response <- cld.mod$lsmean
cld.mod$uSE <- cld.mod$lsmean+cld.mod$SE
cld.mod$lSE <- cld.mod$lsmean-cld.mod$SE
cld.mod[rev(order(cld.mod$species, cld.mod$crosstype)),] crosstype species lsmean SE df lower.CL upper.CL .group response
hybrid kaal 191.5 3.982 91.62 183.6 199.4 c 191.5
within kaal 173.9 3.408 71.69 167.1 180.7 a 173.9
between kaal 183.9 2.630 40.77 178.6 189.2 bc 183.9
hybrid hook 186.4 2.547 26.56 181.1 191.6 bc 186.4
within hook 174.6 3.720 72.22 167.2 182.0 ab 174.6
between hook 168.1 2.870 24.66 162.2 174.0 a 168.1
uSE lSE
195.5 187.5
177.3 170.5
186.5 181.3
188.9 183.8
178.3 170.9
171.0 165.2
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95
P value adjustment: tukey method for comparing a family of 6 estimates
significance level used: alpha = 0.05H.wb <- with(cld.mod[cld.mod$species=="hook",], response[crosstype=="within"]/response[crosstype=="between"] - 1)
K.wb <- with(cld.mod[cld.mod$species=="kaal",], response[crosstype=="within"]/response[crosstype=="between"] - 1)
K.H <- with(cld.mod[cld.mod$crosstype=="between",], response[species=="kaal"]/response[species=="hook"] - 1)
maxsp <- ifelse(K.H>0, "kaal","hook")
minsp <- ifelse(K.H<0, "kaal","hook")
maxresp <- with(cld.mod, response[species==maxsp & crosstype=="between"])
minresp <- with(cld.mod, response[species==minsp & crosstype=="between"])
HK.resp <- with(cld.mod, response[species=="hook" & crosstype=="hybrid"])
KH.resp <- with(cld.mod, response[species=="kaal" & crosstype=="hybrid"])
HK.int <- with(cld.mod, ifelse(HK.resp > minresp & HK.resp < maxresp, (HK.resp-minresp)/(maxresp-minresp),
ifelse(HK.resp < minresp, HK.resp/minresp-1, HK.resp/maxresp-1)))
KH.int <- with(cld.mod, ifelse(KH.resp > minresp & KH.resp < maxresp, (KH.resp-minresp)/(maxresp-minresp),
ifelse(KH.resp < minresp, KH.resp/minresp-1, KH.resp/maxresp-1)))
intermed <- (minresp + maxresp) / 2
with(ff, wilcox.test(ff[species=="kaal" & crosstype=="hybrid","firstflower"], mu=intermed))
Wilcoxon signed rank test with continuity correction
data: ff[species == "kaal" & crosstype == "hybrid", "firstflower"]
V = 1800, p-value = 2e-04
alternative hypothesis: true location is not equal to 176with(ff, wilcox.test(ff[species=="hook" & crosstype=="hybrid","firstflower"], mu=intermed))
Wilcoxon signed rank test with continuity correction
data: ff[species == "hook" & crosstype == "hybrid", "firstflower"]
V = 32000, p-value = 3e-04
alternative hypothesis: true location is not equal to 176round(c(H.wb,K.wb,K.H,HK.int,KH.int),2) [1] 0.04 -0.05 0.09 0.01 0.04ggplot(as.data.frame(cld.mod), aes(y=response, x=relevel(crosstype, "within"), fill=species)) +
geom_col(position=position_dodge2()) +
geom_linerange(aes(ymin=lSE, ymax=uSE), position=position_dodge(0.9)) +
labs(x="", y="Days to flower",fill="Maternal species") +
scale_fill_manual(labels = c("S. hookeri ", "S. kaalae "), values=brewer.pal(name="Set1", n=3)[c(3,2)]) +
scale_x_discrete(labels = c("Intrapopulation", "Interpopulation", "Hybrid")) +
geom_text(aes(label=.group), position=position_dodge(0.9), hjust=0, vjust=-1) +
scale_y_continuous(expand = expand_scale(add=c(0,10)), breaks = scales::pretty_breaks(n = 5)) +
theme_classic() + theme(legend.text=element_text(face="italic", size=rel(1)), legend.position="bottom", axis.text = element_text(colour="black", size=rel(1)), text=element_text(size=14), axis.ticks.x = element_blank()) + geom_segment(aes(x=2.5, y=intermed, xend=3.5, yend=intermed))