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Theoretical Population Biology

Marcy K Uyenoyama, Naoki Takebayashi
We address the evolution of effective number of individuals under androdioecy and gynodioecy. We analyze dynamic models of autosomal modifiers of weak effect on sex expression. In our zygote control models, the sex expressed by a zygote depends on its own genotype, while in our maternal control models, it depends on the genotype of its maternal parent. Our analysis unifies full multi-dimensional local stability analysis with the Li-Price equation, which for all its heuristic appeal, describes evolutionary change over a single generation...
September 11, 2017: Theoretical Population Biology
Philip B Greenspoon, Nicole Mideo
The risk of antibiotic resistance evolution in parasites is a major problem for public health. Identifying factors which promote antibiotic resistance evolution is thus a priority in evolutionary medicine. The rate at which new mutations enter the parasite population is one important predictor; however, mutation rate is not necessarily a fixed quantity, as is often assumed, but can itself evolve. Here we explore the possible impacts of mutation rate evolution on the fate of a disease circulating in a host population, which is being treated with drugs, the use of which varies over time...
September 1, 2017: Theoretical Population Biology
Hisashi Ohtsuki, Hideki Innan
A cancer grows from a single cell, thereby constituting a large cell population. In this work, we are interested in how mutations accumulate in a cancer cell population. We provide a theoretical framework of the stochastic process in a cancer cell population and obtain near exact expressions of allele frequency spectrum or AFS (only continuous approximation is involved) from both forward and backward treatments under a simple setting; all cells undergo cell divisions and die at constant rates, b and d, respectively, such that the entire population grows exponentially...
September 1, 2017: Theoretical Population Biology
Lars Witting
The exponents of inter-specific allometries for several life history (metabolism, lifespan, reproductive rate, survival) and ecological (population density, home range) traits may evolve from the spatial dimensionality (d) of the intra-specific interactive competition that selects net assimilated energy into mass, with 1∕4 exponents being the two-dimensional (2D) case of the more general 1∕2d (Witting, 1995). While the exponents for mass-specific metabolism cluster around the predicted -1/4 and -1/6 in terrestrial and pelagic vertebrates, the allometries of mobile organisms are more diverse than the prediction...
September 1, 2017: Theoretical Population Biology
Max Shpak, Yang Ni, Jie Lu, Peter Müller
The mean pairwise genetic distance among haplotypes is an estimator of the population mutation rate θ and a standard measure of variation in a population. With the advent of next-generation sequencing (NGS) methods, this and other population parameters can be estimated under different modes of sampling. One approach is to sequence individual genomes with high coverage, and to calculate genetic distance over all sample pairs. The second approach, typically used for microbial samples or for tumor cells, is sequencing a large number of pooled genomes with very low individual coverage...
August 24, 2017: Theoretical Population Biology
Reinhard Bürger
The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We investigate a two-locus model in which two diallelic, recombining loci are subject to selection caused by an abrupt environmental change. The habitat is one-dimensional and unbounded, selection at each locus is modeled by step functions such that in one region one allele at each locus is advantageous and in the other deleterious...
August 14, 2017: Theoretical Population Biology
Paul Joyce, Zaid Abdo
In Beisel et al. (2007), a likelihood framework, based on extreme value theory (EVT), was developed for determining the distribution of fitness effects for adaptive mutations. In this paper we extend this framework beyond the extreme distributions and develop a likelihood framework for testing whether or not extreme value theory applies. By making two simple adjustments to the Generalized Pareto Distribution (GPD) we introduce a new simple five parameter probability density function that incorporates nearly every common (continuous) probability model ever used...
July 12, 2017: Theoretical Population Biology
M Reppell, S Zöllner
Coalescent simulations are a widely used approach for simulating sample genealogies, but can become computationally burdensome in large samples. Methods exist to analytically calculate a sample's expected frequency spectrum without simulating full genealogies. However, statistics that rely on the distribution of the length of internal coalescent branches, such as the probability that two mutations of equal size arose on the same genealogical branch, have previously required full coalescent simulations to estimate...
July 11, 2017: Theoretical Population Biology
N H Barton, A M Etheridge, A Véber
Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution...
July 11, 2017: Theoretical Population Biology
Christophe F D Coste, Frédéric Austerlitz, Samuel Pavard
In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models...
August 2017: Theoretical Population Biology
Charles Mullon, Laurent Lehmann
Human evolution depends on the co-evolution between genetically determined behaviors and socially transmitted information. Although vertical transmission of cultural information from parent to offspring is common in hominins, its effects on cumulative cultural evolution are not fully understood. Here, we investigate gene-culture co-evolution in a family-structured population by studying the invasion fitness of a mutant allele that influences a deterministic level of cultural information (e.g., amount of knowledge or skill) to which diploid carriers of the mutant are exposed in subsequent generations...
August 2017: Theoretical Population Biology
Luca Ferreri, Silvia Perazzo, Ezio Venturino, Mario Giacobini, Luigi Bertolotti, Alessandro Mannelli
Spirochetes belonging to the Borrelia burgdoferi sensu lato (sl) group cause Lyme Borreliosis (LB), which is the most commonly reported vector-borne zoonosis in Europe. B. burgdorferi sl is maintained in nature in a complex cycle involving Ixodes ricinus ticks and several species of vertebrate hosts. The transmission dynamics of B. burgdorferi sl is complicated by the varying competence of animals for different genospecies of spirochetes that, in turn, vary in their capability of causing disease. In this study, a set of difference equations simplifying the complex interaction between vectors and their hosts (competent and not for Borrelia) is built to gain insights into conditions underlying the dominance of B...
August 2017: Theoretical Population Biology
Steinar Engen
In spatio-temporal population dynamic models, the most important concept, in addition to mean and variance of local density fluctuations, is the spatial scale of fluctuations in density expressed by studying the spatial autocovariance function. Analytical formulas for this scale in models with local density regulation, dispersal and spatially autocorrelated noise, are rather simple when based on asymptotic theory giving linear models in the limit as the environmental variance approaches zero. The accuracy of these analytical small noise approximations has, however, not been investigated theoretically...
August 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...
August 2017: 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...
June 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...
June 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...
June 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...
June 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...
June 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...
June 2017: Theoretical Population Biology
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