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

For a life history with age at maturity alpha, and stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time-lags of from 1 to alpha 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 = - partial differential lnlambda(T)/partial differential lnN, where lambda 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.