Notes for Lecture #4:

        Population Genetics -- Hardy Weinberg

        Copyrighted 1996. May not be reproduced for commerical purposes

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        The best way to gain an understanding about drift (finite population size) and selection is to play around with them. Try different population sizes (e.g., 5 vs. 25 vs 100 vs 1000) and different survival probabilities in the Hardy-Weinberg simulator . This is a product of our good friends at the University of Chicago. By choosing summarize, one gets the distribution of final allele frequencies. Not choosing this gives the individual sample paths. Have fun!

        The marriage of Mendel and Darwin

      • Heritable Variation
        • One key to Darwin's proposed mechanism of evolution is the existence of heritable variation.
        • How much genetic variation is there in natural populations?
        • What are the properties of this variation?
      • Darwin and Mendel
        • Darwin's Origins had an immediate major impact as soon as it appeared (1859).
        • Mendel's work (1856) was promptly forgotten, then rediscovered with major fanfare in 1900.
        • A result of this was two different schools of the mechanism of evolution, which took nearly 20 years to be reconciled.
      • Darwin's model of inheritance
        • Darwin assumed blending inheritance.
        • Fleeming Jenkin (1867) pointed out that blending inheritance results in genetic variation being halved each generation. Thus, Darwin's mechanism of inheritance does not allow genetic variability to be maintained.

        The Stormy courtship: The Biometricians versus the Mendelians

      • The Biometricians
        • Motivated by Darwin's belief that selection acts on small changes in continuous characters, they developed the framework for the modern theory of statistics.
        • Francis Galton (Darwin's cousin) and Karl Pearson were the key figures.
        • More concerned with the mechanisms of selection than the mechanisms of heritability.
      • The Mendelians
        • Lead by Bateson.
        • Felt that the particulate nature of the gene rules out natural selection (as they thought different alleles had very large effects). They felt mutation generating alleles of large effect was the driving force of evolution.

        The reconciliation: Population Genetics

        The basis for evolution is changes in allele frequencies

      • The founders of population genetics (1920's - 1940's )
        • Sewall Wright
        • R. A. Fisher
        • J. B. S. Haldane
      • Allele and genotypic frequencies
        • Consider a locus with two alleles, A and a
        • In a diploid, three possible genotypes A A, Aa, aa
        • Key questions:
          • What happens to allele frequencies over time?
          • What happens to genotypic frequencies?
          • Example

      • This example illustrates several points
        • In general, populations with the same allele frequency can have different genotypic frequencies.
        • However, when random mating occurs, there is a simple relationship between the two.
        • With only random mating, allele frequencies do not change.

      • Hardy-Weinberg (1908) theorem
        • If only random mating occurs, then
        • Allele frequencies remain unchanged over time
        • After one generation of random-mating, genotypic frequencies are given by

      • The importance of Hardy-Weinberg
        • If the only evolutionary force acting on the population is random mating, allele frequencies remain unchanged and genotypic frequencies (after the first generation) are constant.
        • Thus, Mendelian genetics implies that genetic variability can persist indefinitely, unless other evolutionary forces act to remove it.