scholarly journals On inferring evolutionary stability in finite populations using infinite population models

2021 ◽  
Vol 83 (2) ◽  
Author(s):  
Chai Molina ◽  
David J. D. Earn
Keyword(s):  
Population Size ◽  
Selection Process ◽  
Sufficient Conditions ◽  
Population Models ◽  
Finite Populations ◽  
Phenotypic Effect ◽  
Infinite Population ◽  
Rare Mutations ◽  
Large Populations ◽  
Evolution By Natural Selection

AbstractModels of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations that are selected against always go extinct, whereas in finite populations they can persist and even reach fixation. Nevertheless, for mutations of arbitrarily small phenotypic effect, it is widely believed that in sufficiently large populations, if selection opposes the invasion of rare mutants, then it also opposes their fixation. Here, we identify circumstances under which infinite-population models do or do not accurately predict evolutionary outcomes in large, finite populations. We show that there is no population size above which considering only invasion generally suffices: for any finite population size, there are situations in which selection opposes the invasion of mutations of arbitrarily small effect, but favours their fixation. This is not an unlikely limiting case; it can occur when fitness is a smooth function of the evolving trait, and when the selection process is biologically sensible. Nevertheless, there are circumstances under which opposition of invasion does imply opposition of fixation: in fact, for the $$n$$ n -player snowdrift game (a common model of cooperation) we identify sufficient conditions under which selection against rare mutants of small effect precludes their fixation—in sufficiently large populations—for any selection process. We also find conditions under which—no matter how large the population—the trait that fixes depends on the selection process, which is important because any particular selection process is only an approximation of reality.

scholarly journals Selection may oppose invasion, yet favour fixation: consequences for evolutionary stability

2019 ◽  
Author(s):  
Chai Molina ◽  
David J. D. Earn
Keyword(s):  
Population Size ◽  
Selection Process ◽  
Sufficient Conditions ◽  
Finite Populations ◽  
Phenotypic Effect ◽  
Infinite Population ◽  
Rare Mutations ◽  
Large Populations ◽  
Evolution By Natural Selection ◽  
Limiting Case

AbstractModels of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations that are selected against always go extinct, whereas in finite populations they can persist and even reach fixation. Nevertheless, for mutations of small phenotypic effect, it is widely believed that in sufficiently large populations, if selection opposes the invasion of rare mutants, then it also opposes their fixation. Here, we identify circumstances under which infinite-population models do or do not accurately predict evolutionary outcomes in large, finite populations. We show that there is no population size above which considering only invasion generally suffices: for any finite population size, there are situations in which selection opposes the invasion of mutations of arbitrarily small effect, but favours their fixation. This is not an unlikely limiting case; it can occur when fitness is a smooth function of the evolving trait, and when the selection process is biologically sensible. Nevertheless, there are circumstances under which opposition of invasion does imply opposition of fixation: in fact, for the n-player snowdrift game (a common model of cooperation) we identify sufficient conditions under which selection against rare mutants of small effect precludes their fixation—in sufficiently large populations—for any selection process. We also find conditions under which—no matter how large the population—the trait that fixes depends on the selection process, which is important because any particular selection process is only an approximation of reality.

scholarly journals A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems

2020 ◽  
Vol 28 (1) ◽  
pp. 55-85
Author(s):  
Bo Song ◽  
Victor O.K. Li
Keyword(s):  
Population Dynamics ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Analytical Framework ◽  
Population Models ◽  
Initial Population ◽  
Infinite Population ◽  
Continuous Optimization Problems

Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models are derived from Markov chains by exploiting symmetries between individuals in the population and analyzing the limit as the population size goes to infinity. In this article, we study the theoretical foundations of infinite population models of evolutionary algorithms on continuous optimization problems. First, we show that the convergence proofs in a widely cited study were in fact problematic and incomplete. We further show that the modeling assumption of exchangeability of individuals cannot yield the transition equation. Then, in order to analyze infinite population models, we build an analytical framework based on convergence in distribution of random elements which take values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It also provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Finally, we use the framework to prove the convergence of infinite population models for the mutation operator and the [Formula: see text]-ary recombination operator. We show that these operators can provide accurate predictions for real population dynamics as the population size goes to infinity, provided that the initial population is identically and independently distributed.

scholarly journals Distribution of linkage disequilibrium with selection and finite population size

1979 ◽  
Vol 33 (1) ◽  
pp. 29-48 ◽  
Author(s):  
P. J. Avery ◽  
W. G. Hill
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Large Expansion ◽  
Large Populations ◽  
The Difference ◽  
Successive Generations ◽  
Stable Points

SUMMARYThe effects of finite population size, occurring either as a bottleneck in a single generation followed by a large expansion or in all generations, are considered for models of two linked heterotic loci. Linkage is assumed to be tight because it is required if there is to be stable linkage disequilibrium, D ǂ 0, in infinitely large populations. (D is the difference between gamete frequencies and the product of the gene frequencies.)If a substantial perturbation of frequencies occurs as a result of a bottleneck but the population is subsequently very large, D may take hundreds of generations to return to its stable point. In finite populations, the distribution of D can be ⋃-shaped, unimodal or bimodal. The correlation of D in successive generations is higher with tight linkage and is little affected by selection or the size of the population.The utility of infinite population studies of linkage disequilibrium and its stable points is questioned, and considerable pessimism is expressed about the possibilities of distinguishing selection and sampling effects at linked loci.

scholarly journals Likelihoods and Simulation Methods for a Class of Nonneutral Population Genetics Models

Genetics ◽  
2001 ◽  
Vol 159 (2) ◽  
pp. 853-867 ◽  
Author(s):  
Peter Donnelly ◽  
Magnus Nordborg ◽  
Paul Joyce
Keyword(s):  
Population Genetics ◽  
Population Size ◽  
Mutant Allele ◽  
Mutation Rates ◽  
Simulation Methods ◽  
Large Populations ◽  
Selection Intensities ◽  
Infinite Alleles Model

Abstract Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.

scholarly journals A networked voting rule for democratic representation

2018 ◽  
Vol 5 (3) ◽  
pp. 172265 ◽  
Author(s):  
Alexis R. Hernández ◽  
Carlos Gracia-Lázaro ◽  
Edgardo Brigatti ◽  
Yamir Moreno
Keyword(s):  
Large Scale ◽  
Selection Process ◽  
General Relation ◽  
Community Size ◽  
Rule Based ◽  
Voting Rule ◽  
Large Populations ◽  
Negative Effect ◽  
High Connectivity ◽  
Better Than

We introduce a general framework for exploring the problem of selecting a committee of representatives with the aim of studying a networked voting rule based on a decentralized large-scale platform, which can assure a strong accountability of the elected. The results of our simulations suggest that this algorithm-based approach is able to obtain a high representativeness for relatively small committees, performing even better than a classical voting rule based on a closed list of candidates. We show that a general relation between committee size and representatives exists in the form of an inverse square root law and that the normalized committee size approximately scales with the inverse of the community size, allowing the scalability to very large populations. These findings are not strongly influenced by the different networks used to describe the individuals’ interactions, except for the presence of few individuals with very high connectivity which can have a marginal negative effect in the committee selection process.

Adjustment of fecundity and sex ratio in response to social environments in a haplodiploid mite

2022 ◽  
Author(s):  
Nuwan Weerawansha ◽  
Qiao Wang ◽  
Xiong Zhao He
Keyword(s):  
Population Density ◽  
Sex Ratio ◽  
Population Size ◽  
Local Population ◽  
Female Offspring ◽  
Social Environments ◽  
Positive Interaction ◽  
Offspring Sex Ratio ◽  
Offspring Sex ◽  
Large Populations

Animals can adjust reproductive strategies in favour of corporation or competition in response to local population size and density, the two key factors of social environments. However, previous studies usually focus on either population size or density but ignore their interactions. Using a haplodiploid spider mite, Tetranychus ludeni Zacher, we carried out a factorial experiment in the laboratory to examine how ovipositing females adjust their fecundity and offspring sex ratio during their early reproductive life under various population size and density. We reveal that females laid significantly more eggs with increasing population size and significantly fewer eggs with increasing population density. This suggests that large populations favour cooperation between individuals and dense populations increase competition. We demonstrate a significant negative interaction of population size and density that resulted in significantly fewer eggs laid in the large and dense populations. Furthermore, we show that females significantly skewed the offspring sex ratio towards female-biased in small populations to reduce the local mate competition among their sons. However, population density incurred no significant impact on offspring sex ratio, while the significant positive interaction of population size and density significantly increased the proportion of female offspring in the large and dense populations, which will minimise food or space competition as females usually disperse after mating at crowded conditions. These results also suggest that population density affecting sex allocation in T. ludeni is intercorrelated with population size. This study provides evidence that animals can manipulate their reproductive output and adjust offspring sex ratio in response to various social environments, and the interactions of different socio-environmental factors may play significant roles.

The Wright–Fisher model with varying selection

1986 ◽  
Vol 23 (02) ◽  
pp. 504-508
Author(s):  
N. C. Weber
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Sufficient Conditions ◽  
Selective Advantage ◽  
Fisher Model ◽  
Ultimate Homozygosity ◽  
Varying Population

The Wright–Fisher model with varying population size is examined in the case where the selective advantage varies from generation to generation. Models are considered where the selective advantage is not always in favour of a particular genotype. Sufficient conditions in terms of the selection coefficients and the population growth are given to ensure ultimate homozygosity.

Linkage disequilibrium between neutral genes in finite populations

1974 ◽  
Vol 6 (01) ◽  
pp. 13-15
Author(s):  
William G. Hill
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linkage Disequilibrium ◽  
Finite Populations ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Asymptotic Values

There is now a large literature on linkage disequilibrium between pairs of loci, both for selection in infinite populations and for neutral genes in finite populations, but there have been few studies with more loci. Bennett (1954) showed how the frequencies of chromosomes with any number of neutral genes would change in an infinite population, and the author (unpublished) has extended Bennett's results to find expected changes in chromosome frequencies with up to six loci in finite populations. For two linked neutral genes in finite populations the expected disequilibrium is zero, but the variance of the disequilibrium or the correlation of gene frequencies in segregating populations has been found. This has been done by Monte Carlo simulation (Hill and Robertson (1968)), but an approximation can be obtained by diffusion methods (Ohta and Kimura (1969)) and the asymptotic values using inbreeding theory (Sved (1971)). In this note we discuss the case of disequilibrium between three neutral loci and show how it relates to that between two loci.

scholarly journals Population size, habitat fragmentation, and the nature of adaptive variation in a stream fish

2014 ◽  
Vol 281 (1790) ◽  
pp. 20140370 ◽  
Author(s):  
Dylan J. Fraser ◽  
Paul V. Debes ◽  
Louis Bernatchez ◽  
Jeffrey A. Hutchings
Keyword(s):  
Genetic Variation ◽  
Habitat Fragmentation ◽  
Population Size ◽  
Brook Trout ◽  
Small Populations ◽  
Adaptive Genetic Variation ◽  
Genetic Population ◽  
Fragmented Populations ◽  
Large Populations ◽  
Adaptive Differentiation

Whether and how habitat fragmentation and population size jointly affect adaptive genetic variation and adaptive population differentiation are largely unexplored. Owing to pronounced genetic drift, small, fragmented populations are thought to exhibit reduced adaptive genetic variation relative to large populations. Yet fragmentation is known to increase variability within and among habitats as population size decreases. Such variability might instead favour the maintenance of adaptive polymorphisms and/or generate more variability in adaptive differentiation at smaller population size. We investigated these alternative hypotheses by analysing coding-gene, single-nucleotide polymorphisms associated with different biological functions in fragmented brook trout populations of variable sizes. Putative adaptive differentiation was greater between small and large populations or among small populations than among large populations. These trends were stronger for genetic population size measures than demographic ones and were present despite pronounced drift in small populations. Our results suggest that fragmentation affects natural selection and that the changes elicited in the adaptive genetic composition and differentiation of fragmented populations vary with population size. By generating more variable evolutionary responses, the alteration of selective pressures during habitat fragmentation may affect future population persistence independently of, and perhaps long before, the effects of demographic and genetic stochasticity are manifest.

Asymptotic behavior of near-critical multitype branching processes

1991 ◽  
Vol 28 (03) ◽  
pp. 512-519 ◽  
Author(s):  
Fima C. Klebaner
Keyword(s):  
Asymptotic Behavior ◽  
Population Size ◽  
Discrete Time ◽  
Growth Rates ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Limiting Distribution ◽  
Size Dependent ◽  
Generalized Gamma ◽  
Multitype Branching Processes

Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.

Sign in / Sign up

Export Citation Format

Share Document