Coalescent theory for age-structured random mating populations with two sexes

2011 ◽  
Vol 233 (2) ◽  
pp. 126-134 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Random Mating ◽  
Coalescent Theory ◽  
Age Structured

scholarly journals The probability of survival of a mutant gene in an age-structured population and implications for the evolution of life-histories

1975 ◽  
Vol 26 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Brian Charlesworth ◽  
John A. Williamson
Keyword(s):  
Life Histories ◽  
Random Mating ◽  
Intrinsic Rate ◽  
Mutant Gene ◽  
Intrinsic Rate Of Increase ◽  
Probability Of Survival ◽  
Rate Of Increase ◽  
Evolution Of Life ◽  
Age Structured ◽  
Derivatives Of

SUMMARYAn expression is derived for determining the probability of survival of a new favourable mutation in a large random-mating population with overlapping generations. For a gene of small effect, in a near-stationary population, an approximate formula similar to the usual one for discrete generations is obtained. The implications of these results for the evolution of life histories are discussed, using the partial derivatives of the chance of survival of a gene, with respect to changes in age-specific fecundities and survival probabilities. The properties of these derivatives are very similar to those of the derivatives of the intrinsic rate of increase, analysed by Hamilton (1966), thus providing a genetical basis for his conclusions concerning the evolution of life histories.

scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x 1 N,…,x K N, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes x j N and x i N, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as G ij . Under minimal conditions on the first three moments of G ij for all i and j, a suitable effective population size N e is derived. Then if time is recorded in a backward direction in units of 2N e generations, it can be shown that coalescent theory holds.

scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x1N,…,xKN, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes xjN and xiN, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as Gij. Under minimal conditions on the first three moments of Gij for all i and j, a suitable effective population size Ne is derived. Then if time is recorded in a backward direction in units of 2Ne generations, it can be shown that coalescent theory holds.

scholarly journals NATURAL SELECTION AND AGE-STRUCTURED POPULATIONS

Genetics ◽  
1975 ◽  
Vol 79 (3) ◽  
pp. 535-544
Author(s):  
Lloyd Demetrius
Keyword(s):  
Natural Selection ◽  
Random Mating ◽  
Reproductive Potential ◽  
Demographic Variables ◽  
Rate Of Change ◽  
Structured Populations ◽  
Age Classes ◽  
Malthusian Parameter ◽  
The Difference ◽  
Age Structured

ABSTRACT This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary population. The reproductive potential measures the mean of the contribution of the different age classes to the Malthusian parameter. The Malthusian parameter is precisely the difference between the entropy and the reproductive potential. The effect of these demographic variables on changes in gene frequency is discussed. The concept of entropy of a genotype is introduced and it is shown that in a random mating population in Hardy-Weinberg equilibrium and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the covariance in entropy and reproductive potential. This result is an information theoretic analog of Fisher's fundamental theorem of natural selection.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

Analysis of Quantitative Traits in PP9 Random Mating Sorghum Population 1

Crop Science ◽  
1981 ◽  
Vol 21 (5) ◽  
pp. 664-669 ◽  
Author(s):  
Tom S. Bittinger ◽  
R. P. Cantrell ◽  
J. D. Axtell ◽  
W. E. Nyquist
Keyword(s):  
Quantitative Traits ◽  
Random Mating
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