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John Pollack, Ph.D., Cornell University

Assume a breeder wants to select a population for a quantitative trait. The question arises as to how successful that selection program might be. Quantitative traits are quite different from those inherited as simple Mendelian traits. Many genes are involved in the inheritance, the phenotypes are most often measured characteristics, and the environment often plays an important role in the expression of the phenotype. Enter the concept of heritability. Heritability is a statistic used to evaluate animals and to predict response to selective breeding. It is not easily understood. This article is an attempt to demystify the concept of heritability.

1. Genetic Control Versus Heritability

Heritability is often misinterpreted as a measure of genetic control. Genetic control is simply whether genes are involved in the expression of a phenotype--this is biological. Heritability is a statistic that measures how that control can vary. Consider a trait like reproduction. The development and ovulation of an egg, implantation and support of an embryo, and development of the placenta are well-orchestrated biological events controlled by genes. However, most heritability estimates for reproductive traits are low. So what does heritability measure?

Heritability is a ratio that describes the amount of phenotypic variation that can be attributed to the differences in the "additive genetic merit" of individuals in a population. Differences in additive genetic merit exist if individuals have different alleles at loci that contribute to measurable differences in performance. So, to understand heritability, one must first understand additive genetic merit.

2. Additive Genetic Merit

Assume each genotype at a locus influencing a quantitative trait (e.g., hip dysplasia) has "value" (+ or -). Consider two loci, B and F. With no dominance, the BB genotype has a value of 6, Bb a value of 0, bb a value of -6, and the FF genotype has value 2, Ff value 0, and ff value -2. If there is no epistasis (interaction between these two loci), then the value of a genotype is the sum of the values for each locus. For example, for the genotype BBFF, the value is 8. I haven’t invoked any mysterious statistics or violated any fundamental genetic laws to get here. I also, however, haven’t completely defined additive genetic value. If only it were that simple. Additive genetic merit is a measure of the value that the genes in an individual’s genotype have on the performance of their progeny. Additive genetic merit depends not only on the alleles carried by an individual but also depends on the frequency of alleles in the population. Consider the following animals using our small example.

Animal 1 has genotype BBFF, and all gametes that animal produces have both the B and F genes. The additive genetic merit of the individual producing this gamete depends on the population. If every individual in population A is BBFF, the gametes produced by animal 1 are no better or worse than those produced by any other individual in that population. Animal 1 is an average animal. On the other hand, if the frequencies of b and f in population B are high, the gametes of animal 1 would have considerable value in population B.

Animal 2 is BbFf. This individual produces a variety of gamete types: BF, Bf, bF and bf in equal proportions (25% each). In a population where the frequency of B and F alleles is high, selecting animal 2 for breeding would not improve progeny performance in the next generation. Hence, the additive genetic value of an animal is not only a function of the alleles it carries but of the frequency of alleles in the population as well.

So individuals having different genotypes perform differently and would make different contributions as parents to the next generation. We can estimate the contribution to the phenotypic variance due to these different genotypes. This variance is referred to as the additive genetic variance and is the numerator in the ratio we call heritability.

In real life, we don't know the value of individual genes, nor do we know which genes each individual carries. Because of this lack of knowledge, we estimate additive genetic merit from phenotypic performance of the individual or its relatives using statistical techniques. However, with new DNA technology, there are many projects looking for Quantitative Trait Loci (QTLs). These are loci with genes that have a major impact on quantitative traits and their variance. Several QTLs have been identified in beef (e.g.,marbling), dairy (e.g., milk yield), swine (e.g., litter size), and other species in which the allele differences and contributions to variance were estimated.

3. Environmental Factors

The additive genetic variance is the numerator in the heritability ratio. The denominator is the phenotypic variance. A component of the phenotypic variance is caused by environmental influences. Using our above example, consider animals with identical genotypes, say BBFF, raised in different kennels or exposed to different microenvironments within the same kennel. Their genotypes are the same, but we often see differences in performance caused by the environments each was exposed to. An excellent example of environmental influences in humans is found in studies of identical twins that were reared apart.

We can measure the variation associated with environmental effects much as we do the additive effects. I would point out here that when we do this in genetic evaluation programs for beef and dairy cattle, we only compare performance among animals in the same macroenvironment (i.e., herd, birth years, etc.) and then accumulate these comparisons across environments.

4. Heritability is Simply:

Additive genetic variance / Phenotypic variance

This ratio shows the fraction of total phenotypic variance that is attributed to differences in additive genetic merit. It is, however, a very important statistic for those of us in animal breeding. It is used to take phenotypic measures and convert them to estimates of additive genetic merit for the purpose of selection. This is an area of my research, and we do genetic evaluations for the beef and dairy industry on a routine basis. Heritability is also used to predict response to selection. This is especially useful when there are alternative selection strategies to compare.

To this point, I have only covered heritability in the narrow sense, the heritability estimated with the additive genetic variance in the numerator. A second concept is heritability in the broad sense.

5. Heritability in the Broad Sense

We know from experiences with simply inherited traits (black versus chocolate coat color in Labradors) that there is the potential for dominance (complete and incomplete dominance as well as overdominance). I'll complicate our example now by saying that B is dominant to b and both BB and Bb express the same phenotype. If we were just interested in the individual’s phenotype, it would not matter which of these two animals we owned. However, if we wanted to use one of the two as a parent, then BB is preferable. We also know from examples such as the black, chocolate, and yellow Labrador coat color that alleles at different loci interact. This interaction is referred to as epistasis.

These types of interactions have value just like individual genes do. If the interaction is within a locus, it leads to a dominance value and if between loci, an epistatic value. Differences in these values contribute to the phenotypic variance and are referred to as dominance variance and epistatic variance, respectively.

The sum of additive variance + dominance variance + epistatic variance is the total genetic variance, and heritability in the broad sense is the ratio:

Genetic variance / Phenotypic variance

This brings us to an interesting point. Consider a numerically scored trait controlled by a single gene, with alleles D and d. Since the phenotype is numerically scored, heritability has meaning. Assume D is dominant and that the environment has no influence on these phenotypes. For a single locus, there are no epistatic effects so the phenotypic variance in the absence of important environmental factors is simply the additive plus the dominance variance. Also, because there is no environmental influence, this trait is totally controlled by genetics. Heritability in the broad sense is 1, but heritability in the narrow sense is less than 1, how much so depends on the relative magnitude of the additive and dominance variance. To make the comment that knowing heritability implies something of the importance of the environment implies you are using heritability in the broad sense. In this simplistic example, using heritability in the broad sense does tell us there is no environmental variation in the phenotypes. The same is not implied when looking at estimates of heritability in the narrow sense. Most published estimates are for heritability in the narrow sense as it is the more useful of the two. When selecting animals for breeding, we are interested in the additive component because parents pass on individual genes, not combinations at a locus.

6. Realized Heritability

Is heritability a real thing? Many experiments have been done that compared two populations, one unselected and one selected. If the two populations started from the same gene pool, their performance is relatively similar in the initial generations. If the trait is heritable, the two populations diverge over time. If in each generation, one takes the difference in average performance between the selected and unselected populations, a realized heritability can be estimated. It is simply an estimate of what the heritability needs to be to observe the rate of divergence given the selection practiced. Estimates of realized heritabilities from many of these studies correlate well with estimates based on statistical analysis of data from pedigreed populations.

7. How Should a Breeder Look at Heritability Estimates?

For a breeder, its simplest use is to decide how effective selection might be, particularly phenotypic selection. For a trait with a very low heritability, selecting on phenotypes directly is not a promising approach. For these kinds of traits, combinations of phenotypes from relatives, such as is achieved through progeny testing, is needed to determine more accurately the underlying genetic merit of the potential parents. When heritability for a trait is high, phenotypic selection will be more effective and obtaining additional information on relatives is of less value than when heritability is low. Methods such as selection indices and best linear unbiased prediction have been developed to combine information from relatives to achieve this goal. The latter method is currently being used in evaluations of livestock such as beef and dairy cattle.

John Pollack is a Professor of Animal Genetics at Cornell Animal Sciences Department, working mainly with production species. He teaches both introductory and advanced undergraduate courses in animal genetics, with an emphasis on genetic evaluation and mating stategies. His primary research interest is in statistical analysis of quantitative traits. Please visit his online dog survey course page.

Copyright 1998 John Pollack. No reproduction of any kind without explicit permission of the author.

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