A Misconception About the Hardy–Weinberg Law

Abstract The Hardy–Weinberg law of population genetics is usually associated with the notion of random mating of parents. A numerical example for a triallelic autosomal locus shows that an uncountable set of mating combinations can maintain Hardy–Weinberg proportions. Therefore, one cannot infer random mating in a population from the observation of Hardy–Weinberg equilibrium. The mating system which ensures that the genotypic distribution of offspring is the same as that of the parents is specified.

Genetics of Cronartium ribicola. III. Mating System

Canadian Journal of Botany ◽

10.1139/b96-222 ◽

1996 ◽

Vol 74 (11) ◽

pp. 1852-1859 ◽

Cited By ~ 20

Author(s):

Matthew A. Gitzendanner ◽

Gayle E. Dupper ◽

Eleanor E. White ◽

Brett M. Foord ◽

Paul D. Hodgskiss ◽

...

Keyword(s):

Mating System ◽

Genetic Recombination ◽

Random Mating ◽

Cronartium Ribicola ◽

White Pine Blister Rust ◽

Mendelian Segregation ◽

Weinberg Equilibrium ◽

Forest Pathogen ◽

Genotype Frequencies ◽

Lack of genetic markers has hindered the study of the mating system of Cronartium ribicola, an exotic forest pathogen Meeting natural and cultivated white pines throughout North America. Isozymes, randomly amplified polymorphic DNA (RAPDs), and restriction length polymorphisms (RFLPs) were used to study the mating system of this rust. Heterozygosity (outcrossing) in diploid telia was demonstrated by analysis of cultures derived from the meiotic products (basidiospores) of individual telia. Families of basidiospores cultured from single telia were used to test for Mendelian segregation and for conformance of loci to Hardy–Weinberg equilibrium. A total of 18 polymorphic loci were identified with the three marker systems. All except for three RAPD loci showed Mendelian segregation in the single-telium families. To quantify the level of outcrossing, gene and genotype frequencies were calculated for families from a single population. Up to 24 families were surveyed with isozymes, 14 with RAPDs, and 18 with RFLPs. Except for one isozyme locus (MPI) in one sample, all 14 loci tested with these families were in Hardy–Weinberg equilibrium, indicating random mating. Further studies, with a different sample from the same population, showed all three isozyme loci to be in Hardy–Weinberg equilibrium. The three marker systems were consistent as to the amount of variation detected. Resistance selection and breeding programs must consider the implications of genetic recombination that outcrossing affords the rust. Keywords: isozymes, RAPDs, RFLPs, Hardy–Weinberg equilibrium, white pine blister rust.

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.

A Reality Check on Hardy–Weinberg

Twin Research and Human Genetics ◽

10.1017/thg.2013.40 ◽

2013 ◽

Vol 16 (4) ◽

pp. 782-789 ◽

Cited By ~ 6

Author(s):

Alan E. Stark ◽

Eugene Seneta

Keyword(s):

Random Mating ◽

Weinberg Equilibrium ◽

Reality Check ◽

The Law

G. H. Hardy (1877–1947) and Wilhelm Weinberg (1862–1937) had very different lives, but in the minds of geneticists, the two are inextricably linked through the ownership of an apparently simple law called the Hardy–Weinberg law. We demonstrate that the simplicity is more apparent than real. Hardy derived the well-known trio of frequencies {q2, 2pq, p2} with a concise demonstration, whereas for Weinberg it was the prelude to an ingenious examination of the inheritance of twinning in man. Hardy's recourse to an identity relating to the distribution of types among offspring following random mating, rather than an identity relating to the mating matrix, may be the reason why he did not realize that Hardy–Weinberg equilibrium can be reached and sustained with non-random mating. The phrase ‘random mating’ always comes up in reference to the law. The elusive nature of this phrase is part of the reason for the misunderstandings that occur but also because, as we explain, mathematicians are able to use it in a different way from the man-in-the-street. We question the unthinking appeal to random mating as a model and explanation of the distribution of genotypes even when they are close to Hardy–Weinberg proportions. Such sustained proportions are possible under non-random mating.

A test for Hardy-Weinberg equilibrium on the X chromosome for sex-biased admixed populations

10.1101/552794 ◽

2019 ◽

Author(s):

Daniel Backenroth ◽

Shai Carmi

Keyword(s):

X Chromosome ◽

Random Mating ◽

Allele Frequencies ◽

Ratio Test ◽

Weinberg Equilibrium ◽

Genotype Frequencies ◽

Genome Wide ◽

Control Step ◽

Males And Females

AbstractGenome-wide scans for deviations from Hardy-Weinberg equilibrium (HWE) are commonly applied to detect genotyping errors. In contrast to the autosomes, genotype frequencies on the X chromosome do not reach HWE within a single generation. Instead, if allele frequencies in males and females initially differ, they oscillate for a few generations towards equilibrium. Several populations world-wide have experienced recent sex-biased admixture, namely, their male and female founders differed in ancestry and thus in allele frequencies. Sex-biased admixture makes testing for HWE difficult on X, because deviations are naturally expected, even under random mating post-admixture and error-free genotyping. In this paper, we develop a likelihood ratio test and a χ2 test that detect deviations from HWE on X while allowing for natural deviations due to sex-biased admixture. We demonstrate by simulations that our tests are powerful for detecting deviations due to non-random mating, while at the same time they do not reject the null under historical sex-biased admixture and random mating thereafter. We also demonstrate that when applied to 1000 Genomes project populations (e.g., as a quality control step), our tests reject fewer SNPs (among those showing frequency differences between the sexes) than other tests.

O equilíbrio de Hardy-Weinberg no sistema sanguíneo ABO: um estudo de caso em Engenheiro Coelho – SP

Ciência e Natura ◽

10.5902/2179460x43422 ◽

2021 ◽

Vol 43 ◽

pp. e16

Author(s):

Vinícius Freitas de Oliveira ◽

Guilherme Augusto Pianezzer ◽

Suzete Maria Silva Afonso

Keyword(s):

Random Mating ◽

Natural Populations ◽

Human Populations ◽

Gene Frequencies ◽

Weinberg Equilibrium ◽

Blood Types ◽

Infinite Population ◽

And Migration

The genetics of human populations is the branch of Genetics that studies the dynamics of genes in natural populations, aiming at the elucidation of mechanisms that alter their genetic composition. Among the fundamentals of this science is the Hardy-Weinberg Equilibrium, which determines that gene frequencies remain unchanged and genotypic proportions reach a stable balance, obtaining the same constant relation with each other over time. To demonstrate this principle, it is necessary to admit that the studied population is not subject to evolutionary factors or to those that alter genotypic frequencies, increasing the homozygosity. More specifically, it is necessary to assume that the population obeys the following premises: random mating, infinite population, non-overlapping generations, in addition to the absence of mutation, selection and migration. More than recalling basic concepts of Genetics and Statistics, this article aims to describe the Bernstein Method for verifying the gene equilibrium for blood types. The research is concluded with a case study in the city of Engenheiro Coelho - SP, where the Hardy-Weinberg Equilibrium for blood types in the population is verified.

Hardy–Weinberg Equilibrium and Random Mating

Encyclopedia of Evolutionary Biology ◽

10.1016/b978-0-12-800049-6.00022-6 ◽

2016 ◽

pp. 208-211 ◽

Cited By ~ 1

Author(s):

J. Lachance

Keyword(s):

Random Mating ◽

Weinberg Equilibrium ◽

Population Genetics: Hardy-Weinberg Equilibrium with Two Loci

Wolfram Demonstrations Project ◽

10.3840/003411 ◽

2008 ◽

Keyword(s):

Population Genetics ◽

Weinberg Equilibrium ◽

A Century of Hardy–Weinberg Equilibrium

Twin Research and Human Genetics ◽

10.1375/twin.11.3.249 ◽

2008 ◽

Vol 11 (3) ◽

pp. 249-256 ◽

Cited By ~ 51

Author(s):

Oliver Mayo

Keyword(s):

Gene Locus ◽

Human Genetics ◽

Random Mating ◽

Large Population ◽

Autosomal Gene ◽

Genotypic Frequency ◽

Gene Frequencies ◽

Weinberg Equilibrium ◽

Discrete Generation ◽

AbstractHardy–Weinberg equilibrium (HWE) is the state of the genotypic frequency of two alleles of one autosomal gene locus after one discrete generation of random mating in an indefinitely large population: if the alleles areAandawith frequenciespandq(=1-p), then the equilibrium gene frequencies are simplypandqand the equilibrium genotypic frequencies forAA,Aaandaaarep2, 2pqandq2. It was independently identified in 1908 by G. H. Hardy and W. Weinberg after earlier attempts by W. E. Castle and K. Pearson. Weinberg, well known for pioneering studies of twins, made many important contributions to genetics, especially human genetics. Existence of this equilibrium provides a reference point against which the effects of selection, linkage, mutation, inbreeding and chance can be detected and estimated. Its discovery marked the initiation of population genetics.

CARBONIC ANHYDRASE POLYMORPHISM IN A NEW JERSEY POPULATION OF THE WHITE-FOOTED MOUSE PEROMYSCUS LEUCOPUS

Genetics ◽

10.1093/genetics/71.2.315 ◽

1972 ◽

Vol 71 (2) ◽

pp. 315-318

Author(s):

Patrick L Wilmot ◽

Donald K Underhill

Keyword(s):

New Jersey ◽

Carbonic Anhydrase ◽

Peromyscus Leucopus ◽

Autosomal Locus ◽

Gene Frequencies ◽

Weinberg Equilibrium ◽

Middlesex County ◽

White Footed Mouse

ABSTRACT Two electrophoretic forms of erythrocytic carbonic anhydrase were found to be controlled by one autosomal locus with two codominant alleles, CAf and CA8. The gene frequencies for the CAf and CA8 alleles were found to be.15 and.85, respectively, in a sample of 53 mice from Middlesex County, New Jersey. The observed genotypic frequencies indicated that the population was in Hardy-Weinberg equilibrium.

Population Genetics of Heterosis: Effects of Hardy-Weinberg Disequilibrium

Silvae Genetica ◽

10.1515/sg-2004-0001 ◽

2004 ◽

Vol 53 (1-6) ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Rongling Wu ◽

Ch.-X. Ma ◽

J. Wu ◽

W. Fang ◽

G. Casella

Keyword(s):

Population Genetics ◽

Genetic Structure ◽

Mechanistic Explanation ◽

Hybrid Zones ◽

Gene Effects ◽

Weinberg Equilibrium ◽

Two Populations ◽

Selection Of

SummaryThe mechanistic explanation of heterosis has been traditionally based on quantitative differences of gene effects. However, for outcrossing populations, heterosis is also a property of populations. In this paper, the effects of the deviation of a population from Hardy-Weinberg equilibrium (HWE) on the magnitude of heterosis have been examined numerically. The mating of two populations in HWE may generate directions and magnitudes of heterosis different from the mating of two populations in Hardy-Weinberg disequilibrium (HWD). Such differences of heterosis between these two types of population mating may be due to the release of vigor restored in the parental populations during the process of HWD. Results from this study can provide guidance on the selection of parental populations for the effective exploitation of heterosis and the prediction of genetic structure and organization for hybrid zones in nature.