Efficient Data Collection for Estimating Growth Rates of Structured Populations

Demographic matrix models are used to estimate the population multiplication rate (finite rate of increase) of structured populations. When rates of transitions among age classes or stages (e.g., probabilities of growth or survival, fecundities) are estimated by tagging individuals, the number of individuals tagged from each stage determines the precision of the estimated transition rates, and hence the precision of the estimated population multiplication rate, λ̂. When there is a limit on the total number of individuals that can be tagged, tagging individuals at random does not produce the most precise estimate of λ possible. Here, using a linear approximation to the sampling variance of λ̂, I show how to calculate an allocation of tags among stages that provides a more precise estimate of λ than tagging individuals randomly. I illustrate this calculation with two examples, and show by simulation that stratified sampling based on this efficient sample composition can result in sizable increases in the precision of λ̂. The methods presented can also be used to compare the statistical efficiency of alternative sampling designs.