Spatial variation in abundance created by stochastic temporal variation

Ecology, Sept, 1997 by Anthony R. Ives, Eric D. Klopfer

INTRODUCTION

Spatial variation in the abundance of a species is often attributed to spatial variation in the environmental factors that affect it. For example, the Pied Flycatcher requires suitable holes for nesting, and the density of nesting holes, in part, determines its abundance (Lack 1968). Similarly, energy requirements and thermal tolerance may set a latitudinal limit to the distribution of a species; as this limit is approached, the abundance of the species drops as climatic conditions become marginal (Root 1988a, b). Although ascribing spatial patterns of abundance to spatial patterns of environmental variation is probably a reasonable first guess, there is a growing appreciation for the complex spatial patterns that can be driven by the interaction between temporal fluctuations in species' abundance and dispersal of species in space. This appreciation has come from a variety of conceptual approaches. The concept of metapopulation dynamics has emphasized the role of immigration and extinction in determining the local abundance of species (see references in Hahski and Gilpin 1991). Landscape ecology has highlighted the importance of the spatial arrangement of suitable and unsuitable habitat for local abundances (Turner and Gardner 1991, With and Crist 1995). Models of predator-prey dynamics on an environmentally homogeneous spatial plane have shown how spatial patterns can arise through interactions among species, in the absence of environmental variation (Murray 1989, Comins et al. 1992, Holmes et al. 1994, Molofsky 1994). Thus, spatial variation in the abundance of species can be influenced by numerous factors beyond spatial variation in the environment.

In this article, we illustrate how stochastic temporal environmental variation can create spatial patterns in the abundance of species that appear similar to those patterns created by fixed spatial environmental variation. For this illustration, we start with recent work by Brown, Mehlman, and Stevens (1995), who investigated patterns of spatial variation in animal and plant abundance, particularly focusing on the spatial distribution of birds recorded in the North American Breeding Bird Survey. They discussed four features that suggest that spatial variation in abundance is primarily determined by fixed spatial patterns in the environment.

1) When the log abundance of a bird species at a census site is plotted against the order of the site, ranked by abundance, the resulting curve is decreasing with a broad, flat shoulder (a sigmoidal curve rotated clockwise 90 [degrees]). This implies that a few sites are "hot spots" containing the bulk of the bird population, whereas the majority of sites are "cool spots." Using a computer simulation, Brown et al. (1995) showed that this relationship between log abundance and rank abundance can be created when there are several different environmental factors affecting bird abundance. "Hot spots" occur at sites where several of the environmental factors are coincidentally favorable for the species.

2) For a given species, the same census sites remain "hot spots" year after year. This suggests that spatial variation in abundance is created by fixed spatial variation in environmental factors.

3) There is strong, positive correlation in the abundances of breeding birds at nearby census sites, implying that nearby locations are of similar environmental quality for the species.

4) Breeding birds tend to be less abundant at the edge of their range than in the center. This could result from one or more environmental factors becoming gradually less favorable away from the center of the range, eventually dropping below what is acceptable for the maintenance of the species.

Of four species of passerine birds analyzed in detail by Brown et al. (1995), all showed these four patterns.

We show that all of these patterns can be produced in the absence of spatially fixed environmental variation. To do this, we construct two simulation models for a hypothetical bird species whose population dynamics are affected by two temporally varying environmental factors, one that affects reproduction and the other that affects annual adult survival. We then analyze simulated data from the models to show the four patterns discussed by Brown et al. (1995). Our purpose is not to argue with their view that spatially fixed environmental variability influences the spatial variation in the abundance of species. We agree that spatially fixed environmental variation is almost certainly important. Instead, our purpose is to show that stochastic temporal environmental variation can also generate realistic spatial abundance patterns. Furthermore, we show that some of the most surprising spatial patterns created by stochastic temporal environmental variation occur when density-dependent processes affecting reproduction and/or survival are weak. This highlights the need to study population dynamics to understand the spatial distribution of species.

A NONSPATIAL MODEL OF BIRD DYNAMICS