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Theoretical Population Biology

Coralie Fritsch, Fabien Campillo, Otso Ovaskainen
We propose a numerical approach to study the invasion fitness of a mutant and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds. Our approach is based on a dual representation, which consists of the modeling of the small size mutant population by a stochastic model and the computation of its corresponding deterministic model. The use of the deterministic model greatly facilitates the numerical determination of the feasibility of invasion as well as the convergence-stability of the evolutionary singular strategy...
May 10, 2017: Theoretical Population Biology
Ross Cressman, Abdel Halloway, Gordon G McNickle, Joe Apaloo, Joel S Brown, Thomas L Vincent
A central question in the study of ecology and evolution is: "Why are there so many species?" It has been shown that certain forms of the Lotka-Volterra (L-V) competition equations lead to an unlimited number of species. Furthermore, these authors note how any change in the nature of competition (the competition kernel) leads to a finite or small number of coexisting species. Here we build upon these works by further investigating the L-V model of unlimited niche packing as a reference model and evolutionary game for understanding the environmental factors restricting biodiversity...
May 8, 2017: Theoretical Population Biology
Alexander Singer, Karin Johst
After a disturbance event, population recovery becomes an important species response that drives ecosystem dynamics. Yet, it is unclear how interspecific interactions impact species recovery from a disturbance and which role the disturbance duration (pulse or press) plays. Here, we analytically derive conditions that govern the transient recovery dynamics from disturbance of a host and its obligately dependent partner in a two-species metapopulation model. We find that, after disturbance, species recovery dynamics depend on the species' role (i...
May 4, 2017: Theoretical Population Biology
François Bienvenu, Erol Akçay, Stéphane Legendre, David M McCandlish
Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors...
May 2, 2017: Theoretical Population Biology
Irina Bashkirtseva, Lev Ryashko
A problem of the analysis of the noise-induced extinction in population models with Allee effect is considered. To clarify mechanisms of the extinction, we suggest a new technique combining an analysis of the geometry of attractors and their stochastic sensitivity. For the conceptual one-dimensional discrete Ricker-type model, on the base of the bifurcation analysis, deterministic persistence zones are constructed in the space of initial states and biological parameters. It is shown that the random environmental noise can contract, and even destroy these persistence zones...
April 19, 2017: Theoretical Population Biology
Michael Turelli, Nicholas H Barton
A novel strategy for controlling the spread of arboviral diseases such as dengue, Zika and chikungunya is to transform mosquito populations with virus-suppressing Wolbachia. In general, Wolbachia transinfected into mosquitoes induce fitness costs through lower viability or fecundity. These maternally inherited bacteria also produce a frequency-dependent advantage for infected females by inducing cytoplasmic incompatibility (CI), which kills the embryos produced by uninfected females mated to infected males...
April 12, 2017: Theoretical Population Biology
S Thomas Kelly, Hamish G Spencer
Genomic imprinting is a form of epigenetic modification involving parent-of-origin-dependent gene expression, usually the inactivation of one gene copy in some tissues, at least, for some part of the diploid life cycle. Occurring at a number of loci in mammals and flowering plants, this mode of non-Mendelian expression can be viewed more generally as parentally-specific differential gene expression. The effects of natural selection on genetic variation at imprinted loci have previously been examined in a several population-genetic models...
April 5, 2017: Theoretical Population Biology
Léandra King, John Wakeley, Shai Carmi
The population-scaled mutation rate, θ, is informative on the effective population size and is thus widely used in population genetics. We show that for two sequences and n unlinked loci, the variance of Tajima's estimator (θˆ), which is the average number of pairwise differences, does not vanish even as n→∞. The non-zero variance of θˆ results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by gene genealogies at all loci...
March 21, 2017: Theoretical Population Biology
Hisashi Ohtsuki, Joe Yuichiro Wakano, Yutaka Kobayashi
The success of humans on the globe is largely supported by our cultural excellence. Our culture is cumulative, meaning that it is improved from generation to generation. Previous works have revealed that two modes of learning, individual learning and social learning, play pivotal roles in the accumulation of culture. However, under the trade-off between learning and reproduction, one's investment into learning is easily exploited by those who copy the knowledge of skillful individuals and selfishly invest more efforts in reproduction...
March 16, 2017: Theoretical Population Biology
I Akushevich, A P Yashkin, J Kravchenko, F Fang, K Arbeev, F Sloan, A I Yashin
In this study, we present a new theory of partitioning of disease prevalence and incidence-based mortality and demonstrate how this theory practically works for analyses of Medicare data. In the theory, the prevalence of a disease and incidence-based mortality are modeled in terms of disease incidence and survival after diagnosis supplemented by information on disease prevalence at the initial age and year available in a dataset. Partitioning of the trends of prevalence and mortality is calculated with minimal assumptions...
April 2017: Theoretical Population Biology
Andrew E M Lewis-Pye, Antonio Montalbán
The question as to why most complex organisms reproduce sexually remains a very active research area in evolutionary biology. Theories dating back to Weismann have suggested that the key may lie in the creation of increased variability in offspring, causing enhanced response to selection. Under appropriate conditions, selection is known to result in the generation of negative linkage disequilibrium, with the effect of recombination then being to increase genetic variance by reducing these negative associations between alleles...
April 2017: Theoretical Population Biology
Nienke Hartemink, Trifon I Missov, Hal Caswell
Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity...
April 2017: 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...
April 2017: 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...
April 2017: 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...
April 2017: 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...
April 2017: 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...
April 2017: 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...
April 2017: 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...
April 2017: 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...
April 2017: Theoretical Population Biology
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