149 research outputs found
Establishment versus population growth in spatio-temporally varying environments
We consider situations where repeated invasion attempts occur from a source population into a receptor population over extended periods of time. The receptor population contains two locations that provide different expected off- spring numbers to invaders. There is demographic stochasticity in offspring numbers. In addition, temporal variation causes local invader fitnesses to vary. We show that effects of environmental autocorrelation on establishment success depend on spatial covariance of the receptor subpopulations. In situ- ations with a low spatial covariance this effect is positive, whereas high spatial covariance and/or high migration probabilities between the subpopulations causes the effect to be negative. This result reconciles seemingly contradictory results from the literature concerning effects of temporal variation on popu- lation dynamics with demographic stochasticity. We study an example in the context of genetic introgression, where invasions of cultivar plant genes occur through pollen flow from a source population into wild-type receptor populations, but our results have implications in a wider range of contexts, such as the spread of exotic species, metapopulation dynamics and epidemics.Global Challenges (FGGA
Evolutionary branching in a stochastic population model with discrete mutational steps
Evolutionary branching is analysed in a stochastic, individual-based
population model under mutation and selection. In such models, the common
assumption is that individual reproduction and life career are characterised by
values of a trait, and also by population sizes, and that mutations lead to
small changes in trait value. Then, traditionally, the evolutionary dynamics is
studied in the limit of vanishing mutational step sizes. In the present
approach, small but non-negligible mutational steps are considered. By means of
theoretical analysis in the limit of infinitely large populations, as well as
computer simulations, we demonstrate how discrete mutational steps affect the
patterns of evolutionary branching. We also argue that the average time to the
first branching depends in a sensitive way on both mutational step size and
population size.Comment: 12 pages, 8 figures. Revised versio
Optimal Patch-Leaving Behaviour: A Case Study Using The Parasitoid Cotesia rebecula
1. Parasitoids are predicted to spend longer in patches with more hosts, but previous work on Cotesia rubecula (Marshall) has not upheld this prediction. Tests of theoretical predictions may be affected by the definition of patch leaving behaviour, which is often ambiguous. 2. In this study whole plants were considered as patches and assumed that wasps move within patches by means of walking or flying. Within-patch and between-patch flights were distinguished based on flight distance. The quality of this classification was tested statistically by examination of log-survivor curves of flight times. 3. Wasps remained longer in patches with higher host densities, which is consistent with predictions of the marginal value theorem (Charnov 1976). Under the assumption that each flight indicates a patch departure, there is no relationship between host density and leaving tendency. 4. Oviposition influences the patch leaving behaviour of wasps in a count down fashion (Driessen et al. 1995), as predicted by an optimal foraging model (Tenhumberg, Keller & Possingham 2001). 5. Wasps spend significantly longer in the first patch encountered following release, resulting in an increased rate of superparasitism
Prospects & Overviews Bet hedging or not? A guide to proper classification of microbial survival strategies
Bacteria have developed an impressive ability to survive and propagate in highly diverse and changing environments by evolving phenotypic heterogeneity. Phenotypic heterogeneity ensures that a subpopulation is well prepared for environmental changes. The expression bet hedging is commonly (but often incorrectly) used by molecular biologists to describe any observed phenotypic heterogeneity. In evolutionary biology, however, bet hedging denotes a risk-spreading strategy displayed by isogenic populations that evolved in unpredictably changing environments. Opposed to other survival strategies, bet hedging evolves because the selection environment changes and favours different phenotypes at different times. Consequently, in bet hedging populations all phenotypes perform differently well at any time, depending on the selection pressures present. Moreover, bet hedging is the only strategy in which temporal variance of offspring numbers per individual is minimized. Our paper aims to provide a guide for the correct use of the term bet hedging in molecular biology
Single-crossover dynamics: finite versus infinite populations
Populations evolving under the joint influence of recombination and
resampling (traditionally known as genetic drift) are investigated. First, we
summarise and adapt a deterministic approach, as valid for infinite
populations, which assumes continuous time and single crossover events. The
corresponding nonlinear system of differential equations permits a closed
solution, both in terms of the type frequencies and via linkage disequilibria
of all orders. To include stochastic effects, we then consider the
corresponding finite-population model, the Moran model with single crossovers,
and examine it both analytically and by means of simulations. Particular
emphasis is on the connection with the deterministic solution. If there is only
recombination and every pair of recombined offspring replaces their pair of
parents (i.e., there is no resampling), then the {\em expected} type
frequencies in the finite population, of arbitrary size, equal the type
frequencies in the infinite population. If resampling is included, the
stochastic process converges, in the infinite-population limit, to the
deterministic dynamics, which turns out to be a good approximation already for
populations of moderate size.Comment: 21 pages, 4 figure
How Gaussian competition leads to lumpy or uniform species distributions
A central model in theoretical ecology considers the competition of a range
of species for a broad spectrum of resources. Recent studies have shown that
essentially two different outcomes are possible. Either the species surviving
competition are more or less uniformly distributed over the resource spectrum,
or their distribution is 'lumped' (or 'clumped'), consisting of clusters of
species with similar resource use that are separated by gaps in resource space.
Which of these outcomes will occur crucially depends on the competition kernel,
which reflects the shape of the resource utilization pattern of the competing
species. Most models considered in the literature assume a Gaussian competition
kernel. This is unfortunate, since predictions based on such a Gaussian
assumption are not robust. In fact, Gaussian kernels are a border case
scenario, and slight deviations from this function can lead to either uniform
or lumped species distributions. Here we illustrate the non-robustness of the
Gaussian assumption by simulating different implementations of the standard
competition model with constant carrying capacity. In this scenario, lumped
species distributions can come about by secondary ecological or evolutionary
mechanisms or by details of the numerical implementation of the model. We
analyze the origin of this sensitivity and discuss it in the context of recent
applications of the model.Comment: 11 pages, 3 figures, revised versio
Qualitative Multi-Objective Reachability for Ordered Branching MDPs
We study qualitative multi-objective reachability problems for Ordered
Branching Markov Decision Processes (OBMDPs), or equivalently context-free
MDPs, building on prior results for single-target reachability on Branching
Markov Decision Processes (BMDPs).
We provide two separate algorithms for "almost-sure" and "limit-sure"
multi-target reachability for OBMDPs. Specifically, given an OBMDP,
, given a starting non-terminal, and given a set of target
non-terminals of size , our first algorithm decides whether the
supremum probability, of generating a tree that contains every target
non-terminal in set , is . Our second algorithm decides whether there is
a strategy for the player to almost-surely (with probability ) generate a
tree that contains every target non-terminal in set .
The two separate algorithms are needed: we show that indeed, in this context,
"almost-sure" "limit-sure" for multi-target reachability, meaning that
there are OBMDPs for which the player may not have any strategy to achieve
probability exactly of reaching all targets in set in the same
generated tree, but may have a sequence of strategies that achieve probability
arbitrarily close to . Both algorithms run in time , where is the total bit encoding length
of the given OBMDP, . Hence they run in polynomial time when
is fixed, and are fixed-parameter tractable with respect to . Moreover, we
show that even the qualitative almost-sure (and limit-sure) multi-target
reachability decision problem is in general NP-hard, when the size of the
set of target non-terminals is not fixed.Comment: 47 page
A procedure for the change point problem in parametric models based on phi-divergence test-statistics
This paper studies the change point problem for a general parametric,
univariate or multivariate family of distributions. An information theoretic
procedure is developed which is based on general divergence measures for
testing the hypothesis of the existence of a change. For comparing the accuracy
of the new test-statistic a simulation study is performed for the special case
of a univariate discrete model. Finally, the procedure proposed in this paper
is illustrated through a classical change-point example
Stochasticity in the adaptive dynamics of evolution: The bare bones
First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics
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