11 Pre- and Post-reproduction census

11.1 Background

Population growth estimates depend on when the census is taken relative to reproduction. A pre-breeding census counts individuals before reproduction; a post-breeding census counts them after reproduction. This changes how survival and fecundity are represented in the projection matrix, even if the underlying biology is the same.

11.2 Learning outcomes

Learning outcomes:

  • Explain the difference between pre-breeding and post-breeding census models.
  • Convert a post-breeding matrix to a pre-breeding matrix.
  • Compare growth rates from alternative census timings.

11.3 Worked example

p0 <- 0.2
p1 <- 0.9
p2 <- 0.6
m2 <- 3.0
m3 <- 6.0

A1 <- matrix(c(0.0, m2 * p1, m3 * p2,
               p0, 0.0, 0.0,
               0.0,p1,0), byrow = TRUE, nrow = 3)

Convert to pre-breeding

A2 <- matrix(c(0.0, m2 * p0, m3 * p0,
               p1, 0.0, 0.0,
               0.0,p2,0), byrow = TRUE, nrow = 3)

Compare population growth rates. This uses the eigs function from the popdemo R package.

(popdemo::eigs(A1, what = "lambda"))
## [1] 1.070261
(popdemo::eigs(A2, what = "lambda"))
## [1] 1.070261

11.4 Your task

  • Interpret the two values of \(\lambda\). Are they identical? If not, why might the census timing change the estimate?
  • Modify one survival probability (e.g., p1) and compare how the two census approaches respond.

11.5 Takeaways

  • Census timing changes how fecundity and survival are encoded in the matrix.
  • Pre- and post-breeding models can yield different \(\lambda\) estimates from the same biology.