Quantitative traits have apparently continuous distributions rather than fitting into definite categories. Height in humans is a good example. These traits are generally a combination of many Mendelian genes and possibly environmental noise.
It is clear that they are not single Mendelian genes (plus noise) because for many such traits, if we select artificially we can see long-term responses to selection. Variability in a single gene would become exhausted after a while.
When the response to selection tapers off, as it always will, there are three hypotheses to consider:
You can test these hypotheses by relaxing or reversing selection. If variability is exhausted, a relaxed or reversed line will tend not to change at all. If selection is opposing, on the other hand, relaxed lines will tend to go back to the original value, and reversed lines may be able to go below the original value. And if you are selecting on negatively correlated traits, the relaxed line may tend to stay in the same place, but the reversed line will move.
The distribution of many traits takes on the familiar bell curve shape. Three useful statistics on a bell curve:
It is useful to know that if the distribution is actually a bell curve, about two-thirds of the observations will be within one standard deviation of the mean, and about 95% will be within two standard deviations. This does not hold if the distribution is not a bell curve.
It is useful to think of variability in a population in terms of variance, and ask where that variance comes from. A broad overview:
V = VG + VE + VGE
Total variance is the sum of variance due to genotype ( VG), variance due to environment (VE) and variance due to genotype/environment correlation (VGE). The correlation term comes about from cases in which organisms with different genotypes preferentially end up in different environments. Example: forest trees which are genetically taller than most may get more sunlight (a different environment) so they will also be environmentally taller than most. Most breeding experiments try to avoid having any VGE as it makes things more confusing.
Selection can only work on VG but that is not the whole story.
VG = VA + VD
Here VA is the additive genetic variance. One way to think about this is that VA determines the correlation between parent and offspring. Another way to think about it is that VA is the degree to which adding one A allele increases the phenotype independent of what other alleles are present. VD is the dominance genetic variance-basically all other genetic variance, resulting from forces such as dominance (including under- and over-dominance) and interactions among genes.
Selection for the trait phenotype works only on VA and is completely ineffective if VA is zero. Example: trying to select for a trait which has heterozygote advantage.
Breeding schemes which use more information than just trait phenotype can sometimes make use of VD. Example: creating superior poplar trees by crossing two pure strains and farming the resulting heterozygotes. However, natural selection is generally selecting on a trait phenotype, so VA is critically important for response to natural selection.
There are two ways to think about measuring VA. One comes from breeding experiments. We compare, over many matings, the trait of a child with the mean of its two parents (the mid-parent). The more strongly correlated the child is with its parents, the larger VA is in proportion to total variance.
The other way is to do a selection experiment. The greater the response to selection, the larger VA.
We can define a measure called narrow sense heritability, h2, which expresses this idea:
Narrow-sense heritibility predicts the response to selection:
h2= selection gain / selection differential
Heritability is defined for a specific population in a specific environment. It is very risky to apply it out of that situation; this is a common mistake and can have ethical as well as practical implications.
Two ways to remember that heritability is only defined on one given situation:
Heritability is generally less for traits that are very important to the organism, because there is little genetic variation in such traits.
Heritability is not a measure of how genetic is this trait? It is a measure of In this population, how much of the variability we observe is due to additive genetic variation?