FL_v_rearing

library(tidyverse)

# Previous version of SBM used 120 mm cutoff for rearing
# Exploring idea of using hypothetical continuous relationship between rearing probability and fork length

## Four-parameter logistic model gives nice control over the curve
# a = max value
# b = steepness of the curve
# c = inflection point
# d = min value

logistic_4p <- function(fl, a, b, c, d){
  d + (a - d)/(1 + (fl / c)^b)
}

tibble(FL = 30:150, 
       Prob = logistic_4p(FL, 1, 7, 75, 0)) %>% 
  ggplot(aes(x = FL, y = Prob)) +
  geom_line() +
  labs(x = "Fork length (mm)", y = "Probability of rearing") +
  coord_cartesian(ylim = c(0, 1)) +
  scale_x_continuous(breaks = seq(30, 150, 10)) +
  theme_minimal()


## simple linear relationship with logit transformation
inv_logit = function (x){
  p = 1/(1 + exp(-x))
  p[is.infinite(p)] = 1
  p
}

intercept = 10
slope = -0.12

tibble(FL = 30:150,
       Prob = inv_logit(intercept + slope * FL)) %>%
  ggplot(aes(x = FL, y = Prob)) +
  geom_line() +
  labs(x = "Fork length (mm)", y = "Probability of rearing") +
  coord_cartesian(ylim = c(0, 1)) +
  scale_x_continuous(breaks = seq(30, 150, 10)) +
  theme_minimal()