Abstract

BackgroundVariation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics. Variation is hard to study in the field because of difficulties controlling the environment in order to obtain statistical replicates, and because of the scale and expense of experimenting on populations. There may also be ethical issues. To circumvent these problems we used detailed simulations of the simultaneous behaviours of interacting animals in an accurate facsimile of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of skylarks Alauda arvensis, voles Microtus agrestis, a ground beetle Bembidion lampros and a linyphiid spider Erigone atra. This allows us to quantify and evaluate the importance of spatial and temporal heterogeneity on the population dynamics of the four species.ResultsBoth spatial and temporal heterogeneity affected the relationship between population growth rate and population density in all four species. Spatial heterogeneity accounted for 23–30% of the variance in population growth rate after accounting for the effects of density, reflecting big differences in local carrying capacity associated with the landscape features important to individual species. Temporal heterogeneity accounted for 3–13% of the variance in vole, skylark and spider, but 43% in beetles. The associated temporal variation in carrying capacity would be problematic in traditional analyses of density dependence. Return rates were less than one in all species and essentially invariant in skylarks, spiders and beetles. Return rates varied over the landscape in voles, being slower where there were larger fluctuations in local population sizes.ConclusionOur analyses estimated the traditional parameters of carrying capacities and return rates, but these are now seen as varying continuously over the landscape depending on habitat quality and the mechanisms of density dependence. The importance of our results lies in our demonstration that the effects of spatial and temporal heterogeneity must be accounted for if we are to have accurate predictive models for use in management and conservation. This is an area which until now has lacked an adequate theoretical framework and methodology.

Highlights

  • Variation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics

  • In this paper population density is described by loge(Nt), where Nt is the number of adult females in a specified area in year t; pgr is estimated as loge(Nt+1/Nt); return rate as the negative of the slope of the relationship between density and pgr; i.e. as – [dpgr/dlogeNt]K ≡ - [Nt dpgr/dNt]K, where local carrying capacity, K, is defined as population size in a specified area when pgr = 0

  • The effects of weather year and spatial variation on the fundamental relationships between pgr and local population density are illustrated in Figures. 2 and 3

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Summary

Introduction

Variation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics. The models incorporate as much as possible of the behaviour and ecology of skylarks Alauda arvensis, voles Microtus agrestis, a ground beetle Bembidion lampros and a linyphiid spider Erigone atra. This allows us to quantify and evaluate the importance of spatial and temporal heterogeneity on the population dynamics of the four species. The relationship between pgr and the natural logarithm of density determines whether a population will return to equilibrium after a disturbance, and the slope of the relationship determines how fast any such return will be. Positive return rates less than two indicate population stability, and return rates less than one indicate that population density approaches equilibrium smoothly without oscillating (see [6] for further discussion)

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