Plotting the simulation results

Load packages and results

packages <- c("dplyr", "purrr", "ggplot2", "reshape2", "Cairo", "knitr",  
              "latex2exp", "pander", "grid", "gridExtra", "ggthemes",
              "readr", "tibble", "biglm", "kableExtra")
shh <- suppressMessages(lapply(packages, library, character.only = TRUE, quietly = TRUE))


if(!file.exists("data/all_results.rds")){
  results <- lapply(list.files(path = "data", pattern = "results_", full.names = TRUE), readRDS) %>% 
    do.call("rbind", .) %>%
    filter(cost_A == 0 & cost_B == 0)
  saveRDS(results, file = "data/all_results.rds")
} else results <- read_rds("data/all_results.rds")

results$went_extinct <- ifelse(results$outcome == "Population extinct", 1, 0)

results$migration_type[results$migration_type == "local"] <- "Local"
results$migration_type[results$migration_type == "global"] <- "Global"

find_variable_parameters <- function(dat){
  dat %>% 
    select(-id, -realisations, -generation_extinct, -generation_Zd_extinct, 
           -generation_W_extinct, -generation_Zd_fixed, -outcome, -went_extinct, 
           -mating_table, -initial_Wr, -initial_Zr) %>%
    sapply(function(x) length(unique(x))) %>% 
    keep(~.x > 1) %>% names()
}

variable_parameters <- find_variable_parameters(results)
combinations <- apply(combn(variable_parameters, 2), 2, paste0, collapse = " x ")

# Make a data frame to conver R-friendly names to figure-friendly names
nice_names <- data.frame(original = c(variable_parameters, combinations),
                         new = gsub("_", " ", c(variable_parameters, combinations)),
                         stringsAsFactors = FALSE) %>%
  mutate(
    new = gsub("rel", "Rel", new),
    new = gsub("W shredding rate", "Gene drive in females ($p_{shred}$)", new),
    new = gsub("Z conversion rate", "Gene drive in males ($p_{conv}$)", new),
    new = gsub("Zr creation rate", "Rate of NHEJ ($p_{nhej}$)", new),
    new = gsub("Zr mutation rate", "Z-linked resistance ($\\mu{_Z}$)", new),
    new = gsub("Wr mutation rate", "W-linked resistance ($\\mu{_W}$)", new),
    new = gsub("cost Zdrive female", "Cost of Z* to females ($c_f$)", new),
    new = gsub("cost Zdrive male", "Cost of Z* to males ($c_m$)", new),
    new = gsub("male migration prob", "Male dispersal frequency", new),
    new = gsub("feMale dispersal frequency", "Female dispersal frequency (xf)", new),
    new = gsub("Male dispersal frequency", "Male dispersal frequency (xm)", new),
    new = gsub("xm", "$x_m$", new), 
    new = gsub("xf", "$x_f$", new),
    new = gsub("migration type", "Dispersal type", new),
    new = gsub("n patches", "Number of patches ($k$)", new),
    new = gsub("softness", "Importance of local density ($\\psi$)", new),
    new = gsub("male weighting", "Male effect on density ($\\delta$)", new),
    new = gsub("density dependence shape", "Shape of density dependence ($\\alpha$)", new),
    new = gsub("max fecundity", "Maximum fecundity ($r$)", new),
    new = gsub("initial A", "Intial freq. W-shredding resistance allele A", new),
    new = gsub("initial B", "Intial freq. gene conversion resistance allele B", new),
    new = as.character(TeX(new))) %>% 
  mutate(new = gsub("mu", "\\mu", new))

# Sort the results between those that model a W-shredder, versus those that model a Z* that sterilisies females
W_shredder <- results %>% filter(cost_Zdrive_female != 1)
female_sterilising <- results %>% filter(cost_Zdrive_female == 1)
rm(results)
variable_parameters_W_shredder <- find_variable_parameters(W_shredder)
variable_parameters_female_sterilising <- find_variable_parameters(female_sterilising)

Table showing the frequencies of each possible outcome

Table S1: The number and percentage of simulation runs that ended with the five possible outcomes, for the subset of simulation runs focusing on a W-shredder gene drive.

make_tally_table <- function(dat){
  outcomes <- dat$outcome %>% table() %>% melt() %>% arrange(-value) %>% mutate(p = round(100 * value / sum(value), 1))
  names(outcomes) <- c("Outcome", "Number of simulations", "%")
  outcomes %>% mutate(Outcome = gsub("without", "without causing", Outcome),
                      Outcome = gsub("n extinct", "n went extinct", Outcome),
                      Outcome = gsub("d extinct", "d went extinct", Outcome)) %>% pander()
}

make_tally_table(W_shredder)

Table S2: The number and percentage of simulation runs that ended with the five possible outcomes, for the subset of simulation runs focusing on a female-sterilising Z-linked gene drive.

make_tally_table(female_sterilising)

Make Figure 1

a <- read_rds("data/allele_freqs_1.rds")

plot_run <- function(){
  
  get_data <- function(model_id, allele_freqs_list, result_df, label){
    
    df <- pluck_allele_freqs(model_id, allele_freqs_list) 
    
    alleles_to_plot <- group_by(df, allele) %>% 
      summarise(uniques = length(unique(frequency))) %>% 
      filter(uniques > 1) %>% # Don't plot alleles that stay at 0 whole time
      pull(allele)
    
    alleles_to_plot <- c(alleles_to_plot, "N")
    df <- df[df$allele %in% alleles_to_plot, ]
    df$frequency[df$allele == "N"] <- df$frequency[df$allele == "N"] /
      max(df$frequency[df$allele == "N"])
     
    # paras <- result_df %>% mutate(id = as.character(id)) %>% filter(id == model_id)
    # last_generation <- tail(df,12) %>% select(allele, frequency)
    # print(paras); print(last_generation)
    
    df %>% mutate(facet = label,
                  allele = replace(allele, allele == "Zd", "Z*"),
                  allele = replace(allele, allele == "females", "Females"))
  }
  
  rbind(
    get_data("10024119427447", a, W_shredder, "A. Population extinction"),
    get_data("1002596940286", a, W_shredder, "B. Failure to cause extinction"),
    get_data("10024112958792", a, W_shredder, "C. Resistance prevents extinction")) %>%
    ggplot(aes(x = generation, y = frequency, colour = allele, group = allele)) + 
    geom_vline(xintercept = 50, linetype = 2, colour = "grey10", size = 0.9) + 
    geom_line(size = 0.9, alpha = 0.9) + 
    facet_wrap(~facet, scales = "free_x") +
    theme_hc() + scale_colour_hc(name = "") +
    theme(strip.text = element_text(hjust = 0), 
          strip.background = element_rect(fill = "grey90"),
          legend.position = "top",
          axis.ticks.y = element_blank()) + 
    xlab("Generation") + ylab("Frequency")
}

fig1 <- plot_run()
rm(a)
fig1

Figure 1: Three illustrative runs of the simulation, showing evolution in response to the introduction of XX males carrying a W-shredder at Generation 50 (marked by the dashed line). In panel A, the driving Z* allele fixed very quickly, causing population extinction as the number of females dropped to zero. In panel B, the Z* allele spread up until the point that its fitness costs began to negate its transmission advantage, causing the population to halve in size but not to go extinct. In panel C, the Z* allele invaded, selecting for the resistance alleles A and Zr allele, and causing the Z* allele to reverse course and go extinct. The population size N is shown as a fraction of its maximum value of 10,000. Table SX gives the parameter space used for these three runs.

tabl <- t(rbind(
  data.frame(Panel = "A", W_shredder %>% filter(id == "10024119427447")),
  data.frame(Panel = "B", W_shredder %>% filter(id == "1002596940286")),
  data.frame(Panel = "C", W_shredder %>% filter(id == "10024112958792"))) %>%
  select(release_strategy, W_shredding_rate, 
         Z_conversion_rate, Zr_creation_rate, Zr_mutation_rate,
         Wr_mutation_rate, cost_Zdrive_female, cost_Zdrive_male,
         male_migration_prob, female_migration_prob,
         migration_type, n_patches, softness, male_weighting,
         density_dependence_shape, max_fecundity, initial_A, initial_B))

nice_names2 <- data.frame(original = variable_parameters,
                          new = gsub("_", " ", variable_parameters),
                          stringsAsFactors = FALSE) %>%
  mutate(
    new = gsub("rel", "Rel", new),
    new = gsub("W shredding rate", "Gene drive in females (p-shred)", new),
    new = gsub("Z conversion rate", "Gene drive in males (p-conv)", new),
    new = gsub("Zr creation rate", "Rate of NHEJ (p-nhej)", new),
    new = gsub("Zr mutation rate", "Z-linked resistance (μ-Z)", new),
    new = gsub("Wr mutation rate", "W-linked resistance (μ-W)", new),
    new = gsub("cost Zdrive female", "Cost of Z* to females (c-f)", new),
    new = gsub("cost Zdrive male", "Cost of Z* to males (c-m)", new),
    new = gsub("male migration prob", "Male dispersal frequency", new),
    new = gsub("feMale dispersal frequency", "Female dispersal frequency (x-f)", new),
    new = gsub("Male dispersal frequency", "Male dispersal frequency (x-m)", new),
    new = gsub("migration type", "Dispersal type", new),
    new = gsub("n patches", "Number of patches (k)", new),
    new = gsub("softness", "Importance of local density (ψ)", new),
    new = gsub("male weighting", "Male effect on density (𝛿)", new),
    new = gsub("density dependence shape", "Shape of density dependence (α)", new),
    new = gsub("max fecundity", "Maximum fecundity (r)", new),
    new = gsub("initial A", "Intial freq. W-shredding resistance allele A", new),
    new = gsub("initial B", "Intial freq. gene conversion resistance allele B", new)) 



rownames(tabl) <- nice_names2$new[match(rownames(tabl), nice_names2$original)]
rownames(tabl) <- gsub("[.]", "", rownames(tabl))
colnames(tabl) <- c("Panel A", "Panel B", "Panel C")

Table S3: List of the parameter values used to generate the simulation runs shown in Figure 1.

as.data.frame(tabl) %>% kable(format = "html", escape = FALSE) %>% kable_styling()

Make Figure 2

# Find the proportion of runs that went extinct for each parameter value
get_percent_extinct <- function(dat, parameter){
  dat %>%
    group_by(!! sym(parameter)) %>%
    summarise(extinct = sum(went_extinct),
              not_extinct = n() - sum(went_extinct),
              prob = list(binom.test(extinct, extinct + not_extinct))) %>%
    rowwise() %>%
    mutate(percent_extinct = 100 * extinct/(extinct + not_extinct),
           lower_95_CI = 100 * prob$conf.int[1],
           upper_95_CI = 100 * prob$conf.int[2],
           parameter =  parameter) %>% rename(value = !! sym(parameter)) %>%
    select(parameter, value, everything()) %>% select(-prob) %>% ungroup()
} 

W_shredder_percent_extinct <- lapply(variable_parameters, 
                                     get_percent_extinct, 
                                     dat = W_shredder) %>% do.call("rbind", .)

female_sterilising_percent_extinct <- lapply(variable_parameters, 
                                             get_percent_extinct, 
                                             dat = female_sterilising) %>% do.call("rbind", .)

# Graph these data
make_figure_2 <- function(percent_extinct_data){
  parameter_importance <- percent_extinct_data %>%
    mutate(parameter = nice_names$new[match(parameter, nice_names$original)]) %>%
    group_by(parameter) %>% summarise(range = max(percent_extinct) - min(percent_extinct)) %>%
    arrange(-range) %>% pull(parameter)
  
  levels <- levels(factor(percent_extinct_data$value))
  levels <- c(levels[!(levels %in% c("all_patches", 100))], 100, "all_patches")
  levels <- replace(levels, levels == "all_patches", "Release in\nall patches")
  levels <- replace(levels, levels == "one_patch", "Release in\na single patch")
  
  percent_extinct_data %>% 
    mutate(parameter = nice_names$new[match(parameter, nice_names$original)],
           parameter = factor(parameter, parameter_importance),
           value = replace(value, value == "all_patches", "Release in\nall patches"),
           value = replace(value, value == "one_patch", "Release in\na single patch"),
           value = factor(value, levels)) %>%
    ggplot(aes(value, percent_extinct)) + 
    geom_errorbar(aes(ymin=lower_95_CI, ymax = upper_95_CI), width = 0) +
    geom_point() + 
    xlab("Parameter value") +
    ylab("% simulation runs resulting in extinction (\u00B1 95% CIs)") + 
    theme_bw() + 
    theme(strip.background = element_blank(),
          panel.grid.major.x = element_blank())
  
}

fig2 <- make_figure_2(W_shredder_percent_extinct) 
fig2 + facet_wrap(~parameter, scales = "free", labeller = label_parsed, ncol = 3) 

Figure 2: The percentage of simulations of a W-shredder that ended in extinction, for all runs with a particular value (shown on the x-axis) for a given parameter (shown in the panels). For example, in all the thousands of runs for which I assumed \(p_{shred} = 0.5\), there were no extinctions, while among the runs where \(p_{shred} = 1\), over 60% resulted in extinction. The panels are ordered by the range of the y-axis, which highlights the relative importance of the variables for the probability of extinction. Figure S1 gives a similar plot for simulations of a female-sterilising Z* allele.

Make Figure S1

figS1 <- make_figure_2(female_sterilising_percent_extinct)
cairo_pdf(file = "figures/figureS1.pdf", width = 9, height = 12)
figS1 + facet_wrap(~parameter, scales = "free", labeller = label_parsed, ncol = 4)
dev.off()

quartz_off_screen 
                2 

figS1 + facet_wrap(~parameter, scales = "free", labeller = label_parsed, ncol = 3) 

Figure S1: Analgous information to Figure 2, but showing the results for a female-sterilising Z* allele instfead of a W-shredder.

Finding variables with interacting effects on the extinction probability

run_big_glm <- function(dat, sterilising = FALSE){
  
  if(sterilising){
    variable_parameters <- variable_parameters[!(variable_parameters %in% c("W_shredding_rate", "cost_Zdrive_female"))] 
  }
  
  formula <- paste("went_extinct ~ (",
                   paste0(variable_parameters, collapse = " + "), ")^2",
                   sep = "")
  
  if(!sterilising) formula <- paste(formula, "- W_shredding_rate:cost_Zdrive_female")
  
  my_scale <- function(x) as.numeric(scale(x))
  
  glm_model <- bigglm(as.formula(formula), data = dat %>% mutate_if(is.numeric, my_scale), chunksize = 10000)
  return(glm_model)
  
  output <- data.frame(Parameter = rownames(summary(glm_model)[[2]]), summary(glm_model)[[2]]) %>% 
    as_tibble() %>% arrange(-abs(Coef)) %>%
    mutate(Parameter = gsub(":", " x ", Parameter),
           Parameter = factor(Parameter, rev(Parameter)),
           log10_p = -log10(p + 1e-300)) 
  
  names(output)[2:4] <- c("Estimate", "Lower_95_CI", "Upper_95_CI")
  output
}

if(!file.exists("data/W_shredder_model.rds")) {
  W_shredder_model <- run_big_glm(W_shredder)
  saveRDS(W_shredder_model, "data/W_shredder_model.rds")
  female_sterilising_model <- run_big_glm(female_sterilising, sterilising = TRUE)
  saveRDS(female_sterilising_model, "data/female_sterilising_model.rds")
} else {
  W_shredder_model <- readRDS("data/W_shredder_model.rds")
  female_sterilising_model <- readRDS("data/female_sterilising_model.rds")
}

importance_plot <- function(dat, n = "all"){
  if(n != "all") dat <- dat %>%
      mutate(row=1:n()) %>% filter(row %in% 1:n)
  
  for(i in 1:nrow(dat)){
    if(dat$Estimate[i] < 0){
      lower <- dat$Lower_95_CI[i]
      dat$Lower_95_CI[i] <- dat$Upper_95_CI[i]
      dat$Upper_95_CI[i] <- lower
    }
  }
  
  dat <- dat %>%
    mutate(Parameter = gsub("one_patch", "", as.character(Parameter)),
           Parameter = gsub("Local", "", Parameter),
           Parameter = factor(Parameter, rev(Parameter)),
           tick_label = nice_names$new[match(Parameter, nice_names$original)]) 
  
  print(dat %>% select(Parameter, tick_label))
  
  dat %>%
    ggplot(aes(Parameter, abs(Estimate))) + 
    geom_bar(stat = "identity", fill = "tomato") +
    geom_errorbar(aes(ymin = abs(Lower_95_CI), ymax = abs(Upper_95_CI)), width = 0) + 
    coord_flip() + 
    scale_y_continuous(expand = c(0, 0)) + 
    scale_x_discrete(labels = parse(text = rev(dat$tick_label))) + 
    xlab("Model parameter") + ylab("Absolute effect size")

}
importance_plot(W_shredder_model, n = 25)

# A tibble: 25 x 2
   Parameter                  tick_label                                   
   <fct>                      <chr>                                        
 1 W_shredding_rate           "paste(\"Gene drive in females \", \"(\", \"…
 2 initial_A                  "paste(\"Intial freq\", \". W-shredding resi…
 3 W_shredding_rate x initia… "paste(\"Gene drive in females \", \"(\", \"…
 4 Wr_mutation_rate           "paste(\"W-linked resistance \", \"(\", \"\"…
 5 density_dependence_shape   "paste(\"Shape of density dependence \", \"(…
 6 Z_conversion_rate          "paste(\"Gene drive in males \", \"(\", \"\"…
 7 Z_conversion_rate x cost_… "paste(\"Gene drive in males \", \"(\", \"\"…
 8 W_shredding_rate x Wr_mut… "paste(\"Gene drive in females \", \"(\", \"…
 9 max_fecundity              "paste(\"Maximum fecundity \", \"(\", \"\", …
10 W_shredding_rate x Z_conv… "paste(\"Gene drive in females \", \"(\", \"…
# … with 15 more rows

importance_plot(female_sterilising_model, n = 25)

# A tibble: 25 x 2
   Parameter                    tick_label                                 
   <fct>                        <chr>                                      
 1 Z_conversion_rate            "paste(\"Gene drive in males \", \"(\", \"…
 2 Z_conversion_rate x Zr_crea… "paste(\"Gene drive in males \", \"(\", \"…
 3 Zr_creation_rate             "paste(\"Rate of NHEJ \", \"(\", \"\", \"p…
 4 Z_conversion_rate x male_we… "paste(\"Gene drive in males \", \"(\", \"…
 5 Z_conversion_rate x initial… "paste(\"Gene drive in males \", \"(\", \"…
 6 Z_conversion_rate x density… "paste(\"Gene drive in males \", \"(\", \"…
 7 male_weighting               "paste(\"Male effect on density \", \"(\",…
 8 initial_B                    "paste(\"Intial freq\", \". gene conversio…
 9 density_dependence_shape     "paste(\"Shape of density dependence \", \…
10 Z_conversion_rate x Zr_muta… "paste(\"Gene drive in males \", \"(\", \"…
# … with 15 more rows

get_percent_extinct_double <- function(dat, p1, p2){
  output <-  dat %>%
    group_by(!! sym(p1), !! sym(p2)) %>%
    summarise(extinct = sum(went_extinct),
              not_extinct = n() - sum(went_extinct),
              prob = list(binom.test(extinct, extinct + not_extinct))) %>%
    rowwise() %>%
    mutate(percent_extinct = 100 * extinct / (extinct + not_extinct),
           lower_95_CI = 100 * prob$conf.int[1],
           upper_95_CI = 100 * prob$conf.int[2],
           parameter_1 =  p1, 
           parameter_2 =  p2) 
  names(output)[1:2] <- paste("value", 1:2, sep = "_")
  output %>%
    mutate(value_1 = as.character(value_1), value_2 = as.character(value_2)) %>%
    select(parameter_1, parameter_2, value_1, value_2, everything()) %>% 
    select(-prob) %>% ungroup()
} 

# combinations <- combn(variable_parameters, 2)
# two_way_W_shredder <- map2_df(combinations[1, ], 
#                               combinations[2, ], 
#                               get_percent_extinct_double, dat = W_shredder)

interesting <- c("W_shredding_rate~initial_A", "Z_conversion_rate~cost_Zdrive_female", "W_shredding_rate~Wr_mutation_rate",
                 "W_shredding_rate~Z_conversion_rate", "Zr_creation_rate~cost_Zdrive_female", "W_shredding_rate~density_dependence_shape",
                 "cost_Zdrive_female~n_patches", "W_shredding_rate~max_fecundity", "density_dependence_shape~max_fecundity")
two_way_W_shredder <- map2_df(str_split(interesting, "~", simplify = TRUE)[, 1], 
                              str_split(interesting, "~", simplify = TRUE)[, 2], 
                              get_percent_extinct_double, dat = W_shredder)


two_way_plot <- function(two_way_data, pairwise_combos){
  
  two_way_data <- two_way_data %>%
    mutate(pasted = paste(parameter_1, parameter_2, sep="~"),
           parameter_1 = nice_names$new[match(parameter_1, nice_names$original)],
           parameter_2 = nice_names$new[match(parameter_2, nice_names$original)]) %>%
    filter(pasted %in% pairwise_combos) 
  z_range <- range(two_way_data$percent_extinct) * 1.1
  
  make_one <- function(df){
    
    ggplot(df, aes(value_1, value_2, fill = percent_extinct)) + 
      geom_tile(colour = "black") + 
      scale_fill_distiller(palette = "PuBuGn", direction = 1, limits = z_range, name = "% extinct") + 
      theme_minimal() + 
      theme(panel.border = element_rect(fill = NA, colour = "black")) + 
      scale_x_discrete(expand = c(0,0), name = parse(text = df$parameter_1[1])) + 
      scale_y_discrete(expand = c(0,0), name = parse(text = df$parameter_2[1])) 
      
  }
  
  grid_arrange_shared_legend <- function(...) {
    plots <- list(...)
    g <- ggplotGrob(plots[[1]] + theme(legend.position="bottom"))$grobs
    legend <- g[[which(sapply(g, function(x) x$name) == "guide-box")]]
    lheight <- sum(legend$height)
    plots <- lapply(plots, function(x) ggplotGrob(x + theme(legend.position = "none")))
    
    p <- gtable_cbind(gtable_rbind(plots[[1]], plots[[4]], plots[[7]]),
                      gtable_rbind(plots[[2]], plots[[5]], plots[[8]]),
                      gtable_rbind(plots[[3]], plots[[6]], plots[[9]]))
    
    grid.arrange(p, legend, 
                 nrow = 2, 
                 heights = unit.c(unit(1, "npc") - lheight, lheight))
  }

  dat_list <- vector(mode = "list", length = length(pairwise_combos))
  for(i in 1:length(pairwise_combos)){
    dat_list[[i]] <- two_way_data %>% filter(pasted == pairwise_combos[i])
  }
  
  lapply(dat_list, make_one) %>% do.call("grid_arrange_shared_legend", .)
}

fig3 <- two_way_plot(two_way_W_shredder, interesting)
grid.draw(fig3)

Session information

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] grid      parallel  stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] bindrcpp_0.2.2     kableExtra_0.9.0   biglm_0.9-1       
 [4] DBI_1.0.0          ggthemes_4.0.1     gridExtra_2.3     
 [7] pander_0.6.2       latex2exp_0.4.0    knitr_1.20        
[10] Cairo_1.5-9        ggplot2_3.1.0      future.apply_1.0.1
[13] future_1.11.1.1    tibble_2.0.0       readr_1.1.1       
[16] rslurm_0.4.0       Rcpp_1.0.0         reshape2_1.4.3    
[19] stringr_1.3.1      tidyr_0.8.2        purrr_0.2.5       
[22] dplyr_0.7.8       

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.5   listenv_0.7.0      colorspace_1.3-2  
 [4] viridisLite_0.3.0  htmltools_0.3.6    yaml_2.2.0        
 [7] utf8_1.1.4         rlang_0.3.1        R.oo_1.22.0       
[10] pillar_1.3.1.9000  glue_1.3.0         withr_2.1.2       
[13] R.utils_2.7.0      RColorBrewer_1.1-2 bindr_0.1.1       
[16] plyr_1.8.4         munsell_0.5.0      gtable_0.2.0      
[19] workflowr_1.1.1    rvest_0.3.2        R.methodsS3_1.7.1 
[22] codetools_0.2-15   evaluate_0.11      labeling_0.3      
[25] fansi_0.4.0        backports_1.1.2    scales_1.0.0      
[28] hms_0.4.2          digest_0.6.18      stringi_1.2.4     
[31] rprojroot_1.3-2    cli_1.0.1          tools_3.5.1       
[34] magrittr_1.5       lazyeval_0.2.1     crayon_1.3.4      
[37] whisker_0.3-2      pkgconfig_2.0.2    xml2_1.2.0        
[40] httr_1.3.1         assertthat_0.2.0   rmarkdown_1.10    
[43] rstudioapi_0.9.0   R6_2.3.0           globals_0.12.4    
[46] git2r_0.23.0       compiler_3.5.1