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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
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...
July 27, 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...
July 12, 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
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...
July 6, 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...
June 15, 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
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...
June 2017: Theoretical Population Biology
Heike Lischke, Thomas J Löffler
One way to explore assembly of extant and novel communities from species pools, and by that biodiversity and species ranges, is to study the equilibrium behavior of dynamic competition models such as the Lotka-Volterra competition (LVC) model. We present a novel method (COMMUSTIX) to determine all stable fixpoints of the general LVC model with abundances x from a given pool of n species. To that purpose, we split the species in potentially surviving species (xi>0) and in others going extinct (xi=0). We derived criteria for the stability of xi=0 and for the equilibrium of xi>0 to determine possible combinations of extinct and surviving species by iteratively applying a mixed binary linear optimization algorithm...
June 2017: Theoretical Population Biology
Peter R Wilton, Pierre Baduel, Matthieu M Landon, John Wakeley
Contrary to what is often assumed in population genetics, independently segregating loci do not have completely independent ancestries, since all loci are inherited through a single, shared population pedigree. Previous work has shown that the non-independence between gene genealogies of independently segregating loci created by the population pedigree is weak in panmictic populations, and predictions made from standard coalescent theory are accurate for populations that are at least moderately sized. Here, we investigate patterns of coalescence in pedigrees of structured populations...
June 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
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
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