Genetic diversity and evolution

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Genetic diversity and evolution
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Content

• Summary of previous class
• H.W equilibrium
• Effect of selection
• Genetic Variance
• Drift, mutations and migration

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Hardy-Weinberg assumptions

• If all assumptions were met, the population would
  not evolve
• Real populations do in general not meet all the
  assumptions
• Mutations may change allele frequencies or create
  new alleles
• Selection may favour particular alleles or
  genotypes
• Mating not random -gt Changes in genotype
  frequencies
• Population not infinite -gt random changes in
  allele frequencies Genetic drift
• Immigrants may import alleles with different
  frequencies (or new alleles)

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Fitness

• The average fitness is
• W(1-r)p22pq(1-s)q21-rp2-sq2
• DP((1-r)p2pq/W)-ppqs-(rs)p/W

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Hetrozygote Advantage

• Pn1-(s/(rs))(1-r)pn2pnq/W -(s/(rs))
• (1-r)pn2pnq-(s/(rs))W/W
• (1-r)pn2pnq-(s/(rs)) (1-rpn2-sqn2)/W
• (1-rpn-sqn)/Wpn-(s/(rs)
• The difference decreases to zero only for
  positive r and s. Thus the scenario in which both
  alleles can survive is Hetrozygote Advantage

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Recessive diseases

• If rgt0, and s0, the disadvantage appears only
  homozygotic A1.
• In this case pn1pn(1-rpn)/(1-rpn2)
• 1/pn1-1/pn1/pn(1-rpn2)/(1-rpn)-1
• r(1-pn2)/(1-rpn)
• 1/pn-1/p0nr

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Fitness Summary

• Third fix point is in the range 0,1 only if r
  and s have the same sign.
• It is stable only of both r and s are positive
• In all other cases one allele is extinct.
• If rgt0 and s0 then the steady state is still
  p0, but is is obtained with a rate
  pn1/(nr1/p0)

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New Concepts

• Genetic Variation
• Genetic drift
• Founder effects
• Bottleneck effect
• Mutations
• Selection
• Non Random Mating
• Migration

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Genetic Variation

• Three fundamental levels and each is a genetic
  resource of potential importance to conservation
• Genetic variation within individuals
  (heterozygosity)
• Genetic differences among individuals within a
  population
• Genetic differences among populations
• Species rarely exist as panmictic population
  single, randomly interbreeding population
• Typically, genetic differences exist among
  populationsthis geographic genetic
  differencesCrucial component of overall genetic
  diversity

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heterozygosity

• Several measures of heterozygosity exist. The
  value of these measures will range from zero (no
  heterozygosity) to nearly 1.0 (for a system with
  a large number of equally frequent alleles).  We
  will focus primarily on expected heterozygosity
  (HE, or gene diversity, D). The simplest way to
  calculate it for a single locus is as
•                                                  
                                                    
      
• Eqn 4.1where pi is the frequency of the ith of k
  alleles. Note that p1, p2, p3 etc. may
  correspond to what you would normally think of as
  p, q, r, s etc.. If we want the gene diversity
  over several loci we need double summation and
  subscripting as follows

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Heterozygosity

• In H.W heterozygosity is given by 2pq. The rest
  of the expression (p2 q2) is the homozygosity.
• What does heterozygosity tell us and what
  patterns emerge as we go to multi-allelic
  systems? Lets take an example. Say p q 0.5.
  The heterozgosity for a two-allele system is
  described by a concave down parabola that starts
  at zero (when p 0) goes to a maximum at p 0.5
  and goes back to zero when p 1. In fact for any
  multi-allelic system, heterozygosity is greatest
  when
• p1 p2 p3 .pk                               
                                       
• The maximum heterozygosity for a 10-allele system
  comes when each allele has a frequency of 0.1 --
  D or HE then equals 0.9.  Later, we will see that
  the simplest way to view FST (a measure of the
  differentiation of subpopulations) will be as a
  function of the difference between the Observed
  heterozygosity, Ho, and the Expected
  heterozygosity, HE, 

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Genetic Variation

• HT HP DPT
• where HT total genetic variation
  (heterozygosity) in the species
• HP average diversity within populations
  (average heterozygosity)
• DPT average divergence among populations across
  total species range
• Divergence arise among populations from random
  processes (founder effects, genetic drift,
  bottlenecks, mutations) and from local selection).

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Genetic differentiation

• Inbreeding coefficients can be used to measure
  genetic diversity at different hierachical levels

Individual
Subpopulation
Total population
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Wrights F statistics

• Used to measure genetic differentiation
• Sometimes called fixation index
• Defines reduction in heterozygosity at any one
  level of population hierachy relative to any
  other
• levels Individual - Subpopulation - Total

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Wrights F statistics

• Heterozygosity based on allele frequencies, H
  2pq.
• HI, HS, HT refer to the average heterozygosity
  within individuals, subpopulations and the total
  population, respectively

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Wrights F statistics

• Drop in heterozygosity defined as

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Example

• 2 subpopulations, gene frequencies p1 0.8, p2
  0.3.
• Gene frequency in total population midway between
  them pt 0.55
• HS1 2p1q1 2 x 0.8 x (1-0.8) 0.32
• HS2 2p2q2 2 x 0.3 x (1-0.3) 0.42
• HS average(HS1, HS2) (0.32 0.42)/2 0.37
• HT 2 x 0.55 x (1 - 0.55) 0.495

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Identity by descent

• Imagine self-fertilising plant
• A - A 1,2 - 1,2 X
  ?
• 1/4 of offspring will be of genotype 1,1
• 1/2 of offspring will be of genotype 1,2
• 1/4 of offspring will be of genotype 2,2
• FX (inbreeding coefficient) is probability of IBD
  1/2
• equivalently, let fAA be the probability of 2
  gametes taken at random from A being IBD.

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Mutation occurred once

• Every mutation creates a new allele
• Identity in state identity by descent (IBD)

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The same mutation arises independently
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Identity by descent

• A - B C - D P - Q
  X
• Let fAC be the coancestry of A with C etc., i.e.
  the probability of 2 gametes taken at random, 1
  from A and one from B, being IBD.
• Probability of taking two gametes, 1 from P and
  one from Q, as IBD, FX

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Identity by descent

• Example, imagine a full-sib matingA - B /
  \P - Q X
• Indv. X has 2 alleles, what is the probability of
  IBD?

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Identity by descent

• Example, imagine a half-sib matingA - B - C
  P - Q X

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Mutations
m0.0001
A mutates to a at the rate m a reverts back to A
at the rate v The equilibrium value for the
frequency of A is given by
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SNP

• Single Nucleotide Polymorphism (SNP) naturally
  occuring variants that affect a single nucleotide
     -predominant form of segregating variation at
  the molecular level
• SNPs are classified according to the nature of
  the nucleotide that is affected       
  -Noncoding SNP
• 5' or 3' nontranscribed region (NTR)
• 5' or 3' untranslated region (UTR)
• introns
• intergenic spacers
• Coding SNPs
• replacement polymorphisms
• synonymous polymorphisms
•        Transitions          A to G  OR C to T
•        Transversions A/G to C/T OR C/T to A/G

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Natural Selection

• Tuberculosis (TB) infections have historically
  swept across susceptible populations killing
  many.
• TB epidemic among Plains Indians of QuAppelle
  Valley Reservation
• annual deaths
• 1880s 10
• 1921 7
• 1950 0.2

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Nonrandom mating

• Random mating occurs when individuals of one
  genotype mate randomly with individuals of all
  other genotypes.
• Nonrandom mating indicates individuals of one
  genotype reproduce more often with each other
• Ethnic or religious preferences
• Isolate communities
• Worldwide, 1/3 of all marriages are between
  people born within 10 miles of each other
• Cultures in which consanguinity is more prominent
• Consanguinity is marriage between relatives
• e.g. second or third cousins