Distributional consequences of spatial variation in local demographic PI'OCCSSGS
Brian A. Maurer & James H. Brown
Maurer, B. A. & Brown, J. H. 1989: Distributional consequences of spatial variation in local demographic processes. — Ann. 2001. Fennici 26: 121-131.
The population density of a species in space usually is highest near the center of its geographic range and declines with increasing distance away from the center. Since a large number of biotic and abiotic factors may act simultaneously to limit local densities of species populations, rather than trying to identify these, we focus 0 the general processes by which environmental factors affect population density. Four processes determine the rate of population change: birth, death, immigration, and emigration. These are functions of both space (density independent factors) and population size (density dependent factors).
Death and emigration should be increasing functions of population density. Birth rate should increase with population density up to a point, then begin to decrease. Immigration should decrease with increases in density. Birth and immigration sum to a net rate of population gain and death emigration sum to a net rate of population loss. These two functions intersect to give a stable equilibrium point. The set of equilibrium points of populations in space determines the general pattern of population abundance in space. In order for population density to be a nonincreasing function of the distance from the geographic center, either population gain rate must be a nonincreasing function of distance from the geographic center and population density, or population loss rate must be a nondecreasing function of distance from the geographic center and population size, or both must occur.
Brian A. Maurer, Department of Zoology, Brigham Young University, Provo, UT 84602, USA.James H. Brown, Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA.
1 Introduction
A major activity in ecology has been to attempt to identify the factors that limit local population densi- ties and geographic distributions of species. This has proven to be extremely difficult, because even for a single species many variables are probably important, and often these are not independent either in their ef- fects on organisms, or in their pattern of spatial vari- ation. Recently, multivariate statistical methods have been used to identify complex combinations of vari- ables that appear to account for some spatial variation in population density (e.g. for plants: Kercher & Goldstein 1977, Strahler 1978; for invertebrates: Green 1971, 1974; for birds: Whitmore 1975, 1977; Rotenberry & Wiens 1980; Noon 1981; Collins et a1.
1982; for mammals: Crowell & Pimm 1976; M’Closkey 1976; Dueser & Shugart 1978, 1979). These analyses assume linear responses of organisms to environmental variables, or at least that population responses can be approximated adequately by linear statistics (see review papers in Capen 1981). West- man (1980) has been able to test for curvilinear rela- tionships by fitting Guassian curves to species pop- ulation densities along environmental gradients. Re- gardless of the statistical approach, one problem common to all of these studies is that they seemingly fail to yield satisfying general principles. By defini- tion each species and higher taxon is unique and its abundance and distribution are limited by different combinations of abiotic factors and biotic interac- tions. Consequently, the greater the precision with which these factors are enumerated and their complex interacting effects are elucidated, the less the ability to extrapolate the results to other taxa or even to addi- tional populations of the same species.
An alternative approach to examining in detail the relationships between individual species and their en- vironments (biotic and abiotic) is to search for and attempt to explain general statistical patterns that characterize the variation of local population density of many species over transects or gradients in geo- graphic space (Hengeveld & Haeck 1981, Brown 1984). This procedure has the advantage of elucidat- ing large scale patterns that cannOt be described by studying small collections of local sites.
Species are not equally abundant throughout their ranges; rather, there is a general tendency for popula- tion density to be highest near the center of the geo- graphic range and to decline relatively gradually and often symmetrically toward the boundaries (Whit- taker 1961, Westman 1980, Hengeveld & Haeck 1982). Brown (1984) has proposed the following explanation for this pattern. The local population densities of species are affected by many biotic and abiotic variables that comprise the multiple dimen- sions of the Hutchinsonian (1957) niche. For any widespread species, the relative importance of these different factors varies from site to site over the geo- graphic range. When all factors are considered, the pattern of spatial variation in environmental condi- tions tends to be autocorrelated so that nearby sites tend to have more similar combinations of variables than distant ones. Those places that offer the most favorable conditions support the highest population densities, and these will tend to be clustered together.
With increasing distance away from the most favo- rable sites in any direction, one or more variables will become less favorable and lead to decreasing popula- tion densities. If the number of effectively independ- ent limiting factors is reasonably large, and if envi- ronmental variation in those factors is reasonably gradual, the spatial distribution of population density along any transect which runs through the center of the species’ range will tend to resemble a normal, or bell-shaped, curve (Brown 1984; see also Ramensky 1924, Whittaker 1967, Westman 1980). Brown’s (1984) model applies only to species with a unimodal pattern of abundance in space. Obviously, species abundance patterns which are not unimodal violate one or more of these conditions. We do not consider such patterns here.
The present paper provides a mechanistic model that develops the relationship between the demo- graphic processes (birth, death, immigration, and emigration) that determine local population density and spatial variation in the environment which results in geographic variation of abundance. We begin by considering the processes limiting the density of a single, local population, and then in later sections in- vestigate how these processes vary among collections of spatially distinct populations.
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