Biologists have long been fascinated by species' borders, and with good reason. Understanding the ecological and evolutionary dynamics of species' borders may prove to be the key that unlocks new understanding across a wide range of biological phenomena. After all, geographic range limits are a point of entry into understanding the ecological niche and threshold responses to environmental change. Elucidating patterns of gene flow to, and returning from, peripheral populations can provide important insights into the nature of adaptation, speciation and coevolution. Species' borders form natural laboratories for the study of the spatial structure of species interactions. Comparative studies from the center to the margin of species' ranges allow us to explore species' demographic responses along gradients of increasing environmental stress. Range dynamics further permit investigation into invasion dynamics and represent bellwethers for a changing climate. This set of papers explores ecological and evolutionary dynamics of species' borders from diverse empirical and theoretical perspectives.

With the increasing concern about species conservation, a need exists for quantitaive characterization of species' geographic range and their borders. In this paper, we survey tools appropriate for the quantification of static spatial patterns related to geographical ranges and their borders. We then build on these static methods to consider the problem of changes in geographic range through time. Methods discussed are illustrated using lark sparrow data from the North American Breeding Bird Survey. While there is no such thing as the ``best\''\ or ``only\''\ method to analyze species geographical range and border, we show that a series of methods can be used in sequence to provide complementary and useful quantitative information for species occupancy of range. Indeed, the location of species' borders estimated at different times can be compared to identify locations where species expand or go locally extinct. The ability to delineate accurately species' ranges will be useful to conservation biologists, managers and ecologists.

Statistical models of environment-abundance relationships may be influenced by spatial autocorrelation in abundance, environmental variables, or both, Failure to account for spatial autocorrelation can lead to incorrect conclusions regarding both the absolute and relative importance of environmental variables as determinants of abundance. We consider several classes of statistical models that are appropriate for modeling environment-abundance relationships in the presence of spatial autocorrelation, and apply these to three case studies: 1) abundance of voles in relation to habitat characteristics; 2) a plant competition experiment; and 3) abundance of Orbatid mites along environmental gradients. We find that when spatial pattern is accounted for in the modeling process, conclusions about environmental control over abundance can change dramatically. We conclude with five lessons: 1) spatial models are easy to calculate with several of the most common statistical packages; 2) results from spatially-structured models may point to conclusions radically different from those suggested by a spatially independent model; 3) not all spatial autocorrelation in abundances results from spatial population dynamics; it may also result from abundance associations with environmental variables not included in the model; 4) the different spatial models do have different mechanistic interpretations in terms of ecological processes - thus ecological model selection should take primacy over statistical model selection; 5) the conclusions of the different spatial models are typically fairly similar - making any correction is more important than quibbling about which correction to make.

Theoretical studies of the stability of food webs have generally not incorporated space as a contingency affecting coexistence of species. Here, I considered the importance of spatial heterogeneity on the stability of an individual-based food web model. Individual agents diffused on a lattice of cells and interacted according to a set of probabilistic interaction coefficients. Simulations were run on both uniform and non-uniform lattices. The model had two modes: 1. a mean-field mode with global interactions, and 2. a spatially localized mode in which species interacted within local neighborhoods. Equilibrium number of species were compared among different simulations varying web connectance, interaction strength, and lattice heterogeneity. Local interactions resulted in more species rich webs, indicating greater stability. The addition of spatial heterogeneity to the lattice further altered relationships among species richness, web connectance, and interaction strength, and increased coexistence among species. The results did not support the stability criterion derived by May. However, an inverse relationship between web connectance and species richness was observed suggesting that the product of connectance and species richness may govern the stability of real, finite webs. (C) 1997 Elsevier Science B.V.