scholarly journals Population structure and coalescence in pedigrees: comparisons to the structured coalescent and a framework for inference

2016 ◽  
Author(s):  
Peter R. Wilton ◽  
Pierre Baduel ◽  
Matthieu M. Landon ◽  
John Wakeley
Keyword(s):  
Structured Populations ◽  
Mixture Of Distributions ◽  
Initial Sample ◽  
Migration Rates ◽  
Maximum Likelihood Approach ◽  
Structured Population ◽  
Recent Sample ◽  
Likelihood Approach ◽  
Structured Coalescent

AbstractContrary to what is often assumed in population genetics, independently segregating loci do not have completely independent ancestries, since all loci are inherited through a single, shared population pedigree. Previous work has shown that the non-independence between gene genealogies of independently segregating loci created by the population pedigree is weak in panmictic populations, and predictions made from standard coalescent theory are accurate for populations that are at least moderately sized. Here, we investigate patterns of coalescence in pedigrees of structured populations. We find that the pedigree creates deviations away from the predictions of the structured coalescent that persist on a longer timescale than in the case of panmictic populations. Nevertheless, we find that the structured coalescent provides a reasonable approximation for the coalescent process in structured population pedigrees so long as migration events are moderately frequent and there are no migration events in the recent pedigree of the sample. When there are migration events in the recent sample pedigree, we find that distributions of coalescence in the sample can be modeled as a mixture of distributions from different initial sample configurations. We use this observation to motivate a maximum-likelihood approach for inferring migration rates and mutation rates jointly with features of the pedigree such as recent migrant ancestry and recent relatedness. Using simulation, we show that our inference framework accurately recovers long-term migration rates in the presence of recent migration events in the sample pedigree.

scholarly journals An inclusive fitness analysis of synergistic interactions in structured populations

2012 ◽  
Vol 279 (1747) ◽  
pp. 4596-4603 ◽  
Author(s):  
Peter Taylor ◽  
Wes Maciejewski
Keyword(s):  
Frequency Dependence ◽  
Allele Frequency ◽  
Inclusive Fitness ◽  
Selective Advantage ◽  
Structured Populations ◽  
Weak Selection ◽  
Synergistic Interactions ◽  
Fitness Effects ◽  
Structured Population

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner's dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p . We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.

scholarly journals Evolutionary dynamics in structured populations under strong population genetic forces

2019 ◽  
Author(s):  
Alison F. Feder ◽  
Pleuni S. Pennings ◽  
Joachim Hermisson ◽  
Dmitri A. Petrov
Keyword(s):  
Population Differentiation ◽  
Evolutionary Dynamics ◽  
Structured Populations ◽  
Short Term ◽  
Migration Rates ◽  
Neutral Equilibrium ◽  
Demographic Processes ◽  
And Migration ◽  
Approximate Bayesian

AbstractHigh rates of migration between subpopulations result in little population differentiation in the long-term neutral equilibrium. However, in the short-term, even very abundant migration may not be enough for subpopulations to equilibrate immediately. In this study, we investigate dynamical patterns of short-term population differentiation in adapting populations via stochastic and analytical modeling through time. We characterize a regime in which selection and migration interact to create non-monotonic patterns of the population differentiation statistic FST when migration is weaker than selection, but stronger than drift. We demonstrate how these patterns can be leveraged to estimate high migration rates that would lead to panmixia in the long term equilibrium using an approximate Bayesian computation approach. We apply this approach to estimate fast migration in a rapidly adapting intra-host Simian-HIV population sampled from different anatomical locations. Notably, we find differences in estimated migration rates between different compartments, all above Nem = 1. This work demonstrates how studying demographic processes on the timescale of selective sweeps illuminates processes too fast to leave signatures on neutral timescales.

The structured coalescent process with weak migration

2001 ◽  
Vol 38 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Approximate Solutions ◽  
Coalescence Time ◽  
Migration Rates ◽  
Structured Population ◽  
Moment Generating Functions ◽  
Structured Coalescent ◽  
The Moment ◽  
Segregating Sites

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

scholarly journals The long-term exponentiated complementary exponential geometric distribution under a latent complementary causes framework

2014 ◽  
Vol 15 (1) ◽  
pp. 019 ◽  
Author(s):  
Francisco Louzada ◽  
Cintia Y. Yamachi ◽  
Vitor A. A. Marchi ◽  
Maria A. P. Franco
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Geometric Distribution ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Maximum Likelihood Approach ◽  
Rate Functions ◽  
Likelihood Approach ◽  
Mean Variance

<p><span>A new lifetime distribution which accommodates decreasing and unimodal hazard function is proposed in this paper. It is derived from the exponentiated complementary exponential geometric distribution and has it genesis on the compounding the exponential and geometric distributions. It can be used on a latent complementary causes scenario, where onle thethe minimum lifetime among all causes is observed. We derive the density, quantile, survival and failure rate functions for the proposed distribution, as well as some proprieties such as the characteristic function, mean, variance and r-th order statistics. The estimation is based on maximum likelihood approach. A simulation study performed in order to assess the performance of the maximum likelihood estimates of the parameters of the proposed distribution. The methodology is illustrated in three real datasets. </span></p>

scholarly journals Inferring time-dependent migration and coalescence patterns from genetic sequence and predictor data in structured populations

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Nicola F Müller ◽  
Gytis Dudas ◽  
Tanja Stadler
Keyword(s):  
Population Dynamics ◽  
Phylogenetic Trees ◽  
Sequence Data ◽  
Structured Populations ◽  
Model Parameters ◽  
Effective Population ◽  
Genetic Sequence ◽  
Migration Rates ◽  
Population Sizes ◽  
Structured Coalescent

Abstract Population dynamics can be inferred from genetic sequence data by using phylodynamic methods. These methods typically quantify the dynamics in unstructured populations or assume migration rates and effective population sizes to be constant through time in structured populations. When considering rates to vary through time in structured populations, the number of parameters to infer increases rapidly and the available data might not be sufficient to inform these. Additionally, it is often of interest to know what predicts these parameters rather than knowing the parameters themselves. Here, we introduce a method to  infer the predictors for time-varying migration rates and effective population sizes by using a generalized linear model (GLM) approach under the marginal approximation of the structured coalescent. Using simulations, we show that our approach is able to reliably infer the model parameters and its predictors from phylogenetic trees. Furthermore, when simulating trees under the structured coalescent, we show that our new approach outperforms the discrete trait GLM model. We then apply our framework to a previously described Ebola virus dataset, where we infer the parameters and its predictors from genome sequences while accounting for phylogenetic uncertainty. We infer weekly cases to be the strongest predictor for effective population size and geographic distance the strongest predictor for migration. This approach is implemented as part of the BEAST2 package MASCOT, which allows us to jointly infer population dynamics, i.e. the parameters and predictors, within structured populations, the phylogenetic tree, and evolutionary parameters.

scholarly journals Evolutionary Dynamics in Structured Populations Under Strong Population Genetic Forces

2019 ◽  
Vol 9 (10) ◽  
pp. 3395-3407 ◽  
Author(s):  
Alison F. Feder ◽  
Pleuni S. Pennings ◽  
Joachim Hermisson ◽  
Dmitri A. Petrov
Keyword(s):  
Population Differentiation ◽  
Evolutionary Dynamics ◽  
Structured Populations ◽  
Short Term ◽  
Migration Rates ◽  
Neutral Equilibrium ◽  
Demographic Processes ◽  
And Migration ◽  
Approximate Bayesian

In the long-term neutral equilibrium, high rates of migration between subpopulations result in little population differentiation. However, in the short-term, even very abundant migration may not be enough for subpopulations to equilibrate immediately. In this study, we investigate dynamical patterns of short-term population differentiation in adapting populations via stochastic and analytical modeling through time. We characterize a regime in which selection and migration interact to create non-monotonic patterns of population differentiation over time when migration is weaker than selection, but stronger than drift. We demonstrate how these patterns can be leveraged to estimate high migration rates using approximate Bayesian computation. We apply this approach to estimate fast migration in a rapidly adapting intra-host Simian-HIV population sampled from different anatomical locations. We find differences in estimated migration rates between different compartments, even though all are above Nem = 1. This work demonstrates how studying demographic processes on the timescale of selective sweeps illuminates processes too fast to leave signatures on neutral timescales.

The structured coalescent process with weak migration

2001 ◽  
Vol 38 (01) ◽  
pp. 1-17 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Approximate Solutions ◽  
Coalescence Time ◽  
Migration Rates ◽  
Structured Population ◽  
Moment Generating Functions ◽  
Structured Coalescent ◽  
The Moment ◽  
Segregating Sites

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

scholarly journals Asymmetric competition causes multimodal size distributions in spatially structured populations

2016 ◽  
Vol 283 (1823) ◽  
pp. 20152404 ◽  
Author(s):  
Jorge Velázquez ◽  
Robert B. Allen ◽  
David A. Coomes ◽  
Markus P. Eichhorn
Keyword(s):  
Resource Competition ◽  
Structured Populations ◽  
Necessary Condition ◽  
Small Scale ◽  
Asymmetric Competition ◽  
Size Distributions ◽  
Long Term Study ◽  
Multimodal Distributions ◽  
Using Data

Plant sizes within populations often exhibit multimodal distributions, even when all individuals are the same age and have experienced identical conditions. To establish the causes of this, we created an individual-based model simulating the growth of trees in a spatially explicit framework, which was parametrized using data from a long-term study of forest stands in New Zealand. First, we demonstrate that asymmetric resource competition is a necessary condition for the formation of multimodal size distributions within cohorts. By contrast, the legacy of small-scale clustering during recruitment is transient and quickly overwhelmed by density-dependent mortality. Complex multi-layered size distributions are generated when established individuals are restricted in the spatial domain within which they can capture resources. The number of modes reveals the effective number of direct competitors, while the separation and spread of modes are influenced by distances among established individuals. Asymmetric competition within local neighbourhoods can therefore generate a range of complex size distributions within even-aged cohorts.

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