Post on 03-Apr-2018
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Population geneticsprobability
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Evolutionary Synthesis
Haldane were fathers ofpopulation genetics and
modern evolutionary
theory
Working in early 1920s,worked out how to Fisher,
Wright, and apply
Mendels laws in a
population context toprovide mechanistic
explanation for
evolutionary change
http://www.ars.usda.gov
Sewall Wright
http://www.york.ac.uk
R.A. Fisher
http://www.ucc.ie/
J.B.S. Haldane
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Population Genetics
Study of heritable variation inassemblages of organisms, and how this
is affected by mutation, drift, selection,
and gene flow
Diversity
Mutation+
Drift
-
Selection
+/-
Migration
+
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Population Genetics is Important
Disease susceptibility, genetic testing, and
personalized medicine
Statistical interpretation of forensic DNA
evidence
Human evolution and cultural history
Crop and animal improvement
Traditional breeding
Genetic engineering
Conservation plans for plant and animalcommunities
Responses of plant and animal communities
to climate change
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Mathematical Tools for Population Genetics
Basic algebra
Basic calculus
Basic
statistics Probability
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Population Genetics and Probability
Probability is at the core of much of
population genetics Reproduction is a sampling process
Effects of mutation, gene flow, selection,
and genetic drift must be seen as departuresfrom expectations based on random
processes
Example: 1 genetic locus and two alleles
in a forest of 20 trees determines color of
foliage. Green is dominant.
What proportion of offspring will have white
foliage?
: 4 copies : 36 copies
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Introduction to Probability
What is the probability of an individual event?
Sample Point Method What is the probability of 3 heads on 3 tosses of a coin?
What is the sample space?
What proportion is occupied by 3 heads outcome?
Outcome Toss 1 Toss 2 Toss 3 Shorthand
1 Head Head Head HHH
2 Head Head Tail HHT
3 Head Tail Head HTH4 Tail Head Head THH
5 Tail Tail Head TTH
6 Tail Head Tail THT
7 Head Tail Tail HTT
8 Tail Tail Tail TTT
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Defining Sample Space
Defining sample space manually is tedious to
impossible Combinations provides a shortcut for determining
the sample space
mn rule for number of ways that m elements from one
group can be combined with n elements from another
Permutations and Combinations allow caluculation
of the number of ways numbers or symbols can be
arranged Does the order of elements matter?
If not, then use a combination
If order matters, use a permutation
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Combining Probabilities
Independence and conditional probability
Does probability of one event depend on the
probability of another?
Intersection and union of events
Intersection
Probability of A AND BUnion
Probability of A OR B