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Theoretical Population Biology

Simon Van Wynsberge, Serge Andréfouët, Nabila Gaertner-Mazouni, Georges Remoissenet
Despite actions to manage sustainably tropical Pacific Ocean reef fisheries, managers have faced failures and frustrations because of unpredicted mass mortality events triggered by climate variability. The consequences of these events on the long-term population dynamics of living resources need to be better understood for better management decisions. Here, we use a giant clam (Tridacna maxima) spatially explicit population model to compare the efficiency of several management strategies under various scenarios of natural mortality, including mass mortality due to climatic anomalies...
November 17, 2017: Theoretical Population Biology
Ilana M Arbisser, Ethan M Jewett, Noah A Rosenberg
Many statistics that examine genetic variation depend on the underlying shapes of genealogical trees. Under the coalescent model, we investigate the joint distribution of two quantities that describe genealogical tree shape: tree height and tree length. We derive a recursive formula for their exact joint distribution under a demographic model of a constant-sized population. We obtain approximations for the mean and variance of the ratio of tree height to tree length, using them to show that this ratio converges in probability to 0 as the sample size increases...
November 10, 2017: Theoretical Population Biology
Nicolas P Rebuli, N G Bean, J V Ross
A novel outbreak will generally not be detected until such a time that it has become established. When such an outbreak is detected, public health officials must determine the potential of the outbreak, for which the basic reproductive numberR0 is an important factor. However, it is often the case that the resulting estimate of R0 is positively-biased for a number of reasons. One commonly overlooked reason is that the outbreak was not detected until such a time that it had become established, and therefore did not experience initial fade out...
November 1, 2017: Theoretical Population Biology
Bjarki Eldon, Wolfgang Stephan
We consider a model of viability selection in a highly fecund haploid population with sweepstakes reproduction. We use simulations to estimate the time until the allelic type with highest fitness has reached high frequency in a finite population. We compare the time between two reproduction modes of high and low fecundity. We also consider the probability that the allelic type with highest fitness is lost from the population before reaching high frequency. Our simulation results indicate that highly fecund populations can evolve faster (in some cases much faster) than populations of low fecundity...
October 27, 2017: Theoretical Population Biology
Stephen M Krone
Paul Joyce's work touched on a variety of topics in population genetics-from mathematical models of idealized systems to working closely with biologists on experimental evolution and landscape genetics. I will focus on his earlier mathematical/statistical work that centered on the infinite alleles model.
October 16, 2017: Theoretical Population Biology
Joe Yuichiro Wakano, William Gilpin, Seiji Kadowaki, Marcus W Feldman, Kenichi Aoki
Recent archaeological records no longer support a simple dichotomous characterization of the cultures/behaviors of Neanderthals and modern humans, but indicate much cultural/behavioral variability over time and space. Thus, in modeling the replacement or assimilation of Neanderthals by modern humans, it is of interest to consider cultural dynamics and its relation to demographic change. The ecocultural framework for the competition between hominid species allows their carrying capacities to depend on some measure of the levels of culture they possess...
October 12, 2017: Theoretical Population Biology
Robert Griffiths, Paul A Jenkins, Dario Spanò
This paper considers the coalescent genealogy in a Wright-Fisher diffusion process, modelling the frequency of an allele, when the frequency is fixed in a bridge at two times 0 and T. Particular attention is paid to beginning and ending at zero frequency. The coalescent genealogy of the population at time t is described by two coalescent processes from t to 0 and from t to T. If the frequencies are fixed at zero then the coalescent processes have single lineages at 0 and T. Genealogy of the neutral Wright-Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright-Fisher diffusion...
October 6, 2017: Theoretical Population Biology
Michael Turelli
Mendel (1866) suggested that if many heritable "factors" contribute to a trait, near-continuous variation could result. Fisher (1918) clarified the connection between Mendelian inheritance and continuous trait variation by assuming many loci, each with small effect, and by informally invoking the central limit theorem. Barton et al. (2017) rigorously analyze the approach to a multivariate Gaussian distribution of the genetic effects for descendants of parents who may be related. This commentary distinguishes three nested approximations, referred to as "infinitesimal genetics," "Gaussian descendants" and "Gaussian population," each plausibly called "the infinitesimal model...
October 5, 2017: Theoretical Population Biology
Hans J Skaug
We consider two individuals sampled from an age-structured population, and derive the probability that these have a parent-offspring relationship. Such probabilities play an important role in the recently proposed close-kin mark-recapture methods. The probability is decomposed into three terms. The first is the probability of the parent being alive, the second term involves the mechanism by which individuals are sampled, and the third term is a contribution from the observed age of the parent. A stable age distribution in the population is assumed, and we provide an expression for how this distribution is perturbed by the information that an individual has given birth at a particular time point in the past or in the future...
September 22, 2017: Theoretical Population Biology
Alexey Miroshnikov, Matthias Steinrücken
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly useful for this type of inference. Due to the Markovian structure of these models, an essential building block is the joint distribution of local genealogical trees, or statistics of these genealogies, at two neighboring loci in populations of variable size. Here, we present a novel method to compute the marginal and the joint distribution of the total length of the genealogical trees at two loci separated by at most one recombination event for samples of arbitrary size...
September 21, 2017: 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...
October 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...
October 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...
October 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...
October 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...
October 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
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