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.

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.

scholarly journals Predicting Rates of Inbreeding in Populations Undergoing Selection

Genetics ◽  
2000 ◽  
Vol 154 (4) ◽  
pp. 1851-1864 ◽  
Author(s):  
John A Woolliams ◽  
Piter Bijma
Keyword(s):  
Overlapping Generations ◽  
Linear Models ◽  
Selection Process ◽  
Correction Term ◽  
Random Mating ◽  
Nonrandom Mating ◽  
Selection Processes ◽  
Genetic Contributions ◽  
The Relationship

AbstractTractable forms of predicting rates of inbreeding (ΔF) in selected populations with general indices, nonrandom mating, and overlapping generations were developed, with the principal results assuming a period of equilibrium in the selection process. An existing theorem concerning the relationship between squared long-term genetic contributions and rates of inbreeding was extended to nonrandom mating and to overlapping generations. ΔF was shown to be ~¼(1 − ω) times the expected sum of squared lifetime contributions, where ω is the deviation from Hardy-Weinberg proportions. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express ΔF in terms of expected long-term contributions that are conditional on a set of selective advantages that relate the selection processes in two consecutive generations and are predictable quantities. With random mating, if selected family sizes are assumed to be independent Poisson variables then the expected long-term contribution could be substituted for the observed, providing ¼ (since ω = 0) was increased to ½. Established theory was used to provide a correction term to account for deviations from the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting ΔF with sib indices in discrete generations since previously published solutions had proved complex.

scholarly journals The survival of a mutant gene under selection

1959 ◽  
Vol 1 (1) ◽  
pp. 121-126 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Population Model ◽  
Phenotypic Selection ◽  
Mutant Gene ◽  
Diploid Population ◽  
Genetic Population ◽  
Single Mutant

AbstractThe problem of the survival of a single mutant in a haploid genetic population when there exists selection is considered for a type of population model in which the generations ar overlapping. The results are compared with the previous work of Fisherand others for other models. The need is stressed for a solution of the same problem in a diploid population with general phenotypic selection coefficients.

Evolution in diploid populations by continuity of gametic types

1973 ◽  
Vol 5 (01) ◽  
pp. 55-65
Author(s):  
Ilan Eshel
Keyword(s):  
Random Mating ◽  
Long Term Effects ◽  
Diploid Population ◽  
Selection Pressures ◽  
Genetic Types ◽  
Diploid Populations ◽  
Mutation And Selection

This work studies the long-term effects of mutation and selection pressures on a diploid population embracing many genetic types. A number of results previously established for the simpler asexual case (see [4]) are extended to the cases of random mating and complete inbreeding (Theorem 1), and then, under particular conditions, to certain circumstances of mixed random mating and inbreeding (Theorem 3 and Corollary 1). Several implications for sex and diploidity are drawn from Theorem 2 and its corollaries. Further biological interpretations of these findings, especially of Theorem 2, are given in [3].

A mathematical problem in population genetics

1961 ◽  
Vol 57 (3) ◽  
pp. 574-582 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Population Genetics ◽  
Overlapping Generations ◽  
Mathematical Problem ◽  
Random Mating ◽  
Mathematical Form

A genetical population in which different genotypes have different viabilities will undergo, by selection, changes in its genetical constitution which can be expressed in a simple mathematical form. We here consider a system of m alleles A1, A2, …, Am segregating at one locus, and we assume that the genotype AiAj has viability aij, where aij = aji ≥ 0. We assume discrete, non-overlapping generations and random mating.

scholarly journals The effect of offspring number on the adaptation speed of a polygenic trait

2017 ◽  
Author(s):  
Markus Pfenninger
Keyword(s):  
Phenotypic Change ◽  
Phenotypic Variance ◽  
Genetic Trait ◽  
Hedging Strategy ◽  
Diploid Population ◽  
Offspring Number ◽  
Unpredictable Environments ◽  
Soft Selection ◽  
Polygenic Trait ◽  
Density Dependent Selection

There is increasing evidence that rapid phenotypic adaptation of quantitative traits is not uncommon in nature. However, the circumstances under which rapid adaptation of polygenic traits occurs are not yet understood. Building on previous concepts of soft selection, i.e. frequency and density dependent selection, I developed and tested the hypothesis that adaptation speed of a polygenic trait depends on the number of offspring per breeding pair in a randomly mating diploid population. Using individual based modelling on a range of offspring per parent (2-200) in populations of various size (100-10000 individuals), I could show that the by far largest proportion of variance (42%) was explained by the offspring number, regardless of genetic trait architecture (10-50 loci, different locus contribution distributions). In addition, it was possible to identify the majority of the responsible loci and account for even more of the observed phenotypic change with a moderate population size. The simulation results suggest that offspring numbers may a crucial factor for the adaptation speed of quantitative loci. Moreover, as large offspring numbers translates to a large phenotypic variance in the offspring of each parental pair, this genetic bet hedging strategy increases the chance to contribute to the next generation in unpredictable environments.

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.

The correlations between relatives in a random mating diploid population

1961 ◽  
Vol 57 (2) ◽  
pp. 315-320 ◽  
Author(s):  
G. B. Trustrum ◽  
J. H. Williamson
Keyword(s):  
Maternal Effects ◽  
Random Mating ◽  
Quantitative Character ◽  
Population Variance ◽  
Diploid Population ◽  
Gene Effects ◽  
Additive Gene Effects ◽  
Additive Gene ◽  
Differential Viability

Malecot(4) under certain conditions derived the formula for the covariance of the genotypic values of a quantitative character in two individuals AI and AII, which were related but not by direct descent. This generalized some results of Fisher (l). Kempthorne (2) extended the theory to multiple allelic systems with any degree of epistacy (i.e. interlocular genie interaction) but without linkage. He gave the formula Here is the item in the population variance which can be attributed to the interaction of additive gene effects at r loci and dominance gene effects at s loci. φ and φ′ are the coefficients of relation between the two individuals. The various assumptions normally included under random mating equilibrium were made, i.e. no selection, mutations, maternal effects or differential viability. Kempthorne (2), (3) gave two rather different proofs of this important result. His second proof was the more straightforward, but it was somewhat condensed.

A general theory of the distribution of gene frequencies - I. Overlapping generations

1958 ◽  
Vol 149 (934) ◽  
pp. 102-112 ◽  
Keyword(s):  
General Theory ◽  
Gene Frequency ◽  
Overlapping Generations ◽  
Random Mating ◽  
Phenotypic Selection ◽  
Single Locus ◽  
Heuristic Methods ◽  
Gene Frequencies ◽  
Mating Population

The distribution of gene frequency at a single locus in a population of diploid individuals, with two sexes, subject to mutation, non-random mating and phenotypic selection, is obtained in the case where the generations are overlapping so that individuals die one by one. This distribution is of the same form as that obtained by heuristic methods by S. Wright in a randomly mating population but the coefficients are altered both by the non-randomness of the mating and the overlapping of the generations.

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