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library(tidyverse)
library(brms)
library(mice)
library(future)
library(future.apply)
library(kableExtra)Most studies of the DGRP calculate “line means” simply by averaging
the phenotypes of several individuals per line. Instead, we used
Bayesian generalised linear mixed model (GLMMs) to estimate the true
line means for each of the 4 fitness traits, implemented in the
brms package.
One notable advantage of using a model instead of a simple average is
that a model allows one to statistically remove confounding factors such
as block effects, which would otherwise bias the line means. Note that
we measured line 352 in every block in our experiments, in order to
improve precision when estimating block effects. Additionally, we must
properly account for our experimental design in order to avoid
pseudoreplication. Our design involved repeatedly measuring the same
individuals to determine early- and late-life fitness, which we
incorporate into the model via the random effect vial.
For the progeny count data used to measure early and late female
fitness, we used a multivariate model with two components, one for
early- and one for late-life fitness, which had the following formulae
(in brms-like pseudocode):
Progeny count (early) = Intercept + (1 | p | line) + (1 | q | block) + (1 | r | vial)
Progeny count (late) = Intercept + (1 | p | line) + (1 | q | block) + (1 | r | vial)
Here, the model terms with the form (1 | x | y)
represent random intercepts for line, block, and vial ID
(i.e. y), where the letter between the pipe operators
(x) indicates which random intercepts are assumed to be
correlated with which other random intercepts. Thus, we assume that the
effects of line, block, and vial ID on early-life fitness are
potentially correlated with the effects of these three random variables
on late-life fitness, and estimate this correlation from the data and
prior.
The progeny count data were assumed to follow a Poisson distribution (with the standard log link function).
Similarly, for our measure of male fitness, proportion of offspring sired, we used a multivariate model consisting of a pair of binomial GLMMs (with logit link), with the following formula:
Proportion of progeny sired (early) = Intercept + (1 | p | line) + (1 | q | block) + (1 | r | vial)
Proportion of progeny sired (late) = Intercept + (1 | p | line) + (1 | q | block) + (1 | r | vial)
Where the response variable was a Bernoulli outcome describing the paternity of each offspring observed (either a male from the focal DGRP line, or from one of the competitor males).
For both models, we mostly used the brms default (weak)
priors, except that we chose more informative, ‘skeptical’ priors for
the random intercept terms, of the form cauchy(0, 0.1).
This prior helps the model to converge by making very large estimates
implausible, constraining the parameter space.
# function to load the raw data on male and female fitness, and tidy it for analysis
load_and_tidy_fitness_data <- function(){
female_fitness <- read_csv("data/input/female_fitness.csv") %>%
arrange(line) %>%
split(paste(.$block, .$line)) %>%
map(~ .x %>% mutate(replicate = 1:n())) %>%
bind_rows() %>%
mutate(vial = 1:n(),
vial = paste("F", line, block, replicate, sep = "_"),
line = paste("line_", line, sep = "")) %>%
dplyr::select(-num.F.late1, -num.F.late2, -num.laying.F.early, -replicate) %>%
mutate(female.fitness.early = replace(female.fitness.early, is.na(female.fitness.early), 0),
female.fitness.late = replace(female.fitness.late, is.na(female.fitness.late), 0))
male_fitness <- read_csv("data/input/male_fitness.csv") %>%
arrange(line) %>%
split(paste(.$block, .$line)) %>%
map(~ .x %>% mutate(replicate = 1:n())) %>%
bind_rows() %>%
mutate(vial = paste("M", line, block, replicate, sep = "_"),
line = paste("line_", line, sep = "")) %>%
dplyr::select(-num.DGRP.males, -replicate)
# Save these tidy files, for data archiving
write.csv(female_fitness, file = "data/input/female_fitness_CLEANED.csv", row.names = FALSE)
write.csv(male_fitness, file = "data/input/male_fitness_CLEANED.csv", row.names = FALSE)
list(female_fitness = female_fitness, male_fitness = male_fitness)
}
# A function to calculate each line's expected fitness, using brms models to adjust for block + vial random effects
# For the male late life assay, we also adjust for the number of competitor males that died
# (this assumes that their deaths happened randomly with respect to which line we were measuring)
get_predicted_line_means <- function(overwrite = FALSE){
# If it's already calculated, just load up the file. Otherwise, make the file
out.file <- "data/derived/predicted_line_means.csv"
if(file.exists(out.file) & !overwrite) return(read_csv(out.file))
####### Load the individual-level data for females
female_fitness <- load_and_tidy_fitness_data()[[1]]
####### Load the individual-level data for males, and impute missing values
# For one vial, there is no early-life measurement because the females did not produce offspring.
# Therefore we impute that datapoint and make 5 imputed datasets using the package 'mice'
# See this link for explanation: https://cran.r-project.org/web/packages/brms/vignettes/brms_missings.html
male_fitness <- load_and_tidy_fitness_data()[[2]]
male_fitness <- male_fitness %>%
mutate(early.male.rival = replace(early.male.rival, early.male.rival + early.male.focal == 0, NA),
early.male.focal = replace(early.male.focal, is.na(early.male.rival), NA))
male_fitness_imputed <- mice(male_fitness, m = 5, print = FALSE, seed = 1)
male_fitness_imputed <- lapply(1:5, function(i) { # for each imputed dataset,
complete(male_fitness_imputed, i) %>%
mutate(total1 = early.male.rival + early.male.focal, # tally up the focal+rival offspring for binomial model
total2 = late.male.rival + late.male.focal) %>% # scale this covariate
# For late-life assays where the 5 focal males all died before reaching age 14,
# we need to assign them zero fitness. We did this by assuming that the rivals sired 100/100 offspring.
# This scenario happened in 47 vials (out of 810)
mutate(late.male.focal = replace(late.male.focal, total2 == 0, 100),
total2 = replace(total2, total2 == 0, 100))
})
####### Run model on the female data
# Define the priors for the models
prior_females <-
c(set_prior("cauchy(0, 0.1)", class = "sd", resp = 'femalefitnessearly', group = "line"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'femalefitnessearly', group = "block"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'femalefitnessearly', group = "vial"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'femalefitnesslate', group = "line"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'femalefitnesslate', group = "block"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'femalefitnesslate', group = "vial"))
prior_males <-
c(set_prior("cauchy(0, 0.1)", class = "sd", resp = 'earlymalefocal', group = "line"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'earlymalefocal', group = "block"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'earlymalefocal', group = "vial"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'latemalefocal', group = "line"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'latemalefocal', group = "block"),
set_prior("cauchy(0, 0.1)", class = "sd", resp = 'latemalefocal', group = "vial"))
female1 <- bf(female.fitness.early ~ (1 | p | line) + (1 | q | block) + (1 | r | vial))
female2 <- bf(female.fitness.late ~ (1 | p | line) + (1 | q | block) + (1 | r | vial))
female_model <- brm(female1 + female2,
family = "poisson", data = female_fitness,
prior = prior_females,
iter = 5000, chains = 4, cores = 4,
seed = 1, control = list(adapt_delta = 0.999, max_treedepth = 15))
writeLines(capture.output(summary(female_model)),
con = "data/derived/model_summary_females.txt")
# saveRDS(female_model, "data/derived/female_fitness_prediction_model.rds")
### Run model on male data
male1 <- bf(early.male.focal | trials(total1) ~ (1 | p | line) + (1 | q | block) + (1 | r | vial))
male2 <- bf(late.male.focal | trials(total2) ~ (1 | p | line) + (1 | q | block) + (1 | r | vial))
# Run 5 models, on each of the 5 imputed datasets, and combine the results
male_model <- brm_multiple(male1 + male2,
family = "binomial",
prior = prior_males,
data = male_fitness_imputed,
iter = 5000, chains = 1, cores = 4,
seed = 1, control = list(adapt_delta = 0.999, max_treedepth = 15))
writeLines(capture.output(summary(male_model)),
con = "data/derived/model_summary_males.txt")
# saveRDS(male_model, "data/derived/male_fitness_prediction_model.rds")
####### Define new data for prediction
new.data.female <- female_fitness %>%
select(line) %>% distinct() %>% arrange(line)
new.data.male <- male_fitness %>%
select(line) %>% distinct() %>% arrange(line) %>%
mutate(total1 = 100, # changing this number does not affect the line means, as expected
total2 = 100)
# Get predicted lines means for early and late life *female* fitness on linear predictor scale (i.e. fairly normal)
female_line_preds <- data.frame(
new.data.female,
fitted(female_model,
newdata = new.data.female,
re_formula = "~ (1 | line)",
scale = "linear")) %>%
select(line, Estimate.femalefitnessearly, Estimate.femalefitnesslate) %>%
rename(female.fitness.early = Estimate.femalefitnessearly,
female.fitness.late = Estimate.femalefitnesslate) %>%
mutate(female.fitness.early = as.numeric(scale(female.fitness.early)), # scale the line means
female.fitness.late = as.numeric(scale(female.fitness.late)))
# Get predicted lines means for early and late life *male* fitness on linear predictor scale (i.e. fairly normal)
male_line_preds <- data.frame(
new.data.male,
fitted(male_model,
newdata = new.data.male,
re_formula = "~ (1 | line)",
scale = "linear")) %>%
select(line, Estimate.earlymalefocal, Estimate.latemalefocal) %>%
rename(male.fitness.early = Estimate.earlymalefocal,
male.fitness.late = Estimate.latemalefocal) %>%
mutate(male.fitness.early = as.numeric(scale(male.fitness.early)), # scale the line means
male.fitness.late = as.numeric(scale(male.fitness.late)))
# Record which block(s) each line was measured in. Generally one block, except for ref line (all blocks)
line_blocks <- rbind(female_fitness %>% select(block, line),
male_fitness %>% select(block, line)) %>%
mutate(block = replace(block, line == "352", "reference_line")) %>%
distinct() %>%
group_by(line) %>% summarise(block = paste0(block, collapse = ", "))
predicted_line_means <- female_line_preds %>%
left_join(male_line_preds, by = "line") %>%
left_join(line_blocks, by = "line") %>%
arrange(line)
write.csv(predicted_line_means, out.file, row.names = FALSE)
}The object predicted_line_means is the estimated line
means from the Bayesian models. These means are on the scale of the
linear predictor (i.e. Poisson for females, binomial for males) rather
than on the scale of the original response. They have been scaled to
have a mean of 0 and a variance of 1. You can view the predicted line
means in a table on this
page.
predicted_line_means <- get_predicted_line_means(overwrite = FALSE) cat(readLines('data/derived/model_summary_females.txt'), sep = '\n') Family: MV(poisson, poisson)
Links: mu = log
mu = log
Formula: female.fitness.early ~ (1 | p | line) + (1 | q | block) + (1 | r | vial)
female.fitness.late ~ (1 | p | line) + (1 | q | block) + (1 | r | vial)
Data: female_fitness (Number of observations: 816)
Draws: 4 chains, each with iter = 5000; warmup = 2500; thin = 1;
total post-warmup draws = 10000
Group-Level Effects:
~block (Number of levels: 10)
Estimate Est.Error l-95% CI
sd(femalefitnessearly_Intercept) 0.29 0.09 0.16
sd(femalefitnesslate_Intercept) 1.21 0.35 0.70
cor(femalefitnessearly_Intercept,femalefitnesslate_Intercept) -0.42 0.29 -0.88
u-95% CI Rhat Bulk_ESS Tail_ESS
sd(femalefitnessearly_Intercept) 0.50 1.00 6956 7704
sd(femalefitnesslate_Intercept) 2.05 1.00 7505 8048
cor(femalefitnessearly_Intercept,femalefitnesslate_Intercept) 0.22 1.00 8011 7082
~line (Number of levels: 125)
Estimate Est.Error l-95% CI
sd(femalefitnessearly_Intercept) 0.58 0.05 0.50
sd(femalefitnesslate_Intercept) 1.82 0.17 1.51
cor(femalefitnessearly_Intercept,femalefitnesslate_Intercept) 0.68 0.07 0.53
u-95% CI Rhat Bulk_ESS Tail_ESS
sd(femalefitnessearly_Intercept) 0.68 1.00 5015 7236
sd(femalefitnesslate_Intercept) 2.18 1.00 5994 7883
cor(femalefitnessearly_Intercept,femalefitnesslate_Intercept) 0.79 1.00 7663 7679
~vial (Number of levels: 816)
Estimate Est.Error l-95% CI
sd(femalefitnessearly_Intercept) 0.52 0.02 0.49
sd(femalefitnesslate_Intercept) 1.54 0.07 1.42
cor(femalefitnessearly_Intercept,femalefitnesslate_Intercept) 0.21 0.05 0.12
u-95% CI Rhat Bulk_ESS Tail_ESS
sd(femalefitnessearly_Intercept) 0.55 1.00 4219 6935
sd(femalefitnesslate_Intercept) 1.68 1.00 4543 6625
cor(femalefitnessearly_Intercept,femalefitnesslate_Intercept) 0.30 1.00 7886 7637
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
femalefitnessearly_Intercept 4.40 0.11 4.19 4.62 1.00 11287 6886
femalefitnesslate_Intercept 0.70 0.44 -0.16 1.57 1.00 13408 7848
Draws were sampled 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).
cat(readLines('data/derived/model_summary_males.txt'), sep = '\n') Family: MV(binomial, binomial)
Links: mu = logit
mu = logit
Formula: early.male.focal | trials(total1) ~ (1 | p | line) + (1 | q | block) + (1 | r | vial)
late.male.focal | trials(total2) ~ (1 | p | line) + (1 | q | block) + (1 | r | vial)
Data: male_fitness_imputed (Number of observations: 810)
Draws: 5 chains, each with iter = 5000; warmup = 2500; thin = 1;
total post-warmup draws = 12500
Group-Level Effects:
~block (Number of levels: 10)
Estimate Est.Error l-95% CI u-95% CI Rhat
sd(earlymalefocal_Intercept) 0.75 0.20 0.46 1.23 1.00
sd(latemalefocal_Intercept) 0.30 0.21 0.01 0.78 1.00
cor(earlymalefocal_Intercept,latemalefocal_Intercept) 0.29 0.43 -0.73 0.93 1.00
Bulk_ESS Tail_ESS
sd(earlymalefocal_Intercept) 6267 8051
sd(latemalefocal_Intercept) 1615 5033
cor(earlymalefocal_Intercept,latemalefocal_Intercept) 9194 7696
~line (Number of levels: 124)
Estimate Est.Error l-95% CI u-95% CI Rhat
sd(earlymalefocal_Intercept) 0.54 0.05 0.45 0.64 1.00
sd(latemalefocal_Intercept) 0.85 0.21 0.39 1.23 1.01
cor(earlymalefocal_Intercept,latemalefocal_Intercept) 0.68 0.15 0.36 0.96 1.01
Bulk_ESS Tail_ESS
sd(earlymalefocal_Intercept) 4250 6699
sd(latemalefocal_Intercept) 451 431
cor(earlymalefocal_Intercept,latemalefocal_Intercept) 613 595
~vial (Number of levels: 810)
Estimate Est.Error l-95% CI u-95% CI Rhat
sd(earlymalefocal_Intercept) 0.81 0.03 0.76 0.86 1.01
sd(latemalefocal_Intercept) 2.79 0.11 2.59 3.02 1.00
cor(earlymalefocal_Intercept,latemalefocal_Intercept) 0.18 0.04 0.10 0.27 1.01
Bulk_ESS Tail_ESS
sd(earlymalefocal_Intercept) 3279 7052
sd(latemalefocal_Intercept) 2587 5796
cor(earlymalefocal_Intercept,latemalefocal_Intercept) 1844 4566
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
earlymalefocal_Intercept 0.15 0.25 -0.35 0.64 1.00 6060 5570
latemalefocal_Intercept -0.82 0.18 -1.18 -0.46 1.00 6338 7534
Draws were sampled 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).
sessionInfo()R version 4.2.2 (2022-10-31) Platform: x86_64-apple-darwin17.0 (64-bit) Running under: macOS Big Sur ... 10.16 Matrix products: default BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib LAPACK: /Library/Frameworks/R.framework/Versions/4.2/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] kableExtra_1.3.4 future.apply_1.10.0 future_1.30.0 [4] mice_3.15.0 brms_2.18.0 Rcpp_1.0.10 [7] lubridate_1.9.2 forcats_1.0.0 stringr_1.5.0 [10] dplyr_1.1.0 purrr_1.0.1 readr_2.1.4 [13] tidyr_1.3.0 tibble_3.1.8 ggplot2_3.4.1 [16] tidyverse_2.0.0 knitrhooks_0.0.4 knitr_1.42 [19] workflowr_1.7.0.4 loaded via a namespace (and not attached): [1] colorspace_2.1-0 ellipsis_0.3.2 rprojroot_2.0.3 [4] markdown_1.4 base64enc_0.1-3 fs_1.6.1 [7] rstudioapi_0.14 listenv_0.9.0 farver_2.1.1 [10] rstan_2.21.8 bit64_4.0.5 DT_0.27 [13] fansi_1.0.4 mvtnorm_1.1-3 xml2_1.3.3 [16] bridgesampling_1.1-2 codetools_0.2-18 cachem_1.0.7 [19] shinythemes_1.2.0 bayesplot_1.10.0 jsonlite_1.8.4 [22] broom_1.0.3 shiny_1.7.4 compiler_4.2.2 [25] httr_1.4.5 backports_1.4.1 Matrix_1.5-1 [28] fastmap_1.1.1 cli_3.6.0 later_1.3.0 [31] htmltools_0.5.4 prettyunits_1.1.1 tools_4.2.2 [34] igraph_1.3.5 coda_0.19-4 gtable_0.3.1 [37] glue_1.6.2 reshape2_1.4.4 posterior_1.3.1 [40] jquerylib_0.1.4 vctrs_0.5.2 svglite_2.1.1 [43] nlme_3.1-160 crosstalk_1.2.0 tensorA_0.36.2 [46] xfun_0.37 globals_0.16.2 ps_1.7.2 [49] rvest_1.0.3 timechange_0.2.0 mime_0.12 [52] miniUI_0.1.1.1 lifecycle_1.0.3 gtools_3.9.4 [55] getPass_0.2-2 zoo_1.8-11 scales_1.2.1 [58] vroom_1.6.1 colourpicker_1.2.0 hms_1.1.2 [61] promises_1.2.0.1 Brobdingnag_1.2-9 parallel_4.2.2 [64] inline_0.3.19 shinystan_2.6.0 yaml_2.3.7 [67] gridExtra_2.3 loo_2.5.1 StanHeaders_2.21.0-7 [70] sass_0.4.5 stringi_1.7.12 dygraphs_1.1.1.6 [73] checkmate_2.1.0 pkgbuild_1.4.0 systemfonts_1.0.4 [76] rlang_1.0.6 pkgconfig_2.0.3 matrixStats_0.63.0 [79] distributional_0.3.1 evaluate_0.20 lattice_0.20-45 [82] rstantools_2.2.0 htmlwidgets_1.6.1 bit_4.0.5 [85] processx_3.8.0 tidyselect_1.2.0 parallelly_1.34.0 [88] plyr_1.8.8 magrittr_2.0.3 R6_2.5.1 [91] generics_0.1.3 DBI_1.1.3 pillar_1.8.1 [94] whisker_0.4.1 withr_2.5.0 xts_0.12.2 [97] abind_1.4-5 crayon_1.5.2 utf8_1.2.2 [100] tzdb_0.3.0 rmarkdown_2.20 grid_4.2.2 [103] callr_3.7.3 git2r_0.31.0 threejs_0.3.3 [106] webshot_0.5.4 digest_0.6.31 xtable_1.8-4 [109] httpuv_1.6.9 RcppParallel_5.1.6 stats4_4.2.2 [112] munsell_0.5.0 viridisLite_0.4.1 bslib_0.4.2 [115] shinyjs_2.1.0