Demographic heterogeneity impacts density dependent population dynamics

Background/Question/Methods Among individual variation in vital parameters such as birth and death rates that is unrelated to age, stage, or environmental fluctuations is referred to as demographic heterogeneity. Demographic heterogeneity has been shown to affect demographic stochasticity in small populations and to increase growth rates for density independent populations. The latter is similar to “cohort selection”. If a cohort is composed of two subcohorts, each with a different mortality rate, then as the cohort ages, its crude mortality rate decreases. This occurs because individuals with higher mortality die out and the more robust individuals come to dominate the population. The importance of cohort selection for population dynamics has only recently been recognized. This work explores how demographic heterogeneity affects density dependent population dynamics. We use a continuous time model with density dependence, based on the logistic equation, to study the effects of heterogeneity in the death rates of individuals within a population. The model population is composed of two phenotypes, each of which reproduces offspring of either phenotype. Heterogeneity is introduced by giving the phenotypes different death rates. We also analyzed the abilities of homogeneous models to approximate the dynamics.

Results/Conclusions Heterogeneity in the death rates affects density dependent population dynamics in several ways. Both the low-density growth rate and the equilibrium population size increase as the magnitude of heterogeneity increases. The average death rate within the heterogeneous population decreases over time due to the shifting age structure of the population as the growth rate slows. As the population approaches the stable equilibrium, the age distribution shifts towards a greater abundance of old individuals, so the relative abundance of the longer lived phenotype increases. At equilibrium, the crude mortality rate is the inverse of the average lifespan. This is also true if the population is composed of any number of phenotypes whether discretely or continuously distributed. We can parameterize a homogeneous model that matches the low-density growth rate and carrying capacity. This model also describes the intervening dynamics reasonably well. However, the parameters do not bear a simple relation to the observed birth and death rates. In contrast, a homogeneous model parameterized form observed average vital rates can match either the low-density or equilibrium dynamics but not both.