DOI: 10.5061/dryad.9zw3r22mq
title: Numerical response of predator to prey: Dynamic interactions and population cycles in Eurasian lynx and roe deer

description: 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,
 numerical response remains poorly documented. We studied 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 understand 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 towards 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.
description: # Numerical response of predator to prey: Dynamic interactions and
 population cycles in Eurasian lynx and roe deer
 [https://doi.org/10.5061/dryad.9zw3r22mq](https://doi.org/10.5061/dryad.9zw3r22mq)   Description of data   Henrik Andrén *<sup>a</sup>* and Olof Liberg. **Numerical response of predator to prey: Dynamic interactions and populations cycles in Eurasian lynx and roe deer**. *Ecological Monographs*   *<sup>1</sup> Grimsö Wildlife Research Station, Department of Ecology, Swedish University of Agricultural Sciences, SE-739 93 Riddarhyttan, Sweden* *<sup>a</sup> corresponding author: henrik.andren@slu.se* ORCID – HA: 0000-0002-5616-2426    *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, numerical response remains poorly documented. We studied 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 understand 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 towards 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. Data file: Andren\_lynx\_roedeer\_data.csv   Column names: * year - year * region – region 1 to 7, see figure 1 in Andrén and Liberg * area – area of the region in 1000 km<sup>2</sup> * lynx\_family\_groups – number of lynx family groups registered in the region * lynx\_family\_groups\_intraploted – number of lynx family groups registered in a region. The number of lynx family groups was intrapolated for year without data (NA). This is not used in the analyses, only for illustrations. * lynx\_harvest – number of lynx harvested in a region * roe\_deer\_harvest\_mean – mean estimated number of roe deer harvested in a region * roe\_deer\_harvest\_sd – standard deviation of the estimated number of roe deer harvested in a region * roe\_deer\_harvest\_lower – lower 95% BCI of the estimated number of roe deer harvested in a region * roe\_deer\_harvest\_upper – upper 95% BCI of the estimated number of roe deer harvested in a region