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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
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...
April 26, 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
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...
April 12, 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...
April 8, 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...
April 5, 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
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...
March 27, 2018: Theoretical Population Biology
Jake M Ferguson, Erkan Ozge Buzbas
The distribution of allele frequencies obtained from diffusion approximations to Wright-Fisher models are 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
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
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
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
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...
March 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...
March 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 types 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...
March 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...
March 2018: Theoretical Population Biology
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