Last updated: 2020-04-25

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Knit directory: social_immunity/

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Load data and R packages

# All but 1 of these packages can be easily installed from CRAN.
# However it was harder to install the showtext package. On Mac, I did this:
# installed 'homebrew' using Terminal: ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)" 
# installed 'libpng' using Terminal: brew install libpng
# installed 'showtext' in R using: devtools::install_github("yixuan/showtext")  
library(showtext)

library(brms)
library(bayesplot)
library(tidyverse)
library(gridExtra)
library(kableExtra)
library(bayestestR)
library(cowplot)
library(tidybayes)
library(scales)
source("code/helper_functions.R")

# set up nice font for figure
nice_font <- "PT Serif"
font_add_google(name = nice_font, family = nice_font, regular.wt = 400, bold.wt = 700)
showtext_auto()

files <- c("data/data_collection_sheets/hiveA_touching.csv",
           "data/data_collection_sheets/hiveB_touching.csv",
           "data/data_collection_sheets/hiveC_touching.csv",
           "data/data_collection_sheets/hiveD_touching.csv")

experiment3 <- map(
  files, 
  ~ read_csv(.x) %>%
    gather(minute, touching, -tube) %>%
    mutate(treatment = ifelse(substr(tube, 1, 1) %in% c("A", "B"), "AB", "CD"),
           minute = as.numeric(minute),
           touching = as.integer(touching),
           hive = gsub("hive", "", str_extract(.x, "hive[ABCD]")), 
           tube = paste(hive, tube, sep = "_"))
  ) %>% bind_rows() %>%
  mutate(treatment = replace(treatment, 
                             treatment == "AB" & hive %in% c("A", "B"), 
                             "Ringers"),
         treatment = replace(treatment, 
                             treatment == "AB" & hive %in% c("C", "D"), 
                             "LPS"),
         treatment = replace(treatment, 
                             treatment == "CD" & hive %in% c("A", "B"), 
                             "LPS"),
         treatment = replace(treatment, 
                             treatment == "CD" & hive %in% c("C", "D"), 
                             "Ringers")) %>%
  mutate(hive = replace(hive, hive == "A", "Garden"),
         hive = replace(hive, hive == "B", "Skylab"),
         hive = replace(hive, hive == "C", "Arts"),
         hive = replace(hive, hive == "D", "Zoology"))


expt3_counts <- experiment3 %>%
  group_by(treatment, tube, hive) %>%
  summarise(n_touching = sum(touching),
            n_not_touching = sum(touching== 0),
            percent = n_touching / (n_touching + n_not_touching)) %>% 
  ungroup() %>%
  filter(!is.na(n_touching)) %>%
  mutate(treatment = factor(treatment, c("Ringers", "LPS"))) %>%
  mutate(hive = C(factor(hive), sum)) # sum coding for hive

Inspect the raw data

Sample sizes by treatment

sample_sizes <- expt3_counts %>%
  group_by(treatment) %>%
  summarise(n = n()) 

sample_sizes %>%
  kable() %>% kable_styling(full_width = FALSE)
treatment n
Ringers 220
LPS 219

Sample sizes by treatment and hive

expt3_counts %>%
  group_by(hive, treatment) %>%
  summarise(n = n()) %>%
  kable() %>% kable_styling(full_width = FALSE)
hive treatment n
Arts Ringers 50
Arts LPS 50
Garden Ringers 70
Garden LPS 70
Skylab Ringers 50
Skylab LPS 49
Zoology Ringers 50
Zoology LPS 50

Inspect the results

expt3_counts %>%
  group_by(hive, treatment) %>%
  summarise(pc = mean(100 * percent),
            SE = sd(percent) /sqrt(n()),
            n = n()) %>%
  rename(`% observations in which bees were in close contact` = pc,
         Hive = hive, Treatment = treatment) %>% 
  kable(digits = 3) %>% kable_styling(full_width = FALSE) %>%
  column_spec(3, width = "2in")
Hive Treatment % observations in which bees were in close contact SE n
Arts Ringers 69.509 0.036 50
Arts LPS 72.547 0.033 50
Garden Ringers 76.752 0.033 70
Garden LPS 68.895 0.037 70
Skylab Ringers 70.509 0.040 50
Skylab LPS 65.653 0.034 49
Zoology Ringers 84.075 0.021 50
Zoology LPS 73.019 0.037 50

Plotted as histograms

Note that bees more often spent close to 100% of the observation period in contact in the control group, relative to the group treated with LPS.

histo_data <- expt3_counts %>%
  left_join(sample_sizes, by = "treatment") %>%
  arrange(treatment) %>%
  mutate(treatment = factor(paste(treatment, " (n = ", n, ")", sep = ""),
                            unique(paste(treatment, " (n = ", n, ")", sep = "")))) 

raw_histogram <- histo_data %>% 
  filter(grepl("Ringers", treatment)) %>%
  ggplot(aes(100 * percent, 
             fill = treatment)) + 
  geom_histogram(data = histo_data %>% 
                   filter(grepl("LPS", treatment)), 
                 mapping = aes(y = ..density..), 
                 alpha = 0.5, bins = 11, colour = "black", linetype = 2) +
  geom_histogram(mapping = aes(y = ..density..), 
                 alpha = 0.5, bins = 11, 
                 colour = "black") + 
  scale_fill_brewer(palette = "Set1", 
                    direction = 1, name = "Treatment") + 
  xlab("% Time in close contact") + ylab("Density") + 
  theme_bw() + 
  theme(legend.position = c(0.34, 0.832),
        legend.background = element_rect(fill = scales::alpha('white', 0.7)),
        text = element_text(family = nice_font)) 

rm(histo_data)
raw_histogram

Version Author Date
2235ae4 lukeholman 2020-04-25
99649a7 lukeholman 2020-04-25
1ce9e19 lukeholman 2020-04-21

Binomial model of time spent in contact

Run the models

Fit a binomial model, where the response is either a 0 (if bees were not in contact) or 1 (if they were). To assess the effects of our predictor variables, we compare 5 models with different fixed factors, ranking them by posterior model probability.

# new verison....
if(!file.exists("output/exp3_model.rds")){
  exp3_model_v1 <- brm(
    n_touching | trials(n) ~ treatment * hive + (1 | tube), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = c(set_prior("normal(0, 3)", class = "b")),
    family = "binomial", save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  exp3_model_v2 <- brm(
    n_touching | trials(n) ~ treatment + hive + (1 | tube), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = c(set_prior("normal(0, 3)", class = "b")),
    family = "binomial", save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  exp3_model_v3 <- brm(
    n_touching | trials(n) ~ hive + (1 | tube), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = c(set_prior("normal(0, 3)", class = "b")),
    family = "binomial",  save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  posterior_model_probabilities <- tibble(
    Model = c("treatment * hive + observation_time_minutes",
              "treatment + hive + observation_time_minutes",
              "hive + observation_time_minutes"),
    post_prob = as.numeric(post_prob(exp3_model_v1,
                                     exp3_model_v2,
                                     exp3_model_v3))) %>%
    arrange(-post_prob)
  
  saveRDS(exp3_model_v2, "output/exp3_model.rds") # save the top model, treatment + hive
  saveRDS(posterior_model_probabilities, "output/exp3_post_prob.rds")
}
exp3_model <- readRDS("output/exp3_model.rds")
model_probabilities <- readRDS("output/exp3_post_prob.rds")

Posterior model probabilites

model_probabilities %>% 
  kable(digits = 3) %>% kable_styling(full_width = FALSE)
Model post_prob
hive + observation_time_minutes 0.720
treatment + hive + observation_time_minutes 0.278
treatment * hive + observation_time_minutes 0.001

Fixed effects from the top non-null model

tableS5 <- get_fixed_effects_with_p_values(exp3_model) %>% 
  mutate(mu = map_chr(str_extract_all(Parameter, "mu[:digit:]"), ~ .x[1]),
         Parameter = str_remove_all(Parameter, "mu[:digit:]_"),
         Parameter = str_replace_all(Parameter, "treatment", "Treatment: "),
         Parameter = str_replace_all(Parameter, "observation_time_minutes", "Observation duration (minutes)")) %>%
  arrange(mu) %>%
  select(-mu, -Rhat, -Bulk_ESS, -Tail_ESS) 

names(tableS5)[3:5] <- c("Est. Error", "Lower 95% CI", "Upper 95% CI")

saveRDS(tableS5, file = "figures/tableS5.rds")

tableS5 %>%
  kable(digits = 3) %>% 
  kable_styling(full_width = FALSE) 
Parameter Estimate Est. Error Lower 95% CI Upper 95% CI p
Intercept 1.678 0.141 1.401 1.960 0.000 ***
Treatment: LPS -0.369 0.199 -0.763 0.022 0.033 *
hive1 -0.198 0.175 -0.539 0.137 0.130
hive2 0.145 0.158 -0.157 0.462 0.180
hive3 -0.227 0.179 -0.582 0.121 0.102

Table S5: Table summarising the posterior estimates of each fixed effect in the best-fitting model of Experiment 3 that contained the treatment effect. This was a binomial model where the response variable was 0 for observations in which bees were not in close contact, and 1 when they were. ‘Treatment’ is a fixed factor with two levels, and the effect of LPS shown here is expressed relative to the ‘Ringers’ treatment. ‘Hive’ was a fixed factor with four levels; unlike for treatment, we modelled hive using deviation coding, such that the intercept term represents the mean across all hives (in the Ringers treatment), and the three hive terms represent the deviation from this mean for three of the four hives. The model also included a random effect ‘pair ID’ (XXXXX), which grouped repeated observations made on each pair of bees, preventing pseudoreplication. The \(p\) column gives the posterior probability that the true effect size is opposite in sign to what is reported in the Estimate column, similarly to a p-value.

Plotting estimates from the model

new <- expt3_counts %>% 
  select(treatment) %>% distinct() %>% 
  mutate(n = 100, key = paste("V", 1:n(), sep = ""),
         hive = NA) 
plotting_data <- as.data.frame(fitted(exp3_model, 
                                      newdata=new, re_formula = NA, summary = FALSE))
names(plotting_data) <- c("LPS", "Ringers")
plotting_data <- plotting_data %>% gather(treatment, percent_time_in_contact)

cols <- c("#34558b", "#4ec5a5", "#ffaf12")

dot_plot <- plotting_data %>%
  mutate(treatment = factor(treatment, c("Ringers", "LPS"))) %>%
  ggplot(aes(percent_time_in_contact, treatment)) + 
  stat_dotsh(quantiles = 100, fill = "grey40", colour = "grey40") + 
  stat_pointintervalh(
    mapping = aes(colour = treatment, fill = treatment),
    .width = c(0.5, 0.95), 
    position = position_nudge(y = -0.07),
    point_colour = "grey26", pch = 21, stroke = 0.4) + 
  xlab("Mean % time in close contact") + ylab("Treatment") + 
  scale_colour_brewer(palette = "Pastel1", 
                      direction = -1, name = "Treatment") +
  scale_fill_brewer(palette = "Pastel1", 
                      direction = -1, name = "Treatment") +
  theme_bw() + 
  coord_cartesian(ylim=c(1.4, 2.4)) + 
  theme(
    text = element_text(family = nice_font),
    strip.background = element_rect(fill = "#eff0f1"),
    panel.grid.major.y = element_blank(),
    legend.position = "none"
  ) 
  
# positive effect = odds of this outcome are higher for trt2 than trt1 (put control as trt1)
get_log_odds <- function(trt1, trt2){ 
  log((trt2 / (1 - trt2) / (trt1 / (1 - trt1))))
}

LOR <- plotting_data %>%
  mutate(posterior_sample = rep(1:(n()/2), 2)) %>%
  spread(treatment, percent_time_in_contact) %>%
  mutate(LOR = get_log_odds(Ringers/100, LPS/100)) %>%
  select(LOR)

LOR_plot <- LOR %>%
  ggplot(aes(LOR, y =1)) + 
  geom_vline(xintercept = 0, linetype = 2) +
  stat_dotsh(quantiles = 100, fill = "grey40", colour = "grey40") + 
  stat_pointintervalh(
    colour = "orange", fill = "orange",
    .width = c(0.5, 0.95), 
    position = position_nudge(y = -0.1),
    point_colour = "grey26", pch = 21, stroke = 0.4) + 
  coord_cartesian(ylim=c(0.86, 2)) + 
  xlab("Effect of LPS on mean\n% time in close contact (LOR)") + 
  ylab("Posterior density") + 
  theme_bw() +
  theme(
    text = element_text(family = nice_font),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major.y = element_blank(),
    panel.grid.minor.y = element_blank(),
    legend.position = "none"
  ) 
 
p <- cowplot::plot_grid(raw_histogram, 
                        dot_plot, LOR_plot,  labels = c("A", "B", "C"),
                        nrow = 1, align = 'h', axis = 'l')
ggsave(plot = p, filename = "figures/fig3.pdf", height = 3.2, width = 8.6)
p

Figure 3: Panel A shows the frequency distribution of the % time in close contact, for pairs of bees from the LPS treatment and the Ringers control. Panel B shows the posterior estimates of the mean % time spent in close contact; the details of the quantile dot plot and error bars are the same as described for Figure 1. Panel C shows the effect size (LOR; log odds ratio) associated with the difference in means in Panel B.

Hypothesis testing and effect sizes

get_log_odds <- function(trt1, trt2){ 
  log((trt2 / (1 - trt2) / (trt1 / (1 - trt1))))
}

my_summary <- function(df) {
  
  diff <- (df %>% pull(Ringers)) - (df %>% pull(LPS))
  LOR <- get_log_odds((df %>% pull(Ringers))/100, 
                      (df %>% pull(LPS))/100)
  p <- 1 - (diff %>% bayestestR::p_direction() %>% as.numeric())
  diff <- diff %>% posterior_summary() %>% as_tibble()
  LOR <- LOR %>% posterior_summary() %>% as_tibble()
  output <- rbind(diff, LOR) %>% 
    mutate(p=p, 
           Metric = c("Absolute difference in % time in close contact", 
                      "Log odds ratio")) %>% 
      select(Metric, everything()) %>%
    mutate(p = format(round(p, 4), nsmall = 4))
  output$p[1] <- " "
  output
}

plotting_data %>%
  as_tibble() %>%
  mutate(sample = rep(1:(n() / 2), 2)) %>%
  spread(treatment, percent_time_in_contact) %>%
  mutate(difference = LPS - Ringers) %>%
  my_summary() %>%
  mutate(` ` = ifelse(p < 0.05, "\\*", ""),
         ` ` = replace(` `, p < 0.01, "**"),
         ` ` = replace(` `, p < 0.001, "***"),
         ` ` = replace(` `, p == " ", "")) %>%
  kable(digits = 3) %>% kable_styling() 
Metric Estimate Est.Error Q2.5 Q97.5 p
Absolute difference in % time in close contact 5.538 3.006 -0.330 11.495
Log odds ratio -0.369 0.199 -0.763 0.022 0.0328 *

Table S6: Pairs in which one bee had received LPS were observed in close contact less frequently than pairs in which one bee had received Ringers solution.


sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

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

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

other attached packages:
 [1] scales_1.1.0     tidybayes_2.0.1  cowplot_1.0.0    bayestestR_0.5.1
 [5] kableExtra_1.1.0 gridExtra_2.3    forcats_0.5.0    stringr_1.4.0   
 [9] dplyr_0.8.5      purrr_0.3.3      readr_1.3.1      tidyr_1.0.2     
[13] tibble_3.0.0     ggplot2_3.3.0    tidyverse_1.3.0  bayesplot_1.7.1 
[17] brms_2.12.0      Rcpp_1.0.3       showtext_0.7-1   showtextdb_2.0  
[21] sysfonts_0.8     workflowr_1.6.0 

loaded via a namespace (and not attached):
  [1] colorspace_1.4-1     ellipsis_0.3.0       ggridges_0.5.2      
  [4] rsconnect_0.8.16     rprojroot_1.3-2      markdown_1.1        
  [7] base64enc_0.1-3      fs_1.3.1             rstudioapi_0.11     
 [10] farver_2.0.3         rstan_2.19.3         svUnit_0.7-12       
 [13] DT_0.13              fansi_0.4.1          mvtnorm_1.1-0       
 [16] lubridate_1.7.8      xml2_1.3.1           bridgesampling_1.0-0
 [19] knitr_1.28           shinythemes_1.1.2    jsonlite_1.6.1      
 [22] broom_0.5.4          dbplyr_1.4.2         shiny_1.4.0         
 [25] compiler_3.6.3       httr_1.4.1           backports_1.1.6     
 [28] assertthat_0.2.1     Matrix_1.2-18        fastmap_1.0.1       
 [31] cli_2.0.2            later_1.0.0          htmltools_0.4.0     
 [34] prettyunits_1.1.1    tools_3.6.3          igraph_1.2.5        
 [37] coda_0.19-3          gtable_0.3.0         glue_1.4.0          
 [40] reshape2_1.4.4       cellranger_1.1.0     vctrs_0.2.4         
 [43] nlme_3.1-147         crosstalk_1.1.0.1    insight_0.8.1       
 [46] xfun_0.13            ps_1.3.0             rvest_0.3.5         
 [49] mime_0.9             miniUI_0.1.1.1       lifecycle_0.2.0     
 [52] gtools_3.8.2         zoo_1.8-7            colourpicker_1.0    
 [55] hms_0.5.3            promises_1.1.0       Brobdingnag_1.2-6   
 [58] parallel_3.6.3       inline_0.3.15        RColorBrewer_1.1-2  
 [61] shinystan_2.5.0      curl_4.3             yaml_2.2.1          
 [64] loo_2.2.0            StanHeaders_2.19.2   stringi_1.4.6       
 [67] highr_0.8            dygraphs_1.1.1.6     pkgbuild_1.0.6      
 [70] rlang_0.4.5          pkgconfig_2.0.3      matrixStats_0.56.0  
 [73] evaluate_0.14        lattice_0.20-41      labeling_0.3        
 [76] rstantools_2.0.0     htmlwidgets_1.5.1    processx_3.4.2      
 [79] tidyselect_1.0.0     plyr_1.8.6           magrittr_1.5        
 [82] R6_2.4.1             generics_0.0.2       DBI_1.1.0           
 [85] pillar_1.4.3         haven_2.2.0          whisker_0.4         
 [88] withr_2.1.2          xts_0.12-0           abind_1.4-5         
 [91] modelr_0.1.5         crayon_1.3.4         arrayhelpers_1.1-0  
 [94] rmarkdown_2.1        grid_3.6.3           readxl_1.3.1        
 [97] callr_3.4.3          git2r_0.26.1         threejs_0.3.3       
[100] reprex_0.3.0         digest_0.6.25        webshot_0.5.2       
[103] xtable_1.8-4         httpuv_1.5.2         stats4_3.6.3        
[106] munsell_0.5.0        viridisLite_0.3.0    shinyjs_1.1