Numerical response of predator to prey: Dynamic interactions and population cycles in Eurasian lynx and roe deer

Abstract

The dynamic interactions between predators and their prey have two fundamental processes: numerical and functional responses. Numerical response is defined as predator growth rate as a function of prey density or both prey and predator densities [dP/dt = f(N, P)]. Functional response is defined as the kill rate by an individual predator being a function of prey density or prey and predator densities combined. Although there are relatively many studies on the functional response in mammalian predators, the numerical response remains poorly documented. We studied the numerical response of Eurasian lynx (Lynx lynx) to various densities of its primary prey species, roe deer (Capreolus capreolus), and to itself (lynx). We exploited an unusual natural situation, spanning three decades where lynx, after a period of absence in central and southern Sweden, during which roe deer populations had grown to high densities, subsequently recolonized region after region, from north to south. We divided the study area into seven regions, with increasing productivity from north to south. We found strong effects of both roe deer density and lynx density on lynx numerical response. Thus, both resources and intraspecific competition for these resources are important to understanding the lynx population dynamic. We built a series of deterministic lynx–roe deer models, and applied them to the seven regions. We found a very good fit between these Lotka–Volterra type models and the data. The deterministic models produced almost cyclic dynamics or dampened cycles in five of the seven regions. Thus, we documented population cycles in this large predator–large herbivore system, which is rarely done. The amplitudes in the dampened cycles decreased toward the south. Thus, the dynamics between lynx and roe deer became more stable with increasing carrying capacity for roe deer, which is related to higher productivity in the environment. This increased stability could be explained by variation in predation risk, where human presence can act as prey refugia, and by a more diverse prey guild that will weaken the direct interaction between lynx and roe deer.