Estimating density dependence in time–series of age–structured populations

Abstract

For a life history with age at maturity α, and stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time–lags of from 1 to α years. Contrary to current interpretations, the coefficients for different time–lags in the autoregressive dynamics do not simply measure delayed density dependence, but also depend on life–history parameters. We define a new measure of total density dependence in a life history, D , as the negative elasticity of population growth rate per generation with respect to change in population size, D = –∂lnλ T /∂ln N , where λ is the asymptotic multiplicative growth rate per year, T is the generation time and N is adult population size. We show that D can be estimated from the sum of the autoregression coefficients. We estimated D in populations of six avian species for which life–history data and unusually long time–series of complete population censuses were available. Estimates of D were in the order of 1 or higher, indicating strong, statistically significant density dependence in four of the six species.