Aspects of the reciprocal relationship between the dynamics of a quantitative trait and its variation, and the dynamics of species ranges and biological invasions

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This is the official version, with a timestamp of 20 September 2007. 

Aranne Library (BGU) permalink.

Abstract

The study of distribution limits of species is one of the fundamental goals of ecology and
evolutionary biology. Likewise, understanding biological invasions and determinants of the
invasive potential of species is a major occupation of many ecologists, especially in recent years.
On the other side of the equation, (suggested by the title of this work), the dynamics of quantitative
traits and their variation within and among populations has been the subject of both theoretical and
empirical work for many decades. Recently, ecologists have realized that trait variation has
important consequences for population and community dynamics, not only from a genetic or
evolutionary perspective. The goal of this work is to explore several aspects of the relationship
between trait dynamics and the dynamics of geographic distributions of species, and to provide
some new insights and predictions.

Species range limits are the outcome of many processes, both demographic and
evolutionary, as well as historical and chance events. In the past decade, a theoretical framework
has been gradually developing, which emphasizes the interplay of demography and evolution in
determining species ranges. Specifically, it addresses the effect of gene swamping, i.e., asymmetric
gene flow between high-density central populations and low-density peripheral populations. Gene
swamping is especially important in heterogeneous environments, i.e., if center and periphery have
different adaptive optima. Several theoretical approaches have been taken in modeling the effect of
asymmetric gene flow on the evolution of a species range, and on the closely related problem of
niche evolution. In this work, I follow the general approach of Kirkpatrick and Barton (1997) and
subsequent studies. However, throughout the text I relate my results to those achieved by taking
different approaches (especially the two-habitat-types approach of Holt and his colleagues).

Prior studies of the evolution of species’ niches and ranges have identified the importance
of within-population genetic variance, migration rate and environmental heterogeneity in
determining evolutionary stable patterns of species’ range and habitat use. Different combinations
of these variables can produce either habitat specialists or generalists, and either cause stable range
limits or unbounded expansion across habitats and space. In this work, I consider the joint
evolution of population density and the mean and variance of a quantitative trait along continuous
environmental gradients (represented by spatial variation in the optimum phenotype).

In chapter 2, I examine the effect of density regulation on a species’ range. Given the
inherent interplay of demography and evolution in such models of range evolution, I expect that the
form of density dependence should influence the outcome of range evolution. However, previous
work on the Kirkpatrick-Barton model used only few specific forms of density-dependence.
Moreover, it emphasized the dynamics at the periphery, where density-dependence can be
neglected. I demonstrate in chapter 2 that, generally, density-regulation (i.e., negative density-
dependence) facilitates range expansion, i.e., causes more stringent conditions for achieving stable range limits.

This is because density-regulation makes spatial density gradients more shallow, thus,
weakening gene swamping and its ability to limit a species range.

Additionally, using the theta-logistic formulation I continuously vary the form of density
regulation and demonstrate that: (1) The form of density-regulation should play an important role
in determining whether the equilibrium species range is limited by gene flow; (2) Even when no
such long term limited-range equilibrium occurs, quasi-stable range limits may be maintained for a
long period during the initial phases of an invasion; the length of this period depends on the form
of density regulation; (3) The steady-state invasion speed in heterogeneous environments depends
on the form of density regulation, in contrast to purely demographic invasion models. I also discuss
implications for the study of biological invasions.

In chapter 3, I present a general model for the joint evolution of population density and the
trait-frequency distribution. I also consider a reduced version of the general model, assuming a
Gaussian trait distribution at each position along the environmental gradient. I provide equations
for the dynamics of density, mean phenotype, and genetic variance at each local population. I
derive equations for the equilibrium density, mean phenotype and genetic variance across space.
The major difference between this chapter and the former chapter is that the dynamics of the
genetic variance is also considered, whereas the genetic variance is fixed in the analysis of chapter 2.

I then study how several forms of biased dispersal affect range and trait evolution across the
environmental gradient. In most cases, because the genetic variance also evolves, no limited-range
equilibria are obtained. The species continuously adapts and expands, i.e., invades, for all
parameter values, unless it cannot persist in the environmental gradient and goes globally extinct.
An especially important result obtained in this chapter is that habitat preference based on an
individual’s phenotype (phenotype-dependent habitat preference) increases the effectiveness of the
process of local adaptation. Consequently it facilitates range expansion. I discuss this result in the
context of previous studies that emphasized the role of habitat preference in limiting a species
range (or niche), rather than facilitating its expansion. I also relate my result to recent empirical and
theoretical work on genetic and phenotypic preference-performance covariance.

Chapter 4 is the final chapter concerning range evolution along environmental gradients,
and provides a general discussion of the previous two chapters. In this chapter I first summarize the
previous results. I then demonstrate how optimal habitat preference, as presented in chapter 3,
raises the steady-state invasion speed in heterogeneous environments. This outcome suggests that
preference-performance covariance within a species can determine the invasive potential of that
species, a previously overlooked species characteristic in that context. Finally, I describe some
scenarios that presumably may lead to a limited species range at equilibrium, based on the
expressions derived in chapter 3.

In chapter 5 I move to explore how trait variation (specifically, body size variation) affects
population stability in seasonal environments. Much recent literature is concerned with how
variation among individuals (e.g., variability in their traits and fates) translates into higher-level
(i.e., population and community) dynamics. I describe an analytical model for size-dependent,
seasonal life cycles and evaluate the effect of individual size variation on population dynamics and
stability. I demonstrate that the effect of size variation on the population net reproductive rate
varies in both magnitude and sign, depending on season length. I calibrate the model with field
data on size- and density-dependent growth and survival of the generalist grasshopper Melanoplus
femurrubrum. Under deterministic dynamics (fixed season length), size variation impairs
population stability, given naturally occurring densities. However, in the stochastic case, where
season length exhibits yearly fluctuations, size variation reduces the variance in population growth
rates, thus enhancing stability. This occurs because the effect of size variation on net reproductive
rate is dependent on season length.

The final chapter (ch.6) explores the effect of an externally imposed limited species range
on the evolution of a quantitative trait, namely, how confinement to an island affects the evolution
of dispersability and body mass. Loss of dispersability and change in body-mass (dwarfism and
gigantism) are two commonly observed phenomena on islands. Based on Skellam’s (1951)
formulation of dispersal, I present a new theory of insular evolution that connects island area to the
evolution of dispersability and body mass. Using optimal body mass considerations and allometric
scaling laws, the new theory predicts: (1) The expected direction of body-mass evolution (i.e.,
either dwarfism and gigantism) depends on the relationship between body mass and dispersability;
(2) Rate of body-mass change (i.e. evolution rate) is inversely proportional to the island’s area; (3)
The magnitude of the shift in optimal body mass, either towards gigantism or dwarfism, is also
inversely proportional to island’s area. Available empirical data support the predictions.