5. Population genetics
5.2. Effective population size and
population bottlenecks
5.2.1. Effective population size, Ne
5.2.2. Examples of effective population size
5.2.3. Ne/N
5.2.4. How big population?
5.2.5. Genetic bottlenecks
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5.2.1. Effective population size, Ne
• The number of individuals in an idealized, randomly
mating population with an equal sex ratio that would
– exhibit the same rate of heterozygosity loss over time as
an actual population with a particular census size
– or show the same amount of dispersion of allele
frequencies under random genetic drift as an actual
population with a particular census size
– or show the same amount inbreeding as an actual
population with a particular census size
• ‘A standardized measure, with which populations in
different biological states can be compared’
– You can think it as the effective number of breeding
individuals
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5.2.1. Effective population size, Ne
Assumptions
1.
2.
3.
4.
5.
6.
No immigration
Distinct, non-overlapping generations
Number of reproductive individuals is constant
Reproduction is random (including inbreeding)
No selection
No mutation
Ne is not the same as the census population
size Nc!
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5.2.1. Effective population size, Ne
•
Variance Ne, function of allele frequency
and its variance
– Predicts changes in genetic variance
– Based on number of gametes in a
population – related to number of offspring
•
Inbreeding Ne, function of inbreeding
coefficient
– Predicts changes in heterozygosity
– Based on probability of two gametes
coming from the same parent
•
Eigenvalue Ne, function of loss of
heterozygosity
– Predicts changes in allele frequency
– Based on variability loss at a rate of 1/(2N)
per generation
Var ( p ) =
p (1 - p )
2N
p (1 - p )
Ne =
2Var ( p )
1
Ne =
2f
Ht
Ne =
2( Ht - Ht + 1)
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5.2.1. Effective population size, Ne
If the assumptions do not hold
• No breeding among relatives
→ Ne can be larger than Nc
No inbreeding
Ne = N + ½
No breeding among sisters
Ne = N + 2
This is the aim for example in breeding programs for
endangered species
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5.2.1. Effective population size, Ne
If the assumptions do not hold
• Different number of males and females
→ Ne is smaller than Nc
=
For example, males often are allowed to be hunted
more than females
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• Effective population size decreases fast in
populations with skewed sex-ratios
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cows/bull
• Biased sex-ratios in Finnish moose population
(Nygrén 2009)
• Less biased in the north (Ne > 200), more biased
in the south (Ne ≈ 100) (Kangas et al. 2013)
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5.2.1. Effective population size, Ne
If the assumptions do not hold
• Different number of individuals
in consecutive generations
→ in t generations, the mean Ne
is the harmonic mean
=
+
+ ⋯+
Small Ne has a strong longterm effect (bottlenecks)
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5.2.1. Effective population size, Ne
If the assumptions do not hold
• Variation in number of offspring, that is some
individuals produce more offspring than others
→ Vk = variance in the offspring number (mean
offspring number = 2 in a stable population)
=
if Vk = 2, Ne » N
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5.2.1. Effective population size, Ne
If the assumptions do not hold
• Spatial dispersion
Ne = 4ps2d
where p is the dispersal distance, s2 is the variance of the
dispersal distance and d is the density of individuals. This
formulation is often called the neighborhood size
– changes in the variance of dispersal can affect Ne
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• In an equilibrium
population,
genetic variation
correlates with
effective
population size
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• Genetic variation
decreases as a
function of effective
population size,
1/(2Ne) per generation
• The inbreeding
coefficient (F)
increases as the
effective population
size decreases in
each generation
Δ F = 1/ (2Ne)
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5.2.2. Examples of effective
population size
• If the number of offspring is kept constant, as often
is in breeding programs, Ne might be even two
times larger than in a randomly mating ideal
population
=
4 −2
+2
If Vk = 2, Ne ≈ N
If Vk = 0, Ne = 2N -1
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5.2.2. Examples of effective
population size
• Large variance in the offspring number (k) → Ne
decreases
=
4 −2
+2
If Vk >> k, Ne << N
E. g. large variation in number
and survival of salmon eggs
and fry
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5.2.2. Examples of effective
population size
• One male mates with several females
=
Þ Ne decreases
• E.g. lekking birds
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5.2.2. Examples of effective
population size
• Several males mate with females
Þ Ne increases
• E.g. Small statured salmon males sneak
opportunities to fertilize eggs without fighting with
the big males
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5.2.2. Examples of effective
population size
• Overlapping generations, stable age-structure
Nc = size of a cohort, a function of lifetime and N
L = mean age of parents when they reproduce
=
This is how it usually is in the nature
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5.2.2. Examples of effective
population size
• Metapopulation structure
– Extinction and colonization of small populations
– Decreases the effective population size even to half of the
size without metapopulation structure
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5.2.2. Examples of effective
population size
• Immigration and mutations
– Increase the effective population size
– The effect of mutations is non-existent in ecological time
frame
• The other sex disperses, the other is territorial
– Increases the effective population size
– E.g. many passerine birds (female-biased), social
mammals (male-biased)
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5.2.2. Examples of effective
population size
• Selection
– Decreases the effective population size (by decreasing
the number of offspring)
• Growing, decreasing or spatially structured
populations
– Finding the real Ne is a lot more difficult
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5.2.2. Examples of effective
population size
Ne for X-chromosome (mammals) is ¾ of the autosomal Ne
Ne for Y-chromosome and mitochondrial genes is ¼ of the
autosomal Ne
(if sex determination is XX-XY)
Assumptions are equal sex-ratio and no differences in dispersal
between sexes
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5.2.3.Ne/Nc
• Effective population size is one of the most
important parameters in conservation genetics
– describes the amount of genetic variation and via that, the
inbreeding depression and viability of a population
• Often measures used in order to maintain viability
are:
– Ne = 50 (short term viability)
– Ne = 500 (long-term viability)
– however, it has been realized that these are not enough
(at least 10 x larger)
• What is the relation between effective population
size and census size?
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5.2.3.Ne/Nc
• Usually Ne < Nc, sometimes Ne can artificially be
made bigger with breeding programs
• To estimate Ne, Nc is often multiplied by the ratio of
Ne/Nc
• Theoretically this ratio is about 0.5, seldom below
0.25
• However, empirically ratios have been observed to
be often about 0.1
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5.2.3.Ne/Nc
•
Loss of heterozygosity
100
90
% heterozygosity remaining
Example:
Census size of an endangered
species 250 and Ne/Nc = 0.1
Þ Ne = 25
Þ Half of the heterozygosity will
disappear in 34 generations
Þ Inbreeding increases the risk of
extinction
80
70
60
50
40
30
20
10
0
1
6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96
generations
•
In Sacramento river (California)
~ 2000 Chinook salmons
(Oncorhynchus tshawytscha),
but Ne only 85
Þ Ne/Nc = 0.04
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5.2.4. How big population?
Goal
Ne
Maintenance of
reproductive success
Maintenance of
evolutionary potential
Maintenance of genetic
variation (1 locus)
Avoidance of deleterious
mutations
50
’recovery
time’
500-5000
102-103
105-106
105-107
12-100
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5.2.5. Genetic bottlenecks
• The size of a population decreases at least for
one generation
• If the population is small already before the
bottleneck, the bottleneck can reduce genetic
variation considerably
• Founder effect
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5.2.5. Genetic bottlenecks
Strength of the bottleneck = t / f
Gil McVean (2002)
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5.2.5. Genetic bottlenecks
Example: If a population has gone though a bottleneck
in one generation:
N0 = 1000
N1 = 10
N2 = 1000
The effective population size over these three
generations would be:
1/Ne = (1/t)(1/N0+1/N1 +1/N2)
1/Ne = (1/3)(1/1000 + 1/10 + 1/ 1000) = 0.034
Ne = 1/0.034 = 29.4
(the arithmetic mean would be 670)
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5.2.5. Genetic bottlenecks
Examples of a bottleneck
Lion (Panthera leo ), Driscoll et al 2002, Genome Res
•
Gir-population in eastern India
•
A previously large and continuous population decreased to 20
individuals due to hunting and reduction of habitats
Presently about 250 individuals left
•
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5.2.5. Genetic bottlenecks
Examples of a bottleneck
32
Northern elephant seal (Mirounga angustirostrus)
Weber et al 2004, Mol Ecol
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Hoelzel 1999, Biol J Linn Soc
5.2.5. Genetic bottlenecks
Estimating Ne and bottleneck from genetic data
A. Bottleneck
– Disequilibrium between neutral theory expectations of
allele number and heterozygosity
• Rare alleles are lost more rapidly than heterozygosity
decreases
– Losses of alleles can be seen also in distortion of
distributions of allele frequencies
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5.2.5. Genetic bottlenecks
Estimating Ne and bottleneck from genetic data
Black bars: non-bottlenecked
White bars: bottlenecked
Luikart et al. J. Heredity 1998: 89
X–axis = Allele frequency class
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5.2.5. Genetic bottlenecks
Estimating Ne and bottleneck from genetic data
B. Effective population size
– Methods based on the expectation that genetic drift increases
as effective population size decreases
– Gametic disequilibrium
Where r is the correlation between alleles at different loci and S is
the sample size
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5.2.5. Genetic bottlenecks
Estimating Ne and bottleneck from genetic data
– Heterozygote excess
– Temporal changes of
allele frequency
t is time in generations
S0 and St are samples sizes in the
two generations
Fk = 1/ (A-1) S (xi-yi)2 / ((xi-yi)/2)
A is the number of alleles at a
locus
xi and yi are the frequencies of
allele i in the two sampled
generations
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5.2.5. Genetic bottlenecks
Estimating Ne and bottleneck from genetic data
• More methods based on:
– Maximum likelihood, Ne is estimated as the size of a
population which best explains the variance of allele
frequencies between samplings
– Coalescent theory, when population is known to have
diverged from a common ancestral pool at a specific time
in the past – Bayesian methods
– θ= 4Nem, if the mutation rate is known (but this is a very
long-term estimate)
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