Frequency of Occurrence and Population-Dynamic Consequences of Different Forms of Density-Dependent Emigration

Abstract

Emigration is a fundamental process affecting species' local, regional, and large-scale dynamics. The paradigmatic view in ecology is that emigration is density independent (DIE) or positive density dependent (1DDE). However, alternative forms are biologically plausible, including negative (2DDE), U-shaped (uDDE), and hump-shaped (hDDE) forms. We reviewed the empirical literature to assess the frequency of different forms of density-dependent emigration and whether the form depended on methodology. We also developed a reaction-diffusion model to illustrate how different forms of DDE can affect patch-level population persistence. We found 145 studies, the majority representing DIE (30%) and 1DDE(36%). However, we also regularly found 2DDE (25%) and evidence for nonlinear DDE(9%), including one case of uDDE and two cases of hDDE. Nonlinear DDE detection is likely hindered by the use of few density levels and small density ranges. Based on our models, DIE and 1DDE promoted stable and persistent populations. uDDE and 2DDE generated an Allee effect that decreases minimum patch size. Last, 2DDE and hDDE models yielded bistability that allows the establishment of populations at lower densities. We conclude that the emigration process can be a diverse function of density in nature and that alternative DDE forms can have important consequences for population dynamics.