scholarly journals Genetic load in subdivided populations: interactions between the migration rate, the size and the number of subpopulations

Heredity ◽  
2005 ◽  
Vol 96 (1) ◽  
pp. 69-78 ◽  
Author(s):  
K Theodorou ◽  
D Couvet
Keyword(s):  
Migration Rate ◽  
Genetic Load ◽  
Subdivided Populations

scholarly journals Inbreeding coefficients and coalescence times

1991 ◽  
Vol 58 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Montgomery Slatkin
Keyword(s):  
Migration Rate ◽  
Sequence Data ◽  
Island Model ◽  
Dna Sequence Data ◽  
Local Populations ◽  
Inbreeding Coefficients ◽  
Subdivided Populations ◽  
Stepping Stone Models ◽  
The Relationship ◽  
Coalescence Times

SummaryThis paper describes the relationship between probabilities of identity by descent and the distribution of coalescence times. By using the relationship between coalescence times and identity probabilities, it is possible to extend existing results for inbreeding coefficients in regular systems of mating to find the distribution of coalescence times and the mean coalescence times. It is also possible to express Sewall Wright's FST as the ratio of average coalescence times of different pairs of genes. That simplifies the analysis of models of subdivided populations because the average coalescence time can be found by computing separately the time it takes for two genes to enter a single subpopulation and time it takes for two genes in the same subpopulation to coalesce. The first time depends only on the migration matrix and the second time depends only on the total number of individuals in the population. This approach is used to find FST in the finite island model and in one- and two-dimensional stepping-stone models. It is also used to find the rate of approach of FST to its equilibrium value. These results are discussed in terms of different measures of genetic distance. It is proposed that, for the purposes of describing the amount of gene flow among local populations, the effective migration rate between pairs of local populations, M^, which is the migration rate that would be estimated for those two populations if they were actually in an island model, provides a simple and useful measure of genetic similarity that can be defined for either allozyme or DNA sequence data.

scholarly journals Decay of linkage disequilibrium in a finite island model

1994 ◽  
Vol 64 (2) ◽  
pp. 137-144 ◽  
Author(s):  
Hidenori Tachida
Keyword(s):  
Linkage Disequilibrium ◽  
Migration Rate ◽  
Natural Populations ◽  
Decay Rates ◽  
Island Model ◽  
The Past ◽  
Linkage Disequilibria ◽  
Subdivided Populations ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

SummaryTime-dependent behaviour of linkage disequilibrium when there was initial linkage disequilibrium is studied in a finite island model assuming neutrality. Explicit expressions for linkage disequilibrium parameters are obtained. From these expressions, the initial and the ultimate decay rates of linkage disequilibrium parameters are found to be increased and decreased, respectively, by finiteness of the population when recombination rate, migration rate and inverse of subpopulation size are of comparable order. Thus, linkage disequilibrium created in the past may persist longerin smaller subdivided populations. Also, differentiation of the gametic parameter of linkage disequilibrium among subpopulations is found to diminish quickly compared tothe linkage disequilibrium in the whole population. Implications of these results for the interpretation of linkage disequilibria in natural populations are discussed.

Coalescence times and F ST values in subdivided populations with symmetric structure

2003 ◽  
Vol 35 (03) ◽  
pp. 665-690
Author(s):  
Hilde M. Wilkinson-Herbots
Keyword(s):  
Migration Rate ◽  
Recent Common Ancestor ◽  
Regularity Conditions ◽  
Simple Relationship ◽  
Total Size ◽  
Graph Theoretic ◽  
Most Recent Common Ancestor ◽  
Subdivided Populations ◽  
Structured Coalescent ◽  
Infinite Alleles Model

The structured coalescent is a continuous-time Markov chain which describes the genealogy of a sample of homologous genes from a subdivided population. Assuming this model, some results are proved relating to the genealogy of a pair of genes and the extent of subpopulation differentiation, which are valid under certain graph-theoretic symmetry and regularity conditions on the structure of the population. We first review and extend earlier results stating conditions under which the mean time since the most recent common ancestor of a pair of genes from any single subpopulation is independent of the migration rate and equal to that of two genes from an unstructured population of the same total size. Assuming the infinite alleles model of neutral mutation with a small mutation rate, we then prove a simple relationship between the migration rate and the value of Wright's coefficient F ST for a pair of neighbouring subpopulations, which does not depend on the precise structure of the population provided that this is sufficiently symmetric.

Coalescence times and FST values in subdivided populations with symmetric structure

2003 ◽  
Vol 35 (3) ◽  
pp. 665-690 ◽  
Author(s):  
Hilde M. Wilkinson-Herbots
Keyword(s):  
Migration Rate ◽  
Recent Common Ancestor ◽  
Regularity Conditions ◽  
Simple Relationship ◽  
Total Size ◽  
Graph Theoretic ◽  
Most Recent Common Ancestor ◽  
Subdivided Populations ◽  
Structured Coalescent ◽  
Infinite Alleles Model

The structured coalescent is a continuous-time Markov chain which describes the genealogy of a sample of homologous genes from a subdivided population. Assuming this model, some results are proved relating to the genealogy of a pair of genes and the extent of subpopulation differentiation, which are valid under certain graph-theoretic symmetry and regularity conditions on the structure of the population. We first review and extend earlier results stating conditions under which the mean time since the most recent common ancestor of a pair of genes from any single subpopulation is independent of the migration rate and equal to that of two genes from an unstructured population of the same total size. Assuming the infinite alleles model of neutral mutation with a small mutation rate, we then prove a simple relationship between the migration rate and the value of Wright's coefficient FST for a pair of neighbouring subpopulations, which does not depend on the precise structure of the population provided that this is sufficiently symmetric.

scholarly journals Mutational load, inbreeding depression and heterosis in subdivided populations

2018 ◽  
Author(s):  
Brian Charlesworth
Keyword(s):  
Population Size ◽  
Inbreeding Depression ◽  
Population Genomics ◽  
Local Population ◽  
Genetic Load ◽  
Mutation Rates ◽  
Weak Selection ◽  
Empirical Estimates ◽  
Numerical Predictions ◽  
Subdivided Populations

AbstractThis paper examines the extent to which empirical estimates of inbreeding depression and inter-population heterosis in subdivided populations, as well as the effects of local population size on mean fitness, can be explained in terms of estimates of mutation rates, and the distribution of selection coefficients against deleterious mutations provided by population genomics data. Using results from population genetics models, numerical predictions of the genetic load, inbreeding depression and heterosis were obtained for a broad range of selection coefficients and mutation rates. The models allowed for the possibility of very high mutation rates per nucleotide site, as is sometimes observed for epiallelic mutations. There was fairly good quantitative agreement between the theoretical predictions and empirical estimates of heterosis and the effects of population size on genetic load, on the assumption that the deleterious mutation rate per individual per generation is approximately one, but there was less good agreement for inbreeding depression. Weak selection, of the order of magnitude suggested by population genomic analyses, is required to explain the observed patterns. Possible caveats concerning the applicability of the models are discussed.

scholarly journals LINKAGE DISEQUILIBRIUM IN SUBDIVIDED POPULATIONS

Genetics ◽  
1973 ◽  
Vol 75 (1) ◽  
pp. 213-219
Author(s):  
Masatoshi Nei ◽  
Wen-Hsiung Li
Keyword(s):  
Linkage Disequilibrium ◽  
Migration Rate ◽  
Random Mating ◽  
Isolated Populations ◽  
Gene Frequencies ◽  
Average Linkage ◽  
Subdivided Population ◽  
Overdominant Selection ◽  
Subdivided Populations ◽  
Recombination Value

ABSTRACT The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m  1 + m  2) - (m  1 + m  2)2, whichever is smaller, where r is the recombination value and m  1 and m  2 are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.

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