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Theoretical Population Biology

Luca Ferretti, Alexander Klassmann, Emanuele Raineri, Sebastián E Ramos-Onsins, Thomas Wiehe, Guillaume Achaz
We introduce the conditional Site Frequency Spectrum (SFS) for a genomic region linked to a focal mutation of known frequency. An exact expression for its expected value is provided for the neutral model without recombination. Its relation with the expected SFS for two sites, 2-SFS, is discussed. These spectra derive from the coalescent approach of Fu (1995) for finite samples, which is reviewed. Remarkably simple expressions are obtained for the linked SFS of a large population, which are also solutions of the multi-allelic Kolmogorov equations...
June 28, 2018: Theoretical Population Biology
Lukas Heinrich, Johannes Müller, Aurélien Tellier, Daniel Živković
Population genetics models typically consider a fixed population size and a unique selection coefficient. However, population dynamics inherently generate fluctuations in numbers of individuals and selection acts on various components of the individuals' fitness. In plant species with seed banks, the size of both the above- and below-ground compartments induce fluctuations depending on seed production and the state of the seed bank. We investigate if this fluctuation has consequences on (1) the rate of genetic drift, and (2) the efficacy of selection...
June 27, 2018: Theoretical Population Biology
Steinar Engen, Francisco J Cao, Bernt-Erik Sæther
Harvesting in space affects, in general, the spatial scale of the synchrony in the population fluctuations, which determines the size of the areas subjected to simultaneous quasi-extinction risk. Here we show that harvesting reduces the population synchrony scale if it depends more strongly on population fluctuations than the density dependence of the growth rate in the absence of harvesting. We show that constant and proportional harvesting always increases the spatial scale, using a theta-logistic model for density regulation...
May 31, 2018: Theoretical Population Biology
Adam Thomas Clark, Claudia Neuhauser
Because the Lotka-Volterra competitive equations posit no specific competitive mechanisms, they are exceedingly general, and can theoretically approximate any underlying mechanism of competition near equilibrium. In practice, however, these models rarely generate accurate predictions in diverse communities. We propose that this difference between theory and practice may be caused by how uncertainty propagates through Lotka-Volterra systems. In approximating mechanistic relationships with Lotka-Volterra models, associations among parameters are lost, and small variation can correspond to large and unrealistic changes in predictions...
May 31, 2018: Theoretical Population Biology
Yutaka Kobayashi, Joe Yuichiro Wakano, Hisashi Ohtsuki
A finite-population, discrete-generation model of cultural evolution is described, in which multiple discrete traits are transmitted independently. In this model, each newborn may inherit a trait from multiple cultural parents. Transmission fails with a positive probability unlike in population genetics. An ancestral process simulating the cultural genealogy of a sample of individuals is derived for this model. This ancestral process, denoted by M- , is shown to be dual to a process M+ describing the change in the frequency of a trait...
May 9, 2018: Theoretical Population Biology
Rohan S Mehta, Noah A Rosenberg
Reciprocal monophyly, a feature of a genealogy in which multiple groups of descendant lineages each consist of all of the descendants of their respective most recent common ancestors, has been an important concept in studies of species delimitation, phylogeography, population history reconstruction, systematics, and conservation. Computations involving the probability that reciprocal monophyly is observed in a genealogy have played a key role in criteria for defining taxonomic groups and inferring divergence times...
May 3, 2018: Theoretical Population Biology
Laura S Storch, James M Pringle
In the ocean, propagules with a planktonic stage are typically dispersed some distance downstream of the parent generation, introducing an asymmetry to the dispersal. Ocean-dwelling species have also been shown to exhibit chaotic population dynamics. Therefore, we must better understand chaotic population dynamics under the influence of asymmetrical dispersal. Here, we examine a density-dependent population in a current, where the current has both a mean and stochastic component. In our finite domain, the current moves offspring in the downstream direction...
May 3, 2018: Theoretical Population Biology
Robert C Griffiths, Simon Tavaré
We consider inference about the history of a sample of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting, we implement rejection sampling and importance sampling schemes to perform the inference. The importance sampling scheme addresses an extension of the Ewens Sampling Formula for a configuration of haplotypes and the number of segregating sites in the sample. The implementations include both constant and variable population size models...
April 25, 2018: Theoretical Population Biology
Amaury Lambert
At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth-death process. Stop this process at time T>0. It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid)...
April 25, 2018: Theoretical Population Biology
José M Ponciano, Mark L Taper, Brian Dennis
Change points in the dynamics of animal abundances have extensively been recorded in historical time series records. Little attention has been paid to the theoretical dynamic consequences of such change-points. Here we propose a change-point model of stochastic population dynamics. This investigation embodies a shift of attention from the problem of detecting when a change will occur, to another non-trivial puzzle: using ecological theory to understand and predict the post-breakpoint behavior of the population dynamics...
May 2018: Theoretical Population Biology
Andrew Melfi, Divakar Viswanath
The Kingman coalescent is a commonly used model in genetics, which is often justified with reference to the Wright-Fisher (WF) model. Current proofs of convergence of WF and other models to the Kingman coalescent assume a constant sample size. However, sample sizes have become quite large in human genetics. Therefore, we develop a convergence theory that allows the sample size to increase with population size. If the haploid population size is N and the sample size is N1∕3-ϵ , ϵ>0, we prove that Wright-Fisher genealogies involve at most a single binary merger in each generation with probability converging to 1 in the limit of large N...
May 2018: Theoretical Population Biology
Hilla Behar, Marcus W Feldman
The joint evolutionary dynamics of phenotypes and genotypes are usually couched in terms of genetic variance contributions to changes in the phenotypic mean. Here, we study the evolution of a dichotomous phenotype whose transmission is controlled by one multi-allelic locus. The phenotype is under selection, which may be genotype-dependent. We answer classical population genetic questions about the phenogenotypic evolution, including the conditions for phenotypic and genotypic polymorphism, in terms of selection coefficients and rates of phenotypic transmission...
May 2018: Theoretical Population Biology
Glenn Young, Andrew Belmonte
Through the lens of game theory, cooperation is frequently considered an unsustainable strategy: if an entire population is cooperating, each individual can increase its overall fitness by choosing not to cooperate, thereby still receiving all the benefit of its cooperating neighbors while no longer expending its own energy. Observable cooperation in naturally-occurring public goods games is consequently of great interest, as such systems offer insight into both the emergence and sustainability of cooperation...
May 2018: Theoretical Population Biology
A M Babylon, M G Roberts, G C Wake
New Zealand has one of the highest (per capita) incidences of human leptospirosis in the world. It is the highest occurring occupational disease in New Zealand, often transmitted from livestock such as deer, sheep and cattle to humans. A cyclical model, showing the dynamics of infection of leptospirosis in farmed livestock in New Zealand, is presented. The limit cycle, bifurcation diagram and quasi-R0 value of the system are determined. Leptospire death rate is used as a control parameter. Previously published parameter values are used in a case study to produce figures demonstrating analytical results...
May 2018: 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...
May 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...
May 2018: Theoretical Population Biology
Erkan Ozge Buzbas, Paul Verdu
Signatures of recent historical admixture are ubiquitous in human populations. We present a mechanistic model of admixture with two source populations, encompassing recurrent admixture periods and study the distribution of admixture fractions for finite but arbitrary genome size. We provide simulation-based methods to estimate the introgression parameters and discuss the implications of reaching stationarity on estimability of parameters when there are recurrent admixture events with different rates.
March 28, 2018: Theoretical Population Biology
Jake M Ferguson, Erkan Ozge Buzbas
The distribution of allele frequencies obtained from diffusion approximations to Wright-Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright-Fisher models in which there are two hierarchical levels of genetic variability. The genotypes composed of alleles differing from each other at the selected level have fitness differences with respect to each other and evolve under selection...
March 21, 2018: 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
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...
March 2018: Theoretical Population Biology
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