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library(shiny)
library(bslib)
library(thematic)
library(ggplot2)


thematic::thematic_shiny(font = "auto")


# take a vector, make a histogram

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library(tidyverse)
#> Warning: package 'tibble' was built under R version 4.0.2
#> Warning: package 'tidyr' was built under R version 4.0.2
#> Warning: package 'dplyr' was built under R version 4.0.2
tibble(x = 0:42,
       y1 = pbinom(x, 42, 0.3),
       y2 = 1-pbeta(0.3, x+1, 42-x)) %>% 
  ggplot(aes(x = x, y = y1)) + 
  geom_point(col = "green", size = 3) + 

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---
title: "Exploring observations"
author: "Andrew, based on Tim's lecture!"
date: "18/05/2020"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

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m <- 0.086

o <- (1-m)/m
curve((sqrt(o) - sqrt(o^-1)) / sqrt(x^2 - x + 1), xlim = c(0,50))
abline(h = 1/3)

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library(tidyverse)
cv <- 2.5
sigma = seq(0.2,5,by = 0.2)
list(mean = sigma / cv, sd = sigma) %>% transpose %>%
  set_names(., nm = map_chr(., lift_dl(paste, sep="_"))) %>%
  map(lift_dl(partial, .f = dnorm)) %>%
  map_df(~ tibble(x = seq(-2,3.5,0.01),
               y = .x(x)), .id = "mean_sd") %>%
  ggplot(aes(x = x, ymax = y, ymin = 0, fill = mean_sd)) + geom_ribbon() +

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pwr <- function(S, a, mu = 0.086, phi=240){
  D <- S * (S - 1)
  2 * (D + 1) * (D/(phi + 1) + 1) * mu * ( 1 - mu) + ( a * mu + mu)  * (1 - a * mu - mu) * (2.8)^2 / ((D + 1)*a*mu)^2
}

pwr(6, 0.10)
curve(pwr(x, 0.4), xlim = c(3,30))

curve(pwr(x, 0.2), xlim = c(3,30), log = "y")

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using Plots

# a vector of r values
Rs=collect(0.1:0.001:3)
T = 5000

N=zeros(length(Rs), T)

#Set t0 values to 1
N[:,1] .= 1

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info <- function(x, a, b) {
  a * (exp(a * (x - b)))  / (exp(a * b) + exp(a * x)) ^ 2
}

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library(tidyverse)
set.seed(4812)
islands <- data_frame(area = 
                        # runif(35, min = 0, max = 29)
                        rlnorm(35, meanlog = log(5), sdlog = log(3))
                      )
                      
dragon_response <- function(b0, b1){
  force(b0)
  force(b1)

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simulate_one_cardoso <- function(.cardoso_island = cardoso_island){
  
  spp_names <- unique(.cardoso_island$morphospecies)
  nspp <- length(spp_names)
  bromeliad_names <- unique(.cardoso_island$Bromeliad)
  nbrom <- length(bromeliad_names)
  
  # simulate from the parameters:
  b_intercept <- rnorm(1, 1, 0.2)