Zoology 510, Class Notes for Ridley, Chapter 9
Quantitative Genetics.

No written assignment, but you should try to answer the Study and Review Questions at the end of the chapter.

Brief Outline

• Introductory comments
• Overview
• Checklist of important concepts and terms
• Section-by-section comments
  • 9.1. Beak size in Darwin's finches.
  • 9.2. Continuous traits, polygenic characters.
  • 9.3. Genetic and environmental effects. .
  • 9.4. Genetic and environmental variance.
  • 9.5. Correlation among relatives.
  • 9.6. Heritability.
  • 9.7. Response to selection.
  • 9.8. Non-linear responses.
  • 9.9. Selection reduces genetic variability.
  • 9.10. Variation under stabilizing selection.
  • 9.11. Selection-mutation balance .
  • 9.12. Occurrence of slightly deleterious mutations.
  • 9.13. Conclusion.

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Introductory comments.

"Given the DNA, you cannot specify the organism.  That is not because we are ignorant about it [although we are], but because all the information necessary to specify an organism is not contained in the DNA.  There is also the complete sequence of environments in which the organism develops." Richard Lewontin (from video interview on the CD accompanying Ridley's text)

Genetics is often studied as if genes, all by themselves, determined traits.  Descriptions of Mendelian genetics tend to concentrate on traits that vary sharply with genotype but are relatively unaffected by ordinary environmental variation.  Many features of biological systems are indeed designed to develop similarly under a variety of ordinary environments (i.e., they are not much disturbed by ordinary environmental perturbations or ordinary variations in genetic context).  We describe such features as being "canalized" (like water confined in a canal, or channel, which can only flow one way).

So much of biological organization is so highly canalized, we often forget how much the environment necessarily contributes to each and every phenotypic trait.  However, in our consideration of the quantitative genetics of quantitative traits, we must pay attention to the fact that phenotypic variation is influenced by both genetic variation and by environmental variation.  Selection acts on variation, but only on that portion of variation which is heritable.

There are several issues of major significance associated with quantitative genetics.

• Quantitative genetics deals only with variance, with the quantitative differences among individuals which appear when genotypes and environments vary.  Highly canalized traits which show no variation among individuals are not the subject of quantitative genetics.

• Quantitative genetics (unlike simple versions of Mendelian genetics) recognizes that phenotypes are influenced by many factors so that particular genotypes (especially particular single-locus genotypes) do not neatly and reliably correspond with particular phenotypes.

• Most selection does not act on genotypes, but on phenotypes.
  • Therefore, the selection coefficient associated with a particular genotype is, at best, an average over the various genetic environments (haplotypes) and external environments (ecological circumstances) in which the genotype may find itself.
  • All selection coefficients are thus dependent on many factors besides the genotype itself.

• Heritability depends on a particular mix of genetic combinations and environments.
  • Measurement of heritability, or of genetic and environmental components for phenotypic traits, gives a description within particular circumstances, not a causal explanation.
  • Heritability is not a fixed property of a trait.
  • Heritability may change if the environment changes or if the gene pool is altered.
  • Many discussions of "heredity vs. environment" or "nature vs. nurture" are misguided.
  • "Genetic determinism" is a concept riddled with fallacy and paradox.

• Heritability can be a counter-intuitive concept.  "High heritability" does NOT imply "genetically determined".
  • Heritability is not defined for characters which do not vary.
  • Therefore, characters which are the most strongly "determined" by genetics, which are so strongly canalized that they are unaltered by environmental influence, have NO heritability.

• Concepts of quantitative genetics are central to artificial selection.  Most of the plant and animal breeds that dominate modern agriculture have resulted from an evolutionary process based on principles of quantitative genetics.

Although "quantitative genetics" is, obviously, about quantitative processes, we shall again (as for chapter 8) emphasize qualitative appreciation of the phenomena associated with quantitative genetics.

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Overview.

• The most essential ideas of this chapter are additive genetic variance and heritability.  Both of those are formal (mathematical) concepts whose definitions must be clearly understood.

• The concept of additive genetic variance plays the same role in quantitative genetics that the concept of alleles plays in Mendelian genetics.
  • Other components of measurable phenotypic variance (e.g., variance to environmental influence, developmental noise, dominance, epistasis, and genotype-environment interaction) have the significant effect of obscuring additive genetic variance.
  • But ONLY additive genetic variance contributes to heritability and to the evolutionary response to selection.
• By definition, heritability h² is the proportion of phenotypic variance which is additive genetic variance, h² = V_A / V_P.

• Additive genetic variance is thus that component of total phenotypic variance which is heritable and which will respond to selection.
  • Unfortunately, there is no direct way to measure additive genetic variance; it must be calculated from its consequences.

• The response to selection R is equal to the heritability h² times the selection differential S, or
  R = h² S.

• The action of selection is expected to reduce variability (and hence reduce heritability) over time.
  • However, high variance and heritability remain observable facts for many quantitative traits that are under selection pressure.
  • Explaining this mismatch between expectation and observation remains a challenging problem.

CHECK LIST of important CONCEPTS and TERMS

• Variance
• Phenotypic variance
• Additive genetic variance
• Heritability
  • h² = V_A / V_P
  • h² = R / S

• Selection differential
• Response to selection, R = h² S

Chapter 9, Section-by-Section Comments

9.1. "Climatic changes have driven the evolution of beak size in one of Darwin's finches."

• This section introduces quantitative genetics by describing an example of selection operating on a quantitative trait.
  • Quantitative genetics belongs largely to the domain of artificial selection.
  • In natural populations, it is difficult to obtain direct measures of either heritability or of selective differential.
  • The evolutionary response of beak size in one of Darwin's finches, Geospiza fortis, provides one of the few good examples from nature of selection operating on a quantitative trait.

9.2. "Quantitative genetics is concerned with characters controlled by large numbers of genes."

• Understand the concepts of continuous variation in quantitative traits, and polygenic characters.
• Understand that a particular value for a quantitative trait can be affected by both genes and environment.
• Realize that quantitative genetics presumes large numbers of genes controlling quantitative traits, but the actual number of such genes usually remains unknown.

9.3. "Variation is first divided into genetic and environmental effects."

• This distinction is made on principle. How it is done in practice will be discussed later.
• Concentrate on the meaning of additive genetic variance.  It is the one source of variance that is heritable and upon which selection can operate.
• The idea of dominance effects not being heritable may at first seem counterintuitive.  Here is an example to make it perhaps seem more sensible.
  • Consider a population in Hardy-Weinburg equilibrium with A and a both equal to 0.5, and with values for the dominant and recessive phenotypes being 1 and 0 respectively.
  • The dominant:recessive phenotype frequencies will be 3:1, so the mean phenotype will [(3 x 1)+ (1 x 0)] / 4 = 0.75
  • Now consider a group of heterozygotes, Aa, with phenotype 1.  They will all vary from the mean by 0.25.  The mean variance of this set of heterozygotes is 0.25
  • However, if these heterozygotes breed, they will produce offspring in the standard 3:1 ratio with mean phenotype of 0.75, the same as the original population.
  • Although the mean variance of the parents differed from the whole population by 0.25, the mean variance of these offspring is zero.  On average, they do not differ from the original population.
  • Therefore, the mean variance of the heterozygotes is completely lost in their offspring.
  • Thus the dominance effect which caused the phenotypic variance in the heterozygotes is not heritable.

9.4. "The variance of a character is divided into genetic and environmental effects."

• Understand how variance is calculated.
  V_x = 1/(n-1) {summation over i from i=1 to n}(x_i - mean x)²
  (The expression in braces {} is normally symbolized by a capital Sigma.)

9.5. "Relatives have similar genotypes, producing the correlation between relatives."

• Correlation among relatives is one way to calculate V_A, additive genetic variance.
• V_A = twice the covariance between parents and offspring.
  Caution:  This relation holds only if the environments of parents and offspring are not correlated.
• Correlation of environments is a confounding consideration, whenever genetic correlation is being studied.

9.6. "Heritability is the proportion of phenotypic variance that is additive."

• h² is heritability
• By definition, h² = V_A / V_P.

• Ridley also offers an "intuitive" meaning for heritability:  "Heritability is the quantitative extent to which offspring resemble their parents, relative to the population mean."  Again, caution.  This relation is true only if the environments of parents and offspring are not correlated.  Again, correlation of environments is a confounding consideration, whenever genetic correlation is being studied.
• It is normally very difficult to disentangle environmental correlation from additive genetic variance in natural populations, making heritability practically impossible to determine without careful experimental manipulation.
• Caution:  Heritability is UNDEFINED for characters which do not vary.  Therefore, characters which are the most strongly "determined" by genetics, which are so strongly canalized that they are unaltered by environmental influence, have NO heritability.

9.7. "A character's heritability determines its response to artificial selection."

• The response to artificial (experimental) selection offers the most reliable way to determine heritability.
• In artificial selection, the selection differential for a trait is defined as the difference between the mean of the selected individuals (those which breed the next generation) and the mean of the entire population from which those individuals were selected.
• Similarly, the response to selection is defined as the difference between the offspring mean and the mean of the entire population from which their parents were selected.
• The response to selection R is equal to the heritability h² times the selection differential S, or
  R = h² S.
• This equation tells us how the response to selection depends on h².
• But, since R and S can be directly measured in artificial selection experiments, this equation also gives us another way to determine h².
  h² = R / S

9.8. "The relation between genotype and phenotype may be non-linear, producing remarkable responses to selection."

• This section is not critical for basic understanding, but should be interesting.

9.9. "Selection reduces the genetic variability of a character."

• This section translates the basic ideas from the previous sections into a qualitative description of how selection on quantitative traits is expected to work in nature.
• One standard expectation is for genetic variability to be reduced by consistent directional or stabilizing selection for quantitative polygenic traits.
• Note that selection reduces heritability.  As less fit genotypes are eliminated by selection, the variance which defines heritability is eliminated.  Therefore, one result when selection establishes the "genetic determination" of an adaptive trait, is that the heritability of that trait disappears.  (If this sounds perverse, bear in mind that it is not a paradox but merely a consequence of the formal definition for heritability.)

9.10. "Characters in natural populations subject to stabilizing selection show genetic variation."

• More accurately, SOME (or MANY) characters in natural populations subject to stabilizing selection show genetic variation.
• Nevertheless, this observable fact appears to contradict the conclusion of the preceding section (i.e., selection acts to reduce variation).
• Resolution of this problem remains controversial.  In the next two sections Ridley offers two possible explanations, which we have seen before.
  • Mutation-selection balance
  • Various schemes of selection.

9.11. "Selection-mutation balance is one possible explanation, but there are two models for it."

• Ridley does not explore this issue thoroughly.
• However, if mutation-selection balance is to be an explanation for variation in quantitative traits, it appears to demand a remarkably high mutation rate.  The associated difficulties are discussed in Box 9.2.
• Another resolution is also proposed in Box 9.2, involving shifting selection pressure, frequency dependent selection, or heterozygote advantage (the same suspects we have seen used to explain abundant polymorphism at Mendelian loci).
• Yet another possible resolution involves a role for repetitive DNA as highly mutable loci influencing quantitative traits.  Briefly, such loci may display an extremelyhigh mutation rate, with mutations having a very small effect.
  • This idea remains untested and is too new for the textbooks.
  • For more information (if you're interested) see:
    "Simple sequence repeats as a source of quantitative genetic variation", by Kashi, King (that's me) and Soller, Trends in Genetics 13:74-78 (1997).

9.12. "The rate of slightly deleterious mutations can be observed in experiments in which selection against them is minimized."

• This section emphasizes the significance of deleterious mutations, and the importance of selection to remove the resulting deleterious variation which would otherwise accumulate.

9.13. "Conclusion."

• Ridley's conclusion emphasizes the value of quantitative genetics as a tool to investigate questions involving traits whose underlying genetic basis is not precisely known.
• Ridley also emphasizes here that facts appear to contradict the simple expectations of theory, and that the proper resolution remains unclear.

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