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