pop gen prob 1

7/28/2019 Pop Gen Prob 1

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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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4

1 2224

i i

ii

i

iksibID pppP

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eH

11

141

ee

Nf

m

k

kPP

1


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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

pop gen prob 1

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