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BIOL2007 - INBREEDING AND NEUTRAL EVOLUTION Tutorial work due on Fri 25 Jan by 4:30 pm Put in “BIOL2007 Hand-in box” in Wolfson House office 306. Tutorial times to be announced. PREVIOUSLY Deterministic evolution, via natural selection. TODAY

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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.


Deterministic evolution, via natural selection.


Inbreeding: does not cause evolutionon its own;

-- affects arrangement of genes in populations;

& has important fitness effects.

However, finite population size bothinbreeding and random evolutionary change (or "genetic drift"). Stochastic.Mutation: also causes random genetic change; but genetic drift is usually faster

He’s inbred!

Regular systems of 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).


... 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 ...)

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




Sewall Wright's "path analysis" to calculate F

Only path through female grandparent shown

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).

Inbreeding not all badMany organisms habitually inbreed! 

e.g. fig wasps, parasites, weeds. 

Advantages to inbreeding?

Ecological: a single female can colonize

May also usefully prevent recombination

Deleterious recessives in inbreeding species purged by selection.

Inbreeding in humansAncient 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.


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 + FpqSimilarly, frequency of other homozygotes,

aa= q2 + FpqAll genotype frequencies must add to 1so the extra 2FpqAA 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)

Fmeasures reduction of heterozygosity, or heterozygotedeficit compared to Hardy-Weinberg, as well as probability of identity by descent!


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.


Réunion Vietnam

Native 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.


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:

In a population of size N, the probability that two alleles picked at random mating in generation tareIBDdue 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 in

generation t)

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

take 1–(both sides):

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:

So inbreeding from previous generations, we have at timeheterozygosity 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.

John Liu’s GENETIC DRIFT programme inbreeding from previous generations, we have at time

N inbreeding from previous generations, we have at time=100

15 populations

fixed after 100 generations

FST = 0.41

[N=10, FST ≈ 1.0]

Simulations from John Liu’s drift programme


0 populations

fixed after 100 generations

FST = 0.05

THE FLORIDA PANTHER inbreeding from previous generations, we have at time



... 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 inbreeding from previous generations, we have at time

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. 


1)Separate sexes

2)Unequal sex ratio

3) Some males mate more than others

INBREEDING -- Conclusions inbreeding from previous generations, we have at time

Inbreeding coefficient, F – the measure of inbreeding.

Regular systems of inbreedingFis also a measure of heterozygote deficit.

Inbreeding due to genetic drift in finite populations.The extent of drift can also be measured by F

… orHet = 2pq (1–F).

All evolution is somewhat stochastic:

a mix of randomgenetic drift with deterministic – selection.

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

FURTHER READING inbreeding from previous generations, we have at time

FUTUYMA, DJ 2005. Evolution. 

Chapter 9: 197-199, 201-202, Chapter 10.

FREEMAN & HERRON 2004. Evolutionary Analysis.

Chapter 6. pp. 204-252.