Revised December 5, 2000
Textbook Assignment: Chapter 20, Pages 607-631.
Symbol substitution: Once again, it has been necessary to use "SUM" as a substitute for upper case Greek Sigma to indicate a summation.
Major concepts:
Introduction: In pevious lectures, we have worked almost exclusively with genetic loci that produce discontinuous variation. Alternative alleles at such loci generate phenotypes that differ from each other in discrete steps, such that each phenotype can be clearly distinguished from the others. This lecture focuses on continuous variation, where there is no easily distinguished borderline between phenotypes, such as sizes of individuals or intensity of pigmentation. Continuous phenotypic variation typically reflects the additive effects of alleles at several different loci and is frequently also influenced by environmental factors. Before examining the genetic factors that are involved, it will be helpful to examine the ways in which continuous variation is measured.
Continuous distributions: Any characteristic that is distributed in a continuous manner in a population and is capable of being measured in some way can be described as a metric character. If the variable is truly continuous, such that it is quantified through measurement, it is considered to be a true continuous trait. If it is quantified by counting, rather than measurement, it is considered to be a meristic trait. The textbook points out that there are numerous continuous traits that can be quantified both ways, such as number vs. weight of seeds produced per plant. However, we must be careful in making such generalizations, because total weight of seeds can reflect differences in the weight of individual seeds as well as differences in the number of seeds.
Distributions: Continuous variation results in a distribution of values that must be described in terms of the properties of the distribution. As shown in figure 20.1 and the diagrams on page 609, it is often convenient to divide the continuous variation into a series of increments and then count the number of individuals falling within each increment. Such data can easily be plotted as a histogram, which consists of a series of bars whose heights represent the frequencies of the incremental classes. With large numbers of individuals and very small increments, the histogram becomes smoothed into a distribution curve.
Terms used to describe a distribution: Statisticians use a number of terms to describe a distribution. The mean is the numerical average of all of the values. The median is the measurement for the class that divides the distribution in half, with half of the measurements smaller and the other half larger. The mode is the class that has the highest frequency. If the distribution is symmetrical, the mean, median, and mode will all be at the same point in the center of the distribution. If the distribution is asymmetric, the mode and median will be displaced from the mean. In such cases, the distribution is said to be skewed. Under some circumstances, a distribution may be bimodal, with two different classes more favored than intermediate values. In cases of skewed or bimodal distributions, it becomes difficult to apply statistical methods that are based on the assumption of a symmetrical "normal" distribution.
Variance: As shown on page 610, variance is a measure of how much the individuals in the sample differ from one another. If the variance is small, the distribution curve is narrow and has a sharp peak. If the variance is large, the curve will be wider, with a flatter peak. Variance is defined by the equation
Additive inheritance: Continuous variation occurs when a phenotypic trait is governed by the additive effects of multiple alleles at several different loci. These effects are usually seen in traits like the color of wheat seeds or the heights of individual plants. The example of incomplete dominance in flower color that we examined in chapter 13 (figure 13.1) probably reflects the same basic phenomenon as continuous variation, except that only a single genetic locus is involved. This limits the number of levels of color intensity that can be achieved to 3, making them easy to distinguish as discrete and discontinuous steps. Thus, even though the term "partial dominance" was used, the textbook also said that the amount of pigment in the heterozygote was approximately half as much as in the homozygous red flower. The current chapter describes such a relationship as absence of dominance and additive effects of individual alleles. Thus, the only real difference is that in the current chapter, we are dealing with multiple additive alleles, rather than only two.
Each new locus adds two more steps: With two separate loci whose alleles exhibit additive effects, it is possible to obtain 5 shades of color, which begin to blend together, particularly if there is some phenotypic variation within each of the five genetically determined classes. With three alleles, there are seven shades of color, as shown in figure 20.3. These seven colors represent 0, 1, 2, 3, 4, 5, and 6 copies of the color producing allele, as shown in figure 20.4. The frequency distribution of the seven colors in the F2 generation of a hybrid between true-breeding colorless and true-breeding maximally colored strains of wheat is 1:6:15:20:15:6:1. (figure 20.4) as expected for a binomial with n = 6 (Table 12.4). This distribution begins to look like a normal distribution curve. Also, note how relatively rare 1/64) it is to be completely homozygous for either of the extremes (all colorless or fully colored) in a distribution of this sort.
Multiple gene pairs: As the number of gene pairs at separate loci is increased, the number of different discrete steps increases, such that they become increasingly difficult to distinguish from one another. In addition, the extreme phenotypes (all red or all white in the example in figure 20.4 become increasingly rare, so nearly all of the individually observed phenotypes are distributed around a median value that reflects the relative frequency of the two classes of alleles. When generalized for n loci, the total number of alleles involved is 2n and the total number of different F2 phenotypes is 2n+1. The phenotypic ratios are determined by the binomial coefficients with n equal to the number of alleles involved (twice the number of loci).
Transgressive segregants: In cases where the parents have intermediate phenotypes, the phenotypic range of the progeny will often exceed that of the parents. An extreme case of this occurred in the example discussed above. The F1 generation was heterozygous at all three color loci, and thus was uniformly of a midrange color. The F2 spanned the whole range from all colorless alleles to all colored alleles. If the parents are of an intermediate color either because of heterozygosity or because of being homozygous colored at some loci and homozygous colorless at others, there is a possibility that the progeny will cover a wider range of colors than the parents as shown in figure 20.7. This same principle can cause a child to become taller than either of the parents. Conventional breeding of plant crops often involved a search for transgressive hybrids with particularly desirable properties, which can then be developed into true-breeding lines through multiple generations of self-fertilization. The results of such an experiment are described in Figure 27.12 and boxed example 27.3 (pages 777-778).
Importance of polygenic control: Many traits that are important in agriculture appear to be under polygenic control, such as height, weight, crop yields, etc. Many human traits are probably also under polygenic control, including skin pigmentation, obesity, intelligence, and predisposition to certain diseases. There is an unfortunate tendancy to try to oversimplify such relationships, particularly in cases where there are also major non-genetic influences, such as nutrition, environmental exposures, etc. We will return to this theme at the end of this lecture, and in greater detail in the discussion of eugenics in lecture 41.
Hybrid vigor: In many cases, a cross between two inbred lines will display quantitative traits that exceed those of either parent. This phenomenon, which is referred to as heterosis or hybrid vigor, usually results from increased heterozygosity at a variety of loci at which there are dominant effects on quantitative traits. Each of the inbred lines has become homozygous for recessive alleles at some of the loci. The increased level of heterozygosity allows expression of more of the dominant alleles in the hybrid than in either of the parents, and thus causes an increase in the quantitative trait (figure 20.8). In such cases, several generations of self-fertilization of the hybrids in the absence of selection for the increased trait will result in reversion to the parental states. There are also rare cases of overdominance, in which particular combinations of alleles in a heterozygote will cause a continuous variable to exceed that in either of the true-breeding parents.
Inbreeding depression: Wild populations with a normal pattern of random mating often contain many recessive alleles that produce slightly deleterious phenotypes when homozygous. Any one of these does not have a major effect. However, in a heavily inbred population, enough of these deleterious alleles may become homozygous to have a substantial collective effect, known as inbreeding depression. Typical symptoms include reduced size, vigor, and productivity. Thus, when inbreeding is used to develop a true-breeding strain with a desirable property, it is important to select individuals that are the most fit overall at each generation.
Environmental effects: Environmental factors often have substantial effects on continuously variable traits. In addition, complex interactions between genotype and environment often make the effects difficult to predict. For example, some varieties of a crop may be better adapted to cool climates and others better adapted to hot climates. Thus, when studying the extent to which a particular trait is under genetic control, it is necessary to control for environmental effects. In addition, it is often necessary to do the testing in an environment similar to the one that the strain is being developed for.
Heritability: One of the key issues in quantitative genetics is the extent to which a continuous variable is influenced by inheritance, as opposed to environmental or chance effects. This is often expressed as heritability. Mathematical calculations of heritability become quite complex and involve many assumptions that we do not have time to go into in detail. In general, heritability describes the fraction of total observed phenotypic variance that can be ascribed specifically to genetic factors. Heritability is often divided into broad-sense heritability and narrow-sense heritability.
Broad-sense heritability: Broad-sense heritability includes all aspects of phenotypic variability that can be attributed to genetic effects, as opposed to environmental effects. It is normally expressed as the fraction of the variance that can be altered by genetic manipulation. In some cases, the easiest way to measure heritability is to determine the amount of variance caused by environmental (and chance) factors in genetically identical individuals, such as inbred lines or human identical twins. When the environmental variability is separated from the total variability, the remainder is assumed to be genetic.
Narrow-sense heritability: A better prediction of the potential success of selection is obtained from narrow-sense heritability. In addition to the simple additive effects of non-dominant alleles, phenotype is also influenced by dominance and epistasis. As we saw in the previous lecture, dominance can make it difficult to remove recessive alleles by selection. Epistasis can also reduce the effectiveness of selection by masking the presence of the alleles being selected against. Narrow-sense heritability seeks to measure the isolated effect of additive alleles.
Use of DNA markers: Because of problems associated with selection for quantitative trait loci (those genetic loci that control quantitative traits, often abbreviated QTL), investigators frequently look for DNA markers that appear to segregate with the quantitative traits that are desired. When such markers can be identified, their codominant expression and ease of detection make it much easier to perform selective steps involved in selecting for a QTL. They can also provide a first step toward isolation and cloning of the specific coding (or regulatory) sequence that is responsible for the quantitative effect.
Realized heritability: Selection is done by taking a subset of the population located at one end of a distribution and using it as the parental stock for the next generation. The Selection differential (S) is the difference between the mean of the original overall population and the mean of the selected parental population. The response to selection (R) is the amount that the mean of the progeny is shifted relative to that for the original parental population as a result of the selection. Narrow-sense heritability can be defined as R/S. Realized heritability is defined as the amount of narrow-sense heritability (R/S) that has been demonstrated (achieved) during a period of selection (which may not represent the theoretical maximum that could be achieved with continuing selection).
Limits of selection: In both plant and animal breeding experiments, it becomes important to know how much a particular trait can be enhanced by selective breeding of individuals that express the trait strongly. The amount of change that can be achieved by selection is limited by achieving homozygosity at all of the loci that affect the trait. In addition, physiological limits may be reached, as shown in figure 20.14. The variable that is being selected (both up and down) is litter size in mice. After about 31 generations, no further increases in litter sizes were obtained, presumably because a physiological limit had been reached. If selection has not proceeded to total homozygosity, the process can be reversed, as shown in figure 20.15.
Human quantitative genetics: Studies of quantitative genetics are particularly difficult in humans because controlled matings cannot be done. One of the favorite tools of geneticists is to examine concordance of twins, with particular emphasis on identical twins that have been reared apart, which minimizes possible effects of growing up in similar environments. One major problem that arises in studies of heritability in humans is a tendancy to try to make comparisons between ethnic groups. Heritability studies are only meaningful when they examine the extent of variability that can be attributed to genetic factors within a group, and then only if environmental variables are closely controlled. We will return to human quantitative genetics when we analyze eugenics in lecture 41.