BIOL2007 - INBREEDING AND NEUTRAL EVOLUTION

Tutorial work due on Fri 25 Jan by 4:30 pmPut in “BIOL2007 Hand-in box” in Wolfson House office 306. Tutorial times to be announced.

PREVIOUSLYDeterministic evolution, via natural selection.  TODAYInbreeding: does not cause evolution on its own; -- affects arrangement of genes in populations; & has important fitness effects.

However, finite population size both inbreeding and random evolutionary change (or "genetic drift"). Stochastic.Mutation: also causes random genetic change;

but genetic drift is usually faster

MEASURING INBREEDING Inbreeding: when an individual mates with a relative (or with itself! as in some plants or snails).

Offspring : homozygous for allele which is identical by descent from a single ancestor

Here, a male is homozygous an allele inherited from a single copy in an ancestor.

His mum was also his dad's niece (a type of inbreeding common in many human societies).

Regular systems of inbreeding

He’s inbred!

INBREEDING COEFFICIENT, F, ... used to gauge the strength of inbreeding.

F = probability that two alleles in an individual are identical by descent (IBD).

Identical by descent vs. identical in state

Identity in state (homozygosity) does not necessarily imply recent identity by descent. (Conversely ...)

F for fixation index: homozygosity, or “fixation”, results from inbreeding.

½

½

½

Only path through female grandparent shown

Sewall Wright's "path analysis" to calculate F

Problems of inbreeding:Deleterious recessive alleles in most populations.

Few deleterious recessives per gene (usually << 10-3)…but many deleterious alleles per genome. 

You and I each carry about 1 strongly deleterious recessive mutation, or “lethal equivalent”.

When homozygous, these mutations cause problems,(inbreeding depression).

Frequency of consanguineous marriages

Uncle/niece or

Aunt/nephew

First cousin

s

Av. inbreeding coefficient,

F

India: Andra Pradesh 1957-1958

0.0923 0.3330 0.032

Italy: 1956-60 - 0.0077 0.0007

USA: Catholics 1959-60 Mormons 1920-40

--

0.00080.0061

0.000090.00038

INBREEDING IN HUMAN POPULATIONS

Inbreeding not all bad Many organisms habitually inbreed!  e.g. fig wasps, parasites, weeds. 

Advantages to inbreeding? Ecological: a single female can colonize May also usefully prevent recombinationDeleterious recessives in inbreeding species purged by selection.

Inbreeding in humans  Ancient Egyptians, modern European royals, Indian subcontinent.Mild inbreeding, such as mating between first cousins, or uncle-niece isn't so dangerous.  Example: Charles Darwin: married first cousin, 10 kids.

EFFECT OF INBREEDING ON POPULATIONS

How does inbreeding affect the numbers of heterozygotes?

Consider alleles, A, and a with freqs p,q and inbreeding (IBD) at rate F:

Frequency of homozygotes: AA = (1-F)p2 [outbred] + Fp [inbred]

= p2 + F(p-p2) = p2 + Fp(1-p) = p2 + Fpq

Similarly, frequency of other homozygotes, aa = q2 + Fpq

All genotype frequencies must add to 1so the extra 2Fpq AA and aa homozygotes must have come from the heterozygotes

Inbreeding leads to a reduction in heterozygosity. Heterozygosity (Het, i.e. fraction that are heterozygotes under inbreeding) is reduced by a fraction F compared with the outbred (Hardy-Weinberg) expectation HetHW = 2pq: Het = HetHW (1 - F)

F measures reduction of heterozygosity, or heterozygote deficit compared to Hardy-Weinberg, as well as probability of identity by descent!

genotype

AA Aa aa (Sum)

frequency

p2+Fpq 2pq(1-F)

q2+Fpq p2+Fpq+2pq-2Fpq+Fpq+q2

=1

EFFECT OF INBREEDING ON POPULATIONS

GENETIC DRIFT Deterministic vs. stochastic evolution Hardy-Weinberg: no gene frequency change.

True in an infinitely large population; evolution deterministic.

Only approximately true in populations of finite size. 

Assume a diploid population of constant size N.  Each of 2N alleles are copied into gametes. 

Drift in a small population:N = 6 diploid individuals. Total of 2N = 12 alleles

Identity by descent (IBD) of all alleles by 7th generation. Identity in state earlier. Also, coalescence took place 7 generations ago.

EXAMPLE OF GENETIC DRIFT

Réunion VietnamNative range (Vietnam, right), versus an introduced population (the island of Réunion, left) (from L. Amsellem et al. 2000. Mol. Ecol. 9: 443-455.

Asian bramble (Rubus alceifolius), introduced on Pacific islands.

Genetic variation studied by means of DNA fingerprint technique: "Amplified Fragment Length Polymorphisms" - AFLP for short.

GENETIC DRIFT AS A CAUSE OF INBREEDING  

   As we have seen, inbreeding results from drift because alleles become identical by descent (IBD). We can therefore measure drift in terms of our inbreeding coefficient, F, and hence how the fraction of heterozygosity, Het, declines with time.  We can show:

t

NHettHet

211

0

In a population of size N, the probability that two alleles picked at random mating in generation t are IBD due to copying from generation t-1 is  (on average). 

(inbred in generation t)

This is the rate of inbreeding due to drift per generation.(it measures the strength of drift).

BUT the 2N alleles in the previous generation may be IBD themselves from inbreeding in previous generations. The fraction of alleles in generation t that are IBD because of inbreeding before generation t-1 is:

(outbred ingeneration t)

NtF21

1211

tF

NtF

take 1–(both sides):

111

21

1211

21

tF

tF

NtF

NNtF

11.

211

11

21

111

tF

NtF

NtF

tF

Nt

HettHet211

1

t

NHetHett

211

0

By definition, the heterozygosity after a single generation of inbreeding is reduced by a fraction F, Het = 2pq (1 - F) = HetHW (1 - F), so Het/HetHW = (1 - F).

From the above equation relating Ft to Ft-1 and cancelling HetHW’s:

So, after t generations of drift:

Summing the inbreeding in the current generation with inbreeding from previous generations, we have at time t:

So heterozygosity declines approximately by a factor per generation. However, ...

(a) Only true on average. (And if assumptions met)

(b) F can also measure inbreeding – and drift – as a result of subdivision into finite populations.

It is the heterozygote deficit or identity by descent produced by subdivision. Usually written FST, inbreeding (F) due to subdivision into Subpopulations relative to the Total population.

N21

John Liu’s GENETIC DRIFT programme

N=10015 populationsfixed after 100 generationsFST = 0.41

[N=10, FST ≈ 1.0]N=1000

0 populationsfixed after 100 generationsFST = 0.05

Simulations from John Liu’s drift programme

THE FLORIDA PANTHER

Genus PumaSpecies concolor Subspecies coryi

... may have a few problems of this nature.

Kink at the end of its tail; cowlick on back; 65% males cryptorchid; abnormal sperm – due to inbreeding?

Est. population in the wild: 50-70. Up from 30-50 in 1995.

EFFECTIVE POPULATION SIZE

Alleles usually do not have identical probability of being passed on, as required in simple models. 

Population geneticists get around this by calculating effective population size, Ne that produces the same rate of genetic drift in their simple models with population size N.

Ne may differ from actual population size.  Examples:

1) Separate sexes2) Unequal sex ratio3) Some males mate more than others 

INBREEDING -- Conclusions Inbreeding coefficient, F – the measure of inbreeding.

Regular systems of inbreedingF is also a measure of heterozygote deficit.

Inbreeding due to genetic drift in finite populations.The extent of drift can also be measured by F … or Het = 2pq (1–F).

All evolution is somewhat stochastic: a mix of random genetic drift with deterministic – selection.

– an important equation in conservation, deduced from the effect of drift on inbreeding in population of size N.

t

NHetHett

211

0

FURTHER READING

FUTUYMA, DJ 2005. Evolution.  Chapter 9: 197-199, 201-202, Chapter 10.

FREEMAN & HERRON 2004. Evolutionary Analysis.Chapter 6. pp. 204-252.