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# Heritability Help

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## Heritability

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

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.

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