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Why do we need models
 • Simplicity in a complex world
 • Conceptual vs. Mathematical
 • Models allow us to:
 – Define important parameters
 – Construct testable hypotheses
 – Generalize results
 – Predict the future

The HardyWeinberg Principle
 • A model to estimate genetic diversity of a
 population from a subsample
 – Based on Mendelian segregation and
 probabilities

HW assumptions
 1. Random mating:
 a. Locus specific (e.g. MC1R locus in geese)
 2. No mutation:
 a. Mutation is a longterm process (>100s)
 3. Large population size
 a. Minimal drift
 4. No selection
 5. No immigration/no emigration
 6. Diploids, sexual reproduction, nonoverlapping
 generations, equal allele
 frequencies among sexes

Probability Theory in Genetics
 • The PROBABILITY (P) of an event is the # of times the event will occur
 (a) divided by the total # of possible events (n)
 • What is the probability (P) of sampling a bull trout with haplotype A
 from this population?

Probability Theory in Genetics
 • The Multiplicative (Product) rule: if events A and B are independent,
 then the probability that they both occur is:
 P(A and B) = P(A) x P(B)

The Sum rule
 : the probability of 2 or more mutually exclusive events
 occurring is equal to the sum of their individual probabilities:
 P(A or B) = P(A) + P(B)

HWP
 p2 + 2pq + q2 = 1
 p + q = 1

