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Theoretical Population Biology

Stephanie J Peacock, Juliette Bouhours, Mark A Lewis, Péter K Molnár
Spatial variability in host density is a key factor affecting disease dynamics of wildlife, and yet there are few spatially explicit models of host-macroparasite dynamics. This limits our understanding of parasitism in migratory hosts, whose densities change considerably in both space and time. In this paper, we develop a model for host-macroparasite dynamics that considers the directional movement of host populations and their associated parasites. We include spatiotemporal changes in the mean and variance in parasite burden per host, as well as parasite-mediated host mortality and parasite-mediated migratory ability...
January 6, 2018: Theoretical Population Biology
A Klassmann, L Ferretti
The analysis of patterns of segregating (i.e. polymorphic) sites in aligned sequences is routine in population genetics. Quantities of interest include the total number of segregating sites and the number of sites with mutations of different frequencies, the so-called site frequency spectrum. For neutrally evolving sequences, some classical results are available, including the expected value and variance of the spectrum in the Kingman coalescent model without recombination as calculated by Fu (1995). In this work, we use similar techniques to compute the third moments of the frequencies of three linked sites...
January 5, 2018: Theoretical Population Biology
Soheil Baharian, Simon Gravel
Understanding the historical events that shaped current genomic diversity has applications in historical, biological, and medical research. However, the amount of historical information that can be inferred from genetic data is finite, which leads to an identifiability problem. For example, different historical processes can lead to identical distribution of allele frequencies. This identifiability issue casts a shadow of uncertainty over the results of any study which uses the frequency spectrum to infer past demography...
January 3, 2018: Theoretical Population Biology
Ailene MacPherson, Sarah P Otto
Host-parasite interactions in the form of infectious diseases are a topic of interest in both evolutionary biology and public health. Both fields have relied on mathematical models to predict and understand the dynamics and consequences of these interactions. Yet few models explicitly incorporate both epidemiological and coevolutionary dynamics, allowing for genetic variation in both hosts and parasites. By comparing a matching-alleles model of coevolution, a susceptible-infected-recovered-susceptible compartmental model from epidemiology, and a combined coevolutionary-epidemiology model we assess the effect of the coevolutionary feedback on the epidemiological dynamics and vice versa...
December 28, 2017: Theoretical Population Biology
Torben Tvedebrink, Poul Svante Eriksen, Helle Smidt Mogensen, Niels Morling
Ancestry-informative markers (AIMs) are markers that give information about the ancestry of individuals. They are used in forensic genetics for predicting the geographic origin of the investigated individual in crime and identification cases. In the exploration of the genogeographic origin of an AIMs profile, the likelihoods of the AIMs profile in various populations may be calculated. However, there may not be an appropriate reference population in the database. The fact that the likelihood ratio (LR) of one population compared to that of another population is large does not imply that any of the populations is relevant...
December 23, 2017: Theoretical Population Biology
Roger Arditi, Claude Lobry, Tewfik Sari
The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been fully analyzed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated with dispersal is either favorable or unfavorable to total population abundance. We pay special attention to the case of asymmetric dispersal, i...
December 23, 2017: Theoretical Population Biology
Mathilde Wanneveich, Hélène Jacqmin-Gadda, Jean-François Dartigues, Pierre Joly
Chronic diseases are a growing public health problem due to the population aging. Their economic, social and demographic burden will worsen in years to come. Up to now, the method used to provide projections and assess the future disease burden makes a non-homogeneous Markov assumption in an illness-death model. Both age and calendar year have been taken into account in all parameter estimations, but the time spent with the disease was not considered. This work develops the method with a semi-Markov assumption to model mortality among the diseased and considering the time spent with the disease...
December 16, 2017: Theoretical Population Biology
N H Barton, A M Etheridge
Maladapted individuals can only colonise a new habitat if they can evolve a positive growth rate fast enough to avoid extinction, a process known as evolutionary rescue. We treat log fitness at low density in the new habitat as a single polygenic trait and use the infinitesimal model to follow the evolution of the growth rate; this assumes that the trait values of offspring of a sexual union are normally distributed around the mean of the parents' trait values, with variance that depends only on the parents' relatedness...
December 12, 2017: Theoretical Population Biology
Michael T Pearce, Daniel S Fisher
Genetic exchange in microbes and other facultative sexuals can be rare enough that evolution is almost entirely asexual and populations almost clonal. But the benefits of genetic exchange depend crucially on the diversity of genotypes in a population. How very rare recombination together with the accumulation of new mutations shapes the diversity of large populations and gives rise to faster adaptation is still poorly understood. This paper analyzes a particularly simple model: organisms with two asexual chromosomes that can reassort during rare matings that occur at a rate r...
December 12, 2017: Theoretical Population Biology
Conrad J Burden, Yi Wei
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is presented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral mutations. The asymptotic stationary solution is obtained and has the property that the extant population partitions into subpopulations whose relative sizes are determined by mutation rates. An approximate time-dependent solution is obtained in the limit of low mutation rates...
December 9, 2017: Theoretical Population Biology
Craig R Miller, James T Van Leuven, Holly A Wichman, Paul Joyce
Fitness landscapes map genotypes to organismal fitness. Their topographies depend on how mutational effects interact-epistasis-and are important for understanding evolutionary processes such as speciation, the rate of adaptation, the advantage of recombination, and the predictability versus stochasticity of evolution. The growing amount of data has made it possible to better test landscape models empirically. We argue that this endeavor will benefit from the development and use of meaningful basic models against which to compare more complex models...
November 30, 2017: Theoretical Population Biology
Amy Veprauskas, Azmy S Ackleh, John E Banks, John D Stark
Prolonged exposure to a disturbance such as a toxicant has the potential to result in rapid evolution to toxicant resistance in many short-lived species such as daphniids. This evolution may allow a population to persist at higher levels of the toxicant than is possible without evolution. Here we apply evolutionary game theory to a Leslie matrix model for a daphniid population to obtain a Darwinian model that couples population dynamics with the dynamics of an evolving trait. We use the Darwinian model to consider how the evolution of resistance to the lethal or sublethal effects of a disturbance may change the population dynamics...
November 30, 2017: Theoretical Population Biology
Noah A Rosenberg
No abstract text is available yet for this article.
November 24, 2017: Theoretical Population Biology
Matan Danino, David A Kessler, Nadav M Shnerb
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the relevant timescale depends on the underlying dynamics. The persistence time of the community has been calculated both for neutral models, where the only drive of the system is drift (demographic stochasticity) and for models with strong selection. Following recent analyses that stress the importance of environmental stochasticity in empirical systems, we present here a general theory of persistence time of two-species community where drift, environmental variations and time independent selective advantage are all taken into account...
November 23, 2017: Theoretical Population Biology
F Baumdicker, A M I Huebner, P Pfaffelhuber
Today, the CRISPR (clustered regularly interspaced short palindromic repeats) region within bacterial and archaeal genomes is known to encode an adaptive immune system. We rely on previous results on the evolution of the CRISPR arrays, which led to the ordered independent loss model, introduced by Kupczok and Bollback (2013). When focusing on the spacers (between the repeats), new elements enter a CRISPR array at rate θ at the leader end of the array, while all spacers present are lost at rate ρ along the phylogeny relating the sample...
November 22, 2017: Theoretical Population Biology
José Miguel Ponciano
Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered...
November 22, 2017: 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
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