Inbreeding depression is the average reduction in fitness, or of a character, due to inbreeding.
Why?
Look at a single locus - If there is dominance such that the heterozygote d>0 (or h>1/2), then the weighted average fitness of the two homozygotes is going to be lower than the average of a randomly mating population.
Furthermore, if there is overdominance, then increasing homozygosity will also decrease fitness. In general, it is very difficult to determine whether recessivity or overdominance causes inbreeding depression; there is evidence for both (i.e., clearly, both happen). The general feeling is that deleterious recessives are more important. See a review by Charlesworth and Charlesworth in Annual Review of Ecology and Systematics.
Directional dominance implies that the dominance of genes for a trait is on average biased in one direction.
If there is directional dominance, then a quantitative trait will on average change in mean as a result of inbreeding.
Characters closely related to fitness show more inbreeding depression -- WHY???
Because it is easier to select for dominant alleles.
=> Fitness characters tend to have more dominance variance -- Roff and Mosseau 1996 - Heredity
Without dominance, there can be no inbreeding depression; but epistasis can affect its expression.
Question: Is there evidence for epistasis in determining inbreeding depression? Answer: a qualified yes. Experiments largely show a linear decline in fitness as function of inbreeding coefficient, but there is also often evidence for increased depression with larger inbreeding. See Willis, 1993, Evolution 47:864 for a review, data, and a discussion of the caveats.
Selection can greatly reduce inbreeding depression.
Here's some data from Drosophila melanogaster (Fowler and Whitlock, in prep.) The inbred flies have gone through a single generation bottleneck with N=2 and then have been maintained at moderate size (N=100) for 20 generations.
|
Fitness at time t |
Outbred |
Inbred |
Inbreeding depression as % |
|
t=3 |
196 |
141 |
-29% |
|
t=20 |
222 |
176 |
-21% |
This difference in inbreeding depression is highly significant.
Different episodes of inbreeding can have drastically different effects on the mean. By the same data as above (The vertical axis of the histogram is the mean fitness of an inbred line, 54 lines, 40 families per line):
There's almost a two-fold range in inbreeding depression. In other systems, it is possible to get inbred liens which show no inbreeding depression; occasionally inbred lines even have higher fitness than the outbreds.
Heterosis = hybrid vigor: the increase in fitness of hybrids relative to the inbred lines which were the parents of the cross.
The amount of heterosis in the F1 generation (defined as the deviation of the fitness of the hybrids from the mean fitness of the two parental strains) is proportional to the square of the difference of allele frequencies of the parent populations:
H = d (p1 - p2)2
The fitness of the F2's is expected to be half of this value (essentially because the parental genotypes are being re-created half of the time).
See Figure 14.3.
The fitness of the F2's is also affected by epistasis, even in the absence of dominance. Thus examination of the F2's is a common way to examine the effects of epistasis on traits or fitness.
See Figure 14.5.
Inbreeding on additive characters results in greater genetic variance among populations and lower genetic variance within populations.
Additive genetic variance within populations, on average, decreases by F. VA,w = (1-F)VA.
The additive genetic variance among populations increases in proportion to 2F: VA,b = 2FVA.
The total additive genetic variance is therefore
VA,w + VA,b = (1+F)VA.
The heritability within lines is expected to decrease as a result of this reduction in VA. See p266 in F+M for formulae.
With inbreeding, dominance variance can be "converted" into additive genetic variance.
See Figure 15.2.
If there are relatively many loci with rare recessive alleles, the additive variance can increase on average as a result of inbreeding.
The details of this "conversion" depend on many non-orthogonal terms describing the variance/covariance components of the trait. See Cockerham and Tachida, Genetical Research, 1988.
Similar effects can happen with epistasis. Here the result can be simply expressed:
VA,w = (1-F)VA + 4F(1-F)VAA + ...
Much data suggests that inbreeding often increases VA. See, for example, Bryant et al. 1986, Genetics or Wade et al. 1995, Evolution.
The variance among the offspring of crosses among lines is derivable from the same equation used to tell the variance among families, with r=F and u=F2.
Thus
[sigma]X2 = FVA + F2VD + F2VAA + F3VAD + F4VDD + ...
The mean performance of a line when crossed with other lines is called its general combining ability (GCA). The variance of GCA is also derivable from that general equation, with r=F/2 and u=0.
[sigma]GCA2 = 1/2 FVA + 1/4 F2VAA +...
The variance among the crosses with parents randomly chosen is the sum of the GCA of the two lines, plus the specific combining ability (SCA) of that cross. The variance components of SCA can be found by subtraction:
[sigma]SCA2 = F2VD + 1/2 F2VAA + F3VAD + F4VDD + ...
These combining ability concepts are more important in crop improvement than evolutionary biology. However, they lead to breeding designs such as diallel crosses, which allow estimation of non-additive components of variance, particularly in species which allow easy creation of heavily inbred lines.
The party line is that the sensitivity to environmental perturbations increases with inbreeding; in other words, there is inbreeding depression for homeostasis. The evidence for this is equivocal. (See Whitlock and Fowler, 1996, Evolution).