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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
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The Hardy-Weinberg Principle
- • A model to estimate genetic diversity of a
- population from a subsample
- – Based on Mendelian segregation and
- probabilities
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HW assumptions
- 1. Random mating:
- a. Locus specific (e.g. MC1R locus in geese)
- 2. No mutation:
- a. Mutation is a long-term 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
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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?
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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)
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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)
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HWP
- p2 + 2pq + q2 = 1
- p + q = 1
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