Monoecious Population Research Articles

BREEDING SYSTEMS IN COTULA L. (COMPOSITAE, ANTHEMIDEAE) II. MONOECIOUS POPULATIONS

SummaryThe distribution of male and female florets in heads of monoecious populations is represented by a curve joining points on a graph of percentage of female florets against rank in the same percentage. Comparison of curves for samples from different origins in Cotula minor and C. atrata subsp. atrata shows that sex expression is not greatly influenced by macro‐environmental differences. Much of the total intra‐population variation in sex expression appears in the heads collected at one time from a single plant. The rank‐frequency curves show marked differences between species in the percentages of male and female florets. The average percentage of female florets in seventeen monoecious species is negatively correlated with the floret length, a measure of adaptation to outbreeding. In three species, the seed set and subsequent germination percentages are slightly lower after self‐pollination than after cross‐pollination. Self‐fertilization probably occurs in varying degrees in the monoecious species. Monoecy has arisen independently in sections Leptinella and Strongylosperma.

Linkage disequilibrium and homozygosity of chromosome segments in finite populations

In considering populations of finite size, there are two approaches to studying the correlation of genotype frequencies at two linked loci. The first is based on disequilibrium parameters, and the second on identity-by-descent methods. The basic connection between the two approaches may be stated in the following way. The expected square of the correlation of gene frequencies at two loci r 2 = D 2 p A p a p B p b , is approximately equal to Q, the probability that, given two genes at one locus which are identical by descent, then the two genes at the second locus will be identical by descent through the same pathways. Using this relationship it is shown that for a monoecious population of effective size N e with no selection, the expected value of r 2 will tend to approximately 1 (1 + 4N ec) , where c is the recombination frequency, the rate of approach being given by (1 − 1 2N e )(1 − c) 2 . Computer simulation has shown that this formula holds with reasonable accuracy, and that it is also quite accurate in populations with heterozygote advantage stabilizing gene frequencies. It is suggested that the measurement of linkage disequilibrium in natural populations might thus be used to give information about the effective population size. The identity-by-descent approach is extended to derive the distribution of the length of homozygous chromosome segment surrounding a locus which is identical by descent. The mean such length is approximately 1 2N e ( log N e − 1) . It is suggested that a general theory of stability of the genotype in small populations might be based on parameters such as this.

On the equivalence of random mating and random union of gametes models in finite, monoecious populations

The paper shows that under certain conditions, random mating models for monoecious diploids are equivalent to random union of gametes models, in the case when the population is finite. Two examples are given to illustrate the result, in connection with gametic selection, and for recombination of two loci. It is also shown that under certain conditions three different random mating models can be mathematically equivalent, and likewise three different random union of gametes models can be equivalent.

The effect of linkage in a finite random-mating population

A model is proposed to study the effects of linkage of two loci, at each of which two alleles are possible. In a finite, random-mating monoecious population, it will usually be the case that one locus will fix first, followed by fixation of the other locus. The probabilities for which locus will fix first, which alleles will become fixed, and the rates at which these fixations occur, are found in terms of the recombination fraction for the pair of loci in question, and the initial state of the population. Most of the results are at least qualitatively similar to those found by Karlin and McGregor (1968) ( Genetics 58, 141–159) for a different model, but fixation of the first locus is found to be quickest with tight but not complete linkage, in contrast with their conclusion that looser linkage speeds first-fixation.

Inbreeding function in small populations with an arbitrary number of linked loci

It was attempted to extend the generalized recurrence relationships for the inbreeding function and the panmictic function for an arbitrary number of linked loci developed by Narain (1965) to monoecious populations of size N where the probabilities of selfing and outcrossing are equal. It was found that this is only simple for a single generation. The reason for this is that the step between two parental pools in successive generations will have three branching stages whenever there is more than one gene and more than one individual in the population. The number of branching stages will reduce to two when either the number of genes is one (Wright's F) or the number of individuals in the population is one (selfing). This paper defines a system of gametic states of a Markov chain where the elements are gametic classes or sets and defines the formulatiogns of the inbreeding function in terms of these transition matrices rather than in terms of a genotypic system. A computer program has also been written using the introduced Markov chain to obtain the inbreeding function for populations of size two each with two linked loci. By using the gametic technique the number of possible states can be considerably reduced and the problem becomes solvable at least for a small number of genes. An approximation is also given for the two individual-two locus case.

Demographic effects on the rate of genetic evolution I. constant size populations with two genotypes

SummaryA model is constructed to describe the evolution of a monoecious haploid population in which the population of adults remains of constant size, but for which generations may be overlapping, family size distributions are to a considerable degree arbitrary, and differential survival rates may apply with respect to adult and young individuals. The eigenvalues of the transition probability matrix are obtained, and those which determine the rate of evolution are found as simple functions of mutation rates, the mean lifetime of an individual, and the variance of his viable offspring number. The model builds on, and includes as special cases, certain non-overlapping generation models of Wright (1931), Karlin and McGregor (1965), and an overlapping generation model of Moran (1958).One of the secondary conclusions of the study is that for some models, when evolutionary rates are measured on a mean-lifetime scale, the more offspring that are produced at a mating season may slow down evolution when mutation is absent, but may speed it up if mutation is present.

The Galton-Watson Process with Mean One and Finite Variance

The Galton-Watson Process with Mean One and Finite Variance

NON‐RANDOM MATING, AND ITS EFFECT ON THE RATE OF APPROACH TO HOMOZYGOSITY

SummaryIn this paper, various systems of non‐random mating are considered for both monoecious and dioecious diploid populations. The effect of positive assortative mating on the rate of approach to homozygosity is investigated, at a single chromosome locus in the absence of mutation. The difficulty of setting up an amenable theoretical model for negative assortative mating is discussed. It is found that for a monoecious population, positive assortative mating increases the rate by a factor between 1 and 2 compared with random mating. For a dioecious population, assortative mating may either increase or decrease the rate of approach to homozygosity, depending on the mating system and the divergence of the sex numbers from equality. A population whose birth‐death events occur in succession (a model introduced by Moran), is known to approach homozygosity at twice the rate of a population with non‐overlapping generations, and this result is shown to hold under positive assortative mating. The probability of fixation of an allele is obtained, and depends on the initial gene frequencies.