Heritability Help (page 2)
One of the most important factors in the formulation of effective breeding plans for improving the genetic quality of crops and livestock is a knowledge of the relative contribution made by genes to the variability of a trait under consideration. The variability of phenotypic values for a quantitative trait (as expressed in the phenotypic variance) can, at least in theory, be partitioned into genetic and nongenetic (environmental) components.
Heritability (symbolized H2 or H in some texts) is the proportion of the total phenotypic variance due to all types of gene effects; H represents the corresponding ratio of standard deviations and is not used in this book.
The heritability of a given trait may be any number from 0 to 1.
EXAMPLE 8.3 If all of the phenotypic variability of a trait is genetic in nature (as is true for most classical Mendelian traits, such as blood types), then environmental effects are absent and heritability equals 1; i.e., if σ2G = σ2P, then H2 = 1.
EXAMPLE 8.4 If all of the phenotypic variability of a trait is environmental in nature (as is true for any trait within a genetically homozygous line), then heritability of the trait is zero; i.e., if σ2E = σ2P, then σ2G = 0 and H2 = 0/σ2P = 0.
EXAMPLE 8.5 If half of the phenotypic variability is due to gene effects, then heritability is 50%, i.e., if σ2G = (1/2)σ2P, then 2σ2G = σ2P and H2 = 1/2 = 50%. Note: We cannot say that because heritability of a quantitative trait (such as seed production in a given plant population) is 0.5 that 50% of any one individual's seed productivity is due to gene effects, as explained in the following scenario. One plant may have a superior genotype for seed production, but was grown in a poor environment (e.g., shade, disease, insect damage, etc.) and thus produced fewer seeds than the average number for the population. Another plant in that same population, having only an average genotype, might have grown in an enriched environment (e.g., accidentally fertilized by animal dung) and was thus able to produce a seed number near its genetic potential that actually exceeded the number of seeds produced by the aforementioned plant. Likewise, it is illogical to say that a population with a high heritability for a given trait is genetically superior to another population (in the same or different species) with a lower heritability for that same trait.
EXAMPLE 8.6 If the environmental component of variance is three times as large as the genetic component, heritability is 25%, i.e., if σ2E = 3σ2G, then
Broad-Sense and Narrow-Sense Heritability
The parameter of heritability involves all types of gene action and thus forms a broad estimate of heritability, or referred to as broad sense heritability, (H2) or the degree of genetic determination. In the case of complete dominance, when a gamete bearing the active dominant allele A2 unites with a gamete bearing the null allele A1, the resulting phenotype might be two units. When two A2 gametes unite, the phenotypic result would still be two units. On the other hand, if genes lacking dominance (additive genes) are involved, then the A2 gamete will add one unit to the phenotype of the resulting zygote regardless of the allelic contribution of the gamete with which it unites, Thus, only the additive genetic component of variance (i.e., the variance of breeding values) has the quality of predictability necessary in the formulation of breeding plans. Nonallelic (epistatic) interactions may exist, but they usually make a minor contribution to the total genetic variance, their effects are difficult to access, and they will be ignored in the simple models of this book. If they do occur, all nonadditive genetic variance will be included in the dominance variance. The concept of additive variance does not necessarily involve the assumption of additive gene action. Additive variance can be produced from genes with additive gene action and/or any degree of dominance and/or epistasis. Heritability expressed as the ratio of the additive genetic variance to the phenotypic variance is termed narrow sense heritability:
Unless otherwise specified in the problems of this book, heritability in the narrow sense is to be employed. It must be emphasized that the heritability of a trait applies only to a given population living in a particular environment. A genetically different population (perhaps a different variety, breed, race, or subspecies of the same species) living in an identical environment is likely to have a different heritability for the same trait. Likewise, the same population is likely to exhibit different heritabilities for the same trait when measured in different environments because a given genotype does not always respond to different environments in the same way. There is no one genotype that is adaptively superior in all possible environments. That is why natural selection tends to create genetically different populations within a species, each population being potentially adapted to local conditions rather than generally adapted to all environments in which the species is found.
Several methods can be used to estimate heritabilities of quantitative traits.
Consider the simple, single-locus model (below) with alleles b1 and b2.
The midparent value m = (1/2)(b1b1 + b2b2). If the heterozygote does not have a phenotypic value equal to m, some degree of dominance (d) exists. If no dominance exists, then the alleles are completely additive. However, quantitative traits are governed by many loci and it might be possible that genotype b1b2 is dominant in a positive direction whereas genotype c1c2 is dominant in a negative direction, so that they cancel each other, giving the illusion of additivity. Dominance of all types can be estimated from the variances of F2 and backcross generations. All of the phenotypic variance within pure lines b1b1 and b2b2, as well as in their genetically uniform F1 (b1b2), is environmental. Hence, the phenotypic variances of each pure parental line (VP1 and VP2) as well as that of the F1 (VF1) serve to estimate the environmental variance (VE). The F2 segregates (1/4)b1b1 : (1/2)b1b2 : (1/4)b2b2. If each genotype departs from the midparent value as shown in the above model, then the average phenotypic value of F2 should be (1/4)(–a) + 1/2 (+d) + 1/4 (+a) = (1/2)d. The contribution that each genotype makes to the total is its squared deviation from the mean (m) multiplied by its frequency . Therefore, the total F2 variance (all genetic in this model) is the mean of squared deviations from the mean:
If we let a2 = A; d2 = D, and E = environmental component, then the total F2 phenotypic variance (VF2) = (1/2)A + (1/4)D+E, representing the additive genetic variance (VA) + the dominance genetic variance (VD) + the environmental variance (VE), respectively. Likewise it can be shown that VB1 (the variance of backcross progeny F1 × P1) or VB2 (the variance of backcross progeny F1 × P1), = (1/4)A + (1/4)D+E, and VB1 + VB2 = (1/2)A + (1/2)D+2E. The degree of dominance is expressed as
Heritability can be easily calculated from these variance components. The same is true of variance components derived from studies of identical (monozygotic) vs. nonidentical (fraternal, dizygotic) twins. If twins reared together tend to be treated more alike than unrelated individuals, the heritabilities will be overestimated. This problem, and the fact that the environmental variance of fraternal twins tends to be greater than for identical twins, can be largely circumvented by studying twins that have been reared apart.
Genetic Similarity of Relatives
If offspring phenotypes were always exactly intermediate between the parental values regardless of the environment, then such traits would have a narrow heritability of 1.0. On the other hand, if parental phenotypes (or phenotypes of other close relatives) could not be used to predict (with any degree of accuracy) the phenotypes of offspring (or other relatives), then such traits must have very low (or zero) heritabilities.
The regression coefficient (b) is an expression of how much (on the average) one variable (Y) may be expected to change per unit change in some other variable (X).
EXAMPLE 8.7 If for every egg laid by a group of hens (X) the average production by their respective female progeny (Y) is 0.2, then the regression line of Y on X would have a slope (b) of 0.2 (symbol Δ = increment of change).
The regression line of Y on X has the formula
where a is the "Y intercept" (the point where the regression line intersects the Y axis), and and are the respective mean values. The regression line also goes through the point (, ) and establishing these two points allows the regression line to be drawn. Any X value can then be used to predict the corresponding Y value. Let = estimate of Y from X; then
Since daughters receive only a sample half of their genes from each parent, the daughter-dam regression estimates only one-half of the narrow heritability of a trait (e.g., egg production in chickens). If the variances in the two populations are equal (Sx = Sy), then
Similarly, the regression of offspring on the average of their parents (midparent) is also an estimate of heritability
Full sibs (having the same parents) are expected to share 50% of their genes in common; half-sibs share 25% of their genes. Therefore,
If the variances of the two populations are unequal, the data can be converted to standardized variables (as discussed later in this chapter) and the resulting regression coefficients equated to heritabilities as described above.
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