Generalized population models and the nature of genetic drift

Der, Ricky; Epstein, Charles L.; Plotkin, Joshua B.

doi:10.1016/j.tpb.2011.06.004

Cited by 83 publications

(112 citation statements)

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“…As described in Der et al (2011), it is possible to define a significantly larger natural class of discrete population processes (those whose first two conditional moments coincide with that of the Wright-Fisher process), and derive their continuum limits, without restrictions on the offspring distribution P U . This class of discrete processes contains the Cannings processes and the Eldon-Wakeley processes discussed above as special cases.…”

Section: Continuum Approximations Of Population Models With Reproductmentioning

confidence: 99%

“…In fact, it can be shown that the relationship between the space-scaling b N and time-scaling c N is fixed, in the sense that no other relationship leads to nontrivial limiting processes. We wish to study allele frequencies and hence impose the natural scaling b N = N. The general theory (Der et al 2011;Möhle 2001) then indicates that the timescaling must be proportional towhere s 2 N is the offspring variance of the discrete-time process (2).Once a time-scaling is fixed, then so is the appropriate scaling regime for the mutation rates, to produce a nontrivial balance of mutation and drift. This scaling must satisfy…”

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The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

Der

Plotkin

2014

Genetics

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We study the population genetics of two neutral alleles under reversible mutation in a model that features a skewed offspring distribution, called the L-Fleming-Viot process. We describe the shape of the equilibrium allele frequency distribution as a function of the model parameters. We show that the mutation rates can be uniquely identified from this equilibrium distribution, but the form of the offspring distribution cannot itself always be so identified. We introduce an estimator for the mutation rate that is consistent, independent of the form of reproductive skew. We also introduce a two-allele infinite-sites version of the L-Fleming-Viot process, and we use it to study how reproductive skew influences standing genetic diversity in a population. We derive asymptotic formulas for the expected number of segregating sites as a function of sample size and offspring distribution. We find that the WrightFisher model minimizes the equilibrium genetic diversity, for a given mutation rate and variance effective population size, compared to all other L-processes. MANY questions in population genetics concern the role of demographic stochasticity and its interaction with mutation and selection in determining the fates of allelic types. The foundational work of Fisher, Wright, Haldane, Kimura (Wright 1931;Haldane 1932;Fisher 1958;Kimura 1994), and others has been instrumental in shaping our intuition about the powerful role that genetic drift plays in evolution and especially its role in maintaining diversity. This classical theory, which views genetic drift as a strong force, emanates from the Wright-Fisher model of replication and its large-population limit, the Kimura diffusion (Kimura 1955). The diffusion approximation has been particularly well studied, not only because it is mathematically tractable, but also because it is robust to variation in many of the underlying model details. Many discrete population-genetic models, including a large number of Karlin-Taylor and Cannings processes (Karlin and McGregor 1964;Cannings 1974;Ewens 2004), share the same diffusion limit as the Wright-Fisher model, and they therefore exhibit qualitatively similar behavior.Nevertheless, Kimura's classical diffusion is not appropriate in every circumstance. Its central assumption is the absence of skew in the reproduction process-that is, the assumption that no single individual can contribute a sizable proportion to the composition of the population in a single generation. Recent studies have suggested that this assumption is violated in several species, especially in marine taxa but also including many types of plants (Beckenbach 1994;Hedgecock 1994), whose mode of reproduction involves a heavy-tailed offspring distribution.While the number of empirical studies on heavy-tailed offspring distributions is limited, there is a rich mathematical theory to describe the dynamics of populations with heavy reproductive skew. Beginning with Cannings' (1974) paper on neutral exchangeable reproduction processes, this literature has le...

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Section: Continuum Approximations Of Population Models With Reproductmentioning

confidence: 99%

mentioning

confidence: 99%

The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

Der

Plotkin

2014

Genetics

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“…Note also that the strong efficacy of selection under MMC models (see above, Der et al 2011) (Stukenbrock et al 2011(Stukenbrock et al , 2012Brunner et al 2013) and other species (Wicker et al 2013). The proportion of the genome which is affected by genetic draft due to selection (Neher & Hallatschek 2013;, and thus the extent of linkage disequilibrium (Eldon & Wakeley 2008;Birkner et al 2012), will depend on the frequency of recombination in a given parasite species .…”

Section: Selective Mechanisms: Parasitic Life Cycle and Fast Adaptationmentioning

confidence: 99%

“…The frequencies of a and A are then given by binomial sampling at every generation. Such a case represents an upper limit to the strength and occurrence of drift (Der et al 2011). In a model where both alleles a and A are neutral and their frequencies are only driven by drift, MMC models generate long period of frequency stasis (unchanged values) only interrupted by multiple merger events.…”

Section: Effect On Genetic Drift and Linkage Disequilibriummentioning

confidence: 99%

“…In a model where both alleles a and A are neutral and their frequencies are only driven by drift, MMC models generate long period of frequency stasis (unchanged values) only interrupted by multiple merger events. The fixation probability of a new allele is unchanged in MMC models compared to a WrightFisher model and is equal to its initial frequency (namely 1/2N; Der et al 2011). However the time to fixation of a mutant allele entering the population at frequency 1/2N decreases from 2N in the WrightFisher model to N×log (N) in MMC models.…”

Section: Effect On Genetic Drift and Linkage Disequilibriummentioning

confidence: 99%

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Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Tellier

Lemaire

2014

Preprint

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Population genetics theory has laid the foundations for genomics analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species. Identifying SNPs under natural selection and underpinning species adaptation relies on disentangling the respective contribution of random processes (mutation, drift, migration) from that of selection on nucleotide variability. Most theory and statistical tests have been developed using the Kingman's coalescent theory based on the Wright-Fisher population model. However, these theoretical models rely on biological and life-history assumptions which may be violated in many prokaryote, fungal, animal or plant species. Recent theoretical developments of the so called multiple merger coalescent models are reviewed here (Λ-coalescent, beta-coalescent, Bolthausen-Snitzman, Ξ-coalescent). We explicit how these new models take into account various pervasive ecological and biological characteristics, life history traits or life cycles which were not accounted in previous theories such as 1) the skew in offspring production typical of marine species, 2) fast adapting microparasites (virus, bacteria and fungi) exhibiting large variation in population sizes during epidemics, 3) the peculiar life cycles of fungi and bacteria alternating sexual and asexual cycles, and 4) the high rates of extinction-recolonization in spatially structured populations. We finally discuss the relevance of multiple merger models for the detection of SNPs under selection in these species, for population genomics of very large sample size and advocate to potentially examine the conclusion of previous population genetics studies.

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Rethinking Hardy–Weinberg and genetic drift in undergraduate biology

Masel

2012

BioEssays

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Population genetics is often taught in introductory biology classes, starting with the Hardy-Weinberg principle (HWP) and genetic drift. Here I argue that teaching these two topics first aligns neither with current expert knowledge, nor with good pedagogy. Student difficulties with mathematics in general, and probability in particular, make population genetics difficult to teach and learn. I recommend an alternative, historically inspired ordering of population genetics topics, based on progressively increasing mathematical difficulty. This progression can facilitate just-in-time math instruction. This alternative ordering includes, but does not privilege, the HWP and genetic drift. Stochastic events whose consequences are felt within a single generation, and the deterministic accumulation of the effects of selection across multiple generations, are both taught before tackling the stochastic accumulation of the effects of accidents of sampling.

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Generalized population models and the nature of genetic drift

Cited by 83 publications

References 43 publications

The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Rethinking Hardy–Weinberg and genetic drift in undergraduate biology

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