population genetics halliburton chapter 8 inbreeding 1 panmixa is an important prerequisite for the...

Population geneticsHalliburton 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)

InbreedingBetween individuals sharing a (relatively recent) ancestor. One of the consequences is an increase inthe 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 inbreedingConsanguinity ("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, aftersome time, be ignored. A generation of forefathers where "no individuals are related" is called the reference- or base-population..

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Inbreeding 2

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 thecoefficient 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 = 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] = 1/4For 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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Halliburton Chapter 8

Inbreeding 3

The inbreeding coefficientWe now define the inbreeding coefficient as the probability that an individual has two alleles that areibd 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).



Inbreeding 4

BI3010H07 Population geneticsHalliburton Chapter 8

Inbreeding 5

NB! Table 8.1 contains anerror in the "path" for parent B (K should be F).



Inbreeding 6

The effect of inbreeding on heterozygosity:Inbreeding increases the frequency of homozygotes and reduces the frequencyof heterozygotes in a population, compared to the reference population in a formergeneration. 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 expression3.19 page 81 in Halliburton, and see that if no other forces than inbreedingaffect genotype proportions in the population, the inbreeding coefficient can beexpressed 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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Inbreeding 7

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 aninbred population relative to an non-inbred reference (base) population.

If no other evolutionary processes are are in action, these two meanings areequivalent.


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Inbreeding 8

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 willincrease 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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Inbreeding 9

Selfing:

With selfing, the heterozygosity is reduced by 50 % each generation, andrapidly 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 10

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 11

Inbreeding and "purging" of harmful alleles:

It has been suggested that inbreeding, because of the increased homo-zygosity 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 co-adapted 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 stocksunder the influence of escapees from the salmon farming plants).


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Inbreeding 12

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 13Population geneticsHalliburton Chapter 8

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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population genetics halliburton chapter 8 inbreeding 1 panmixa is an important prerequisite for the...

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inbreeding mating

population average3

alle alleles

coefficient of kinship

consanguinity g

cr coefficient of relationship

coefficient of relationship

degree of inbreeding