Pulse disturbances in age-structured populations: Life history predicts initial impact and recovery time.

Understanding population responses to discrete 'pulsed' environmental disturbances is essential to conservation and adaptive management. Populations of concern can be driven to low levels by disturbance, and understanding interspecific differences in recovery trajectories is necessary for evaluating management options. We analysed single-species models to investigate the demographic and management factors determining the two components of population 'resilience': the magnitude of initial impact on population abundance, and duration of the recovery time. We simulated age-structured populations with density-dependent recruitment, subjected to a pulse disturbance consisting of a period of increased mortality of either the juvenile age class or all age classes, and calculated both impact and return time. For illustration, we used demographic parameters from a suite of 16 fish species. We formulated the model as a renewal equation, allowing us to describe disturbance impacts mathematically as a convolution. We also included nonlinear dynamics, representing populations that recover to a steady state; this is more realistic (in most cases) than prior analyses of resilience in linear models without density-dependence. When the disturbance affected only one or a few young age-classes, longevity was the major life-history determinant of impact and recovery time. Shorter-lived species endured greater impacts when disturbed because each age class is a greater proportion of the population. However, shorter-lived species also had faster recovery times, for the same reason. When disturbance affected adult age-classes, the impact was more immediate and no longer affected by species' longevity, though the effect of longevity on recovery time remained. These results improve our understanding of interspecific differences in resilience and increase our ability to make predictions for adaptive management. Additionally, formulating the problem as a renewal equation and using mathematical convolutions allows us to quantify how disturbances with different time courses (not just an immediate, constant level of disturbance but gradually increasing or decreasing levels of disturbance) would have different effects on population resilience: delayed responses for species in which biomass is concentrated in older age classes, and for disturbances that become progressively more severe.