hs18 popgen 03 effectivepopulationsizeevolution.unibas.ch/teaching/evol_genetics/c_population... ·...

Evolutionary Genetics

LV 25600-01 | Lecture with exercises | 6KP

HS2018

Effective Population Size

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Population Genetics ▷ Genetic Drift

HS18 | UniBas | JCW

A Primer of Ecological Genetics Chapter 3 - Genetic Drift - Page 62-65

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Population Genetics ▷ Effective Population Size

HS18 | UniBas | JCW

Population size has a major impact on the dynamics of a population. For example genetic drift reduces allelic diversity much faster in small populations than in large ones. Population size also influences the chances of extinction through random change in population size over time due to random variation in individual survival and reproductive success (demographic stochasticity).

A1A2

A1A2

A1A2

A1A2

A1A2

A1A1

A1A1

A1A1

A1A1

A1A1

A2A2

A2A2

A1A2

A1A2

A1A2

A1A2

A1A1

A1A2

Nc = 18

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Natural population have many different structures and breeding systems that have different genetic consequences. Therefore the effective size of a population (Ne) is usually less than the census size (Nc), or the number of potential breeders, as real population deviate in structure from the assumptions of the idealised population in sex-ratio, distribution of family size, constancy of numbers in successive generations (population size), and having overlapping, rather than discrete generations.

Ne = 6

A1A2

A1A2

A1A2

A1A2

A1A2

A1A1

A1A1

A1A1

A1A1

A1A1

A2A2

A2A2

A1A2

A1A2

A1A2

A1A2

A1A1

A1A2 A1A1

A1A2

A2A2

A2

A2

A2

A1

A2 A2

Gamete pool

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N>100 unequal sex-ration variance in reproductive success

Ne

Nc

⇒10%

Frankham (1995)

Ne

Nc

⇒ 20%

Waples (2002)

Ne

Nc

⇒15%

Palstra & Ruzzante (2008)

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Ne =4NmN f

Nm +N f

Unequal sex-ratios reduce the effective size of the population towards the number in the sex with the fewest breeding individuals.

A skewed sex ratio will not have a large effect on the Ne/N ratio unless there is a great excess of one sex over the other.

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Ne

N

%−males 7


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Nm = NF = 1

Ne =4NmN fNm+N f

= 42= 2

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Nf

Ne

N f→∞

Ne ≈ 4

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For alleles at a X-linked gene or alleles in a haplo-diploid organism, the effective population size is somewhat different than that for autosomal genes because females contain two-third and males one-third of the alleles.

Ne =9NmN f

4Nm +2N f

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Nm = NF = 1

Ne =9NmN f4Nm+2N f

= 32

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Family sizes (number of progeny) in wild population typically show greater variation than random (Poisson) distribution assumed for the idealised population. In general, to include variance in the number of progeny and the population is changing in size so that k≠2, the effective population size is approximately

where N is the number of adults in the previous generation, k is the number of progeny (gametes) per parent, and Vk is the variance in family size (variance in the number of progeny).

Ne = Nk −1k −1+ Vk

k

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Lets assume that we have an idealised population with an expected number of offsprings of 2 (i.e. k=2). The equation for effective population size would change to

Ne = Nk−1k−1+Vkk

= N 2−12−1+Vk2

= 4N−22+VK

Furthermore, in this idealised populations the expected number of offsprings would follow a Poisson distribution where the mean is equal to the variance (k=Vk=2).

Ne = 4N−22+VK = 4N−2

2+2 ≈ N

N = N f + Nm

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Vkf: variance in number of progeny of females Vkm: variance in number of progeny of males

Ne = 8NVkf +Vkm +4

Many species are not monogamous and therefore differ in the number of offsprings. When males mate with more than one female, Vk is likely to be different for females and males.

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Ne = 8NVkf +Vkm+4 =

8N2+2+4 = N

In an idealised, random mating population …

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For many animal species, the variance of progeny number in males is expected to be larger than that for females. For example, according to the Guinness Book of World Records*, the greatest number of children produced by a human mother is 69; in great contrast, the last Sharifian Emperor of Morocco is estimated to have fathered some 1400 children! The current use of sperm donors can also result in males with many progeny.

* http://www.guinnessworldrecords.com/world-records/3000/most-prolific-mother-ever

Vkf < Vkm

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http://www.guinnessworldrecords.com/world-records/3000/most-prolific-mother-ever


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Wild population vary in numbers as a consequence of variation in climatic conditions, disease, epidemics, varying hunting pressure and many more factors. Fluctuation in population size over generations reduce Ne below the average number of adults.

1Ne

= 1t

1N1+ 1

N2+ ...+ 1

Nt⎡⎣ ⎤⎦

Moose and wolf population fluctuations on Isle Royale National Park in Lake Superior depend on factors like weather, disease and possibly genetic problems.

harmonic mean

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probability = 12N

t t+1allele

probability = 1− 12N

t t+1

A1/A2

A3/A4

A5/A6

A7/A8

A9/A10

A11/A12

A13/A14

A15/A16

Gamete pool

equal freq of all alleles

randomly pick of two gametes

Axx

Axx

h=1 N=8

self-fertilization

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probability = 12N

t t+1allele

probability = 1− 12N

t t+1

H1 = 1− 12N( )H0

Ht = 1− 12N( )t H0

Heterozygosity after one generation:

Heterozygosity after t generations:

➥ The equation indicates that the heterozygosity declines each generation at a rate inversely dependent on the population size.

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Year N2000 1402001 1202002 32003 1002004 130

ht = 1− 12N

⎛⎝⎜

⎞⎠⎟t

h0 = 1− 12 *130

⎛⎝⎜

⎞⎠⎟5

h0 = 0.981h0

→ We expect to lose 2% of the heterozygosity.

Year N

2004 130

0

40

80

120

160

2000 2001 2002 2003 2004

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→ If we consider population size fluctuations over time the loss of heterozygosity is 17%.

1Ne= 1

51140 + 1

120 + 13 + 1

100 + 1130[ ]= 0.0733⇒ Ne = 13.6

ht = 1− 12Ne

⎛⎝⎜

⎞⎠⎟

t

h0 = 1− 12*13.6

⎛⎝⎜

⎞⎠⎟5

h0 = 0.829h0

Year N2000 1402001 1202002 32003 1002004 1300

40

80

120

160

2000 2001 2002 2003 2004

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⇒ ?

⇒ ?

⇒ ?Nm = 1

Nm = N f = 1

Nm = N f

Ne =4NmN f

Nm +N f

Unequal sex-ratios reduce the effective size of the population towards the number in the sex with the fewest breeding individuals.

⇒ ?Nm = 1N f = ∞

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?⇒Nm = N f ⇒

Nm = N f = 1

For alleles at an X-linked gene or alleles in a haplo-diploid organism, the effective population size is somewhat different than that for autosomal genes because females contain two-third and males one-third of the alleles.

Ne =9NmN f

4Nm +2N f?

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For genes that are inherited only though one sex such as mtDNA, cpDNA, and the Y Chromosome, the effective population size for the appropriate sex determines the effect of genetic drift on those genes.

Ne =Nef

2 or Ne =Nem

2

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Nm = 4

Nf = 200

Nm = 200

Nf= 200

Nm = 200

Nf = 4

autosome Ne=? Ne=400 Ne=?

chromosome X Ne=? Ne=300 Ne=?

chromosome Y Ne=? Ne=? Ne=?

mitochondrial Ne=? Ne=? Ne=?

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hs18 popgen 03 effectivepopulationsizeevolution.unibas.ch/teaching/evol_genetics/c_population... ·...

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