In cboettig/multiple_uncertainty: Multiple Uncertainty

library("dplyr")
library("tidyr")
library("ggplot2")
library("multipleuncertainty")
library("parallel")
knitr::opts_chunk$set(cache = TRUE)

Robustness to model

We consider a variety of functional forms for the population growth model. We use the following functional forms for the models:

logistic
bevertonholt
ricker
gompertz
allen

fig3 <- function(model, noise_dist){  
  grid <- seq(0, 200, length = 401)
  model <- get(as.character(model))
  small     <- multiple_uncertainty(f = model, x_grid = grid, sigma_g = 0.1, sigma_m = 0.1, sigma_i = 0.1, noise_dist = noise_dist)
  growth    <- multiple_uncertainty(f = model, x_grid = grid, sigma_g = 0.5, sigma_m = 0.1, sigma_i = 0.1, noise_dist = noise_dist)
  measure   <- multiple_uncertainty(f = model, x_grid = grid, sigma_g = 0.1, sigma_m = 0.5, sigma_i = 0.1, noise_dist = noise_dist)
  implement <- multiple_uncertainty(f = model, x_grid = grid, sigma_g = 0.1, sigma_m = 0.1, sigma_i = 0.5, noise_dist = noise_dist)
  ## Combine records by scenario
  df <- data.frame(y_grid = grid, small = small, growth = growth, 
                   measure = measure, implement = implement) %>%
    tidyr::gather(scenario, value, -y_grid)
}


expand.grid(model = c("logistic", "bevertonholt", "ricker", "gompertz"), 
            noise_dist = c("uniform", "lognormal")) %>%
  dplyr::group_by(model, noise_dist) %>%
  dplyr::do(fig3(.$model, .$noise_dist)) -> df

df %>%
  ggplot(aes(x = y_grid, y = value, col = scenario)) + 
    geom_line()  + 
    facet_grid(model ~ noise_dist) + 
    xlab("Stock") + 
    ylab("Escapement") + 
    coord_cartesian(xlim = c(0, 150), ylim = c(0,100)) + 
    theme_bw()

Visualizing models at different parameter values

First we include plots of the growth function at different

case <- function(model, r){
  x <- seq(0,200, by=1)
  f <- get(as.character(model))
  data.frame(x = x, f = sapply(x, f, h = 0, r = r))
}

options(stringsAsFactors = FALSE)

expand.grid(model = c("logistic", "bevertonholt", "ricker", "gompertz", "allen"), 
            r = c(0.1, 0.5, 0.75, 1)) %>%
  dplyr::group_by(model, r) %>%
  dplyr::do(case(.$model, .$r)) -> 
  df

ggplot(df, aes(x = x, y = f, color = model)) + 
  geom_line() + 
  #geom_segment(aes(x = 0, xend = 100, y = 100, yend = 100), col='black', linetype = 2) + 
  #geom_segment(aes(x = 100, xend = 100, y = 0, yend = 100), col='black', linetype = 2) +
  facet_grid(model ~ r)

Recall or observe that the parameter r does not change the carrying capacity of the Logistic, Ricker or Allen models, but does for the Beverton-Holt and Gompertz model. This makes it difficult to directly consider how

cboettig/multiple_uncertainty documentation built on May 13, 2019, 2:08 p.m.