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Rmd	3fdbcb2	lukeholman	2020-11-30	Tweaks Nov 2020

Load packages

library(tidyverse)
library(ggridges)

library(coxme)
library(lme4)
library(nlme)
library(brms)
library(tidybayes)

library(kableExtra)
library(knitrhooks) # install with devtools::install_github("nathaneastwood/knitrhooks")

output_max_height() # a knitrhook option

options(stringsAsFactors = FALSE)

Load data

# load eclosion data
eclosion.dat <- read.csv("data/1.eclosion_times.csv")

# remove vials seeded with more than 100 larvae
#unique(eclosion.dat[which(eclosion.dat$eclosing < 0), "ID"]) # 4 vials overseeded

eclosion.dat.trim <- eclosion.dat %>% 
  filter(ID %in% eclosion.dat[which(eclosion.dat$eclosing < 0), "ID"] == FALSE)

# expand data frame so each row is a single fly
ecl.dat <- reshape::untable(eclosion.dat.trim[ ,c(1:7, 9, 10)], 
                           num = eclosion.dat.trim[, 8])

# load wing length data
wing_length <- read.csv("data/1.wing_length.csv") %>% 
  filter(Side == 'L') %>% 
  # scale wing vein length to make effect size comparisons with other data sets?
  mutate(Length = as.numeric(scale(Length)))

# add replicate
wing_length$LINE <- paste0(wing_length$Treatment, substr(wing_length$Rep, 2, 2))

Survival analysis

We modeled juvenile development time using survival analysis. We measured the time in days from 1st instar larvae until eclosion (EVENT = 1) upon which flies were stored in ethanol before counting. Of the initially seeded 100 flies per vial, the remaining flies not emerging after two consecutive days of no observed eclosions were right censored (EVENT = 0) on the last observation day. In total 14400 larvae were seeded (100 larvae x 2 Treatment x 4 LINE per Treatment x 6 VIAL per LINE x 3 SEED days). For P1 only three vials were seeded on day B so we seeded 3 additional vials on day C. Four vials were seeded with too many larvae and excluded from analysis. In total 10448 flies eclosed during the observation period leaving 3552 individuals to be right censored on day 9. Censored flies were assigned sex based on the observed sex ratio of eclosees. We calculated the number of flies of each sex that emerged from each vial, and assigned the remaining censored individuals (of unknown sex) sex based on the proportion of individuals of each sex that did emerge, so that overall an equal sex ratio of females:males was assigned to each vial.

Kaplan-Meier survival curve

First we plot Kaplan-Meier survival curves without considering our full experimental design.

survminer::ggsurvplot(survfit(Surv(DAY, EVENT) ~ TRT + SEX, data = ecl.dat),
                      conf.int = TRUE,
                      risk.table = FALSE,
                      linetype = "SEX",
                      palette = c("pink", "skyblue", "red", "blue"),
                      fun = "event",
                      xlim = c(12, 21),
                      xlab = "Days",
                      ylab = "Cumulative proportion eclosed",
                      legend = 'right',
                      legend.title = "",
                      legend.labs = c("M \u2640","M \u2642",'P \u2640','P \u2642'),
                      break.time.by = 2,
                      ggtheme = theme_bw())

Version	Author	Date
989e86f	lukeholman	2020-12-18
96d1188	Martin Garlovsky	2020-12-13
df61dde	Martin Garlovsky	2020-12-03

Figure X: Kaplan-Meier curve for eclosion time (in days) for flies in each treatment and sex. +’s indicate censored individuals (n = 3552).

Check proportional hazards assumption

Next we need to check that the proportional hazards assumption is not violated before fitting the model, where crossing hazards (lines) indicate violation of the proportional hazards assumption.

survminer::ggsurvplot(survfit(Surv(DAY, EVENT) ~ TRT + SEX, data = ecl.dat),
                      conf.int = TRUE,
                      risk.table = FALSE,
                      linetype = "SEX",
                      palette = c("pink", "skyblue", "red", "blue"),
                      fun = "cloglog",
                      xlim = c(13, 21),
                      legend = 'right',
                      legend.title = "",
                      legend.labs = c("M \u2640","M \u2642",'P \u2640','P \u2642'),
                      break.time.by = 2,
                      ggtheme = theme_bw())

Version	Author	Date
989e86f	lukeholman	2020-12-18
96d1188	Martin Garlovsky	2020-12-13
7d4b609	Martin Garlovsky	2020-12-05
df61dde	Martin Garlovsky	2020-12-03

Figure X: ln(-ln(survival))

Fit the model in `brms`

We fit a Cox Proportional hazards model in brms using family = cox(), with time (days) to event (eclosion) as the response and sexual selection treatment (TRT; Monogamy or Polyandry), SEX (female or male) and their interaction as predictors with Seed day as a covariate. See here for a helpful explanation on fitting survival models in brms. We also include replicate treatment as a random intercept term for each of the 8 lines and a random slope term to allow the effect of selection treatment to vary across replicate lines. We also include vial ID as a random intercept term as individuals emerging from the same vial may show a correlated response.

Define priors

We set fairly conservative normal priors on the fixed effects (mean = 0, sd = 1) and half Cauchy priors on the random effects - LINE - (mean = 0, scale = 0.1). All other priors were left at the default in brms.

Run the model

The model is run over 4 chains with 5000 iterations each (with the first 2500 discarded as burn-in), for a total of 2500*4 = 10,000 posterior samples. Note that some of the brms functionality is not currently available for models using the cox family (e.g. posterior predictive checks).

if(!file.exists("output/cox_brms.rds")){
  
  cox_brm <- brm(DAY | cens(1 - EVENT) ~ TRT * SEX + SEED + (TRT|LINE) + (1|ID),
               iter = 5000, chains = 4, cores = 4,
               control = list(max_treedepth = 20,
                              adapt_delta = 0.999),
               data = ecl.dat, family = cox())
  
  saveRDS(cox_brm, "output/cox_brms.rds")
} else {
  cox_brm <- readRDS('output/cox_brms.rds')
}

Table of model parameter estimates - eclosion time

Formatted table

This tables shows the fixed effects estimates on eclosion time. The p column shows 1 - minus the “probability of direction”, i.e. the posterior probability that the reported sign of the estimate is correct given the data and the prior; subtracting this value from one gives a Bayesian equivalent of a one-sided p-value. Click the next tab to see a complete summary of the model and its output.

hyp_test <- bind_rows(
  hypothesis(cox_brm, 'TRTP = 0')$hypothesis,
  hypothesis(cox_brm, 'SEXm = 0')$hypothesis,
  hypothesis(cox_brm, 'TRTP:SEXm = 0')$hypothesis,
  hypothesis(cox_brm, 'SEEDB = 0')$hypothesis,
  hypothesis(cox_brm, 'SEEDC = 0')$hypothesis
) %>% 
  mutate(Parameter = c('Treatment (P)', 'Sex (M)', 'Treatment (P) x Sex (M)', 'Seed (B)', 'Seed (C)'),
         across(2:5, round, 3)) %>% 
  relocate(Parameter, Estimate, Est.Error, CI.Lower, CI.Upper, Star)

pvals <- bayestestR::p_direction(cox_brm) %>% 
  as.data.frame() %>%
  mutate(vars = map_chr(str_split(Parameter, "_"), ~ .x[2]),
         p_val = 1 - pd, 
         star = ifelse(p_val < 0.05, "\\*", "")) %>%
  select(vars, p_val, star)

hyp_test %>% 
  mutate(vars = c('TRTP', 'SEXm', 'TRTP.SEXm', 'SEEDB', 'SEEDC')) %>% 
  left_join(pvals %>% filter(vars != 'Intercept'), 
            by = c("vars")) %>% 
  select(Parameter, Estimate, Est.Error, CI.Lower, CI.Upper, `p` = p_val, star) %>% 
  rename(` ` = star) %>%
  mutate(p = ifelse(p > 0.001, round(p, 3), '< 0.001')) %>% 
  kable() %>% 
  kable_styling(full_width = FALSE)

Parameter	Estimate	Est.Error	CI.Lower	CI.Upper	p
Treatment (P)	-0.798	0.301	-1.332	-0.164	0.012	*
Sex (M)	-0.174	0.027	-0.227	-0.122	< 0.001	*
Treatment (P) x Sex (M)	0.009	0.040	-0.070	0.086	0.41
Seed (B)	0.096	0.095	-0.084	0.285	0.155
Seed (C)	0.338	0.092	0.161	0.525	< 0.001	*

Complete output from `summary.brmsfit()`

cox_brm

 Family: cox 
  Links: mu = log 
Formula: DAY | cens(1 - EVENT) ~ TRT * SEX + SEED + (TRT | LINE) + (1 | ID) 
   Data: ecl.dat (Number of observations: 14000) 
Samples: 4 chains, each with iter = 5000; warmup = 2500; thin = 1;
         total post-warmup samples = 10000

Group-Level Effects: 
~ID (Number of levels: 140) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.43      0.03     0.38     0.50 1.00     1723     2858

~LINE (Number of levels: 8) 
                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)           0.24      0.15     0.03     0.58 1.01      807     1158
sd(TRTP)                0.32      0.30     0.01     1.02 1.01      719     2196
cor(Intercept,TRTP)     0.17      0.54    -0.89     0.97 1.00     2731     3923

Population-Level Effects: 
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept     0.67      0.15     0.35     0.98 1.00     2621     4058
TRTP         -0.80      0.30    -1.33    -0.16 1.00     2766     2324
SEXm         -0.17      0.03    -0.23    -0.12 1.00     5984     6212
SEEDB         0.10      0.09    -0.08     0.29 1.00     1235     2024
SEEDC         0.34      0.09     0.16     0.52 1.00     1257     2189
TRTP:SEXm     0.01      0.04    -0.07     0.09 1.00     5976     6909

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Posterior effect size of treatment on eclosion time for each sex

As posterior_eprid() is not available for brms models using the cox family, we manually calculate the estimates for each group from the posterior predictions. The \(\beta\) coefficients from a Cox model measure the impact of covariates and give an estimate of the effect size (see here). Taking the exponent of the coefficients give the hazard ratio. In short, hazard ratios give the probability of the event occurring compared to the ‘control’ group, in our case compared to Monogamy females, where:

Hazard ratio = 1 (\(\beta\) = 0): no effect
Hazard ratio > 1 (\(\beta\) > 0): reduced hazard (higher probabilty of eclosion)
Hazard ratio < 1 (\(\beta\) < 0): increased hazard (lower probabilty of eclosion)

posterior_samples(cox_brm) %>% 
  as_tibble() %>%
  select(starts_with("b_")) %>% 
  mutate(draw = 1:n()) %>% 
  mutate(M_f = b_Intercept,
         P_f = b_Intercept + b_TRTP,
         M_m = b_Intercept + b_SEXm,
         P_m = b_TRTP + b_SEXm + `b_TRTP:SEXm`) %>% 
  select(draw, M_f, P_f, M_m, P_m) %>% 
  pivot_longer(cols = 2:5) %>% 
  mutate(SEX = str_sub(name, -1),
         TRT = str_sub(name, 1, 1)) %>%
  select(draw, value, SEX, TRT) %>% 
  pivot_wider(names_from = TRT,
              values_from = value) %>%
  mutate(`Difference in means (Poly - Mono)` = P - M) %>%
  ggplot(aes(x = SEX, y = `Difference in means (Poly - Mono)`, fill = SEX)) +
  geom_hline(yintercept = 0, linetype = 2) +
  stat_halfeye() + 
  scale_fill_brewer(palette = 'Pastel1', direction = 1, name = "") +
  scale_colour_brewer(palette = 'Pastel1', direction = 1, name = "") +
  labs(y = 'Difference in means between\nselection treatments (P - M)') +
  theme_bw() +
  theme(legend.position = 'none',
        strip.background = element_blank(),
        panel.grid.major.x = element_blank()) +
  NULL

Version	Author	Date
989e86f	lukeholman	2020-12-18
df61dde	Martin Garlovsky	2020-12-03

Figure X: Difference in mean \(\beta\) coefficients for the survival analysis on eclosion time between the selection treatments (Polyandry - Monogamy).

Body size differences (wing vein IV length)

We measured the length of wing vein VI as a proxy for body size to test for differences between sexes and treatments as body size may influence development time. Prior to measurement, wing images were anonymised using a custom python script provided by Henry Barton and then decoded for statistical analysis. Wing length was scaled by subtracting the mean (across all measurements) and dividing by the standard deviation.

Inspecting the raw data

Violin plots

wing_length %>% 
  mutate(var = paste(Treatment, Sex)) %>% 
  ggplot(aes(x = Sex, y = Length)) +
  geom_violin(aes(fill = var), alpha = .5) + 
  geom_boxplot(aes(fill = var), width = .1, position = position_dodge(width = .9)) +
  scale_colour_manual(values = c("pink", "skyblue", "red", "blue"), name = "") +
  scale_fill_manual(values = c("pink", "skyblue", "red", "blue"), name = "",
                    labels = c('Monogamy Females', 'Monogamy Males',
                               'Polandry Females', 'Polandry Males')) +
  labs(y = 'Wing vein IV length') +
  theme_bw() +
  theme() +
  NULL

Version	Author	Date
989e86f	lukeholman	2020-12-18
df61dde	Martin Garlovsky	2020-12-03

Figure X: Wing vein IV length has been scaled (subtracted the mean and divided by the standard deviation).

Means and standard errors

wing_length %>% 
  group_by(Treatment, Sex) %>% 
  summarise(Mean = mean(Length),
            `Std. Errors` = sd(Length)/sqrt(n()),
            N = n()) %>%
  mutate(Treatment = recode(Treatment, M = "Monogamy", P = 'Polyandry'),
         Sex = recode(Sex, M = "Male", F = 'Female')) %>% 
  mutate(across(2:4, round, 2)) %>% 
  kable() %>% 
  kable_styling(full_width = FALSE)

Treatment	Sex	Mean	Std. Errors	N
Monogamy	Female	0.85	0.04	152
Monogamy	Male	-0.91	0.04	154
Polyandry	Female	0.94	0.05	118
Polyandry	Male	-0.79	0.05	127

Fitting the model for wing length in `brms`

We fit a model in brms to test for differences in wing length between the sexes and sexual selection treatments. We fit treatment, sex and the treatment x sex interaction as fixed effects as well as Seed day as a covariate. As above, we included replicate treatment as a random intercept for each of the 8 lines and a random slope term for selection to allow the effect of treatment to vary across replicate lines.

Define priors

As above we set conservative normal priors on the fixed effects (mean = 0, sd = 1) and half Cauchy priors on the random effects - LINE - (mean = 0, scale = 0.1). All other priors were left at the default in brms.

Run the model

The model is run over 4 chains with 10000 iterations each (with the first 2500 discarded as burn-in), for a total of 7500*4 = 30,000 posterior samples.

if(!file.exists("output/wing_brms.rds")){
  
  wing_brms <- brm(Length ~ Treatment * Sex + Seed + (Treatment|LINE),
                 data = wing_length,
  iter = 10000, chains = 4, cores = 4,
  prior = c(set_prior("normal(0,1)", class = "b"),
            set_prior("cauchy(0,0.1)", class = "sd")),
  control = list(max_treedepth = 20,
                 adapt_delta = 0.999)
  )
  
  saveRDS(wing_brms, "output/wing_brms.rds")
} else {
  wing_brms <- readRDS('output/wing_brms.rds')
}

Posterior predictive check of model fit

pp_check(wing_brms)

Version	Author	Date
989e86f	lukeholman	2020-12-18
96d1188	Martin Garlovsky	2020-12-13
7d4b609	Martin Garlovsky	2020-12-05
df61dde	Martin Garlovsky	2020-12-03

Table of model parameter estimates - body size

Formatted table

wing_test <- bind_rows(
  hypothesis(wing_brms, 'TreatmentP = 0')$hypothesis,
  hypothesis(wing_brms, 'SexM = 0')$hypothesis,
  hypothesis(wing_brms, 'TreatmentP:SexM = 0')$hypothesis,
  hypothesis(wing_brms, 'SeedB = 0')$hypothesis,
  hypothesis(wing_brms, 'SeedC = 0')$hypothesis,
) %>% 
  mutate(Parameter = c('Treatment (P)', 'Sex (M)', 'Treatment (P) x Sex (M)',
                       'Seed (B)', 'Seed (C)'),
         across(2:5, round, 3)) %>% 
  relocate(Parameter, Estimate, Est.Error, CI.Lower, CI.Upper, Star)

pvals <- bayestestR::p_direction(wing_brms) %>% 
  as.data.frame() %>%
  mutate(vars = map_chr(str_split(Parameter, "_"), ~ .x[2]),
         p_val = 1 - pd, 
         star = ifelse(p_val < 0.05, "\\*", "")) %>%
  select(vars, p_val, star)

wing_test %>% mutate(vars = c('TreatmentP', 'SexM', 'TreatmentP.SexM', 'SeedB', 'SeedC')) %>% 
  left_join(pvals %>% filter(vars != 'Intercept'), 
              by = c("vars")) %>% 
    select(Parameter, Estimate, Est.Error, CI.Lower, CI.Upper, `p` = p_val, star) %>% 
  mutate(p = ifelse(p > 0.001, round(p, 3), '< 0.001')) %>% 
  rename(` ` = star) %>%
  kable() %>% 
  kable_styling(full_width = FALSE)

Parameter	Estimate	Est.Error	CI.Lower	CI.Upper	p
Treatment (P)	0.111	0.261	-0.406	0.638	0.317
Sex (M)	-1.733	0.045	-1.823	-1.644	< 0.001	*
Treatment (P) x Sex (M)	0.020	0.068	-0.114	0.154	0.384
Seed (B)	-0.098	0.042	-0.181	-0.017	0.008	*
Seed (C)	-0.030	0.043	-0.115	0.054	0.24

Complete output from `summary.brmsfit()`

wing_brms

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: Length ~ Treatment * Sex + Seed + (Treatment | LINE) 
   Data: wing_length (Number of observations: 551) 
Samples: 4 chains, each with iter = 10000; warmup = 5000; thin = 1;
         total post-warmup samples = 20000

Group-Level Effects: 
~LINE (Number of levels: 8) 
                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept)                 0.33      0.12     0.16     0.61 1.00     7540
sd(TreatmentP)                0.16      0.18     0.00     0.65 1.00     6252
cor(Intercept,TreatmentP)     0.09      0.55    -0.91     0.95 1.00    15048
                          Tail_ESS
sd(Intercept)                10324
sd(TreatmentP)                7152
cor(Intercept,TreatmentP)    10995

Population-Level Effects: 
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept           0.87      0.18     0.51     1.22 1.00     8584     9556
TreatmentP          0.11      0.26    -0.41     0.64 1.00    10015    10628
SexM               -1.73      0.05    -1.82    -1.64 1.00    20172    15736
SeedB              -0.10      0.04    -0.18    -0.02 1.00    22473    15468
SeedC              -0.03      0.04    -0.11     0.05 1.00    22268    15614
TreatmentP:SexM     0.02      0.07    -0.11     0.15 1.00    19758    15712

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.40      0.01     0.37     0.42 1.00    26769    14763

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Posterior effect size of treatment on body size for each sex

We predict the mean wing vein IV length for each treatment and sex from the model averaged across the eight replicate selection lines and seeding days. The plots show the difference in posterior estimates between the P and M treatment for each sex separately. Note that females are larger than males but effect sizes are plotted for each sex separately.

new <- expand_grid(Sex = c("M", "F"),
                   Treatment = c("M", "P"),
                   LINE = NA, Seed = NA) %>%
  mutate(type = 1:n())

posterior_epred(
  wing_brms, newdata = new, re_formula = NA,
  summary = FALSE, resp = 'Length') %>%
  reshape2::melt() %>% rename(draw = Var1, type = Var2) %>%
  as_tibble() %>%
  left_join(new, by = "type") %>%
  select(draw, value, Sex, Treatment) %>% 
  pivot_wider(names_from = Treatment, 
              values_from = value) %>%
  mutate(`Difference in means (Poly - Mono)` = P - M) %>% 
  ggplot(aes(x = Sex, y = `Difference in means (Poly - Mono)`, fill = Sex)) +
  geom_hline(yintercept = 0, linetype = 2) +
  stat_halfeye() + 
  scale_fill_brewer(palette = 'Pastel1', direction = 1, name = "") +
  scale_colour_brewer(palette = 'Pastel1', direction = 1, name = "") +
  labs(y = 'Difference in means between\nselection treatments (P - M)') +
  theme_bw() +
  theme(legend.position = 'none',
        strip.background = element_blank(),
        panel.grid.major.x = element_blank()) +
  NULL

Version	Author	Date
989e86f	lukeholman	2020-12-18
96d1188	Martin Garlovsky	2020-12-13

Figure XX: Posterior estimates of treatment effects on wing vein IV length (proxy for body size).

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

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

other attached packages:
 [1] knitrhooks_0.0.4 knitr_1.30       kableExtra_1.3.1 tidybayes_2.3.1 
 [5] brms_2.14.4      Rcpp_1.0.5       nlme_3.1-149     lme4_1.1-26     
 [9] Matrix_1.2-18    coxme_2.2-16     bdsmatrix_1.3-4  survival_3.2-7  
[13] ggridges_0.5.3   forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2     
[17] purrr_0.3.4      readr_1.4.0      tidyr_1.1.2      tibble_3.0.4    
[21] ggplot2_3.3.3    tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
  [1] readxl_1.3.1         backports_1.2.1      plyr_1.8.6          
  [4] igraph_1.2.6         splines_4.0.3        svUnit_1.0.3        
  [7] crosstalk_1.1.1      rstantools_2.1.1     inline_0.3.17       
 [10] digest_0.6.27        htmltools_0.5.0      rsconnect_0.8.16    
 [13] fansi_0.4.1          magrittr_2.0.1       openxlsx_4.2.3      
 [16] modelr_0.1.8         RcppParallel_5.0.2   matrixStats_0.57.0  
 [19] xts_0.12.1           prettyunits_1.1.1    colorspace_2.0-0    
 [22] rvest_0.3.6          ggdist_2.4.0         haven_2.3.1         
 [25] xfun_0.20            callr_3.5.1          crayon_1.3.4        
 [28] jsonlite_1.7.2       zoo_1.8-8            glue_1.4.2          
 [31] survminer_0.4.8      gtable_0.3.0         webshot_0.5.2       
 [34] V8_3.4.0             distributional_0.2.1 car_3.0-10          
 [37] pkgbuild_1.2.0       rstan_2.21.2         abind_1.4-5         
 [40] scales_1.1.1         mvtnorm_1.1-1        DBI_1.1.0           
 [43] rstatix_0.6.0        miniUI_0.1.1.1       viridisLite_0.3.0   
 [46] xtable_1.8-4         foreign_0.8-80       km.ci_0.5-2         
 [49] stats4_4.0.3         StanHeaders_2.21.0-7 DT_0.17             
 [52] htmlwidgets_1.5.3    httr_1.4.2           threejs_0.3.3       
 [55] RColorBrewer_1.1-2   arrayhelpers_1.1-0   ellipsis_0.3.1      
 [58] reshape_0.8.8        pkgconfig_2.0.3      loo_2.4.1           
 [61] farver_2.0.3         dbplyr_2.0.0         labeling_0.4.2      
 [64] tidyselect_1.1.0     rlang_0.4.10         reshape2_1.4.4      
 [67] later_1.1.0.1        munsell_0.5.0        cellranger_1.1.0    
 [70] tools_4.0.3          cli_2.2.0            generics_0.1.0      
 [73] broom_0.7.3          evaluate_0.14        fastmap_1.0.1       
 [76] yaml_2.2.1           processx_3.4.5       fs_1.5.0            
 [79] zip_2.1.1            survMisc_0.5.5       whisker_0.4         
 [82] mime_0.9             projpred_2.0.2       xml2_1.3.2          
 [85] compiler_4.0.3       bayesplot_1.8.0      shinythemes_1.1.2   
 [88] rstudioapi_0.13      gamm4_0.2-6          curl_4.3            
 [91] ggsignif_0.6.0       reprex_0.3.0         statmod_1.4.35      
 [94] stringi_1.5.3        highr_0.8            ps_1.5.0            
 [97] Brobdingnag_1.2-6    lattice_0.20-41      nloptr_1.2.2.2      
[100] markdown_1.1         KMsurv_0.1-5         shinyjs_2.0.0       
[103] vctrs_0.3.6          pillar_1.4.7         lifecycle_0.2.0     
[106] bridgesampling_1.0-0 insight_0.11.1       data.table_1.13.6   
[109] httpuv_1.5.4         R6_2.5.0             promises_1.1.1      
[112] rio_0.5.16           gridExtra_2.3        codetools_0.2-16    
[115] boot_1.3-25          colourpicker_1.1.0   MASS_7.3-53         
[118] gtools_3.8.2         assertthat_0.2.1     rprojroot_2.0.2     
[121] withr_2.3.0          shinystan_2.5.0      bayestestR_0.8.0    
[124] mgcv_1.8-33          parallel_4.0.3       hms_0.5.3           
[127] grid_4.0.3           coda_0.19-4          minqa_1.2.4         
[130] rmarkdown_2.6        carData_3.0-4        ggpubr_0.4.0        
[133] git2r_0.28.0         shiny_1.5.0          lubridate_1.7.9.2   
[136] base64enc_0.1-3      dygraphs_1.1.1.6

Juvenile development time

Load packages

Load data

Survival analysis

Kaplan-Meier survival curve

Check proportional hazards assumption

Fit the model in brms

Define priors

Run the model

Table of model parameter estimates - eclosion time

Formatted table

Complete output from summary.brmsfit()

Posterior effect size of treatment on eclosion time for each sex

Body size differences (wing vein IV length)

Inspecting the raw data

Violin plots

Means and standard errors

Fitting the model for wing length in brms

Define priors

Run the model

Posterior predictive check of model fit

Table of model parameter estimates - body size

Formatted table

Complete output from summary.brmsfit()

Posterior effect size of treatment on body size for each sex

Fit the model in `brms`

Complete output from `summary.brmsfit()`

Fitting the model for wing length in `brms`

Complete output from `summary.brmsfit()`