Zoology 510, Class Notes for Ridley, Chapter 5
The Theory of Natural Selection

Brief Outline

• Overview of chapters 5 through 9.

• Chapter 5 overview (check-list of important ideas).

• Summary of Equations (listing all numbered equations from Chapter 5).

• Section-by-section comments
  • 5.1. Gene frequencies
  • 5.2. Modelling population genetics
  • 5.3 - 5.5. Hardy-Weinberg equilibrium
  • 5.6. Single-locus selection
  • 5.7. Peppered moth
  • 5.8. Pesticide resistance
  • 5.9. Estimating fitness
  • 5.10. Real-world complications
  • 5.11. Mutational equilibrium
  • 5.12. Heterozygous advantage
  • 5.13. Frequency-dependent selection
  • 5.14. Multiple-niche polymorphism
  • 5.15. Subdivided populations

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Overview of Chapters 5 through 9

• Our modern theory of evolution embraces several processes, including:

  • Natural selection.
  • Mendelian genetics.
  • Molecular mutation.
  • Genetic drift.

• Chapters 5, 8 and 9 concentrate on DETERMINISTIC PROCESSES.
  • Gene and genotype frequencies in large populations (Chapter 5).
  • Single locus selection (Chapter 5)
  • Two-locus and multilocus selection (Chapter 8)
  • Genetics of quantitative traits (Chapter 9)

• Chapter 6 and 7 concentrate on RANDOM PROCESSES.
  • Genetic drift (Chapter 6)
  • Molecular mutation and neutral theory (Chapter 7)

• In all of these chapters, mathematical models are of central importance.
  • You will be expected to understand the models at the level presented by Ridley.
  • You will be expected to know or be able to derive all numbered equations.
  • You will be expected to solve problems comparable to end-of-chapter exercises.
  • You will be expected to interpret graphs and/or to reproduce properly labelled graphs to summarize important concepts.

• All of these chapters also include particular examples illustrating each process.
  • You will be expected to be familiar with the text-book examples.

• In future chapters (and in real-life biology), understanding particular evolutionary phenomena requires attention to all of these processes, as well as the basics of natural selection and genetics from Chapters 2 and 4.

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Overview of Chapter 5

Chapter 5 introduces several major ideas.
There is a LOT of important material in this chapter. To make sure you don't miss anything, use the following as a check-list.

• Gene frequency and genotype frequency (5.1).
• Modelling population genetics (5.2).
• Equilibrium models (Hardy-Weinberg equilibrium) (5.3-5.5).
• Single-locus selection models (5.6-5.8).
  • Mathematical explanation (5.6).
  • Famous example: The peppered moth, Biston betularia (5.7).
    Less famous complications (5.7.4)
  • Famous example: Pesticide resistance (5.8).
• Fitness estimation (5.9).
• Mechanisms which maintain allele polymorphism (5.11 - 5.14).
  • Mutational equilibrium (5.11).
  • Heterozygote advantage (5.12).
    • Mathematical explanation (5.12).
    • Famous example: Sickle-cell anemia (5.12.2).
  • Frequency-dependent selection (5.13).
  • Multiple-niche polymorphism (5.14).
• Modelling subdivided populations (5.15).
  • Higher homozygote frequency (Wahlund effect) (5.15.1).
  • Gene flow (migration) (5.15.2-5.15.3).
  • Migration-selection balance (5.15.4).

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Chapter 5, Section-by-Section Comments

Most of this chapter of Ridley's text is straightforward and clearly explained. The following comments will therefore concentrate on highlighting certain essential goals for your study.

5.1. "Population genetics is concerned with genotype and gene frequencies."

• Know how to calculate gene frequencies, when given genotype frequencies.
• Given Hardy-Weinberg conditions, know how to calculate genotype frequencies when given gene frequencies.
• Be able to do these calculations either numerically or algebraically.

5.2. "An elementary population genetics model has four main steps."

• Understand the steps which must be included in a population genetics model, and how those steps can be simplified (e.g., by assuming some or all of the Hardy-Weinberg conditions).
• These steps can be made as complex and realistic as one wishes, but in this course we will concentrate on the simplest models.

5.3. "Genotype frequencies in the absence of selection go to the Hardy-Weinberg equilibrium."

• Know what simplifying conditions are assumed for the Hardy-Weinberg theorem.
  • Random mating.
  • No selection.
  • Large population.
  • No mutation.
  • No migration in or out.

• Be able to state the Hardy-Weinberg theorem, either in words or algebraically.  That is, assuming Hardy-Weinberg conditions, know how to describe both gene frequencies and genotype frequencies in terms of gene frequencies in the immediately preceding generation.
• Be able to calculate genotype frequencies using the Hardy-Weinberg theorem.  Be able to reproduce (sketch) Figure 5.2.
• Understand (and be able to explain) reasons why a population might NOT be in Hardy-Weinberg equilibrium (some of these will be discussed in later sections).
• Understand (and be able to explain) how various departures from the Hardy-Weinberg assumptions will affect gene and genotype frequencies (such departures will be the subject of several later sections; also see Review Question 1, p. 131).

5.4. "We can test, by simple observation, whether genotypes in a population are at the Hardy-Weinberg equilibrium."

• When given genotype frequencies (or numberical counts), be able to determine whether the population is in Hardy-Weinberg equilibrium.  For example, given the "observed numbers" in Table 5.2, be able to calculate the "expected proportions" and "expected numbers".

5.5. "The Hardy-Weinberg theorem is important conceptually and historically, and in practical research and the workings of theoretical models."

• Understand (and be able to explain) the three points of value for the Hardy-Weinberg theorem, as listed by Ridley on p. 99.

5.6. "The simplest model of selection is for one favored allele at one locus."

• Understand the simplifying assumptions in this model (i.e., Hardy-Weinberg conditions, modified by selection operating on survival).
• Understand the derivation of all equations in this section.
• Know how selection coefficient is defined algebraically in this model.
• Given parental gene or genotype frequencies and the selection coefficient, be able to derive an algebraic expression for and know how to calculate the following:
  • Gene and genotype frequencies in the next generation, after selection.
  • Mean fitness.

• Given a change in gene frequency from one generation to the next, be able to derive an algebraic expression for and know how to calculate the selection coefficient.
• Understand how, using the above procedure, to calculate changes in gene frequency due to selection over many generations.
• Be able to sketch graphically the result of selection over many generations, such as the data presented in Table 5.4.

5.7. "The model of selection can be applied to the peppered moth."

• This is one of the most famous examples of well-documented selection in nature.  You should understand (and be able to explain) the basic biology of this example, and also be familiar with complications that are often omitted from introductory biology texts.

• 5.7.1. "Industrial melanism in moths evolved by natural selection."
  • Know the basic facts of environment, selection, and genetics of Biston betularia that are relevant for this example.

• 5.7.2. "One estimate of the fitnesses is made by using the rate of change in gene frequencies."
  • Understand (and be able to explain) how the model of section 5.6 applies to enable calculation of the selection coefficient for the peppered moth, and how the data tabulated in Table 5.5 were derived.

• 5.7.3. "A second estimate of the fitnesses is made from the survivorship of the different genotypes in mark-recapture experiments."
  • Understand (and be able to explain) how these experiments relate to the calculation of section 5.7.2.
  • Understand the assumptions underlying these experiments (see Review Question 5, p. 132.)
  • Understand how the fitness values in in Table 5.6 were derived.

• 5.7.4. "The details of the story are now known to be more complex."
  • Be able to list and discuss some of the complications affecting the evolution of melanism in peppered moths.

5.8. "Pesticide resistance in insects is an example of natural selection."

• This section gives another example of applying the simple model of selection to real-world observations.  Be able to discuss the basic biology, the relevant assumptions of this example.
• Understand the tabulated data (Table 5.7), the graph (Figure 5.6) and the calculations (applying algebraic expression derived in section 5.6).

5.9. "Fitnesses are important numbers in evolutionary theory and can be estimated by three main methods."

• Two of the three methods have already been discussed.
  • Direct measures of survival (e.g., mark-recapture experiments).
  • Calculations from gene-frequency changes between generations.
• The third method is by calculation based on departures from Hardy-Weinberg expectations, in situations where gene frequencies are not changing (see section 5.12).
• Note the emphasis in the concluding paragraph in this section, that "the fitnesses of different genotypes are among the most important variables -- perhaps the most important variables -- in the theory of evolution."  But in most cases fitnesses are extremely difficulty to determine.

5.10. "Natural selection operating on a favored allele at a single locus is not meant to be a general model of evolution."

• The ideal, simplified conditions of single-locus, two allele models in large, randomly mating populations are not realistic.  But such models do constitute proof-in-principle of the basic idea of selection operating through rules of Mendelian genetics.  Any appropriate complications can be readily incorporated into models of population genetics, albeit with loss of mathematical simplicity.  However, making complicated models realistic requires that the model be supplied with accurate parameters like fitnesses, and these are often difficult to obtain.

5.11. "A recurrent disadvantageous mutation will evolve to a calculable equilibrial frequency."

• This is a very simple concept, recognizing the importance of mutation in maintaining a supply of variation.
• Understand how the processes of mutation (which adds mutant alleles to a population at some rate) and selection (which removes mutant alleles from the population, at a rate that depends on how many are present) will necessarily strike a balance at mutational equilibrium.
• Understand the mathematical expression of this concept.
• Be able to calculate the gene frequency at mutational equilibrium for a disadvantageous allele.
• Understand how mutational equilibrium can contribute to polymoprhism.

5.12. "Heterozygous advantage."

• 5.12.1. "Selection can maintain a polymorphism when the heterozgote is fitter than either homozygote."
  • Understand (and be able to explain) the basic concept of heterozygote advantage in terms of genotype fitnesses.
  • Understand the significance of heterozygote advantage as an explanation for genetic polymorphism (why more than one allele are so commonly found at any given locus).

• 5.12.2. "Sickle-cell anemia is a polymorphism with heterozygote advantage."
  • Understand how selection coefficients against the homozygotes can be calculated, from data such as that presented in Table 5.9.

5.13. "The fitness of a genotype may depend on its frequency."

• The modelling continues to grow complicated.
• Understand why fitness may depend on genotype frequency; mimicry provides an example.
• Understand that frequency-dependent selection can maintain allele polymorphism.

5.14. "Multiple niche polymorphism can evolve in a heterogeneous environment."

• Understand that polymorphism can be maintained by selection IF different genotypes have different fitnesses in various niches.
• Understand that this polymorphism can evolve more readily if habitat selection occurs, i.e., if each genotype can choose its preferred niche.

5.15. "Subdivided populations require special population genetic principles."

• 5.15.1. "A subdivided set of populations has a higher proportion of homozygotes than an equivalent fused population:  this is the Wahlund effect".
  • Understand why this must be so, at least when the subdivisions do not all share the same gene frequency distribution.
  • Understand the significance of this effect for sampling populations to determine if they are in Hardy-Weinberg equilibrium.
  • Understand the significance of this effect when previously separate populations merge.

• 5.15.2. "Migration acts to unify gene frequencies between populations.
  • In this situation, Ridley makes rather a muddle of his derivation; so...
  • Simply appreciate that non-selective migration must act in this way.

• 5.15.3. "The convergence of gene frequencies by gene flow is illustrated by the human population of the United States."
  • This example makes some unstated assumptions, which you might wish to consider and criticize.

• 5.15.4. "A balance of selection and migration can maintain genetic differences between subpopulations."
  • Understand that selection-migration balance can maintain a polymorphism which would be eliminated by either selection or migration acting alone.
  • Skip the equations 5.14 and 5.15 in this section.  (I can't make head nor tail of Ridley's derivations.)

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