## Measuring Variance in Traits and Estimating Heritability

The differing degree of genetic versus environmental contribution to a trait is called heritability. Many Mendelian, or single-gene traits are unaffected by the environment. An extreme example is our blood type, which is unaffected by the environment and thus is 100 percent heritable. For polygenic traits, genetic factors contribute a portion of the trait, and the environment contributes the rest. If we wish to select animals or plants for a given trait, heritability is an important consideration. Heritability predicts how successful we will be in selecting for a trait by breeding individuals with the favorable trait. A trait that is highly heritable can be selected for, whereas if a trait is mostly determined by the environment, selection will not help in producing animals or plants with that trait.

Many traits of agricultural crops and animals, such as milk production in cattle and oil content in corn, are polygenic traits. We saw that polygenic traits such as these do not produce easily distinguishable phenotypic categories. So how do we measure the phenotypic differences brought about by polygenic traits among individuals in a population? How do we estimate the influence of the environment on these traits when phenotypes are the only thing we can directly observe?

If we measure traits from many individuals and plot them, poly-genic traits approximate normal, bell-shaped distributions, as we saw in figure 12.2. This type of distribution can be analyzed statistically using two measures, the mean and the variance of these plots. The mean (or average) is the sum of all the measurements of a trait in a population of organisms (for example, weight), divided by the number of organisms measured. Variance is the flatness or the sharpness of the normal distribution around the mean. Figure 12.3 illustrates these concepts. You can see in this figure three normal curves that have the same mean but are very different in their spread. The flatness of the curve is indicative of the spread of the measurements, or variance.

Mean

Figure 12.3 Overlapping Graphs of Normal Distributions or Bell-Shaped Curves. All three distributions have the same mean but very different variances. The sharpest one has the least variance and the flatter ones have higher variance. Plots of measurements of polygenic traits from many individuals would have shapes similar to these. Both genes and the environment contribute to the variance in plots of polygenic traits.

Mean

Figure 12.3 Overlapping Graphs of Normal Distributions or Bell-Shaped Curves. All three distributions have the same mean but very different variances. The sharpest one has the least variance and the flatter ones have higher variance. Plots of measurements of polygenic traits from many individuals would have shapes similar to these. Both genes and the environment contribute to the variance in plots of polygenic traits.

In the case of polygenic traits, the variance observed for a particular phenotype (VP) depends on the variance due to the genotype (VG) plus the variance due to the environment (VE). In order to determine heritability, defined as the genetic contribution to the phenotype, researchers try to make the environmental variance as close as possible to zero, that is, to keep the organisms under study in the same environment. With animals and plants, this can be done by growing these individuals under conditions that are as close as possible for all the individuals under study. Under constant environmental conditions, which mean a small VE, almost all the variance is due to the genes. Conversely, if one wants to know the contribution of the environment, one can raise in a natural setting highly inbred, thus genetically very similar, animals and plants characterized by small genetic variance, VG. These estimates of variance due mostly to genetics or environment are then used to determine heritability, that is, the genetic contribution to a polygenic trait.

Determining heritability involves producing many offspring and detailed bookkeeping of the trait in question to allow for statistical analysis, as described above. For example, we may wish to increase egg production by either selecting chickens that produce larger eggs or ones that produce more eggs during the year. It was determined that for white leghorn chickens, heritability for egg weight was 60 percent whereas heritability of number of eggs per year was only 30 percent. This means that the trait for the weight of eggs has a larger genetic contribution than that for the number of eggs per year. Thus selection for egg weight would result in a faster change in total egg mass than selection for number of eggs per year. In other words, environmental conditions influence the number of eggs laid more than they influence the weight of eggs. Therefore, artificial selection would produce chickens that produce larger eggs, whereas controlling the environmental conditions such as lighting and feed would be more effective in increasing the number of eggs.