Transcript E-Halliburton chapter 8

BI3010H07
Population genetics
Halliburton Chapter 8
Inbreeding 1
Panmixa is an important prerequisite for the Hardy-Weinbergs law. What would be the result if it
does not hold? There are many examples of non-random mating in nature: selfing in plants, mate choise
based on size or external attributes in animals and humans, first cousin marriages etc.
In the broad sense there are three types of non-random mating:
1. Inbreeding (mating between individuals more related than average in the population)
2. Assortative mating (between individuals that are more phenotypically similar than population average)
3. Dissortative mating (between individuals less phenotypically similar than the population average)
Inbreeding
Between individuals sharing a (relatively recent) ancestor. One of the consequences is an increase in
the frequency of homozygotes in the population. Recessive harmful genes will then manifest themselves,
such as developmental and morphological effects, and reduced viability and fertility. This reduces the
mean absolute fitness of the population. How can we quantify the degree of inbreeding at autosomal
loci in a population of diploid individuals?
Consanguinity and inbreeding
Consanguinity ("same blood") means that individuals share a relatively recent common ancestor; they
have received copies of the same allele from that ancestor. Such alleles are ibd (identical by descent;
cf Chapter 7.2), and their hosts have a non-zero probability that two alleles at a locus are ibd.
Generally, an individual has 2n forefathers after n generations from the ancestor. Genetic consequences
of consanguinity decreases with increasing number of generations from the forefather and can, after
some time, be ignored. A generation of forefathers where "no individuals are related" is called the
reference- or base-population.
.
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Various ways of estimating the degree of relatedness between two individuals are:
(CR) Coefficient of relationship = the expected proportion of the alleles that are ibd.
In a group of offspring (full-sibs) from non-related parents the proportion is ½ (i.e. half of the
alleles are ibd).
(CC) Coefficient of consanguinity (after Malecót) is a more useful measure; it is the probability
that two alleles, each drawn randomly from the same locus, are ibd. This measure is identical to
the coefficient of coancestry and coefficient of kinship.
To sum up; the probability that two individuals have received the same allele is the coefficient of
relationship (CR), while the probability of drawing just that allele from the population gene pool is the
coefficient of coancestry (CC), which is exactly half the CR and is often referred to as g.
[Coeff. of consanguinity (g)] = [coeff. of kinship] = [coeff. of coancestry] = [ ½ coeff. of relationship ]
gxy = S 1/2 Pr(X=Ai) x 1/2Pr(Y=Ai)
(summed over alle alleles at a locus)
We will hereafter call g the coefficient of coancestry
"Path analysis" for the coefficient of coancenstry (g).
(Fig. 8.1 in Halliburton):
For two fullsibs, in total 4 alleles in two individuals: g = 4[ ½(½) x (½(½) ] = 4[1/16] = 1/4
For first cousins, in total 4 alleles in two individuals: g = 4[ ½(¼) x (½(¼) ] = 4[1/64] = 1/16
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The inbreeding coefficient
We now define the inbreeding coefficient as the probability that an individual has two alleles that are
ibd at a locus. Because the alleles of an individual are randomly sampled (half from each of its
parents), its inbreeding coefficient (f) is the same as the coancestry coefficient of its parents, i.e. g.
The symbol used for the coefficient of inbreeding is f, with a subscript which indicates which of the
individuals in the pedigree are involved (see Fig. 8.3 page 275 in Halliburton). Again:
The inbreeding coefficient (f) of an individual = the "coancestry coefficient" (g) of its parents
By "path analysis" it is fairly easy to find the inbreeding coefficient when the pedigree is known.
(see examples on the following pages).
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NB! Table 8.1 contains an
error in the "path" for
parent B (K should be F).
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The effect of inbreeding on heterozygosity:
Inbreeding increases the frequency of homozygotes and reduces the frequency
of heterozygotes in a population, compared to the reference population in a former
generation. NB! In an inbred population the homozygosity is caused both by ibs
alleles from the reference population and ibd alleles due to inbreeding since the
reference population.
If we let the subscripts r and f refer to the reference (base) population and the
inbred population, respectively, the following is valid:
Hf = Hr (1-f), which means that f can be interpreted as a measure of the
proportional reduction in the frequency of heterozygotes relative to the reference
population. (cf expression 8.4 page 275 in Halliburton). Recapitulate expression
3.19 page 81 in Halliburton, and see that if no other forces than inbreeding
affect genotype proportions in the population, the inbreeding coefficient can be
expressed as:
f = (Hexp - Hobs) / (Hexp)
cf. expr. (8.7)
NB! Reduction in heterozygosity does not affect allele frequencies (cf page 278).
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Halliburton Chapter 8
Summing up:
At the individual level f is the probability that two alleles are ibd.
At the population level f is the proportional reduction in heterozygosity in an
inbred population relative to an non-inbred reference (base) population.
If no other evolutionary processes are are in action, these two meanings are
equivalent.
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Inbreeding in small populations:
Small populations have a non-zero probability that two alleles are ibd
even under panmixia. In the first generation after the reference population
this probability is 1/(2N) (Halliburton Chapter 7.2 and Fig. 8.4)), and it will
increase each generation so that:
ft+1 = 1/(2N) + (1 - 1/(2N)) ft
(Box 8.1)
if the reference population itself was not inbred, then
ft = 1 - (1 - 1/(2N))t
and the heterozygosity ...
Ht = H0(1 - 1/(2N))t
(NB! Important formula!)
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Selfing:
With selfing, the heterozygosity is reduced by 50 % each generation, and
rapidly approaches zero. After only 10 generations it is practically zero.
In many plants, selfing is not obligatory, and they may maintain a certain
(although low) heterozygosity (e.g. H = 0.00024 in Arabidopsis thaliana).
Repeated full-sib mating:
Ht+1 = ½ Ht + ¼ Ht-1 (Halliburton Expression (8.22) and Fig. 8.10)
For other types of repeated inbreeding mating systems, see Halliburton
Table 8.4 page 287).
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Inbreeding depression:
Also at single-locus traits the result of inbreeding is an increased
frequency of homozygotes, and thereby inreased frequency of harmful,
recessive alleles in double dose so that they manifest in disease/death.
This has been thoroughly documented in studies on offspring from related
parents.
For multilocus traits (quantitative traits) the manifested effects are quite
diverse, like higher frequencies of harmful morphological deformities,
miscarriages, infant deaths, and mental retardations in man.
In captive animals (livestocks and pets), typical effects can also relate to
health, longeivity, fertility, general vigour, heart disease, egg shell
thickness (poultry, fish) and hip dysplasia (e.g. dogs).
At the population level, Frankham (1998) showed that small, isolated
island populations increased their probability of extinction when the
inbreeding coefficient increased beyond 0.5. He also showed that such
values are quite common in many small populations.
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Inbreeding and "purging" of harmful alleles:
It has been suggested that inbreeding, because of the increased homozygosity with harmful alleles in double doses and lower frequencies of
heterozygotes, can serve a useful cleansing of the genepool. It gives
selection the chance to get rid of harmful alleles in a process called
purging. Even if it is in principle possible, opinions are divided as to how
efficient his process can be in natural populations and domesticated
brood stocks.
Outbreeding, hybrid vigour, and outbreeding depression.
Outbreeding is the opposite of inbreeding; i.e. mating between individuals
less related than the average in the population. The outbred population
can have higher fitness than any of the involved inbred populations
because of so-called "hybrid vigour". However, if local populations have
been adapting to their milieu in many generations and so-called coadapted gene complexes have been formed, these complexes can be
broken up by outbreeding and result in so-called otbreeding depression.
(This has been suggested as a threath to Norwegian wild salmon stocks
under the influence of escapees from the salmon farming plants).
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Assortative and disassortativ mating (non-panmixia):
Assortative: Mating between individuals that are (phenotypically) more
similar than the average in the population ("alike seeks alike"). This will
reduce the population's heterozygosity for the trait. Assortative mating
may play an important role in speciation processes (e.g. for ”sympatric
speciation”; page 301 ff).
(Speciation: Read about pre- and post-mating isolation mechanisms, sympatric
and allopatric speciation on page 301 ff in Halliburton).
Disassortative: Mating between individuals that are phenotypically less
alike than the average in the population. "Contrasts attract each other").
In this case the heterozygosity increases compared to a panmictic
scenario. This phenomenon is strongly associated with selection (incl.
sexual selection).
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Inbreeding and Gametic (genetic) disequilibrium:
In section 4.2, the coefficient of gametic disequilibrium was defined as
D = g1g4 - g2g3
Where the g’s are the frequencies of the two-locus gamete types. The
disequilibrium decays over generations (if no selection) at a rate that
depends on the recombination rate r. The recursion equiation is:
Dt+1 = (1-r)Dt
Since recombinations only occur in double heterozygotes, and inbreeding reduces
heterozygosity at all loci, the frequency of double heterozygotes would expected to
be lower under strong inbreeding (e.g. under selfing). Hence initial gametic
combinations will rarely be broken up, and decay to gametic equilibrium will be
much slower than in a panmictic population. We should therefore expect to find
high levels of D in predominantly self-fertilizing species. This has been confirmed in
many studies. (cf page 294 ff).
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