Dorian J. Garrick
Department of Animal Sciences, Colorado State University, Fort Collins, Colorado, U.S.A.
Strictly speaking, genetics refers to the study of inheritance. Its usual interpretation is based on cell biology, referring to the transmission of hereditary factors, such as deoxyribonucleic acid (DNA), or, more specifically, genes, from parents to offspring. Population genetics is concerned with inheritance from a population perspective considering gene and genotypic frequencies.[1'2]
Gene and genotypic frequencies may reflect equilibrium or non-equilibrium conditions. A well known equilibrium condition with respect to a single locus is known as Hardy Weinberg equilibrium. This always occurs in the absence of forces that influence gene frequency such as selection, migration, or mutation. It has a counterpart in relation to the concurrent consideration of two or more loci known as linkage equilibrium.
Traditionally, interest in population genetics was of a theoretical nature or was applied to simply inherited Mendelian characteristics such as the inheritance of coat color, horns, or blood groups. The recent explosion in knowledge relating to individual genes that has arisen from DNA markers and the discovery of so-called quantitative trait loci has increased interest in population genetics.
Many loci may be involved in the expression of any characteristic, but only loci that exhibit polymorphisms and therefore contribute to variation in observed performance are of interest from a population genetics perspective. If a characteristic is determined by a single locus, it is said to be monogenic. Characteristics influenced by a small number of loci are oligogenic and those determined by genes at a large number of loci are described as polygenic (infinitesimal). At any such locus, there must be at least two alleles in order to produce variation. We denote a particular locus with a capital letter such as A, or an abbreviation to represent the trait or gene function. Alleles at a particular locus might be denoted by the same letter in upper case or lower case or with various superscripts. For convenience, suppose the A-locus contains two alleles A and a. In diploid organisms, such as animals and birds, individuals carry two alleles at each autosomal locus, one inherited from the sire and another from the dam. Individuals can therefore have one of three genotypes, AA, Aa, and aa. Two of these, AA and aa, are said to be homozygous because the individual can only produce one kind of zygote, carrying either A or a. The other genotype Aa is known as a heterozygote as such an individual can produce two kinds of zygotes, those carrying A and those carrying a. From a population perspective, the interest often is in the frequency of these alternate alleles (A vs. a) and the frequency of the various genotypes (AA, Aa, and aa).
Suppose the frequencies of the A and a alleles are p and q, respectively. That is, a fraction, p, of the gametes contain A and the remainder, representing the fraction q = 1 — p carry the a allele. If mating is at random, the frequency of the three genotypes can be calculated from the independent frequencies of each gamete. A proportion p of the sperm will carry A and p of the ova carry A so that p2 represents the frequency of AA offspring. A similar argument shows that the frequency of aa is q2 and the frequency of Aa is 2pq. These genotype frequencies, in the absence of migration, mutation, or selection, represent what is known as Hardy Weinberg equilibrium. At equilibrium, the frequency of gametes produced by these genotypes in the next generation will remain at the earlier values of p and q. Only migration in or out of the population, mutation of alleles, or selection of parents will change the allele and genotype frequencies. Of course, in small populations, allele and genotype frequencies can drift each generation due to chance sampling, which is, in a sense, undirected selection.
The principle of Hardy Weinberg equilibrium can be used to determine allele frequencies from genotypic frequencies. Suppose a rare recessive condition occurs in 1 in 10,000 births. If the locus is denoted with the letter R, the affected individuals will be rr. Their frequency, q2, is therefore 1/10,000 or 0.0001. The square root of this is q, which in this case is 0.01. The frequency of the alternate allele R must therefore be 0.99 = 1.00 — 0.01. The frequency of carriers, the heterozygous individuals who can pass on a copy of the recessive r allele without themselves having shown its effect, will be 2pq or 2 x 0.99 x 0.01 = 0.02. There are therefore 200 times as many individuals in the population carrying the gene for the condition as there are exhibiting the condition.
The presence of another locus, say the B locus, provides the opportunity to consider pairwise frequency of various alleles and genotypes. In the absence of migration, mutation, and selection, the A and B alleles will be in Hardy Weinberg equilibrium. In some cases, the A and B alleles will also be in equilibrium, a condition known as Mendel's law of independent assortment. For example, if the frequency of the A allele is p and the frequency of the B allele is m, then there will be a frequency of pm gametes that carry the A and B alleles together. If the A and B loci are located near each other on the same chromosome, or if the traits affected by the A and B loci are subject to selection, this pairwise equilibrium may not exist and the two loci will be said to be in linkage disequilibrium. For example, if the a and b alleles were very rare alleles representing recent mutations or introductions to the population, it may be that the only gametes that carry a also carry b. An offspring created as the product of such a gamete would be doubly heterozygous AaBb. In one generation, without further migration or selection, both the A and B loci would exhibit Hardy Weinberg equilibrium. However, if the A and B loci were very close together so that a recombination event between the two loci was very rare, most gametes produced by the doubly heterozygous individual would carry the haplotype ab or the haplotype AB. The pairwise disequilibrium may take many generations to disappear. This mechanism provides a basis for marker-assisted selection.
Some loci that influence one trait may have so-called pleiotropic effects and influence other traits. These effects may be complementary when an allele is favorable for both traits or it may be that the allele that is favorable for one trait is unfavorable for another. The effect of such genes creates a correlation between the genotypes for the traits. These genetic correlations may be positive or negative and will influence the performance of one trait when the other trait is subject to selection. They will also influence the rate at which the traits respond to simultaneous selection, such as with an index.
The phenotypes of individuals represented by genotypes AA, Aa, and aa will be influenced by the mode of gene action. The relative frequency of the three genotypes will be determined by the gene frequencies that determine the fraction of gametes that carry the A or the alternate a allele. One interesting issue from a population perspective, is the relative performance of a number of offspring that inherit say the A allele from one parent, with the other parents being random representatives of the population. The difference in performance of such offspring from all offspring in the population represents the average effect of allele A. An average effect can be similarly obtained for allele a. The average effects so obtained will be population dependent as they vary with gene frequency. These effects can then be used to quantify the merit of particular parents having the AA, Aa, or aa genotypes. An AA parent has twice the value of the average effect of A. A heterozygous parent has the average effect of A and the average effect of a. This sum of average effects of each allele is known as their genetic merit or breeding value. The same phenomenon can be considered for the infinitesimal model when many genes are involved in the expression of a trait, even though the loci, their gene frequencies, and modes of action are not known. In that context, the breeding value can be estimated by statistical analysis of animal performance over a number of generations. Such breeding values are useful tools for selection and are routinely estimated in many livestock species. The estimates have a variety of names (EPD, EBV, PTA) depending upon the species and country and are sometimes scaled to assist in interpretation of the likely phenotypic performance of offspring.
Variation in genetic merit can come about from variation in the merit of sires, variation in merit of dams, and variation arising from chance sampling of various gene combinations. Chance sampling comes about from two processes: first, because chromosomes are in pairs but only one member of the pair is passed on to the offspring; second, because there is typically crossing over between the pair of homologous chromosomes, which produces chromosomes in offspring that are no longer identical to those the parent inherited from its sire or its dam. The variation produced by this chance sampling is known as Mendelian sampling and can be shown in the infinitesimal model to contribute half of the genetic variation in the population, which explains why offspring of the same sire and dam (such as lit-termates) can vary considerably in genetic merit.
Population genetics is involved with study of inheritance at the population level. Early work focused on theoretical mathematical aspects associated with the forces that alter gene frequency. Modern work has the luxury of having much data as a result of computerized record collection and the advent of DNA technologies that has introduced many new aspects to studies of population genetics, particularly with respect to the use of wild populations.
Gene Action, Types of, p. 456 458. Genetics: Mendelian, p. 463 465. Genetics: Quantitative. Published online only. Quantitative Trait Loci, p. 760 762. Selection: Marker Assisted, p. 781 783. Selection: Traditional Methods, p. 784 786.
1. Bourdon, R.M. Understanding Animal Breeding; Prentice Hall: Englewood Cliffs, NJ, 1997.
2. Falconer, D.S.; Mackay, T.F.C. Introduction to Quantitative Genetics; Prentice Hall: Englewood Cliffs, NJ, 1996.
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