###############################################################################
### Figure 4 - Spatiotemporal correlations and chaos ##########################
###############################################################################

# Nick Lowery and Tristan Ursell
# 2018
# 
# 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
# 
# The script reads in correlation and metadata files generated from the LV_competition_chaos
# and chaos_spatial_correlation_function scripts. The functions to generate the data from the
# raw .mat data files are included but commented out.

###############################################################################

# load required libraries
#library(R.matlab)
library(tidyverse)
library(cowplot)
library(colorspace)

# # read in raw data files
# chaos.corr.raw <- list.files("E:/ecological_modelling/3sp_chaos_robust_cor", pattern = ".mat", full.names = T) %>%
#   lapply(., readMat)
# 
# chaos.metadata.raw <- list.files("E:/ecological_modelling/3sp_chaos_robust_metadata", 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 files for later use
# write_csv(chaos.corr, "3sp_chaos_corr.csv")
# write_csv(chaos.metadata, "3sp_chaos_metadata.csv")


# read in proccessed data files
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))

# calculate t to extinction
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))

# prep data 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)

# color palette (function generated using choose_palette() GUI)
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)
}

# generate 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"))