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Theoretical Population Biology

Alfonso Ruiz-Herrera
In this study, I explored the impact of constructing a new dispersal route between two different patches in a metapopulation. My results indicated that its success/failure on the population abundance greatly depends on the patches directly involved and negligibly on the network topology. Specifically, constructing a dispersal route is highly recommended if it connects a source to a source that is close to becoming a sink or a sink that is close to becoming a source. This biological property is the basis for understanding the influence of the network topology on the population abundance...
March 12, 2018: Theoretical Population Biology
Yoav Ram, Lee Altenberg, Uri Liberman, Marcus W Feldman
Generation of variation may be detrimental in well-adapted populations evolving under constant selection. In a constant environment, genetic modifiers that reduce the rate at which variation is generated by processes such as mutation and migration, succeed. However, departures from this reduction principle have been demonstrated. Here we analyze a general model of evolution under constant selection where the rate at which variation is generated depends on the individual. We find that if a modifier allele increases the rate at which individuals of below-average fitness generate variation, then it will increase in frequency and increase the population mean fitness...
February 26, 2018: Theoretical Population Biology
Carsten Wiuf
In many areas of genetics it is of relevance to consider a population of individuals that is founded by a single individual in the past. One model for such a scenario is the conditioned reconstructed process with Bernoulli sampling that describes the evolution of a population of individuals that originates from a single individual. Several aspects of this reconstructed process are studied, in particular the Markov structure of the process. It is shown that at any given time in the past, the conditioned reconstructed process behaves as the original conditioned reconstructed process after a suitable time-dependent change of the sampling probability...
February 13, 2018: Theoretical Population Biology
A C Fowler, H F Winstanley
We propose a model for the growth of microbial populations in the presence of a rate-limiting nutrient which accounts for the switching of cells to a dormant phase at low densities in response to decreasing concentration of a putative biochemical signal. We then show that in conditions of nutrient starvation, self-sustained oscillations can occur, thus providing a natural explanation for such phenomena as plankton blooms. However, unlike results of previous studies, the microbial population minima do not become unrealistically small, being buffered during minima by an increased dormant phase population...
February 12, 2018: Theoretical Population Biology
Richard Arratia, A D Barbour, W J Ewens, Simon Tavaré
This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum...
February 9, 2018: Theoretical Population Biology
Alex McAvoy, Nicolas Fraiman, Christoph Hauert, John Wakeley, Martin A Nowak
Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended Wright-Fisher process with variable population size. In such a scenario, it is possible that the entire population becomes extinct. Survival of the population may depend on which strategy prevails in the game dynamics. Studying cooperative dilemmas, it is a natural feature of such a model that cooperators enable survival, while defectors drive extinction...
February 2, 2018: Theoretical Population Biology
Masahiro Anazawa
This paper explores the effects of increasing spatial subdivision of habitat on competition between two species. An increase in the degree of subdivision without any increase in the total amount of resources in the environment leads to smaller patch sizes, and thus, fewer individuals supported per patch. This fact suggests that when the degree of subdivision is high, the minimum resources that an individual must obtain before reproduction become important. Competition equations derived from first-principles that incorporate the minimum resource requirement are employed to investigate the effects of spatial subdivision and how these effects depend on the minimum requirements of the two species, type of resource competition such as scramble or contest, and spatial aggregation level of individuals...
January 30, 2018: Theoretical Population Biology
A Carvajal-Rodríguez
In this work, mate choice is modeled by means of the abstract concept of mutual mating propensity. This only assumes that different type of couples can have different mating success. The model is adequate for any population where mating occurs among distinct types. There is no extra assumption about particular mating scheme or preference model. The concept of mutual mating propensity permits to express the observed change in the mating phenotypes as the gain in information with respect to random mating. The obtained expression is a form of the Price equation in which the mapping between ancestral and descendant population is substituted by a mapping between random mating and non random mating population...
January 29, 2018: Theoretical Population Biology
Gregory Roth, Hal Caswell
As an individual moves through its life cycle, it passes through a series of states (age classes, size classes, reproductive states, spatial locations, health statuses, etc.) before its eventual death. The occupancy time in a state is the time spent in that state over the individual's life. Depending on the life cycle description, the occupancy times describe different demographic variables, for example, lifetime breeding success, lifetime habitat utilisation, or healthy longevity. Models based on absorbing Markov chains provide a powerful framework for the analysis of occupancy times...
January 26, 2018: Theoretical Population Biology
Anna Tovo, Marco Favretti
In this paper we are concerned with the analytical description of the change in floristic composition (species turnover) with the distance between two plots of a tropical rainforest due to the clustering of the individuals of the different species. We describe the plant arrangement by a superposition of spatial point processes and in this framework we introduce an analytical function which represents the average spatial density of the Sørensen similarity between two infinitesimal plots at distance r. We see that the decay in similarity with the distance is essentially described by the pair correlation function of the superposed process and that it is governed by the most abundant species...
January 18, 2018: 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
Mathilde Wanneveich, Hélène Jacqmin-Gadda, Jean-François Dartigues, Pierre Joly
No abstract text is available yet for this article.
March 2018: 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...
March 2018: 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...
February 2018: Theoretical Population Biology
Noah A Rosenberg
No abstract text is available yet for this article.
February 2018: 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 driving force 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 the persistence time of a two-species community where drift, environmental variations and time independent selective advantage are all taken into account...
February 2018: 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...
February 2018: Theoretical Population Biology
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