Equilibrium population dynamics of site-dependent species

Abstract

Adults of site-dependent species require a discrete structure, e.g., a cavity, for breeding, which they are unable to construct and must locate and occupy. The environment provides only a limited number of such sites, which may vary in overall quality due to their environmental context. Heterogeneity of site quality can result in population equilibrium, often construed as source-sink dynamics. Rodenhouse et al. (Ecology 78:2025-2042, 1997) proposed a mechanism of site-dependent equilibrium that they claimed was more general than source-sink dynamics. After defining notions of source and sink, I use explicit dynamical models for a site-dependent population, based on the life history of golden eagles (Aquila chrysaetos), with two levels of site quality, to investigate the existence of population equilibria under several scenarios: source-source, source-sink, and source-floater. The life history traits I employ are not overly restrictive and serve the purpose only of providing models explicit enough to be treated analytically. I use a generalized notion of “golden eagle” since site dependency is often discussed in the literature on raptors, and I have exploited details from Hunt et al. (PLoS ONE 12:e0172232, 2017) for numerical simulations. The crucial features of the modeling, however, are those of site dependency. The modeling emphasizes that equilibrium results from the limited supply of source sites and that vital rates averaged across site qualities do not provide a compelling explanation of equilibria, contra Rodenhouse et al. Counterintuitively, equilibria are theoretically possible, even when both site qualities are intrinsically source sites.