Genetic drift with polygamy and arbitrary offspring distribution

1974 ◽  
Vol 6 (1) ◽  
pp. 3-4
Author(s):  
C. Cannings
Keyword(s):  
Simple Model ◽  
Genetic Drift ◽  
Overlapping Generations ◽  
Fixed Size ◽  
Diploid Population ◽  
Offspring Distribution

Wright (1931) introduced a simple model for a bisexual, diploid population of fixed size and with non-overlapping generations. With N1 males and N2 females, the rate of drift was λ0 = 1 – (N/8N1N2) where N = N1 + N2.

Genetic drift with polygamy and arbitrary offspring distribution

1974 ◽  
Vol 6 (01) ◽  
pp. 3-4
Author(s):  
C. Cannings
Keyword(s):  
Simple Model ◽  
Genetic Drift ◽  
Overlapping Generations ◽  
Fixed Size ◽  
Diploid Population ◽  
Offspring Distribution

Wright (1931) introduced a simple model for a bisexual, diploid population of fixed size and with non-overlapping generations. WithN1males andN2females, the rate of drift wasλ0= 1 – (N/8N1N2) whereN=N1+N2.

Genetic drift with polygamy and arbitrary offspring distribution

1974 ◽  
Vol 11 (04) ◽  
pp. 633-641
Author(s):  
C. Cannings
Keyword(s):  
Genetic Drift ◽  
Mating Systems ◽  
Random Mating ◽  
Female Offspring ◽  
Autosomal Locus ◽  
Fixed Size ◽  
Expected Number ◽  
Diploid Population ◽  
Male And Female ◽  
Sib Mating

The rate of genetic drift at an autosomal locus for a bisexual, diploid population of fixed size is studied. The generations are non-overlapping. The model encompasses a variety of mating systems, including random monogamy, random polygamy in one sex and random mating. The rate of drift is shown for several models to depend on the expected number of parents that two randomly selected individuals have in common. The male and female offspring are assigned to families in a fairly general way, which permits the study of a model in which each family has offspring of one sex only. The equation arising in this last case is identical to one of Jacquard for a system in which sib-mating is excluded.

Genetic drift with polygamy and arbitrary offspring distribution

1974 ◽  
Vol 11 (4) ◽  
pp. 633-641 ◽  
Author(s):  
C. Cannings
Keyword(s):  
Genetic Drift ◽  
Mating Systems ◽  
Random Mating ◽  
Female Offspring ◽  
Autosomal Locus ◽  
Fixed Size ◽  
Expected Number ◽  
Diploid Population ◽  
Male And Female ◽  
Sib Mating

The rate of genetic drift at an autosomal locus for a bisexual, diploid population of fixed size is studied. The generations are non-overlapping. The model encompasses a variety of mating systems, including random monogamy, random polygamy in one sex and random mating. The rate of drift is shown for several models to depend on the expected number of parents that two randomly selected individuals have in common. The male and female offspring are assigned to families in a fairly general way, which permits the study of a model in which each family has offspring of one sex only. The equation arising in this last case is identical to one of Jacquard for a system in which sib-mating is excluded.

The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models

1974 ◽  
Vol 6 (2) ◽  
pp. 260-290 ◽  
Author(s):  
C. Cannings
Keyword(s):  
Markov Chains ◽  
Genetic Drift ◽  
Overlapping Generations ◽  
Branching Processes ◽  
Multiple Alleles ◽  
New Approach ◽  
Constant Size ◽  
Latent Roots

Haploid models of genetic drift in populations of constant size are considered. Generalizations of the models of Moran and Wright have been developed by Karlin and McGregor (for multiple alleles and non-overlapping generations), by Chia and Watterson (for two alleles and overlapping or non-overlapping generations) and by Chia (for multiple alleles and overlapping or non-overlapping generations), using conditioned branching processes. A new approach is developed which contains the models mentioned above and provides simpler expressions for the latent roots. A greater dependence between the birth events and death events can be permitted, and non-independent mutations treated.

The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models

1974 ◽  
Vol 6 (02) ◽  
pp. 260-290 ◽  
Author(s):  
C. Cannings
Keyword(s):  
Markov Chains ◽  
Genetic Drift ◽  
Overlapping Generations ◽  
Branching Processes ◽  
Multiple Alleles ◽  
New Approach ◽  
Constant Size ◽  
Latent Roots

Haploid models of genetic drift in populations of constant size are considered. Generalizations of the models of Moran and Wright have been developed by Karlin and McGregor (for multiple alleles and non-overlapping generations), by Chia and Watterson (for two alleles and overlapping or non-overlapping generations) and by Chia (for multiple alleles and overlapping or non-overlapping generations), using conditioned branching processes. A new approach is developed which contains the models mentioned above and provides simpler expressions for the latent roots. A greater dependence between the birth events and death events can be permitted, and non-independent mutations treated.

The Hardy-Weinberg law with overlapping generations

1974 ◽  
Vol 6 (1) ◽  
pp. 4-6 ◽  
Author(s):  
Brian Charlesworth
Keyword(s):  
Population Genetics ◽  
Genetic Drift ◽  
Age Structure ◽  
Continuous Time ◽  
Arbitrary Number ◽  
Overlapping Generations ◽  
Birth Rate ◽  
Allele Frequencies ◽  
Autosomal Locus ◽  
Weak Ergodicity

The Hardy-Weinberg law is generally regarded as one of the most important results of population genetics. It was originally proved for the case of populations with distinct generations (Hardy (1908), Weinberg (1908)); a general proof for populations with overlapping generations has apparently not been given before. The case of a single autosomal locus with an arbitrary number of alleles is considered here. Births and deaths are assumed to occur in continuous time. The weak ergodicity property of the birth rate and age structure of such a population, first derived by Norton (1928), is used to establish the fact that allele frequencies tend to constant limits in the absence of mutation, migration, selection and genetic drift.

On the offspring number distribution in a genetic population

1966 ◽  
Vol 3 (1) ◽  
pp. 129-141 ◽  
Author(s):  
M. W. Feldman
Keyword(s):  
Overlapping Generations ◽  
Random Mating ◽  
Diploid Population ◽  
Genetic Population ◽  
Offspring Number ◽  
Number Distribution

We consider a dioecious diploid population of N individuals, N1 males and N2 = N – N1 females. The alleles will be represented by a and A, and the population reproduces according to the Wright scheme, that is, by random mating with non-overlapping generations.

scholarly journals Exploring the causes of small effective population sizes in cyst nematodes using artificial Globodera pallida populations

2019 ◽  
Vol 286 (1894) ◽  
pp. 20182359 ◽  
Author(s):  
Josselin Montarry ◽  
Sylvie Bardou-Valette ◽  
Romain Mabon ◽  
Pierre-Loup Jan ◽  
Sylvain Fournet ◽  
...  
Keyword(s):  
Genetic Drift ◽  
Overlapping Generations ◽  
Temporal Analysis ◽  
Globodera Pallida ◽  
Effective Population ◽  
Cyst Nematodes ◽  
The Real ◽  
Real Population ◽  
Population Sizes ◽  
The Ideal

The effective size of a population is the size of an ideal population which would undergo genetic drift at the same rate as the real population. The balance between selection and genetic drift depends on the effective population size ( N e ), rather than the real numbers of individuals in the population ( N ). The objectives of the present study were to estimate N e in the potato cyst nematode Globodera pallida and to explore the causes of a low N e / N ratio in cyst nematodes using artificial populations. Using a temporal analysis of 24 independent populations, the median N e was 58 individuals (min N e = 25 and max N e = 228). N e is commonly lower than N but in the case of cyst nematodes, the N e / N ratio was extremely low. Using artificial populations showed that this low ratio did not result from migration, selection and overlapping generations, but could be explain by the fact that G. pallida populations deviate in structure from the assumptions of the ideal population by having unequal sex ratios, high levels of inbreeding and a high variance in family sizes. The consequences of a low N e , resulting in a strong intensity of genetic drift, could be important for their control because G. pallida populations will have a low capacity to adapt to changing environments.

On the offspring number distribution in a genetic population

1966 ◽  
Vol 3 (01) ◽  
pp. 129-141 ◽  
Author(s):  
M. W. Feldman
Keyword(s):  
Overlapping Generations ◽  
Random Mating ◽  
Diploid Population ◽  
Genetic Population ◽  
Offspring Number ◽  
Number Distribution

We consider a dioecious diploid population ofNindividuals,N1males andN2=N–N1females. The alleles will be represented byaandA, and the population reproduces according to the Wright scheme, that is, by random mating with non-overlapping generations.

A Simple Model of Linkage Disequilibrium and Genetic Drift in Human Genomic SNPs: Importance of Demography and SNP Age

2005 ◽  
Vol 60 (4) ◽  
pp. 181-195 ◽  
Author(s):  
Joanna Polanska ◽  
Marek Kimmel
Keyword(s):  
Linkage Disequilibrium ◽  
Simple Model ◽  
Genetic Drift ◽  
Human Genomic
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