Stochastic models for the ecology and population genetics of introduced species

The long-term success of an introduced population depends on the
ecological conditions in its new environment, but is also
influenced by stochasticity. This is particularly clear in the
first stage of an invasion when the population is still small and
either goes extinct quickly or establishes a self-sustaining
population. Once established, some populations grow and spread
spatially, with potential impacts on native communities and
ecosystems. The role of stochasticity during these later invasion
stages remains unclear. Furthermore, little is known about the
population genetic and evolutionary consequences of stochastic
invasion trajectories. With this dissertation, I would like to
contribute to a stochastic eco-genetic theory of the entire
invasion process—from the first introduction up to potential
impacts. The overarching questions in this dissertation are: a) How
does a population’s movement through the invasion process depend on
ecological factors influencing its average growth rate? b) How does
it depend on factors influencing the stochastic variability in the
population dynamics? c) How much genetic diversity do introduced
populations harbor on average upon reaching a certain point in the
invasion process? d) To what extent can the population-genetic
consequences of invasion trajectories feed back onto the population
dynamics? Together with my advisors and coauthors, I have conducted
four studies, each addressing two or more of these questions for
specific ecological scenarios. We employ several types of
stochastic models: Markov chains, Markov processes, their diffusion
approximations, and coalescent-like genealogy simulations. In
Chapter 1 (Wittmann et al., 2013a, appeared in Theoretical
Population Biology), we focus on a factor influencing the
introduced population’s average growth rate: the intensity of
competition with an ecologically similar native species. Our
results indicate that the expected time until the introduced
species drives the native competitor to extinction is smallest for
intermediate competition intensity. This phenomenon results from
the opposing effects of competition intensity at different points
of the invasion process: On the one hand, intense competition
renders the establishment of the introduced population more
difficult; on the other hand, it facilitates the later exclusion of
the native species. In Chapter 1, we also investigate to what
extent the native species’ extinction is accelerated if a reduction
in population size entails a reduction in genetic diversity and
thus a reduced ability to adapt to a changing environment. We find
this eco-genetic feedback to be particularly strong at small
competition intensities. In Chapter 2 (Wittmann et al., 2013b, in
press at Oikos), we compare introduction regimes with the same
average number of individuals introduced per time unit, but with a
different temporal distribution. Relative to regimes with many
small introduction events, regimes with few large introduction
events generate more variability in population-size trajectories.
We show that this variability helps introduced populations to
overcome difficult stages in the invasion process (those with a
negative average growth rate), but is disadvantageous during easy
stages (those with a positive average growth rate). In the light of
our results, we can reinterpret three published data sets on
invasion success under different introduction regimes. In Chapters
3 and 4 (Wittmann et al., 2013c,d), we examine levels of genetic
diversity in populations that have successfully overcome a strong
demographic Allee effect. In this ecological scenario, the average
population growth rate is negative below a certain critical
population size and positive above, such that the first stage in
the invasion process is difficult and the second one easy. In
Chapter 3, we assume Poisson-distributed offspring numbers. We show
that compared to successful populations without an Allee effect,
successful Allee-effect populations are expected to harbor either
more or less genetic diversity, depending on the magnitude of
typical founder population sizes relative to the critical
population size. Part of the explanation is that,
counter-intuitively, successful Allee-effect populations escape
particularly fast from the range of small population sizes where
genetic drift is strongest. In Chapter 3, we also identify
conditions under which the critical population size can be
estimated from genetic data. In Chapter 4, we consider a range of
offspring-number models leading to either more or less variability
in population dynamics than the Poisson model. For a fixed founder
population size, we observe that the Allee effect has a negative
influence on genetic diversity for small amounts of variability,
but a positive influence for large amounts of variability. We show
that the differences between our various offspring-number models
are so substantial that they cannot be resolved by rescaling the
parameters of the Poisson model. Taken together, these results
offer some general conclusions with respect to the four main
questions raised above. a) How fast an introduced population
completes the invasion process is mainly determined by the presence
and severity of difficult stages. Therefore, an ecological change
promotes invasion success if it lessens such difficult stages. b)
From the perspective of the introduced population, variability is
advantageous during difficult but not during easy stages of the
invasion process. c) Because the strength of genetic drift depends
on population size, a key to understanding the population genetic
consequences of invasion trajectories is to consider how much time
the population of interest spends in different population-size
ranges. d) Feedbacks between a reduction in population size and a
loss of genetic diversity are strongest in ecological scenarios
where the population of interest spends considerable time at small
population sizes. Some of the most striking results in this
dissertation cannot be understood from a deterministic point of
view, but only when considering stochasticity. Thus, stochasticity
does not just add “noise” to some average outcome, but can
qualitatively change the behavior of biological systems.