1. Lecture 7 Effective population size Bottlenecks Coalescence theory basics Sonja Kujala

2. Effective population sizeNe
the number of individuals in a Wright-Fisher model that would produce the same amount of genetic drift as in the real population
reminder!
the actual number of individuals in a population
2N=10
N=5
2N=100
N=50

3. Effective population size
population size has an effect on genetic drift
effective population size is a measure on the
amount of drift taking place in a population
effective population size can be measured in various ways - for instance by estimating heterozygosity:
”population that harbours the amount of heterozygosity as does a Wright-Fisher
population of 100 individuals, has effective population size of 100 individuals, even if
the census size was much larger”

4. Effective population size
Factors that affect effective population size:
Not all individuals are reproductive
not all leave offspring
preproductive stage
postproductive stage
number of breeding individuals effective population size

5. Effective population size
Factors that affect effective population size:
1) unequal sex ratio
2) variance in offspring number
3) mode of inheritance - special cases in the genome
4) real change in population size
5) level of inbreeding
all of these factors influence the genetic contribution to the next generation
Ne/N describes how much the population deviates from the ideal

6. Effective population size
3 approaches to estimate Ne
Inbreeding effective population size
relates to increase in inbreeding in a given population to that in the ideal population
Variance effective population size
relates to the increase in variance in allele frequency in a given population to that of the ideal population
Eigenvalue effective population size
relates to the loss of heterozygosity in a given population to that in the ideal population
Usually give very similar estimates

7. Effective population size
In populations of 16 Drosophila, the changes were similar as in ideal populations of size Ne=9

8. Effective population size
unequal sex ratio
often the number of breeding males is smaller than the number of breeding females
sometimes opposite, e.g. honeybees
Ne, Nf, Nm
𝑁 𝑒 = 4 𝑁 𝑓 𝑁 𝑚 𝑁 𝑓 + 𝑁 𝑚

9. Effective population size
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)

10. Effective population size
generation t
generation t-1
imagine monoecious population
N individuals
Pr(two alleles in generation t came from the same parent in generation t-1) = (1/N)2
Pr(any two individuals inheriting alleles from the same parent) = N x (1/N)2 =1/N

11. Effective population size
dioecious population
half of the gametes must come from females and half from males
Pr(two alleles in generation t came from a female in t-1) = (1/2)2
Nf females
-> Pr(two alleles in generation t came from a same female in t-1) = 1/Nf
Nm males
-> Pr(two alleles in generation t came from a same male in t-1) = 1/Nm

12. Effective population size
Pr(two alleles in generation t came from a same parent in generation t-1) =
if equal numbers of females and males, what is Ne?
Nf=Nm=1/2N
substitute in the equation
-> Ne=N
in general
separate sexes
𝑁 𝑒 = 4 𝑁 𝑓 𝑁 𝑚 𝑁 𝑓 + 𝑁 𝑚
rearranges to

13. Effective population size
the effective population size as a function of the proportions of males, for three different total numbers of individuals:

14. Effective population size
Southern elephant seal Mirounga leonina
polygynous mating structure
behavioral observations suggest 40 females/male
genetic data: 4-5 females/male
(Slade et al Genetics 149, )
success of matings overestimated
one male dominates only for a couple of years

15. Effective population size
variance in offspring number
imagine a Wright-Fisher population of constant size
-> average number of offspring must be 2
the distribution of progeny size (family size, k) is often described with the Poisson distribution

16. Effective population size
Poisson distribution
“expresses the probability of a given number of events (k) occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event”
known expected value λ
mean = variance

17. Effective population size
if the distribution of progeny size is non-Poisson, Ne is affected
when ≠ 2, i.e. population size is changing
when = 2, i.e. population size is constant
= average of family size
Vk = variance of family size

18. Effective population size
large variation in number and survival
of salmon eggs and fry
family size has become very uniform in Japan through birth control
-> Ne got larger than N due to decreasing variation in k

19. Effective population size
what if the variance in progeny number is different between males and females?

20. Effective population size
Pumas (Puma concolor) in Yellowstone
Murphy 1998, Culver et al. 2004
number of lifetime offspring produced by individual females and males in a population
microsatellite markers
Nef / Nf = 9.14 / 14
Nem / Nm = 4.45 / 24
-> Ne = 11.97

21. Effective population size
3) mode of inheritance
- special cases in the genome
- X-linked genes
if Nf = Nm -> Ne of X-linked genes is 3/4 of the Ne of autosomes
if Nf ≠ Nm :
- genes inherited only through one sex
if Nf = Nm -> Ne of these genes is 1/4 of the Ne of autosomes
(transmitted through one sex only AND haploid in this sex)
Y chromosome (if paternally inherited)
mtDNA (if maternally inherited)
XX female
XY male

22. Effective population size
4) change in real population size
if population size varies in time, across generations
e.g. N0=1000, N1=10, N2=1000 (a bottleneck),
what is Ne across these three generations?
Ne = 29.4
(the arithmetic mean would be 670)
= the harmonic mean

23. Effective population size
the lowest population numbers determine, to a large extent, the overall Ne
because after the size reduction, all individuals are decendants of the bottleneck survivors

24. Effective population size
Estimating Ne from genetic data
methods based on the expectation that genetic drift increases as effective population size decreases
data over generations
- temporal changes of allele frequency
- greater change in allele frequencies between generations is expected in small populations
- heterozygote excess
- small population size will increase allele frequency differences between males and females
-> results in excess of heterozygotes in their progeny
- loss of heterozygosity
- after a bottleneck event
- due to founder effect
short term estimates

25. Reminder

26. Bottlenecks
the size of a population decreases at least for one generation
founder effect

27. Bottlenecks
strength of the bottleneck =  / f (Gil McVean 2002)

28. Bottlenecks 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

29. Bottlenecks & Coalescence theory
Coalescence theory basics
very sequence data oriented way of thinking about population genetic processes
what kind of processes generated the current data
genealogical trees describe the history of a piece of DNA (a gene)
genealogical trees phylogenetic trees!)
based on models such as Wright-Fisher model
this is about drift – probability that two sequences share a common ancestor - coalesce – in the previous generation

30. Bottlenecks & Coalescence theory
modelling backwards in time
coalescence event ( )
most recent common ancestor (MRCA)
time in 2N generations
present
past
MRCA

31. Bottlenecks & Coalescence theory
stochastic variation among gene genealogies

32. Bottlenecks & Coalescence theory
adding mutations
the expected number of mutations on a branch is proportional to the branch length

33. Bottlenecks & Coalescence theory
coalescence time is proportional to the population size
lineages in small populations coalesce quickly (short branches, fitting fewer mutations)
in large populations lineages coalesce slowly (longer branches, fitting more mutations)
if pop size changes, so will the rate of coalescence
population size growth -> long external branches
population size decrease -> short external branches
”average” shape of the tree:
past
present
constant expanding decreasing

34. Bottlenecks & Coalescence theory
what do the gene genealogies look like after bottleneck?
past
present

35. Bottlenecks & Coalescence theory
age of bottleneck
- t2 represent sampling shortly after bottleneck
- t1 sampling after a longer time
severity of bottleneck
throw in mutations, where will they land?
shape of the tree determines the relative abundance of common vs. rare variants

36. Bottlenecks & Coalescence theory
𝜃=4 𝑁 𝑒 𝜇
bottlenecks reduce diversity
long term effective population size
parameters estimated from sequence data
Ne of the African populations is larger
DOES NOT mean that there are more individuals
DOES mean that African populations have been able to maintain more genetic diversity than other populations
bottleneck effects in other populations, ”Out of Africa”
Wall et al. 2008
Genome Research