In a previous post, I briefly discussed something called genetic correlation and how this might be important for the evolution of a trait. Now, I hope to further clarify that concept and add to that a discussion of a very important concept in evolutionary biology—*heritability—*and tie it back to my initial discussion of the evolution of pesticide resistance.

Consider your siblings or the siblings of a friend and you will likely observe that inheritance of a trait is not a binary distinction. In other words, it is not always as simple as either having or not having a trait from a parent. Chances are, neither you nor your siblings are exactly the same height as either of your parents, or their mean (or average). This is because height–and virtually every other quantitative trait, or one that is variable along some continuum—has an associated heritability (or *h*^{2}). As an aside, the notation of this is a bit confusing; we’re not actually squaring anything, but this notational weirdness is an accident of history. At any rate, the most straightforward, but perhaps least intuitive way of thinking about heritability is that it is the slope of the best-fit linear regression of offspring trait means on parent trait means. If your parents’ mean height is *x*, and you and your siblings’ mean height is *y*, and you plot this as a point (*x*,*y*) on a coordinate plane along with those of many other families, heritability is the slope of the line that most closely follows this cluster of points. Incidentally, the technique of linear regression taught in introductory statistics was developed for just this purpose.

To explain that in another way, heritability is the proportion of variation transmitted to offspring by parents. Because this proportion is often of less than 1, heritability is frequently less than complete. For example, if *h*^{2}=0.6 for pesticide resistance (it actually varied in the study I described), on average, offspring will have 60% of the resistance of the selected group. This affects the rate of evolution and can be used to predict the evolutionary trajectory of a population. Higher heritability means the trait evolves faster; fewer generations are required for the trait to increase to the same degree as a trait with lower heritability.

There is another layer of complexity to be found here: heritability can be thought of as the proportion of variability in a trait that is due to genetic variation, which implies that if the total amount of variation in a trait changes, heritability will also be affected. This can happen due to environmental changes. In the case of pesticide resistance, if the amount of spraying changes and this affects the amount of variation in a resistant phenotype, heritability may change as well.

What does this mean for genetic correlation? Well, through a bit of mathematical manipulation, it can be shown that heritability is the genetic correlation of a trait with itself. Thus parents having a higher trait value tend to have offspring with a higher trait value. For this reason, we can use genetic correlation and heritability to show how a trait might change from one generation to the next and into the future. In the pesticide study, we found that alternately selecting on anticorrelated traits resulted in retarded evolution of pesticide resistance. Could there be other ways in which we might take advantage of these relationships to change the evolutionary fates of populations? For example–if the amount of spraying affects heritability, as mentioned above, might there be some optimal level of application that optimizes efficacy and rate of resistance evolution? These are all questions that can be approached with an understanding of heritability, one of the foundational measures of evolutionary theory.

Edited by Kerri Donohue and Ed Basom