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Theoretical Population Biology

Peter Czuppon, Chaitanya S Gokhale
In population genetics, fixation of traits in a demographically changing population under frequency-independent selection has been extensively analysed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. A combination of demographic fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics has received comparatively little attention. We consider a stochastic, competitive Lotka-Volterra model with higher order interactions between two traits...
October 22, 2018: Theoretical Population Biology
Loic Yengo, Peter M Visscher
Mate choice through direct assortment on heritable traits, assortative mating (AM), is predicted in theory to inflate the genetic variance in a population and the correlation between relatives. Here, we revisit the theory of AM, first established in the landmark 1918 paper from RA Fisher, and provide new theory and analytical results. In particular, we shed light on inconsistencies in the literature regarding the correlation between double first cousins under AM and provide a solution. We derive new theory for AM due to X-chromosome loci...
October 11, 2018: Theoretical Population Biology
Conrad J Burden, Robert C Griffiths
The stationary distribution of the diffusion limit of the 2-island, 2-allele Wright-Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for approximating the forward Kolmogorov equation, the stationary distribution is obtained to leading order as a set of line densities on the edges of the sample space, corresponding to states for which one island is bi-allelic and the other island is non-segregating, and a set of point masses at the corners of the sample space, corresponding to states for which both islands are simultaneously non-segregating...
October 9, 2018: Theoretical Population Biology
Andrew Melfi, Divakar Viswanath
The first terms of the Wright-Fisher (WF) site frequency spectrum that follow the coalescent approximation are determined precisely, with a view to understanding the accuracy of the coalescent approximation for large samples. The perturbing terms show that the probability of a single mutant in the sample (singleton probability) is elevated in WF but the rest of the frequency spectrum is lowered. A part of the perturbation can be attributed to a mismatch in rates of merger between WF and the coalescent. The rest of it can be attributed to the difference in the way WF and the coalescent partition children between parents...
October 9, 2018: Theoretical Population Biology
P Pfaffelhuber, A Wakolbinger
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected frequency spectrum for low levels of frequency-dependent selection. Specifically, we rederive and extend the one-third rule of evolutionary game theory (Nowak et al., 2004) and effects of stochastic slowdown (Altrock and Traulsen, 2009). Since similar effects are of interest in other application areas, we formulate our results for general one-dimensional diffusions...
September 28, 2018: Theoretical Population Biology
Johannes Wirtz, Martina Rauscher, Thomas Wiehe
We revisit the classical, and introduce a novel, concept of two-locus linkage disequilibrium (LD). In contrast to defining haplotypes as allele combinations at two marker loci, we concentrate on the clustering of a sample of chromosomes induced by their coalescent genealogy. The root of a binary coalescent tree defines two clusters of chromosomes, each one of them containing the left and right descendants of the root. At two different loci this assignment may be different as a result of recombination. We show that the proportion of shared chromosomes among clusters at two different loci, measured by the squared correlation, constitutes a natural measure of LD...
September 19, 2018: Theoretical Population Biology
Antony M Dean
I analyze the joint impact of directional and fluctuating selection with reversible mutation in finite bi-allelic haploid populations using diffusion approximations of the Moran and chemostat models. Results differ dramatically from those of the classic Wright-Fisher diffusion. There, a strong dispersive effect attributable to fluctuating selection dissipates nascent polymorphisms promoted by a relatively weak emergent frequency dependent selective effect. The dispersive effect in the Moran diffusion with fluctuations every birth-death event is trivial...
September 9, 2018: Theoretical Population Biology
C Y Chen, J P Ward, W B Xie
In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the past. We use simple mathematical models to describe this process with the aim to better understand the emergence of an epidemic resulting from such a mutation and the extent of measures that are needed to control it. The feared outbreak of a human-human transmissible form of avian influenza leading to a global epidemic is the paradigm for this study. We extend the SIR approach to derive a deterministic and a stochastic formulation to describe the evolution of two classes of susceptible and infected states and a removed state, leading to a system of ordinary differential equations and a stochastic equivalent based on a Markov process...
August 27, 2018: 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...
September 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...
September 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...
September 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...
September 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...
September 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...
September 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...
September 2018: Theoretical Population Biology
Tanjona Ramiadantsoa, Ilkka Hanski, Otso Ovaskainen
Empirical studies have shown that, unlike species with specialized resource requirements, generalist species may benefit from habitat destruction. We use a family of models to probe the causes of the contrasting responses of these two types of species to habitat destruction. Our approach allows a number of mechanisms to be switched on and off, thereby making it possible to study their marginal and joint effects. Unlike many previous models, we do not assume any intrinsic competitive asymmetry between the species, and we assume pre-emptive rather than displacement competition...
August 16, 2018: Theoretical Population Biology
Raazesh Sainudiin, Amandine Véber
We develop a novel importance sampler to compute the full likelihood function of a demographic or structural scenario given the site frequency spectrum (SFS) at a locus free of intra-locus recombination. This sampler, instead of representing the hidden genealogy of a sample of individuals by a labelled binary tree, uses the minimal level of information about such a tree that is needed for the likelihood of the SFS and thus takes advantage of the huge reduction in the size of the state space that needs to be integrated...
July 23, 2018: Theoretical Population Biology
Simon Tavaré, Erkan Ozge Buzbas
No abstract text is available yet for this article.
July 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...
July 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)...
July 2018: Theoretical Population Biology
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