Fig4_chaos_analysis.md

Figure 4 - Decorrelation time and chaos

Nick Lowery

Background

This script generates Figure 4 from our preprint: Structured environments fundamentally alter dynamics and stability of ecological communities https://www.biorxiv.org/content/early/2018/07/10/366559

It shows that the more densely packed pillars are in the simulation environment, replicate simulations decorrelate more rapidly and become more sensitive to smaller perturbations in the initial conditions - i.e. pillars induce chatoic fluctuations within simulated communities.

First, load the requisite libraries

library(R.matlab)
library(tidyverse)
library(cowplot)
library(colorspace)

Wrangle raw data files

The following code chunk reads in the raw .mat files and writes organized flat .csv data files. It's not run here, but included for clarity.

# read in raw data files
chaos.corr.raw <- list.files("/path/to/files", pattern = ".mat", full.names = T) %>%
  lapply(., readMat)

chaos.metadata.raw <- list.files("/path/to/files", pattern = ".mat", full.names = T) %>%
  lapply(., readMat)

# organize into tbl
chaos.corr <- chaos.corr.raw %>% {
  tibble(
    L = map_dbl(., "L"),
    R = map_dbl(., "R"),
    dx = map_dbl(., "dx"),
    dinit = map_dbl(., "dinit"),
    cor.mat = map(., "cor.mat"),
    cor.mean = map(., "cor.mean"),
    cor.sd = map(., "cor.sd")
  )
} %>%
  filter(dinit %in% c(0.1, 0.01, 0.001, 0.0001)) %>%
  select(-cor.mat) %>%
  unnest() %>%
  group_by(R, dx, dinit) %>%
  mutate(t.step = seq_along(cor.mean))

chaos.metadata <- chaos.metadata.raw %>% {
  tibble(
    P = map_dbl(., "P"),
    pillars = map_dbl(., "pillarq"),
    R = map_dbl(., "R"),
    dx = map_dbl(., "dx"),
    dinit = map_dbl(., "dinit"),
    rep = map_dbl(., "rep"),
    data = map(., `[`, c("meanA.out", "meanB.out", "meanC.out")) %>% map(data.frame)
  )
} %>%
  unnest() %>%
  rename(A = meanA.out, B = meanB.out, C = meanC.out) %>%
  group_by(R, dx, dinit, rep) %>%
  mutate(t.step = seq_along(A))

# write organized data files
write_csv(chaos.corr, "3sp_chaos_corr.csv")
write_csv(chaos.metadata, "3sp_chaos_metadata.csv")

Calculate time to extinction

We'll use the flat data files for the rest of the analysis. We'll also need a file that gives the number of pillar vs. non-pillar pixels in each simulation environment, to accurately determine when extinctions occur (see below).

chaos.corr <- read_csv("3sp_chaos_corr.csv")
chaos.metadata <- read_csv("3sp_chaos_metadata.csv")
pillar.weights <- read_csv("filt_all_weights.csv", col_names = c("L","R","dx","pillar.weight")) %>%
  mutate(dx = round(dx*R))

Now, we'll calculate whether a simulation went extinct, and if so at which time step. Extinction is defined as any species abundance falling below a minimum threshold (specifically, the area that could be pinned between a pillar and the edge of the simulation box, and thereby not in contact with the rest of the simulation environment).

chaos.ext <- chaos.metadata %>%
  left_join(pillar.weights) %>%
  mutate(extinct = ifelse(A <= ((2*R)^2 - pi*R^2)/4/pillar.weight |
                          B <= ((2*R)^2 - pi*R^2)/4/pillar.weight |
                          C <= ((2*R)^2 - pi*R^2)/4/pillar.weight , 1, 0)) %>%
  group_by(R,dx,dinit,rep) %>%
  summarise(extinction = max(extinct),
            t.extinct = ifelse(max(extinct), which.max(extinct), NA)) %>%
  group_by(R,dx,dinit) %>%
  summarise(t.stop = floor(min(t.extinct, na.rm = T)/5)) # round to whole time step
    # this will generate a bunch of warnings when nothing goes extinct, which are safe to ignore

Next is to combine the extinction data with the between-rep correlation data, and prep for plotting:

chaos.corr.plot <- chaos.corr %>%
  ungroup() %>%
  left_join(chaos.ext) %>%
  filter(t.step <= t.stop) %>% 
  mutate(R = round(R/sqrt(15), digits = 2),
         R = fct_relevel(factor(R), "0", after = Inf),
         dinit = 100*dinit)

Generate Plot

Before making the final plot, I'm using the following function from the colorspace package to generate the color palette for this (and other) plots. Full disclosure: I almost always use the colorspace GUI to pick the palettes I want.

pal <- function (n, h = c(300, 75), c. = c(35, 95), l = c(15, 90), 
                 power = c(0.8, 1.2), fixup = TRUE, gamma = NULL, alpha = 1, 
                 ...) 
  {
  if (!is.null(gamma)) 
    warning("'gamma' is deprecated and has no effect")
  if (n < 1L) 
    return(character(0L))
  h <- rep(h, length.out = 2L)
  c <- rep(c., length.out = 2L)
  l <- rep(l, length.out = 2L)
  power <- rep(power, length.out = 2L)
  rval <- seq(1, 0, length = n)
  rval <- hex(polarLUV(L = l[2L] - diff(l) * rval^power[2L], 
                       C = c[2L] - diff(c) * rval^power[1L], H = h[2L] - diff(h) * 
                         rval), fixup = fixup, ...)
  if (!missing(alpha)) {
    alpha <- pmax(pmin(alpha, 1), 0)
    alpha <- format(as.hexmode(round(alpha * 255 + 1e-04)), 
                    width = 2L, upper.case = TRUE)
    rval <- paste(rval, alpha, sep = "")
  }
  return(rval)
}

And, finally, the code to generate the plot:

chaos.corr.plot %>%
  ggplot(aes(x = t.step, y = cor.mean, color = as.factor(dinit), group = dinit)) +
  geom_hline(yintercept = 0, linetype = "dashed", size = 1.5, color = "grey50") +
  geom_ribbon(aes(ymin = cor.mean - cor.sd/sqrt(10), 
                  ymax = cor.mean + cor.sd/sqrt(10), 
                  fill = as.factor(dinit), color = NULL), alpha = 0.4) +
  geom_line(size = 1, lineend = "round") +
  facet_wrap(~ R) +
  scale_color_manual(values = pal(4)) +
  scale_fill_manual(values = pal(4)) +
  labs(x = "time step (doubling times)",
       y = "mean pairwise correlation",
       color = paste("percentage of","reassigned","pixels at t = 0", sep = "\n"),
       fill = paste("percentage of","reassigned","pixels at t = 0", sep = "\n"),
       title = expression(paste("pillar radius ( R / ", lambda, ")"))) +
  theme(plot.title = element_text(size = 14, face = "plain"))