Lecture 3

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Evolving Probabilities

• Genetic Variations:
  • Genotype: Single Nucleotide Polymorphisms (SNPs)
  • Phenotype: Dominant/Recessive Traits

  What are the processes generating and maintaining such variations?

• Elements of Population Genetics (GIF):

  • Mutations
  • Random Matings:
    • Hardy-Weinberg Equilibrium in very Large (Diploid) Populations
    • Genetic Drift in Finite Populations; Loss of Heterozygosity (Absorbing States)
  • Selection

  How does the probability distribution for an allele (alternate forms of a gene at a given locus) change with time?

• Quantifying Evolving Probabilities:

  • The Continuous Random Walk (GIF):
    • The Central Limit Theorem
    • The Diffusion Equation
  • Position-dependent Random Walks (GIF):
    • The Master Equation for Discrete Jumps
    • The Fokker Planck Equation in the Continuum
  • Probability of an Aallele in a Finite Population (GIF):
    • Binomial Sampling for Random Mating
    • The (forward) Kolmogorov Equation
    • Steady State Distributions (GIF)
    • The Backward Kolmogorov Equation (GIF)
    • Probability of Fixation (GIF)