  Geographic ranges of communities of species evolve in response to
environmental, ecological, and evolutionary forces. Understanding the effects
of these forces on species' range dynamics is a major goal of spatial ecology.
Previous mathematical models have jointly captured the dynamic changes in
species' population distributions and the selective evolution of
fitness-related phenotypic traits in the presence of an environmental gradient.
These models inevitably include some unrealistic assumptions, and biologically
reasonable ranges of values for their parameters are not easy to specify. As a
result, simulations of the seminal models of this type can lead to markedly
different conclusions about the behavior of such populations, including the
possibility of maladaptation setting stable range boundaries. Here, we
harmonize such results by developing and simulating a continuum model of range
evolution in a community of species that interact competitively while diffusing
over an environmental gradient. Our model extends existing models by
incorporating both competition and freely changing intraspecific trait
variance. Simulations of this model predict a spatial profile of species' trait
variance that is consistent with experimental measurements available in the
literature. Moreover, they reaffirm interspecific competition as an effective
factor in limiting species' ranges, even when trait variance is not
artificially constrained. These theoretical results can inform the design of,
as yet rare, empirical studies to clarify the evolutionary causes of range
stabilization.
