Transcript Effective population size

中国科学院上海生命科学研究院研究生课程 人类群体遗传学
人类群体遗传学
基本原理和分析方法
徐书华
金 力
中科院-马普学会计算生物学伙伴研究所
第五讲
遗传漂变效应及有效群体大小的估计
基本概念
► 遗传漂变（Genetic
drift）
 群体内由于抽样误差造成的等位基因频率的随机
波动.
► 有效群体大小（Effective
population size）
 一个理想遗传学群体中繁育群体的大小.
中性突变 – 随机漂变学说
►在分子水平上，仅很少一部分突变
是有利的，多数突变是有害的、中
性的。
►自然选择是一种保存有利突变和消
灭有害突变的进化过程。
►大部分新突变都将消失，少量新突
变的固定依赖于随机漂变。
mutations create new alleles
evolutionary fate of alleles is
governed by 3 other forces:
-selection
- migration
- random drift
The influence of evolutionary forces on
populations: Genetic Drift
All populations are finite in size.
AB
A
Generation: n
A B B
A
B Gene Pool A B B
B
A
A
A
A
B
BA B A B A
Each generation is a
random sample of the
previous generation
A
A
A
A
A B
B
A
Next Generation B
B
A
A
A
A B
Generation: n + 1
A
B
A
AB
A
A B B
A
B Gene Pool A B B
B
A
A
A
A
B
BA B A B A
f(A) = p = 0.48
f(B) = q = 0.52
A
A
A
A
A B
B
A
Next Generation B
B
A
A
A
A B
A B
A
f(A) = p = 0.67
f(B) = q = 0.33
Genetic drift occurs when changes in
gene frequencies from one generation
to another occur because of chance
events (sampling errors) that occur
when populations are finite in size.
Situations in natural populations that magnify drift:
1. Continuously small populations.
2. Founder effect.
3. Bottleneck effect.
Consequences of continuously small populations
The bottleneck effect
Founder Effect
► Bottlenecking
is an important concept in
conservation biology of endangered
species.
 Populations that have suffered bottleneck incidents
have lost at least some alleles from the gene pool.
 This reduces individual variation and adaptability.
 For example, the genetic variation
in the three small surviving wild
populations of cheetahs is very low
when compared to other mammals.
►Their genetic variation is
similar to highly inbred
lab mice!
Northern Elephant Seal:
Example of Bottleneck
Hunted down to 20 individuals
in 1890’s
Population has recovered to
over 30,000
No genetic diversity at 20 loci.
The Founder Effect is Another Variation of Genetic Drift
The South Atlantic island of Tristan da Cunha was colonized by 15 Britons in 1814,
one of them carrying an allele for retinitis pigmentosum. Among their 240
descendents living on the island today, 4 are blind by the disease and 9 others are
carriers.
The Founder Effect
Old Order Amish populations are derived from a few dozen colonists who
escaped religious persecution in Germany in 1719 to settle in Pennsylvania.
The community is closed.
Allele and genetic disease frequencies in Amish are significantly different from
the German ancestral and the surrounding local populations.
The Founder Effect
in a population:
only a fraction of individuals will produce progeny
each generation:
- some genes may increase in frequency
- others decrease in frequency
- some may be lost
genetic drift randomly alters gene frequencies
generation
0
f(“white’)
0.50
0.50
1
0.60
0.60
2
0.80
0.80
3
0.40
Genetic Drift: Population Size Matters
4 populations
2 at N=25
2 at N=250
From Li (1997) Molecular Evolution, Sinauer Press, via A. Sidow BIOSCI 203
Simulation 演示
How big is big enough??
 As a general rule, an Ne of 50 is necessary to
prevent immediate harmful effects of
inbreeding, and an Ne of ~500 is necessary
to maintain long-term evolutionary potential.
50/500 rule of thumb
Genetic drift -Summary
► Genetic
drift occurs because the population size
is not infinite, allowing chance events (sampling
error) to occur.
► Genetic drift is a random process. The outcome
of genetic drift cannot be stated with certainty.
► Genetic drift removes genetic variation from the
population.
► The rate of fixation of a selectively neutral
alleles is inversely related to the population size:
 P(fixation)=1/2N
► The
rate of loss is:
 P(loss)=1-(1/2N)
How much variation will there be in allele
frequency from one population to the next
as a consequence of genetic drift?
How much variation will there be in allele
frequency from one population to the next
as a consequence of genetic drift?
p
x
q
Variance = Sp2 = 2 N
e
Standard error = Sp =
pxq
2 Ne
Important point –
influence of drift increases as Ne gets smaller.
For a binomial distribution
Applying this to our situation
Effects of drift on natural populations:
•Genetic drift is a random process.
•Changes will be non-adaptive.
•Will cause isolated populations to diverge.
•Will result in loss of genetic diversity over time.
Genetic drift drives the decay of
heterozygosity
► Genetic
drift removes genetic variation from
the population.
Ht = (1 - 1 )tH0
2N
if 2N is large, 1/2N ~ 0, and (1 - 1 ) ~ 1, Ht ~ H0
2N
if 2N is small, 1/2N ~ ‘very , and (1 large
1 )
2N
~ 0, Ht ~ 0
The decay of heterozygosity
Effective Population Size (concept)

“The number of individuals in a population who
contribute offspring to the next generation.”

“The size of an ideal population which acts the
same as the real population in question.”

“The size of an ideal population that has the
same properties with respect to genetic drift as
our actual population does.”
The influence of genetic drift is directly
related to the size of a population.
How big is that population?
Census population size vs. effective population size
Effective population size = equivalent number of
adults contributing gametes to the next generation.
How big is that population?
Census population size vs. effective population size
Effective population size = equivalent number of
adults contributing gametes to the next generation.
Formula for calculating
Ne when there is a bias
in the sex ratio
4 x Nf x Nm
Ne =
Nf + Nm
importance of genetic drift is related to population size
maximum effect in small populations
effective population size = Ne
= theoretical population where every individual has
the same probability of contributing genes to the next
generation
Effective population size (Ne)

the size of a genetically idealized
population with which an actual
population can be equated genetically,
Ne = N , if

equal sex ratio

equal probability of mating

constant dispersal rate

progeny per family randomly distributed
Effective population size Ne

Sewall Wright (1931, 1938)



“The number of breeding individuals in an idealized population that
would show the same amount of dispersion of allele frequencies
under random genetic drift or the same amount of inbreeding as the
population under consideration".
Usually, Ne < N (absolute population size)
Ne != N can be due to:




fluctuations in population size
unequal numbers of males/females
skewed distributions in family size
age structure in population
Effective population size affected
by fluctuating population size
Influence of fluctuating population size
on the effective number
individuals in each generation
1
1
(
1/N1
+
1/N2
+
N =
.....1/Nt)
e
t
#
generations
Effective
Number
Influence of fluctuating population size
on the effective number

e.g., if a population of 100 individuals drops
to only 25 in the tenth generation the effective
number during these 10 generations would
be 77
1
1
( 1/100 + 1/100 +
=
N
10
.....1/25)
e
From this example it’s clear that
a single generation with a low
population size has a large
negative influence on the
effective number
Effective population size affected
by bottlenecks and founder
effects
Effective Population Size
•
Influenced by bottlenecks and founder effects
•
Reduced genetic variation from the original
population
•
Founder effect: non-random sample of the genes
from the original population
Effective population size
Effective size and census size fluctuations
1 1 t 1 1
 
Ne t i  0 N(i)
Current effective size is the harmonic
mean of previous population sizes
Harmonic mean is strongly influenced by the smallest samples
Assuming the size of the ancestral
human population was 10’000 ,
100’000 years ago and that it grew
Exponentially until today, what is the
present day effective population size?
Census size
100 kyears
Effective size
Answer: Less than 20’000
(assuming a generation time of
20 years)
Generations
The diversity of the human species much depends on
its past demography, and not much on its present size
Effective population size affected
by reproductive sex ratio
Effective Population Size
Made the assumption that the number of
males and females contributing to each
subsequent generation is the same
If the sex ratio is not 1:1 for each
generation then the population loses
genetic variability more rapidly
This is because the “effective number” of
individuals is smaller than the actual number
of individuals in the population
Effective Number can be calculated
as follows:
Effective Number
# breeding
females in pop.
Ne = 4Nm Nf
Nm + Nf
# breeding males in pop.
For a sex ratio of 1 male:9 females in
a population of 100 individuals
4(10
X
90)
Ne =
= 36
10 + 90
Which means that a population of 100
individuals, consisting of 10 breeding
males and 90 breeding females would
lose genetic variability as rapidly as a
population consisting of only 18 males
and 18 females or 36 individuals
Effective population size
Effective population size and
reproductive sex ratio
4N m N f
Ne 
Nm  N f

Effective size of a population
of census size 100 as a function of
the number of males in the population
The effective population size is strongly
influenced by the rarer of the two sexes.
Examples:
A flock of Geese:
50 males
50 females
(N = 100)
4 x Nf x Nm
Ne =
N f + Nm
A harem of Elephant seals:
4 males
96 females
(N = 100)
Examples:
4 x Nf x Nm
Ne =
N f + Nm
A flock of Geese:
50 males
50 females
(N = 100)
A harem of Elephant seals:
4 males
96 females
(N = 100)
Will be over represented
in the next generation.
Examples:
A flock of Geese:
50 males
50 females
(N = 100)
4 x Nf x Nm
Ne =
N f + Nm
4 x 50 x 50
Ne =
= 100
50 + 50
A harem of Elephant seals:
4 males
4 x 96 x 4
96 females N =
= 15.36
e
96 + 4
(N = 100)
Effective population size affected
by family size
Influence of family size on the
effective number
Actual # of breeding individuals
4N - 4
Ne = Vk + 2
Effective Variance in number of
number Offspring
Rearrange equation
Ne/N ~ 4/(Vk + 2)
Ne/N ~ 4/(2+2) = 1.0N
Ne/N ~ 4/(4+2) = 0.67N
Factors that affect effective population size (Ne):
Factors that affect effective population size (Ne):
1. Bias in male/female sex ratios
Factors that affect effective population size (Ne):
1. Bias in male/female sex ratios
2. Differential production of offspring
Factors that affect effective population size (Ne):
1. Bias in male/female sex ratios
2. Differential production of offspring
3. Fluctuating population size
(As might occur from periodic catastrophes)
Factors that affect effective population size (Ne):
1. Bias in male/female sex ratios
2. Differential production of offspring
3. Fluctuating population size
(As might occur from periodic catastrophes)
4. Overlapping generations
Estimate effective population size
Effective Population Size

A variable in the following equation:
 = 4Ne

( = mutation rate)
Using  as an estimator of Ne, the
effective population size of humans is ~
10,000
Human recombination rate (C)





=4Ner
=4 x 10000 x 1cM/Mb
=4 x 10000 x 0.01 M/1000000 bp
=0.0004/bp
=0.4/kb
Estimate Ne from LD
Populations for Genetic Studies
►Outbred
+ Easy to recruit
+ Directly relevant to patients
►Inbred
 Isolation
►Why
does it matter?
►Specific example: Kosrae
 Consanguinity
Isolates are Intensively Studied
Québequois
Icelanders
Finns
Sardinians
Ashkenazim
Hutterites
Bedouins
Polynesians
Amish
Ticuna
Afrikaners
Aborigines
Indirect (LD-based) Association
►A
new mutation is in LD with its background
► Recombination bounds co-inherited LD segment
Time to Most Recent
Common Ancestor
Matters
► Phylogenetic
LD segment
history in
tmrca
► If
all samples from
a sub-phylogeny:
longer LD
Effects of Population Bottleneck
► Elimination
variation:
of
 Recombinants
Effects of Population Bottleneck
► Elimination
variation:
of
 Recombinants
 Polymorphic sites
Mild Bottlenecks Affect Rare Alleles
► Elimination
variation:
of rare
 Recombinants
 Polymorphic sites
 “memory” of ancestral
state
Isolated Populations &
Association Studies
► Reduced
diversity
 bottleneck eliminates rare alleles
► Rare
alleles become common (detectable)
► Longer
LD
► Characteristic
phenotype frequencies
 good candidates for association studies
Genetics in Kosrae, Micronesia
► Non
genetics:
 Isolated
 Inhabited: 2000 ya
 European exposure:
19th century
► High
prevalence of
common metabolic diseases
 Kosraen HapMap (100k x 30 trios)
towards genome scan
Less common variation on Kosrae
Slower decay of LD in Kosrae
常用软件
►Arlequin 3.01
 http://anthro.unige.ch/software/arlequin/
练习
► 利用HapMap数据进行有效群体大小估计；
 http://www.hapmap.org