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POPULATION GENETICS
I. GENETIC DIVERSITY
17 March 2016
I. GENETIC DIVERSITY – ANALYSIS OF SINGLE POPULATIONS
SPECIES
SUBPOPULATIONS
POPULATIONS
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POPULATION
and problems of definition
• a population is a group of interbreeding
indiviuals that exist together in time and
space
• to develop the basic concepts of
population genetics, we initially consider
the ideal population = large, random-
mating
ALLELE FREQUENCY
• proportion of an allele in comparison to all the others alleles of the
same locus (gene) in a population sample
• basic characteristics for genetic diversity (variation) of a population
• population genetics studies genetic diversity and processes that
have created it and influence it – i.e. the dynamics of distribution and
frequency of alleles (genotypes → phenotypes), i.e. processes
shaping evolution:
increase of gen. diversity: mutation and migration
decrease of gen. diversity: genetic drift (and natural selection)
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1. substitutions (transitions, transversions)
non-coding regions
synonymous
nonsynonymous
missense
nonsense
= silent substitutionsGTC  GTA
Val  Val
GTC  TTC
Val  Phe
AAG  TAG
Lys  ochre (stop)
MUTATIONS
= indels
 frameshift mutations
2.
insertion ACGGT  ACAGGT
deletion ACGGT  AGGT
increase genetic diversity
responsible for variation/heterogeneity in
populations – essential to evolution
Mutation rate – rate at which number of various types of
mutations occur in a given position over time
OBSERVATION
Callimorpha
dominula
přástevník
hluchavkový
Scarlet tiger moth
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OBSERVATION
Callimorpha
dominula
přástevník
hluchavkový
Scarlet tiger moth
Genotype and allele frequency
Genotype A1A1 A1A2 A2A2 Total
Number n1 n2 n3 N
Frequency P=n1/N Q=n2/N R=n3/N
p = (2n1 + n2)/2N q = (n2 + 2n3)/2N
Relative numbers = frequencies: genotype f.: P (GAA), Q (GAa), R (Gaa)
allele (gene) f.: p (A), q (a)
P + Q + R = 1
p + q = 1
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Hardy-Weinberg Equilibrium (HWE)
Allele Allele frequency
A p
a q
Ex. Single locus with 2 alleles
p + q = 1
p, q - Allele frequencies known
from our samples
Genotype Expected genotype
frequency
AA p2
Aa 2pq
aa q2
= Hardy-Weinberg equilibrium
 Observed genotype frequencies
(Ho) are known from our samples
 deviation of Ho from HWE
conditions  for example 2 test
Expected heterozygosity, (He) under HWE
He=1-(p2+q2) ..... for 1 locus with the allele frequencies p and q
Assumptions for ideal population in HWE
• random-mating
• negligible effect of mutations and migration („closed populations“)
• infinitely large population (negligible effect of random fluctuations in allele
frequencies in time – genetic drift) – in HWE population the allele
frequencies are stable = do not change between generations
• Mendelian inheritance of the analysed loci
• neutral loci – not under selection
• diploid, sexually reproducing organisms with discrete generations
• loci are independent from each other – test for „linkage disequilibrium“
2 loci physically close to each other
(decreased probability of recombination
- linkage disequilibrium)
vs.
2 loci physically distant
(probability of recombination not influenced
- linkage equilibrium)
or
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LINKAGE DISEQUILIBRIUM (LD)
loci in LINKAGE EQUILIBRIUM – segregate independently
of each other during meiosis
the most common reason for non-random association
among loci (LD) is the proximity of two loci on a
chromosome (others e.g. small pop. size – gen. drift,
immigration, overlapping generations, admixture, etc.)
in presence of LD:
we have fewer independent loci for our genetic analysis
than anticipated
neutral loci (alleles) linked to selected ones will appear
non-neutral
presence of LD needs to be tested when analysing data
from multiple loci
haplotype diversity – p(AB) ≠ p(A) x p(B)
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Example of genetic diversity estimation
in a sample of 4 individuals (on 4 loci)
Individual Locus 1 Locus 2 Locus 3 Locus 4 Average
Ind 1 170/170 223/227 116/116 316/316
Ind 2 170/172 223/225 112/112 316/316
Ind 3 172/172 223/225 112/112 316/316
Ind 4 170/172 223/227 112/112 316/316
Počet alel 2 3 2 1 2
Ho 0,5 1,00 0 0 0,375
p 0,5 p = 0,5 0,75 1,00
q 0,5 q = 0,25 r = 0,25 0,25 0
He 0,5 0,625 0,375 0 0,375
He=1-(p2+q2)
He=1-(p2+q2+r2)
Proportion of polymorphic loci (polymorphism) = 0,75
Callimorpha
dominula
přástevník
hluchavkový
Scarlet tiger moth
Is our population in HWE?
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Is our population in HWE?
Deviation from HWE
• HWE test – e.g. Genepop software („exact
probability tests“) – any case of significant
deviations from HWE indicates that some of
HWE assumptions were not fulfilled → detailed
inspection required:
• heterozygote excess
– negative assortative mating (i.e. intentional mating of distinct individuals)
– used loci are advantageous in heterozygote situation (= balancing selection
favouring heterozygotes, e.g. MHC genes)
– mutation
– migration
• heterozygote deficit
– inbreeding (all loci are equally affected), assortative mating
– genetic structure in populations
– null alleles (only some loci affected by heterozygote deficit )
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Quantifying genetic diversity
Polymorfism (proportion of polymorphic loci) - P
• polymorphic locus = with at least two alleles
with having frequency of more numerous allele
being less or equal 0.95 (or 0.99)
• e.g. a population sample with four polymorphic
loci out of five → P = 0.8
Number of alleles - Na
• number of alleles per locus (mean over loci)
Allelic richness - Ar
• number of alleles corrected for sample size
(rarefaction method e.g. in FSTAT software)
Observed heterozygosity - Ho
• observed frequency of heterozygote genotypes
(mean over loci)
Sample size
Numberofalleles
Ar
Na
HAPLOID DIVERSITY
• genetic diversity for haploid data
HAPLOTYPE DIVERSITY (h; Nei et Tajima 1981) –
frequency of different haplotypes
NUCLEOTIDE DIVERSITY (π; Nei 1987)
– quantifies the mean nucleotide divergence between
sequences
– probability that two randomly chosen homologous
nucleotides will be identical
xi and xj – respective frequencies of the ith and jth sequences
πij – number of nucleotide differences per nucleotide site
between the ith and jth sequences
xi –haplotype frequency of each haplotype in the sample
N – sample size
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WHAT INFLUENCES
GENETIC DIVERSITY?
• influenced by a multitude of factors
• varies considerably between populations
MOST IMPORTANT DETERMINANTS OF
GENETIC DIVERSITY:
 genetic drift
population bottlenecks
natural selection
methods of reproduction
GENETIC DRIFT
population not infinitely large → population not in HWE →
increase of influence of CHANCE → allele freqencies
vary between generations
in absence of selection, each allele goes to:
1. fixation
2. extinction
more quickly in smaller populations
genetic drift – process causing a population´s allele frequencies to change from
one generation to the next as a result of CHANCE
DECREASE of
genetic diversity
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GENETIC DRIFT
very profound effect of genetic drift in
small populations – founder effect,
bottleneck
inextricable link between genetic drift
and population size – the effective
population size
Founder effect
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Bottleneck
Ne – effective population size
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Ne – effective population size
vs. Nc – census population size (may be estimated from Ne
– see Luikart et al. 2010 Conserv Genet)
all else being equal, LARGE pops are MORE LIKELY to
survive than small pops
Ne – reflects the rate at which genetic diversity will be lost
following genetic drift (this rate is inversely proportional
to a population´s Ne)
single-sample estimators of Ne – level of LD due to drift
double sample estimators of Ne – temporal changes in
allele frequencies due to genetic drift
Freeland et al. 2011
OVERVIEW