genetic diversity and evolution
DESCRIPTION
Genetic diversity and evolution. Content. Summary of previous class H.W equilibrium Effect of selection Genetic Variance Drift, mutations and migration. Hardy-Weinberg assumptions. If all assumptions were met, the population would not evolve - PowerPoint PPT PresentationTRANSCRIPT
Genetic diversity and evolution
Content
Summary of previous classH.W equilibrium
Effect of selection
Genetic VarianceDrift, mutations and migration
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 -> Changes in genotype frequencies Population not infinite -> random changes in allele
frequencies: Genetic drift Immigrants may import alleles with different frequencies
(or new alleles)
Fitness
The average fitness is:
W=(1-r)p2+2pq+(1-s)q2=1-rp2-sq2
P=([(1-r)p2+pq]/W)-p=pq[s-(r+s)p]/W
)/(),/(
0,1
1,0
],[
srrsrs
qp
Hetrozygote Advantage
Pn+1-(s/(r+s))=[(1-r)pn2+pnq]/W -(s/(r+s))
=[(1-r)pn2+pnq]-(s/(r+s))W]/W=
=[(1-r)pn2+pnq]-(s/(r+s)) (1-rpn
2-sqn2)]/W
= (1-rpn-sqn)/W[pn-(s/(r+s)]
The difference decreases to zero only for positive r and s. Thus the scenario in which both alleles can survive is Hetrozygote Advantage
Recessive diseases
If r>0, and s=0, the disadvantage appears only homozygotic A1.
In this case: pn+1=pn(1-rpn)/(1-rpn2)
1/pn+1-1/pn=1/pn[(1-rpn2)/(1-rpn)-1]=
[r(1-pn2)/(1-rpn)]
1/pn-1/p0=nr
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 r>0 and s=0 then the steady state is still
p=0, but is is obtained with a rate pn=1/(nr+1/p0)
New Concepts
Genetic Variation
Genetic drift
Founder effects
Bottleneck effect
Mutations
Selection
Non Random Mating
Migration
Genetic Variation
Three fundamental levels and each is a genetic resource of potential importance to conservation:
1) Genetic variation within individuals (heterozygosity)2) Genetic differences among individuals within a
population3) Genetic differences among populations Species rarely exist as panmictic population = single,
randomly interbreeding population Typically, genetic differences exist among populations
—this geographic genetic differences=Crucial component of overall genetic diversity
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
21 ipH
i j
ijpH 21
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? Let’s 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,
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).
Genetic differentiation
Inbreeding coefficients can be used to measure genetic diversity at different hierachical levels
Individual
Subpopulation
Total population
Wright’s 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
Wright’s 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
Wright’s F statistics
Drop in heterozygosity defined as
S
ISIS H
HHF
FST HT HS
HT
T
ITIT H
HHF
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
FST HT HS
HT
0.495 0.37
0.4950.252
Identity by descent
Imagine self-fertilising plantA - A 1,2 - 1,2 | | X ?
1/4 of offspring will be of genotype 1,11/2 of offspring will be of genotype 1,21/4 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.
•Every mutation creates a new allele•Identity in state = identity by descent (IBD)
A1A1
A2A2
A1A2A1A1
A1A2 A1A2
Mutation occurred once
A1A1
A2A2
A1A2A1A1
A1A2 A1A2
A1A1
A2A2
A1A2 A1A1
A1A2A1A2
A2 A2 IBD A2 A2 IBD
A2 A2 alike in state (AIS)
not identical by descent
The same mutation arises independently
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
FX fPQ 1
4fAD
1
4fAC
1
4fBC
1
4fBD
Identity by descent
Example, imagine a full-sib matingA - B / \P - Q | X
Indv. X has 2 alleles, what is the probability of IBD?
FX fPQ 1
4fAD
1
4fAC
1
4fBC
1
4fBD
1
42 fAB fAA fBB 1
40 1
2 1
2
1
4
Identity by descent
Example, imagine a half-sib matingA - B - C | | P - Q | X
FX fPQ 1
4fAD
1
4fAC
1
4fBC
1
4fBD
1
42 fAB fAC fBC fBB
1
40 0 0
1
2
1
8
νˆ
μ+νp
A mutates to a at the rate a reverts back to A at the rate vThe equilibrium value for the frequency of A is given by
0
1/ 2
0.5
0.5 1
ln 0.56931 generations
ln 1
t
t
p p
t
Mutations
=0.0001
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]
Natural Selection
Tuberculosis (TB) infections have historically swept across susceptible populations killing many.
TB epidemic among Plains Indians of Qu’Appelle Valley Reservation
annual deaths 1880s 10 % 1921 7 % 1950 0.2%
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