Transcript 1 - F

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
Inbreeding: 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
Regular systems of inbreeding
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).
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.
Sewall Wright's "path analysis" to calculate F
½
½
½
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 IN HUMAN POPULATIONS
Frequency of consanguineous marriages
Uncle/niece or
First
Av. inbreeding
cousins
coefficient, F
Aunt/nephew
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
-
0.0008
0.0061
0.00009
0.00038
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 recombination
Deleterious 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 1
so the extra 2Fpq AA and aa homozygotes must
have come from the heterozygotes
EFFECT OF INBREEDING ON POPULATIONS
genotype
AA
Aa
aa
(Sum)
frequency
p2+Fpq
2pq(1-F)
q2+Fpq
p2+Fpq+2pq
-2Fpq+Fpq+q2
=1
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!
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
Asian bramble (Rubus
alceifolius), introduced on
Pacific islands.
Genetic variation studied
by means of DNA
fingerprint technique:
"Amplified Fragment
Length Polymorphisms" AFLP for short.
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.
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
1
Hett  Het 1 
0 2N 





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
Ft  1
generation t)
2N
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:












Ft  1 1 F
2N t 1
(outbred in
generation t)
Summing the inbreeding in the current generation with
inbreeding from previous generations, we have at time t:


1
1
1 1 F   F


Ft 
 1
F




 t 1

t 1 t 1
2N  2N 
2N 



 

1
1


 




1 F   1 F

1

F

1
.1 F





take 1–(both sides): 
t  
t 1 2N 
t 1  2N  
t 1
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:


1


Hett  Het 1

t 1 2N 
So, after t generations of drift:





Hett  Het0 1 1
2N
t





So heterozygosity declines approximately by a
factor 1 per generation. However, ...
2N
(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
N=100
15 populations
fixed after 100
generations
FST = 0.41
[N=10, FST ≈ 1.0]
Simulations from John Liu’s drift programme
N=1000
0 populations
fixed after 100
generations
FST = 0.05
THE FLORIDA
PANTHER
Genus
Puma
Species
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: 5070. 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 sexes
2) Unequal sex ratio
3) Some males mate more than others
INBREEDING -- Conclusions
Inbreeding coefficient, F – the measure of inbreeding.
Regular systems of inbreeding
F 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.





Hett  Het0 1 1
2N
t





– an important equation in conservation, deduced from the
effect of drift on inbreeding in population of size N.
FURTHER READING
FUTUYMA, DJ 2005. Evolution.
Chapter 9: 197-199, 201-202, Chapter 10.
FREEMAN & HERRON 2004. Evolutionary Analysis.
Chapter 6. pp. 204-252.