Consortium for Comparative Genomics
University of Colorado School of Medicine
Population Genetics
The study of naturally occurring genetic differences
among organisms
Biochemistry and Molecular Genetics
Consortium for Comparative Genomics
Human Medical Genetics, Computational Bioscience
University of Colorado School of Medicine
David.Pollock@UCDenver.edu
www.EvolutionaryGenomics.com
Sexual reproduction
What is Sex?
Mixing
Gender
Ploidy
Recombination
Multiple Loci: Linkage
2 loci, A and B, in a good
population, each in HW
equilibrium
The gametes may have
nonrandom associations
Multiple Loci: Linkage
Gametes are A1B1, A1B2, A2B1, and A2B2
A1
B1
A1
B2
P11
P12
A2
B1
P21
A2
B2
P22
Allele frequencies of A and B, separately, are
p1 and p2 for A, q1 and q2 for B
Linkage and Recombination
A new mutation is in disequilibrium with
existing variants at other loci
It arose linked to one variant or the other
Linkage is disrupted through genetic
exchange (breakage and reunion of gametes)
Recombination, frequency r
proportion of gametes with combination of
alleles not present in either parent
Range is 0 to 0.5
Linkage Disequilibrium
Measurement of the degree of nonrandom
association
D = P11 P22 – P12 P21
Linkage and Recombination
r determines the rate of approach to linkage
equilibrium
P11’ = r p1 q1 + (1-r) P11
= (1-r) D
In each gen, D is only (1-r) times as large
Falloff in LD with Distance
Linkage and Time
Starting with initial D0
Dt = D0 (1-r)t
Values of D depend on allele frequencies
Difficult to compare from one locus to the next
Sometimes expressed as percentage of its minimum (if
negative) or maximum (if positive) value
E.g., Dmin = larger of –p1q1 and –p2q2
Incest is Best
Riff
Raff
Mating between relatives
Increased frequency of homozygotes
Consider selfing (plants)
AA x AA => AA
aa x aa => aa
Aa x Aa => 0.5 Aa + 0.25 AA + 0.25 aa
Magenta
Incest is Best
Riff
Raff
Magenta
Inbreeding coefficient
AA: p2(1-F) + pF
Aa: 2pq(1-F)
aa: q2(1-F) + qF
H0  H 

F
H0
Incest is Best
Identical by Descent (IBD)
Relative to some ancestral population
F is the probability that alleles are IBD
Autozygous (always homozygous)
Allozygous
Not IBD; may be heterozygous or homozygous
The difference can be important!
Example of T1D and MHC alleles
Inbreeding Depression
Well, maybe not always best
If individuals in
normally
outcrossed species
are inbred,
inbreeding harmful
Data from Neal,
1935
Average Yield of Corn (Bushels/acre)
70
20
0
0.25 0.5
0.75 1.0
Inbreeding Coefficient, F
Inbreeding Depression
Well, maybe not always best
Frequency of
homozygous recessives
for rare deleterious
allele in first cousin
mating
F = 1/16
aa: q2(1-F) + qF

aa: q2(1-1/16) + q/16
Relative Risk (RR)
 the
The rarer the allele,
greater the RR
 1   1 
q 1  q 
 16  16 
RR 
2
q
2
0.0625
RR  0.9375 
q
q  0.01, RR  700%
Regular Systems of Mating
Selfing, Sib mating, half-sib mating, or
backcrossing to produce strains
Calculate F at any time
Hybrid vigor (heterosis)
F => 0 after one generation of outcrossing
Inbred lines unlikely to have same inbred rare
deleterious recessive variants
And the worst get weeded out
Uniform progeny
test for the best hybrids
Mutation & Fate
Absorbing States
Extinction
Fixation
Ideal Population
Constant N
Hardy-Weinberg
Fitness
Fitness landscape
Two pictures of evolution
Adaptionists: (Dawkins, etc.)
Neutralists
(Kimura, Gould)
Every day, in every way,
I'm getting better and better!
- Emile Coue
“Nearlyneutral
model”
The Panglossian
Paradigm
The Spandrels of
San Marcos
A Force to be
Reckoned With
“Mankind is so
unstable a species that
he may one day
become obsolete.”
“This game is an
exercise In controlling
genetic drift.”
Remote Inbreeding
Getting ready for the coalescent
IBD of any two alleles in a finite population
Often FST to distinguish it
Go back 1 generation, N alleles, a1…aN
Probability that two alleles are the same
1/2N => the force of genetic drift
Probability that two alleles are different, but
related due to previous remote inbreeding
(1-1/2N)Ft-1
 1 
1 Ft  1 F0 1

 2N 
t
Heterozygosity Requires Mutation
Mutation breaks the chain of IBD
Mutation rate m
Probability no mutation = 1-m
Infinite Alleles Model (all mutants different)
 1  1  
2
Ft    1
Ft11 m
2N  2N  
At Equilibrium
Ft  Ft1  Fˆ
Fˆ 


1
4Nm  1
4N
m

Hˆ  1 Fˆ 

4Nm  1 1 
Effective Population Size
The population size of an ideal population that
would produce the same outcome (i.e., same
heterozygosity, given mutation rate)
  4Ne m
Variance in expected reproduction, changing
population size, male to female ratios (and different
mating success), dispersion (neighborhood size) all
reduce the effective population size
Migration
Migration limits genetic divergence
Remarkably little: 1-4 migrants per generation
(Nm)
Low migration rates is like increased remote
inbreeding
Apparent inbreeding
FST 
Due to population substructure
Variance over expected variance
Happens even though each subpopulation is
undergoing random mating, in HWE

2
pq
The Driving Force
Natural Selection
Inherited differences in the ability of
organisms to survive and reproduce
Through time, better genotypes increase in
frequency in a population
Natural selection chooses between different
variants
Variants compete with one another
Leads to greater adaptation of organisms to
their environment
Accumulation of ability to survive and reproduce
Strategies to Produce More Offspring
Survival (zygotic selection)
Fertility (mating success, sexual selection)
Fecundity (production of zygotes)
Gametic selection (distorted segregation in zygotes)
Parenting (increase the probability that your young will
survive)
There are usually trade-offs
E.g., More offspring at younger age = lower survival
Mostly Competition Between
Individuals
Modeling Natural Selection
AA  p   AA
aa  q   aa
2
2
Aa  2pq Aa
2

  p   AA  2 pq   Aa  q   aa
2

f xy 
f xy   xy

Dominant
Recessive
From CA Andrews, 2010
Selection Needs to Overcome
Genetic Drift
10 replicates, N=20
From CA Andrews, 2010
Predictions
Mutation-selection balance
Time required for changes in gene frequency
Overdominance, underdominance, frequencydependent selection (e.g., MHC)
Selection versus drift
Diffusion approximations
Effective population size
The genetic architecture of
complex traits
Phenotypic variation due to population
average plus
Genotypic variance
Environmental variance
Interaction between the two
Heritability: ratio of genotypic to phenotypic
variance
Depends on variant frequencies!
Quantitative traits, multiple genes
Pleiotropy (antagonistic?)
During a drought, Finch N decreased due to decline in seed supply. Size
and hardness of seeds increased, as did the size of the finches (larger
birds can eat bigger seeds)