Polygenic Traits and Estimates of Heritability

Goals: the goals of this lecture are to introduce polygenic (quantitative) traits and to define and explain how to measure heritability, an estimate of the amount of genetic variation in quantitative traits.

Related Textbook Material: Freeman and Herron (2001) Chapters 3 (some information) and 7 (the main source of information on this topic)

Lab Manual Questions over this material are in Lab Manual Chapter IX

The Lecture:

As we have seen, the potential for evolution through mechanisms such as natural selection depends on the presence of genetic variation: there must be genetically determined differences among the individuals in populations for there to be genetic change over time through natural selection, genetic drift, or gene flow. We have also seen that natural selection, gene flow, and genetic drift may affect the amount of genetic variation in a population in different ways. It is thus crucial for the study of evolution to be able to estimate the amount of genetic variation in a trait. For traits coded by a single gene, we can often directly evaluate the genetic variation simply by counting up different alleles and determining allele and genotype frequencies (you have seen how this can be done with allozymes, for example, in lecture 2 from week 4.)

For polygenic (quantitative) traits, we can't directly determine allele and genotype frequencies affecting a trait because there are too many genes affecting the trait for this to be practical (we can't find and study all the genes for a trait if there are a hundred or more genes affecting it, and polygenic traits can have this many genes affecting them.)

In this lecture, we'll figure out how to estimate genetic variation for a quantitative (polygenic) trait. First, we will consider the typical pattern of variation in a population for such a trait, then we'll look at what determines this pattern of variation and how we can estimate how much of the variation is genetic.

Polygenic (quantitative) traits are often aspects of organisms' bodies that can be measured in some way. Examples include height, sizes of different parts of the body, degree of some aspects of coloration. The specific phenotype of an individual (for example, how tall it is) is often referred to as its trait value.

The following graph shows the typical pattern of the frequency of individuals with different trait values in a population.

As you can see, this is a bell curve indicating that there are few individuals with extremely small trait values, that most individuals have about the average trait value, and that there are few individuals with extremely large trait values. Human height is an example of a quantitative trait that fits this pattern; most people are of average height, a few people are very short and a few people are very tall.

Two major factors, separately or working together, can cause such a distribution:

1. Genetic variation in quantitative (polygenic) traits. If individuals differ in the alleles at the many genes that code for such a trait, they can have different phenotypes. Such genetic variation is typically additive. Additive genetic variation refers to genetic effects where each allele at each of the many genes that codes for a trait has a small effect on the phenotype and the phenotype depends on the sum of the effects of all these alleles with each allele contributing equally. For example, the alleles at the many genes that affect height might all code for height that is either a little taller or a little shorter, and your height would depend on the sum of all the alleles for being taller and all the alleles for being shorter. Additive genetic variation results in a distribution like this because most individuals will have a combination of "tall" and "short" alleles and be of average height; only a few will get mostly "tall" alleles (and be tall) or mostly "short" alleles (and be short.) Because there are many genes, and many alleles, affecting the trait, and the effect of each allele is small, variation in the trait is continuous. We can't divide it up into clear, discrete categories (like gray versus black) in moths -- instead, there is a continuous range of variation from short to tall.
2. Environmentally determined variation in traits. The phenotype of an individual can depend directly on the environment in which it develops -- individuals could be genetically the same but differ in appearance because of the environment within which they live and develop. Some examples of this include: human height is influenced by prenatal and childhood nutrition as well as genetics. People are on average taller now than they were a hundred years ago because we receive better nutrition -- we aren't different genetically, we just get better food. Hair color in humans is influenced by a variety of factors including exposure to the sun and exposure to hair dyes -- people with the same alleles for hair color could have different color hair if one has been in the sun more or if they have dyed their hair. Environmentally determined variation typically also results in a continuous, bell-shaped distribution in a trait; most individuals develop in some average environment but some are exposed to more extreme environmental conditions and end up with the extreme forms of the trait.

The main measure of genetic variation in polygenic (quantitative) traits is called heritability. Heritability is defined as the proportion of all the variation in a quantitative trait in a population that is present because of genetic variation (genetic differences among individuals.) Remember that the total variation of a trait in a population can depend on genetic variation or environmental variation, so heritability is the proportion that is genetic, not environmental, out of that total.

Note that heritability is a measure of genetic differences among individuals, NOT simply of whether or not a trait is inherited. A trait can be inherited but if all individuals in the population inherit the same thing there is no genetic variation and therefore no heritability. For example, people almost all inherit having five fingers; a very small number of people inherit a different number but there is very little genetic variation in this trait so heritability is very low (even though having five fingers is clearly something we inherit.)

Since heritability is a proportion, it can vary in value from 0 (meaning none of the phenotypic variation in the population is genetic) to 1 (meaning all of the phenotypic variation in the population is genetic.) For many traits in many populations, values of heritability are somewhere between 0 and 1, meaning that some of the differences among individuals are genetic and contribute to heritability but other differences depend directly on the environment and do not contribute to heritability.

Now that we have defined heritability, our measure of genetic variation in quantitative (polygenic) traits in populations, we need to consider how we measure heritability. A standard method for measuring heritability is a mid-parent offspring regression. To conduct a mid-parent offspring regression, we measure the trait value for some trait in a large number of individuals. When these individuals have offspring, and these offspring grow up, we measure the trait value for that trait in the offspring. The idea behind the test is that if the differences between the individuals in the first generation (the parents) are genetic, then offspring will tend to resemble their parents -- smaller parents have smaller offspring, larger parents have larger offspring. If the differences between the individuals in the first generation (the parents) are environmental, then they won't be passed on to the offspring, so small parents could have large or small offspring and large parents could have large or small offspring.

To analyze the degree to which smaller parents have smaller offspring and larger parents have larger offspring, we make a plot of the average trait value of the offspring of each family versus the average trait value of the two parents of each family (the average value for the two parents is called the mid-parent value.) We then conduct a statistical test called a regression, which allows us to draw the straight line that best fits the points we've plotted.

FOR THIS class, we're NOT going to do the actual statistical test (haven't you done enough mathematical/statistical analysis already in this class?) It's something any statistical computer package can do and it's messy to do by hand, so we won't. You should, however, be able to eyeball the plots you see and draw an approximate straight line that fits the points well; you should also be able to interpret what such lines mean in terms of heritability. So let's look at what these plots might look like and how we would interpret such lines.

Suppose all the variation in some quantitative (polygenic) trait among the parents in a population is determined by genetic differences among those parents. In this case, the average offspring trait value for each family should equal the average (mid-parent) value of the two parents: parents who are small will have small offspring, parents who are medium sized will have medium size offspring, parents who are large will have large offspring. Here's what a mid- parent offspring regression graph would look like in this case (each dot on the graph represents a family, indicating the average parent trait value for that family and the average offspring trait value for the family):

Note that since the mid-parent values equal the offspring values the slope of this line equals 1. Note that since all the variation among the parents is genetic, this means that the heritability is equal to 1. In general, the slope of the line of a mid-parent offspring regression will vary from 0 to 1 and the slope gives us our estimate of the value of the heritability.

Now let's consider the other extreme. Suppose all the variation among parents depends on direct environmental influences, not on genetic differences. As shown in the following graph, this results in a scatter of points with no tendency to slope up or down, because parents of any size can have offspring of any size. The line that best fits such a plot is a flat line -- a line with zero slope -- as shown.

Again, we can see that the slope of the line, in this case zero, gives us our estimate of heritability, which is zero because none of the differences among the parents are genetic.

For many traits in many populations, we might see a mid-parent offspring graph like the following:

In this case, there is clearly some tendency for smaller parents to have smaller offspring and larger parents to have larger offspring, but there is also some other variation, and heritability would be between 0 and 1 indicating both genetic and environmental influences on the variation in this trait.

The mid-parent offspring regression method just described is a good way to estimate heritability but it is not perfect. We will consider one potential problem with the method. The problem is that if parents and their offspring tend to be in environments that are similar, and different from other families, then parents and offspring may resemble each other for reasons that are environmental and not genetic. Suppose for example that some families occur in areas with good nutrients and others occur in areas with poor nutrients. Both the parents and the offspring in areas with good nutrients might get larger because of those good nutrients, while parents and offspring in areas with poor nutrients might be smaller because of those poor nutrients. This could happen even if the individuals in the areas with good nutrients are genetically the same as those in the areas with poor nutrients. As a result, it would appear that the size of individuals had higher heritability than it should -- the mid- parent offspring regression would overestimate heritability because of environmental similarities between parents and offspring.

This problem has been dealt with in different ways in studies of heritability. Consider two possible ways to correct for this problem:

1. We could study aspects the environment and see whether the variation we observe in traits can be explained by differences in the environment. In the Darwin's Finches studied by the Grants, as described in your textbook, there was no evidence of direct environmental effects on traits such as bill size and body size, so the heritability estimates for these studies are more likely to be correct. However, it is never possible to study EVERY aspect of the environment that could affect a trait, so there is still some potential for error.
2. For some species, we can raise offspring of many families in constant environmental conditions. If offspring are still more like their parents than like each other, even though they raised in environments just like each other, then we can rule out differences in the environment as causes of differences among the offspring, and conclude that these differences are genetic. Raising offspring of many families in constant environmental conditions like this is called doing a common garden experiment. The basic procedure is to raise offspring of many families in constant environmental conditions to rule out the effects of the environment, and then to measure parents and offspring and do a mid-parent offspring regression to estimate heritability. The common garden experiment makes this estimate more accurate. As implied by the name ("garden") it is generally easiest to do with plants, especially small, relatively fast growing plants that can be grown in a greenhouse. It clearly can't be done with species that can't be raised in constant conditions in captivity. Where it has been done, it has provided more accurate estimates of heritability.

Click here to return to the index of lectures