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Theoretical Population Biology

Dominik Schrempf, Asger Hobolth
Recently, Burden and Tang (2016) provided an analytical expression for the stationary distribution of the multivariate neutral Wright-Fisher model with low mutation rates. In this paper we present a simple, alternative derivation that illustrates the approximation. Our proof is based on the discrete multivariate boundary mutation model which has three key ingredients. First, the decoupled Moran model is used to describe genetic drift. Second, low mutation rates are assumed by limiting mutations to monomorphic states...
December 29, 2016: Theoretical Population Biology
Luděk Berec, Eva Janoušková, Michal Theuer
Infectious diseases can seriously impact dynamics of their host species. In this study, we model and analyze an interaction between a sexually transmitted infection and its animal host population affected by a mate-finding Allee effect. Since mating drives both host reproduction and infection transmission, the Allee effect shapes the transmission rate of the infection which we show takes a saturating form. Our model combining sexually transmitted infections with the mate-finding Allee effect in the host produces quite rich dynamics, including oscillations, several multistability regimes, and infection-induced host extinction...
December 27, 2016: Theoretical Population Biology
Laura S Storch, James M Pringle, Karen E Alexander, David O Jones
There is an ongoing debate about the applicability of chaotic and nonlinear models to ecological systems. Initial introduction of chaotic population models to the ecological literature was largely theoretical in nature and difficult to apply to real-world systems. Here, we build upon and expand prior work by performing an in-depth examination of the dynamical complexities of a spatially explicit chaotic population, within an ecologically applicable modeling framework. We pair a classic chaotic growth model (the logistic map) with explicit dispersal length scale and shape via a Gaussian dispersal kernel...
December 19, 2016: Theoretical Population Biology
Noemi Kurt, Mathias Rafler
For the seedbank coalescent with mutation under the infinite alleles assumption, which describes the gene genealogy of a population with a strong seedbank effect subject to mutations, we study the distribution of the final partition with mutation. This generalizes the coalescent with freeze by Dong et al. (2007) to coalescents where ancestral lineages are blocked from coalescing. We derive an implicit recursion which we show to have a unique solution and give an interpretation in terms of absorption problems of a random walk...
December 18, 2016: Theoretical Population Biology
Simon Maccracken Stump, Peter Chesson
Optimal foraging is one of the major predictive theories of predator foraging behavior. However, how an optimally foraging predator affects the coexistence of competing prey is not well understood either in a constant or variable environment, especially for multiple prey species. We study the impact of optimal foraging on prey coexistence using an annual plant model, with and without annual variation in seed germination. Seed predators are modeled using Charnov's model of adaptive diet choice. Our results reveal that multiple prey species can coexist because of this type of predator, and that their effect is not greatly modified by environmental variation...
December 18, 2016: Theoretical Population Biology
Bendix Koopmann, Johannes Müller, Aurélien Tellier, Daniel Živković
Seed banks are common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation...
December 10, 2016: Theoretical Population Biology
Olivier David, Christian Lannou, Hervé Monod, Julien Papaïx, Djidi Traore
The role of environmental heterogeneity in the evolution of biological diversity has been studied only for simple types of heterogeneities and dispersals. This article broadens previous results by considering heterogeneities and dispersals that are structured by several environmental factors. It studies the evolution of a metapopulation, living in a network of patches connected by dispersal, under the effects of mutation, selection and migration. First, it is assumed that patches are equally connected and that they carry habitats characterized by several factors exerting selection pressures on several individual traits...
December 7, 2016: Theoretical Population Biology
Fernando L Mendez
Difference in male and female effective population sizes has, at times, been attributed to both sexes having unequal variance in their number of offspring. Such difference is paralleled by the relative effective sizes of autosomes, sex chromosomes, and mitochondrial DNA. I develop a simple framework to calculate the inbreeding effective population sizes for loci with different modes of inheritance. In this framework, I separate the effects due to mating strategy and those due to genetic transmission. I then show that, in addition to differences in the variance in offspring number, skew in the male/female effective sizes can also be caused by family composition...
November 30, 2016: Theoretical Population Biology
Thomas W Carr
In an SIRS compartment model for a disease we consider the effect of different probability distributions for remaining immune. We show that to first approximation the first three moments of the corresponding probability densities are sufficient to well describe oscillatory solutions corresponding to recurrent epidemics. Specifically, increasing the fraction who lose immunity, increasing the mean immunity time, and decreasing the heterogeneity of the population all favor the onset of epidemics and increase their severity...
February 2017: Theoretical Population Biology
Ferdinand Pfab, Odo Diekmann, Souvik Bhattacharya, Andrea Pugliese
Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two parasitoids that attack different juvenile stages of a common host. Their main result was that coexistence of the parasitoids is only possible when there is sufficient variability in the maturation delays of the host juvenile stages. Here, we analyze the phenomenon of coexistence in that model more deeply. We show that with some distribution families for the maturation delays, the coexistence equilibrium is unique, while with other distributions multiple coexistence equilibria can be found...
February 2017: Theoretical Population Biology
Conrad J Burden, Yurong Tang
A procedure is described for estimating evolutionary rate matrices from observed site frequency data. The procedure assumes (1) that the data are obtained from a constant size population evolving according to a stationary Wright-Fisher or decoupled Moran model; (2) that the data consist of a multiple alignment of a moderate number of sequenced genomes drawn randomly from the population; and (3) that within the genome a large number of independent, neutral sites evolving with a common mutation rate matrix can be identified...
February 2017: Theoretical Population Biology
Alex McAvoy, Christoph Hauert
Repeated games have a long tradition in the behavioral sciences and evolutionary biology. Recently, strategies were discovered that permit an unprecedented level of control over repeated interactions by enabling a player to unilaterally enforce linear constraints on payoffs. Here, we extend this theory of "zero-determinant" (or, more generally, "autocratic") strategies to alternating games, which are often biologically more relevant than traditional synchronous games. Alternating games naturally result in asymmetries between players because the first move matters or because players might not move with equal probabilities...
February 2017: Theoretical Population Biology
Kris De Jaegher
The game-theoretic model in this paper provides micro-foundations for the effect a harsher environment on the probability of cooperation among multiple players. The harshness of the environment is alternatively measured by the degree of complementarity between the players' cooperative efforts in producing a public good, and by the number of attacks on an existing public good that the players can collectively defend, where it is shown that these two measures of the degree of adversity facing the players operate in a similar fashion...
February 2017: Theoretical Population Biology
O Hössjer, Linda Laikre, Nils Ryman
Many versions of the effective population size (Ne) exist, and they are important in population genetics in order to quantify rates of change of various characteristics, such as inbreeding, heterozygosity, or allele frequencies. Traditionally, Ne was defined for single, isolated populations, but we have recently presented a mathematical framework for subdivided populations. In this paper we focus on diploid populations with geographic subdivision, and present new theoretical results. We compare the haploid and diploid versions of the inbreeding effective size (NeI) with novel expression for the variance effective size (NeV), and conclude that for local populations NeV is often much smaller than both versions of NeI, whenever they exist...
December 2016: Theoretical Population Biology
Kavita Jain, Sona John
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and fitness is additive. When beneficial mutations are ignored, the exact solution for the frequency distribution is known to be a Poisson distribution. Here we include beneficial mutations and obtain exact expressions for the frequency distribution at all times using an eigenfunction expansion method. We find that the stationary distribution is non-Poissonian and related to the Bessel function of the first kind...
December 2016: Theoretical Population Biology
Matteo Detto, Helene C Muller-Landau
Spatial interactions are widely acknowledged to play a significant role in sustaining diversity in ecological communities. However, theoretical work on this topic has focused on how spatial processes affect coexistence of species that differ in their strategies, with less attention to how spatial processes matter when competitors are equivalent. Furthermore, though it is recognized that models with local dispersal and local competition may sustain higher diversities of equivalent competitors than models in which these are not both localized, there is debate as to whether this reflects merely equalizing effects or whether there is also a stabilizing component...
December 2016: Theoretical Population Biology
Daniel Maxin, Laurentiu Sega, Lisa Eaton
We study several epidemic models (with and without gender structure) that incorporate risk compensation behavior in response to a lower chance of acquiring the infection as a result of preventive measures that are only partially effective. We show that the cumulative risk compensation that occurs between a high risk susceptible and infectious individual may play an important role in whether the implementation of these measures is successful in lowering the epidemic reproductive number. In addition, we show that certain levels of risk compensation may cancel the benefit of the low infection risk practiced by diagnosed infectious individuals when the goal is a reduction of the epidemic reproductive number...
December 2016: Theoretical Population Biology
Ashish Goyal, John M Murray
BACKGROUND: Hepatitis delta virus (HDV) in conjunction with hepatitis B virus (HBV) increases adult morbidity and mortality. A number of studies have performed cost-benefit analyses for HBV interventions, but they have ignored the impact of HDV on these outcomes. METHODS: Using a mathematical model of HBV-HDV epidemiology, we compare health benefits and cost outcomes of four interventions: testing with HBV adult vaccination (diagnosis), diagnosis with antiviral treatment for HBV infections (mono-infections), diagnosis with antiviral treatment for HBV-HDV infections (dual-infections), and awareness programs...
December 2016: Theoretical Population Biology
Robert C Griffiths, Paul A Jenkins, Sabin Lessard
Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the Wright-Fisher diffusion for genetic drift and its genealogical counterpart, the coalescent. There have been a number of articles extending this relationship to include other evolutionary processes such as mutation and selection, but little has been explored for models also incorporating crossover recombination...
December 2016: Theoretical Population Biology
R McVinish, P K Pollett, Y S Chan
We study a variant of Hanski's incidence function model that allows habitat patch characteristics to vary over time following a Markov process. The widely studied case where patches are classified as either suitable or unsuitable is included as a special case. For large metapopulations, we determine a recursion for the probability that a given habitat patch is occupied. This recursion enables us to clarify the role of landscape dynamics in the survival of a metapopulation. In particular, we show that landscape dynamics affects the persistence and equilibrium level of the metapopulation primarily through its effect on the distribution of a local population's life span...
December 2016: Theoretical Population Biology
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