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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...
December 1, 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 size, skew in the male/female effective sizes can also be caused by family composition...
November 30, 2016: 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...
November 17, 2016: 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...
November 4, 2016: Theoretical Population Biology
C Merle, R Leblois, F Rousset, P Pudlo
Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become inefficient when the population size varies in time, making likelihood-based inferences difficult in many demographic situations. In this work, we modify a previous sequential importance sampling algorithm to improve the efficiency of the likelihood estimation. Our procedure is still based on features of the model with constant size, but uses a resampling technique with a new resampling probability distribution depending on the pairwise composite likelihood...
October 3, 2016: 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...
September 29, 2016: 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...
September 21, 2016: 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
Alberto Maltz, Gabriel Fabricius
An epidemic model with births and deaths is considered on a two-dimensional L×L lattice. Each individual can have global infective contacts according to the standard susceptible-infected-recovered (SIR) model rules or local infective contacts with their nearest neighbors. We propose a deterministic approach to this model and, for the parameters corresponding to pertussis and rubella in the prevaccine era, verify that there is a close agreement with the stochastic simulations when epidemic spread or endemic stationarity is considered...
December 2016: Theoretical Population Biology
Uri Liberman, Hilla Behar, Marcus W Feldman
Most models for the evolution of mutation under frequency-dependent selection involve some form of host-parasite interaction. These generally involve cyclic dynamics under which mutation may increase. Here we show that the reduction principle for the evolution of mutation, which is generally true for frequency-independent selection, also holds under frequency-dependent selection on haploids and diploids that does not involve cyclic dynamics.
December 2016: Theoretical Population Biology
J M Kitayimbwa, J Y T Mugisha, R A Saenz
One of the serious threats facing the administration of antiretroviral therapy to human immunodeficiency virus (HIV-1) infected patients is the reported increasing prevalence of transmitted drug resistance. However, given that HIV-1 drug-resistant strains are often less fit than the wild-type strains, it is expected that drug-resistant strains that are present during the primary phase of the HIV-1 infection are replaced by the fitter wild-type strains. This replacement of HIV-1 resistant mutations involves the emergence of wild-type strains by a process of backward mutation...
December 2016: Theoretical Population Biology
D Abu Awad, S Billiard, V C Tran
When predicting the fate and consequences of recurring deleterious mutations in self-fertilising populations most models developed make the assumption that populations have discrete non-overlapping generations. This makes them biologically irrelevant when considering perennial species with overlapping generations and where mating occurs independently of the age group. The few models studying the effect of perennial life-histories on the genetic properties of populations in the presence of self-fertilisation have done so considering age-dependent selection...
December 2016: Theoretical Population Biology
Mitchell G Newberry, David M McCandlish, Joshua B Plotkin
Underdominant mutations have fixed between divergent species, yet classical models suggest that rare underdominant alleles are purged quickly except in small or subdivided populations. We predict that underdominant alleles that also influence mate choice, such as those affecting coloration patterns visible to mates and predators alike, can fix more readily. We analyze a mechanistic model of positive assortative mating in which individuals have n chances to sample compatible mates. This one-parameter model naturally spans random mating (n=1) and complete assortment (n→∞), yet it produces sexual selection whose strength depends non-monotonically on n...
December 2016: Theoretical Population Biology
Conrad J Burden, Yurong Tang
We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex...
December 2016: Theoretical Population Biology
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