Population Genetics

POPULATION GENETICS IS OFTEN THOUGHT TO BE A DIFFICULT SUBJECT. To some extent, difficulties are inevitable in a field where some quite basic points are controversial. However, problems are most acute when theoretical points are discussed, despite the fact that there has been very little controversy over the mathematics. In my experience, the actual mathematical manipulations rarely cause much difficulty. Rather it is that the biologist, lacking the physicist's or chemist's experience in "reading" mathematical formulae, finds it difficult to appreciate what is happening in a mathematical treatment and to grasp the implications of the results obtained, when these are given in mathematical form. Accordingly, I have followed a procedure, which students seem to find helpful, of giving a rough-and-ready verbal treatment of a problem before attempting a much more exact mathematical treatment; when the results of the latter are not readily interpretable, I have given an elucidation. Another problem which often concerns students is the reliability of results obtained using approximate methods; I have, therefore, discussed this in fair detail in critical cases. When dealing with controversial issues, I have done my very best to be fair. To conceal one's opinions entirely would probably make for a very dull book. I trust, however, that I have given enough for the reader previously unfamiliar with these controversies to form his own judge­ ment.

1. Introduction.- Natural selection.- Problems studied by population geneticists.- Approaches to our problems.- The Mendelian population.- Factors affecting the genetic composition of populations.- Summary.- 2. Selfing.- Inbreeding.- Inbreeding depression.- Difficulties in allowing for natural selection during inbreeding.- Species inbreeding to some extent in nature.- Effect of selling on genotype frequencies at a single locus.- Information needed to discuss the effect of inbreeding on the entire genotype.- The start (generation 0).- A later stage (generation n).- Proportion of lines completely homozygous at a late stage.- To determine the average number of tracts in a given generation.- To determine the average number of heterozygous ends.- To determine the average number of external junctions.- Proportion of lines homozygous at all loci.- An illustrative example.- Total length heterozygous.- Summary.- 3. Random Genetic Drift.- On the word “probability”.- Intuitive notions on the effects of drift.- Probability distribution of allele frequency.- Mean allele frequency: mean frequency of heterozygotes.- Extreme versus intermediate allele frequencies.- Circumstances under which drift may be ignored.- Long-term effects of drift.- Variable fertilities Variable population size.- Summary.- 4. Survival and Fixation of Advantageous Mutants.- Factors affecting the chance of fixation.- Genic selection. Mean and variance of the change in allele frequency.- The probability of fixation: Kimura’s formula.- Accuracy of Kimura’s formula.- The probability of fixation: some conclusions.- Initial frequency larger than 1/(2N).- Variable population size (initial frequency 1/(2N)).- Dominance in fitness.- Summary.- 5. What is the role of Drift in Evolution? I. Morphological Characters.- The problem.- Harmful mutants.- Obviously adaptive characters.- “Minor” morphological variants.- Chromosomal inversions in Drosophila pseudoobscura.- Colour and banding in Cepaea nemoralis.- Sternopleural chaetae in Drosophila melanogaster.- Wing colour in Panaxia dominula.- Conclusions on morphological characters.- 6. What is the role of Drift in Evolution? II. Protein Variation.- Protein polymorphism.- Rate of nucleotide substitution: theory Rate of nucleotide substitution in practice.- A different approach Allele frequencies in geographically distant areas.- Effect of migration.- Frequency of heterozygotes.- Testing the neutral theory from frequency data: summary.- Experimental approach.- Experiments involving several loci.- Predicting selective response from biochemical studies.- Tentative conclusions.- Summary.- 7. Hitch-Hiking Effect of a Favourable Gene.- The hitch-hiking effect defined.- Effect of recombination.- The setup most favourable for hitch-hiking.- Some other situations leading to hitch-hiking.- Summary.- 8 Changes of Allele Frequency Under Natural Selection in Large Random Mating Populations.- Conditions under which the problem can be simplified.- Genic selection.- Wright’s formula.- Change in allele frequency per generation (mild selection).- Time required for a given change Allowance for drift.- Industrial melanism.- Summary.- 9. Evolution of Dominance.- Modifiers of dominance.- Disadvantageous mutants.- Advantageous mutants.- Balanced polymorphism.- Metrical characters.- Summary.- 10. Polymorphism.- Frequency of polymorphism.- Some possible explanations for polymorphism.- Heterozygous advantage: theory.- Sickle-cell anaemia.- Is heterozygous advantage common?.- Variable selective advantage: formal theory.- Measuring selective advantage: formal approach.- The ecological genetic approach.- Inversions in Drosophila pseudoobscura.- Batesian mimicry in butterflies.- Final comments.- Summary.- 11. Evolution of Altruism.- Altruistic behaviour.- Kin selection.- Social insects.- Group selection.- Summary.- 12. Summary. Some Tentative Conclusions.- Appendix 1. A Misapplication of the Hardy-Weinberg Law.- If genotype frequencies do not obey the Hardy-Weinberg law what can we conclude?.- Problem.- Solution.- General comment.- Appendix 2. Some Points in Statistics.- Probability.- Mean and variance.- Probability distributions.- Binomial distribution.- Poisson distribution.- Poisson approximation to binomial distribution.- Continuous distributions.- Normal distribution.- Normal approximation to binomial distribution.- A note on chapter 3.- Some mathematical points.- Suggestions for Further Reading.