file4ca1dcc46fe.R

#' # Lake Ontario Cormorant matrix
cormorant_post_pop <- function(S = c(0.5, 0.87, 0.88, 0.89), 
                               B = c(0, 0.5, 0.99), 
                               F_ = c(0, 1.6, 2.4),
                               R = 0.5){
  A <- matrix(0, nrow=3, ncol=3)
  A[2,1] <- S[1]
  A[3,2:3] <- S[2:3] # ends up slightly different than pre-breeding matrix
  A[1,] <- B*F_*S[2:4]*R
  A
}

#' This is the **pre-breeding** matrix that Blackwell et al. calculated. Note that it doesn't match the 
#' values given in their Table 1. Careful reading of the text and captions of Table 2 is needed to figure
#' out the parameters.

cormorant_blackwell <- function(S = c(0.5, 0.87, 0.88, 0.89), 
                                B = c(0, 0.5, 0.99), 
                                F_ = c(0, 1.6, 2.4),
                                R = 0.5){
  A <- matrix(0, nrow=3, ncol=3)
  A[2,1] <- S[2]
  A[3,2:3] <- S[3:4]
  A[1,] <- B*F_*S[1]
  A
}

A_blackwell <- cormorant_blackwell()
A_blackwell 

A <- cormorant_post_pop()
popbio::lambda(A)
S <- popbio::sensitivity(A, zero=TRUE)
S


A_blackwell <- matrix(c(0, 0.2, 0.5940,
                        0.87, 0, 0,
                        0, 0.881, 0.89), nrow=3, byrow=TRUE)

popbio::lambda(A_blackwell)

#' # 4, 5 if we were interested in the effect of the sex ratio R
#' Calculate the matrix of *partial derivatives* with respect to R
#' Any element without R is 0
#' Any element with R is just the other parameters
P <- c(0.5, 0.87, 0.88, 0.89)
B <- c(0, 0.5, 0.99)
F_ <- c(0, 1.6, 2.4)
R <- 0.5
pd_R <- matrix(c(0, B[2]*F_[2]*P[2], B[3]*F_[3]*P[3],
                 0, 0, 0,
                 0, 0, 0), nrow = 3, ncol = 3, byrow = TRUE)

pd_R

#' Now we multiply each element here by the same element of the sensitivity matrix, and sum.
#' 

sum(pd_R * S) # This is the sensitivity of lambda to changes in the sex ratio (towards more females)

#' Here is an example of the code to produce q 6 plot