Definition and Properties of Disequilibrium Statistics for Associations Between Nuclear and Cytoplasmic Genotypes

ABSTRACT We define and establish the interrelationships of four components of statistical association between a diploid nuclear gene and a uniparentally transmitted, haploid cytoplasmic gene: an allelic (gametic) disequilibrium (D), which measures associations between alleles at the two loci; and three genotypic disequilibria (D 1, D 2, D 3), which measure associations between two cytotypes and the three respective nuclear backgrounds. We also consider an alternative set of measures, including D and the residual disequilibrium (d). The dynamics of these disequilibria are then examined under three conventional models of the mating system: (1) random mating; (2a) assortative mating without dominance (the "mixed-mating model"); and (2b) assortative mating with dominance ("O'Donald's model"). The trajectories of gametic disequilibria are similar to those for pairs of unlinked nuclear loci. The dynamics of genotypic disequilibria exhibit a variety of behaviors depending on the model and the initial conditions. Procedures for statistical estimation of cytonuclear disequilibria are developed and applied to several real and hypothetical data sets. Special attention is paid to the biological interpretations of various categories of allelic and genotypic disequilibria in hybrid zones. Genetic systems for which these statistics might be appropriate include nuclear genotype frequencies in conjunction with those for mitochondrial DNA, chloroplast DNA, or cytoplasmically inherited microorganisms.

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The Effects of Pollen and Seed Migration on Nuclear-Dicytoplasmic Systems. II. A New Method for Estimating Plant Gene Flow From Joint Nuclear-Cytoplasmic Data

Genetics ◽

10.1093/genetics/155.2.833 ◽

2000 ◽

Vol 155 (2) ◽

pp. 833-854 ◽

Cited By ~ 2

Author(s):

Maria E Orive ◽

Marjorie A Asmussen

Keyword(s):

Gene Flow ◽

Simulated Data ◽

Likelihood Method ◽

Data Sets ◽

Mixed Mating ◽

Hybrid Zones ◽

Plant Gene ◽

Seed Migration ◽

Genotype Frequencies ◽

Source Populations

Abstract A new maximum-likelihood method is developed for estimating unidirectional pollen and seed flow in mixed-mating plant populations from counts of joint nuclear-cytoplasmic genotypes. Data may include multiple unlinked nuclear markers with a single maternally or paternally inherited cytoplasmic marker, or with two cytoplasmic markers inherited through opposite parents, as in many conifer species. Migration rate estimates are based on fitting the equilibrium genotype frequencies under continent-island models of plant gene flow to the data. Detailed analysis of their equilibrium structures indicates when each of the three nuclear-cytoplasmic systems allows gene flow estimation and shows that, in general, it is easier to estimate seed than pollen migration. Three-locus nuclear-dicytoplasmic data only increase the conditions allowing seed migration estimates; however, the additional dicytonuclear disequilibria allow more accurate estimates of both forms of gene flow. Estimates and their confidence limits for simulated data sets confirm that two-locus data with paternal cytoplasmic inheritance provide better estimates than those with maternal inheritance, while three-locus dicytonuclear data with three modes of inheritance generally provide the most reliable estimates for both types of gene flow. Similar results are obtained for hybrid zones receiving pollen and seed flow from two source populations. An estimation program is available upon request.

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Mating system of Racosperma auriculiforme in a seed production area in Zaire

Canadian Journal of Botany ◽

10.1139/b93-089 ◽

1993 ◽

Vol 71 (6) ◽

pp. 779-785 ◽

Cited By ~ 5

Author(s):

P. Damase Khasa ◽

William M. Cheliak ◽

Jean Bousquet

Keyword(s):

Mating System ◽

Seed Production ◽

Random Mating ◽

Single Locus ◽

Acacia Auriculiformis ◽

Mixed Mating ◽

Outcrossing Rates ◽

Production Area ◽

Mixed Mating Model ◽

Mating Model

Analysis of the mating system of Racosperma auriculiforme (formerly Acacia auriculiformis) in a seed production area in Zaire was conducted using a mixed mating model at five polymorphic loci (Est-2, Est-3, G6p-dh, Nadhdh-2, Pgm-1). Single-locus estimates of outcrossing rate varied widely between 0.615 and 1.204 and were significantly heterogenous among and within the stands. Weighted means of single-locus estimates of outcrossing rates (ts) ranged from 0.859 to 1.032 while multilocus estimates of outcrossing rates (tm) ranged from 0.863 to 1.059. Comparisons between the single-locus estimates and the multilocus estimates of outcrossing rates indicated that most of the inbreeding detected was due to consanguineous (sibling) matings rather than selfing. Comparisons of observed and expected inbreeding coefficients indicated a general deficit of heterozygotes over the frequencies expected from random mating in the single stands and the pooled stands. Locus to locus variation in outcrossing rates suggested that violation of the mixed mating model might have occurred. Implications for seed production, collection, and distribution for reforestation are discussed. Key words: Acacia, mating system, Racosperma, seed production area, Zaire.

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Outcrossing rate of Couratari multiflora (J.Smith) Eyma (Lecythidaceae), a low-density tropical tree species from a central Amazonian rainforest

Acta Amazonica ◽

10.1590/s0044-59672011000100018 ◽

2011 ◽

Vol 41 (1) ◽

pp. 153-162 ◽

Cited By ~ 1

Author(s):

Nadja Lepsch-Cunha ◽

Paulo Yoshio Kageyama ◽

Roland Vencovsky ◽

Henrique E. M. Nascimento

Keyword(s):

Tree Species ◽

Random Mating ◽

Small Sample ◽

Outcrossing Rate ◽

Reproductive Phenology ◽

Mixed Mating ◽

Long Distance ◽

Sample Number ◽

Mixed Mating Model ◽

Mating Model

A multilocus mixed-mating model was used to evaluate the mating system of a population of Couratari multiflora, an emergent tree species found in low densities (1 individual/10 ha) in lowland forests of central Amazonia. We surveyed and observed phenologically 41 trees in an area of 400 ha. From these, only four mother trees were analyzed here because few of them set fruits, which also suffered high predation. No difference was observed between the population multilocus outcrossing rate (t mp = 0.953 ± 0.040) and the average single locus rate (t sp = 0.968 ± 0.132). The four mother trees were highly outcrossed (t m ~ 1). Two out of five loci showed departures from the Hardy-Weinberg Equilibrium (HWE) expectations, and the same results occurred with the mixed-mating model. Besides the low number of trees analyzed, the proportion of loci in HWE suggests random mating in the population. However, the pollen pool was heterogeneous among families, probably due to both the small sample number and the flowering of trees at different times of the flowering season. Reproductive phenology of the population and the results presented here suggest, at least for part of the population, a long-distance pollen movement, around 1,000 m.

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The effects of assortative mating and migration on cytonuclear associations in hybrid zones.

Genetics ◽

10.1093/genetics/122.4.923 ◽

1989 ◽

Vol 122 (4) ◽

pp. 923-934 ◽

Cited By ~ 1

Author(s):

M A Asmussen ◽

J Arnold ◽

J C Avise

Keyword(s):

Assortative Mating ◽

Hybrid Zone ◽

Evolutionary Dynamics ◽

Initial Conditions ◽

Likelihood Method ◽

Hybrid Population ◽

Hybrid Zones ◽

Gene Frequencies ◽

Nonrandom Mating ◽

And Migration

Abstract We examine the influence of nonrandom mating and immigration on the evolutionary dynamics of cytonuclear associations in hybrid zones. Recursion equations for allelic and genotypic cytonuclear disequilibria were generated under models of (1) migration alone, assuming hybrid zone matings are random with respect to cytonuclear genotype; and (2) migration in conjunction with refined epistatic mating, in which females of the pure parental species preferentially mate with conspecific males. Major results are as follows: (a) even the slightest migration removes the dependency of the final outcome on initial conditions, producing a unique equilibrium in which both pure parental genotypes are maintained in the hybrid zone; (b) in contrast to nuclear genes, the dynamics of cytoplasmic allele frequencies appear robust to changes in the assumed mating system, yet are particularly sensitive to gene flow; (c) continued immigration can generate permanent cytonuclear disequilibria, whether mating is random or assortative; and (d) the order of population censusing (before versus after reproduction by immigrants) can have a dramatic effect on the magnitude but not the pattern of cytonuclear disequilibria. Using the maximum likelihood method, the parameter space of migration rates and assortative mating rates was examined for best fit to observed cytonuclear disequilibria data in a hybrid population of Hyla tree frogs. An epistatic mating model with a total immigration rate of about 32% per generation produces equilibrium gene frequencies and cytonuclear disequilibria consistent with the empirical observations.

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Cytonuclear Theory for Haplodiploid Species and X-Linked Genes. I. Hardy-Weinberg Dynamics and Continent-Island, Hybrid Zone Models

Genetics ◽

10.1093/genetics/147.1.321 ◽

1997 ◽

Vol 147 (1) ◽

pp. 321-338

Author(s):

Michael A D Goodisman ◽

Marjorie A Asmussen

Keyword(s):

Assortative Mating ◽

Hybrid Zone ◽

Random Mating ◽

Diploid Species ◽

Specific Gene ◽

Hybrid Zones ◽

Pure Type ◽

Special Cases ◽

Source Populations ◽

And Migration

Abstract We develop models that describe the cytonuclear structure for either a cytoplasmic and nuclear marker in a haplodiploid species or a cytoplasmic and X-linked marker in a diploid species. Sex-specific disequilibrium statistics that summarize nonrandom cytonuclear associations in such systems are defined, and their basic Hardy-Weinberg dynamics and admixture formulae are delimited. We focus on the context of hybrid zones and develop continent-island models whereby individuals from two genetically differentiated source populations migrate into and mate within a single zone of admixture. We examine the effects of differential migration of the sexes, assortative mating by pure type females, and census time (relative to mating and migration), as well as special cases of random mating and migration subsumed under the general models. We show that pure type individuals and nonzero cytonuclear disequilibria can be maintained within a hybrid zone if there is continued migration from both source populations, and that females generally have a greater influence over these cytonuclear variables than males. The resulting theoretical framework can be used to estimate the rates of assortative mating and sex-specific gene flow in hybrid zones and other zones of admixture involving haplodiploid or sex-linked cytonuclear data.

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Bayesian Inference of Recent Migration Rates Using Multilocus Genotypes

Genetics ◽

10.1093/genetics/163.3.1177 ◽

2003 ◽

Vol 163 (3) ◽

pp. 1177-1191 ◽

Cited By ~ 13

Author(s):

Gregory A Wilson ◽

Bruce Rannala

Keyword(s):

Probability Distributions ◽

Gray Wolf ◽

Data Sets ◽

Genotype Data ◽

Migration Rates ◽

Multilocus Genotypes ◽

Monte Carlo Techniques ◽

Inbreeding Coefficients ◽

Genotype Frequencies ◽

Marker Loci

Abstract A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.

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THE EFFECTIVE PROPORTION OF SELF-FERTILIZATION WITH CONSANGUINEOUS MATINGS IN INBRED POPULATIONS

Genetics ◽

10.1093/genetics/106.1.139 ◽

1984 ◽

Vol 106 (1) ◽

pp. 139-152

Author(s):

Kermit Ritland

Keyword(s):

Mixed Mating ◽

Selfing Rate ◽

Genotypic Distribution ◽

Self Fertilization ◽

Allelic Segregation ◽

Mixed Mating Model ◽

Mating Model ◽

Inbred Populations ◽

Biased Estimates ◽

Independent Parameters

ABSTRACT Allelic segregation at a single locus among offspring derived from matings, including those between inbred relatives, is a combination of two patterns, corresponding to self-fertilization and random outcrossing. The proportion of effective self-fertilization is termed the "effective selfing rate," and it is specified with identity coefficients. The description of the offspring genotypic distribution for a population with mating among relatives requires a set of three independent parameters of genetic and mating structure. One such set is the inbreeding coefficient of parents, the coefficient of kinship between mates and the effective selfing rate. The model used to derive the effective selfing rate distinguishes between the effective selfing rates of inbred vs. outbred parents; the mixed mating model does not distinguish between these two rates. As a result, the mixed mating model usually gives biased estimates of effective selfing, if there is mating among inbred relatives. The procedure for estimation of effective selfing, based upon progeny array data distributed according to the "effective selfing model," is presented, and an example is given.

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Deviation from Hardy–Weinberg proportions in finite populations

Genetics Research ◽

10.1017/s0016672300034224 ◽

1996 ◽

Vol 68 (3) ◽

pp. 249-257 ◽

Cited By ~ 13

Author(s):

Jinliang Wang

Keyword(s):

Sampling Error ◽

Random Mating ◽

Random Selection ◽

Stochastic Simulations ◽

Gene Frequencies ◽

Dioecious Species ◽

Male And Female ◽

Census Size ◽

Genotype Frequencies ◽

Gene Frequency Difference

SummaryFor a finite diploid population with no mutation, migration and selection, equations for the deviation of observed genotype frequencies from Hardy–Weinberg proportions are derived in this paper for monoecious species and for autosomal and sex-linked loci in dioecious species. It is shown that the genotype frequency deviation in finite random-mating populations results from the difference between the gene frequencies of male and female gametes, which is determined by two independent causes: the gene frequency difference between male and female parents and the sampling error due to the finite number of offspring. Previous studies have considered only one of the causes and the equations derived by previous authors are applicable only in the special case of random selection. The general equations derived here for both causes incorporate the variances and covariances of family size and thus they reduce to previous equations for random selection. Stochastic simulations are run to check the predictions from different formulae. Non-random mating and variation in census size are considered and the applications of the derived formulae are exemplified.

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Difficulties in parentage analysis: the probability that an offspring and parent have the same heterozygous genotype

Genetics Research ◽

10.1017/s0016672301005237 ◽

2001 ◽

Vol 78 (2) ◽

pp. 163-170 ◽

Cited By ~ 6

Author(s):

A. C. FIUMERA ◽

M. A. ASMUSSEN

Keyword(s):

Random Mating ◽

Parentage Analysis ◽

Mixed Mating ◽

Heterozygous Genotype ◽

Heterozygous Parent ◽

Mendelian Segregation ◽

Maximum Value ◽

Potential Applicability ◽

System 2 ◽

Increasing Function

Parentage studies often estimate the number of parents contributing to half-sib progeny arrays by counting the number of alleles attributed to unshared parents. This approach is compromised when an offspring has the same heterozygous genotype as the shared parent, for then the contribution of the unshared parent cannot be unambiguously deduced. To determine how often such cases occur, formulae for co-dominant markers with n alleles are derived here for Ph, the probability that a given heterozygous parent has an offspring with the same heterozygous genotype, and Pa, the probability that a randomly chosen offspring has the same heterozygous genotype as the shared parent. These formulae have been derived assuming Mendelian segregation with either (1) an arbitrary mating system, (2) random mating or (3) mixed mating. The maximum value of Pa under random mating is 0·25 and occurs with any two alleles each at a frequency of 0·5. The behaviour with partial selfing (where reproduction is by selfing with probability s, and random mating otherwise) is more complex. For n [les ] 3 alleles, the maximum value of Pa occurs with any two alleles each at a frequency of 0·5 if s < 0·25, and with three equally frequent alleles otherwise. Numerically, the maximum value of Pa for n [ges ] 4 alleles occurs with n* [les ] n alleles at equal frequencies, where the maximizing number of alleles n* is an increasing function of the selfing rate. Analytically, the maximum occurs with all n alleles present and equally frequent if s [ges ] 2/3. In addition, the potential applicability of these formulae for evolutionary studies is briefly discussed.

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EVOLUTION OF INTERACTIONS IN FAMILY-STRUCTURED POPULATIONS: MIXED MATING MODELS

Genetics ◽

10.1093/genetics/96.1.275 ◽

1980 ◽

Vol 96 (1) ◽

pp. 275-296

Author(s):

Richard E Michod

Keyword(s):

Mating System ◽

Mating Systems ◽

Random Mating ◽

Additive Model ◽

Multiplicative Model ◽

Structured Populations ◽

Mixed Mating ◽

Genotypic Distribution ◽

Individual Fitness ◽

Recessive Genes

ABSTRACT The effect of inbreeding on sociality is studied theoretically for the evolution of interactions between siblings in certain mixed mating systems that give rise to inbreeding: sib with random mating and selfing with random mating. Two approaches are taken. First, specific models of altruism are studied for the various mating systems. In the case of the additive model, inbreeding facilitates the evolution of altruistic genes. Likewise, for the multiplicative model this is usually the case, as long as the costs of altruism are not too great. Second, the case of total altruism, in which the gene has zero individual fitness but increases the fitness of associates, is studied for a general fitness formulation. In this case, inbreeding often retards the ability of such genes to increase when rare, and the equilibrium frequency of those recessive genes that can increase is totally independent of the mating system and, consequently, of the amount of inbreeding. It appears from the results presented that inbreeding facilitates most forms of altruism, but retards extreme altruism. These results stem from the fact that inbreeding increases the within-family relatedness by increasing the between-family variance in allele frequency. In most cases this facilitates altruism. However, in the case of total altruism, only heterozygotes can pass on the altruistic allele, and inbreeding tends to decrease this heterozygote class. In either case, the important effect of inbreeding lies in altering the genotypic distribution of the interactions.

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