ZOOL 304, Class Notes

Chapter 4, Feb. 14 - 19.  

Text reading:  Chapter 4.

• Assignment for written preparation.
• Discussion.
  • Introduction
  • Review fitness
  • Comment on text Chapter 4.
    • Genetic systems, sexual and asexual
    • Mendelian population genetics
    • Quantitative population genetics
      • Heritability
      • Response to selection
      • Evolutionary implications
      • Quantitative trait loci (QTLs)
  • Additional commentary
    • Mathematical models of population genetics
      • HARDY-WEINBERG EQUILBRIUM
      • Modelling selection
      • Modelling genetic drift
    • Quantitative genetics
• Study questions for text reading.

Notes for chapter 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17

Introductory comments.

In the previous two chapters (Chapters 2 and 3), we briefly examined adaptive and neutral evolution.  In this chapter (Chapter 4), we learn about genetic processes that affect genetic variation within populations.  Ultimately, all evolution must be explained in terms of these processes.  These chapters present the core concepts for understanding the genetic mechanisms of evolution.

• New variation may be introduced into a population.
  • Mutation, the ultimate source of all genetic variation, introduces new ("mutant") alleles into a population by spontaneous "random" change of preexisting alleles.
  • Immigration may introduce alleles from neighboring populations having a different history of mutation, selection, and drift.
     
• Variation may be reduced or eliminated.  When all but one variant has been eliminated from a population, the single remaining variant is said to be fixed.  The following processes can lead to allele fixation, unless opposed by other processes.
  
  • Selection generally removes from a population alleles whose bearers are, on average, less fit than bearers of alternative alleles.
  • Genetic drift eliminates alleles by random statistical fluctuations.  Drift is more effective in smaller populations.
  • Genetic bottlenecks and the founder effect reduce variation through drastic reduction in population size.
  • Inbreeding exaggerates the effects of genetic drift and genetic bottlenecks.
     
• Variation may be actively maintained, in the form of allele polymorphism (which can also be measured as heterozygosity).
  • Processes based on selection actively prevent variation from being lost.
    • Selection in progress (after mutational introduction of an advantageous allele, but prior to fixation)
    • Heterozygote advantage (also called heterosis)
    • Multiple-niche selection (a type of disruptive selection)
    • Fluctuating environmental conditions (conditions of selection change repeatedly, before any given allele can be selected to fixation)
    • Frequency-dependent selection
  • Other processes involve persistent introduction of new variation.
    • Mutation-drift balance (new mutant alleles appear as often as others drift to elimination)
    • Migration-selection balance (alleles are introduced from outside populations at a rate faster than they can be eliminated by selection)
    • Mutation-selection balance (new mutant alleles occur as often as they are eliminated by selection)

Chapter 4 introduces the use of equations to describe the genetic structure of populations.

For additional explanation, see

• Mathematical Models in Population Genetics.
• Quantitative Genetics

Also, please review the basic concept of fitness, from Chapter 3..

Comments on Chapter 4

• Genetic systems, sexual and asexual
• Mendelian population genetics
• Quantitative population genetics
  • Heritability
  • Response to selection
  • Evolutionary implications
  • quantitative trait loci (QTLs)

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Genetic systems, sexual and asexual

This section (Chapter 4, pp. 72-75) reviews some basic biology.  Hopefully, this material is familiar.  If not, let your instructor know, ASAP (As Soon As Possible).

Be sure you know the meanings of the following words.  We shall be using this terminology as if everyone understands.

• haploid
• diploid
• meiosis
• fertilization
• gamete
• zygote
• sexual reproduction
• asexual reproduction

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Population genetic change under selection

This section (Chapter 4, pp. 75-81) introduces the basic mathematical model for analyzing allele frequencies within populations.  The model is based on Mendelian principles of segregation and independent assortment of discrete alleles.

This model is extremely important in the history of evolutionary biology.

Esssential concepts include the following.

• Hardy-Weinberg frequencies
• selection coefficient
• mean fitness

For extended commentary, see:

• Mathematical models in population genetics
• HARDY-WEINBERG EQUILBRIUM
• Modelling selection
• Modelling genetic drift

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Quantitative genetic change under selection

This section (Chapter 4, pp. 81-89) introduces the basic features of quantitative genetics.

Esssential concepts include the following.

• variance (a statistical measure)
  • phenotypic variance
  • genetic variance
  • environmental variance
• heritability (h²)
  • h² = Var[A] / Var[P]
  • h² = R / S
• Selection differential (S)
• Response to selection (R)
  • R = h² / S

Quantitative genetics analyzes the heritability of measurable, continuously-varying ("quantitative") traits, and the response to selection of those traits.  The allelic basis for quantitative genetic variation is generally unknown, so Mendelian principles cannot be directly applied.  

However, most observations in quantitative genetics can in principle be explained by presuming that allelic variation at several independent loci contributes to phenotypic variation, and that phenotypes are additionally affected by environmental (i.e., non-genetic) variation.  

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One of the significant challenges for quantitative genetics is distinguishing between that proportion of phenotypic variance [P] which is due to genetic variance [G] and that proportion which is due to environmental variance [E].  Variance is a mathematically-defined statistical measure, equivalent to the square of the standard deviation.

In the simplest case of additive genetic and environmental variance, we have:

variance [P] = genetic variance [G] + environmental variance [E]

The textbook presentation of variance is quite sketchy.  For additional discussion, see Quantitative Genetics.

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The heritability of a trait refers to the proportion of phenotypic variance in the trait which is based on genetic variance.  Basically, the "broad sense" measure of heritability is defined as:

H² = Var[G] / Var[P]

A somewhat more useful "narrow sense" heritability measure is defined as:

h² = Var[A] / Var[P]

where Var[A] is the mathematically-defined additive genetic variance.

If the genetic component of variance is limited (i.e., if most phenotypic variation is environmentally induced), then heritability is low.  Conversely, if genetic variance is extensive AND environmentally-imposed variance is low, then heritability is high.

VERY IMPORTANT:  Heritability measures are always specific to the conditions under which they are measured.  One must not generalize a heritability measure from one population to a different or larger population.  Within-population heritability measures cannot be properly applied to between-population differences.  That is, two populations may show very high within-population heritability, while the difference between the populations may be entirely due to environmental differences.  

Rather infamously, this error is often made in characterizing human racial differences.  The observation that IQ shows high heritability is often used as a basis for a claim that racial differences in average IQ must be caused by genetic differences between the races.  But heritability can say nothing about between-race differences, which may be entirely due to environmental effects.  (An analogy may make this evident.  Take corn seed from two different sources ["races"].  Plant seeds from one source in a well-watered, well fertilized field.  Within that field, environmental conditions are fairly uniform.  So most variation in height and productivity among the corn plants in that field is measurably due to genetic variation.  Plant seeds from the other source in a different field, one that is arid and infertile.  Again, within-field conditions are uniform so most variation in height and productivity is measurably due to genetic variation.  Thus, heritability is high in each field.  But the average difference between the two populations tells you nothing about genetic differences.  Although racial variation might exist, this experiment does not illuminate the difference.  Rather; the observed between-population difference is plausibly due entirely to environmental difference.)  Heritability is context-specific.  To quote the textbook (p. 87), "[Heritability] does not tell us to what extent a trait is genetic or environmental...  Estimates of heritabilities are only reliable for the population and environment in which they are measured.

As for variance (above), the textbook presentation of heritability is quite sketchy.  For additional discussion, see Quantitative Genetics.

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Heritability is directly related to response to selection.  That is, if you know the heritability of a trait in a population, you can predict how much that trait will respond to selection.  Conversely, if you know how a trait has responded to selection, you can calculate its heritability.

For the simple case of "truncation selection" (in which only individuals beyond a certain threshold reproduce successfully), if you measure the "selection differential" [defined as S, the mean of the parental generation before selection subtracted from the mean of the reproducing individuals from that generation], and you measure the "response to selection" [R, the mean of the parental generation before selection subtracted from the mean of the offspring generation], these will be related to heritability [h²] by the following equation.

h² = R / S  or   R = h² / S

The textbook presentation of the response to selection is concentrated in the caption for Fig. 4.10 on p. 86. Again, as for variance (above) and heritability (above), this presentation is quite sketchy.  For additional discussion, see Quantitative Genetics.

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Perhaps the most significant concept in this chapter is presented on page 87:

"When heritability is high, the response to strong directional selection can quickly produce very large phenotypic changes."

That is, under appropriate circumstances evolutionary change can be quite rapid.  The principal evidence comes from experiments in artificial selection, but similarly large responses to selection have been measured in natural populations.  Galapagos finches studied by Rosemary and Peter Grant offer the classic example (more) . (Jonathan Weiner earned a Pulitzer Prize for his account the Grants' research, The Beak of the Finch: A Story of Evolution in Our Time.)

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Chapter 4 closes with an aside about quantitative trait loci or QTLs.   Quantitative trait loci are specific chromosomal sites which have been associated, by genetic mapping, with quantitative genetic variation.  Study of QTLs may play an increasingly important role in evolutionary biology as our knowledge of the genome expands.

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Notes for chapter 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17

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