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Date Posted: 12:16:30 03/12/04 Fri
Author: DaVid I.
Subject: Analysis of Dr. Willis article on inbreeding.

Sorry about the accidentally truncated URL for the Willis article:
http://www.nvfr.nl/willisInbreed.html

Under the assumption that you have already become familiar with
Willis' comments, I will repeat only those sections that I hope to
address. It is important to note up front that Willis makes a lot of
excellent points in his discussion and with these I find no fault.
Perhaps the most important is the observation that, even though a
breeder may be inbreeding, he does not do so without also using
selection. However, Willis' use of quotations and references in this
commentary is highly selective, and he might just as easily have
introduced a number of counterpoints to his own arguments, some from his
own text.

References cited:

Willis, "Genetics of the Dog, 1989 (W)
Falconer & Mackay, "Intro to Quantitative Genetics," 4th ed, 1996
(F&M)

Willis states: "What we do know is that inbreeding brings about
something called inbreeding depression. This depends on a formula which
is: -2F dpq " He provides definitions for each element in the formula
so I will not repeat those here. A more complete formula (F&M, p250)
is:

Mf = Mo - 2F SUM (dpq) where Mf is the mean population value (for some
trait) of a population with COI = F and Mo is the mean population value
with COI = 0. Willis observes correctly "If there is no dominance
[i.e., d = 0] there is no depression for that trait. The critics of
inbreeding rarely, if ever, tell you this." But we already know that d
is NOT zero in most cases of interest. In fact, Willis himself
observes: "Most deleterious traits tend to be recessive." For
recessive traits, d = 1, that is the heterozygous genotype has the same
value as the homozygous dominant genotype. In such cases, the net loss
in genotype value is 2F SUM (pq) which increases linearly with
inbreeding, F, and can be substantial. N.B. I did not need the sigma
symbol to write this formula ;-)

But we already knew this. Willis' book (W, p329), (F&M, p248) gives
us substantial evidence that inbreeding generally reduces the average
breed fitness, so why would we need even to speculate on the issue of
the possibility that dominance effects might be zero -- breeders of
plants and animals have known for centuries that inbreeding carried far
enough results in inbreeding depression.


"Inbreeding depression as it is called is likely to be most obvious in
what are called fitness traits (fertility traits) and least obvious in
traits like some aspects of conformation which tend to be quite
heritable, often in excess of 0.40 (40%). ...A breeder would rightly
argue that maintaining fertility was desirable since without it the
breeder cannot function. However what about prolificacy (litter size)?
A pig breeder wants as large a litter as he can rear and thus
inbreeding, if it reduced litter size, would be very damaging to a pig
breeder. That is not true of a dog breeder." Maternal effects,
unfortunately, do not merely influence rather benignly the number of
pups whelped, they also relate to neonatal deaths, average weight at
birth, etc. Although a breeder might be quite willing to forego large
litter sizes to attain some objective requiring inbreeding, it is not so
certain that the breeder will be equally willing to deal with high
levels of neonatal deaths and generally unthrifty pups. Further, Rehfeld
(1970) in his beagle colony study did not discover increases in neonatal
deaths starting at 78% inbreeding, such increases were evident at far
lower inbreeding levels (W, p329)

Willis writes: "Nobody would dispute the fact that high levels of
inbreeding can be damaging but in some cases the effect of inbreeding is
not apparent at less than 20% (brother/sister and parent/offspring is
25%). ...The idea that increased inbreeding will increase the incidence
of defects is unlikely (Alderson & Bodo, 1992) if the defect has a high
frequency." Quite so, but Willis seems never to have encountered
extended, multi-generational pedigrees for dogs. He actually, treats
3-generation pedigrees as meaningful when computing COIs. (W, p331).
With such a paucity of pedigree data, I am not surprised that he finds
that "the overall average of Boxer champions is a mere 4.2% inbreeding."
Willis' assertion, "Extending pedigrees would increase these values
slightly but breeders have no means of doing this" is not true on both
counts. These 3-generation COIs are virtually meaningless, a fact to
which anyone doing pedigree analysis and computing COIs for extended
pedigrees can testify. The 20% inbreeding "trouble zone" is not a
remote possibility for most breeds, it is the rule rather than the
exception for many dogs.

Risking the likelihood of becoming overlong and tedious, I would
like to address one more point with regard to selection for polygenic
traits. Willis observes: "Genetic theory states quite clearly that
response to selection per year is given by the formula:

R = h^2 x St , where h^2 is the heritability of the trait, R is the
response per year, S is the selection differential and t is the
generation interval.

Willis implies in this section that restricting the extensive use of
some desirable sires will limit the breeders ability to employ selection
to improve his breed line with respect to one or more traits. He fails
to emphasize that his formula for response to selection is based
entirely on phenotypic class. That is, one need not inbreed to achieve
improvement through selection when dealing with polygenes. On the
contrary, one need only select the breeding animals from the class of
dogs that best epitomizes the trait(s) being selected for. This implies
assortative selection, which may but need not lead to inbreeding.
Surely, Willis is not recommending that one use so large a selection
differential, S, that only one or a few sires in the entire breed can
satisfy the selection criteria.

I could extend this review indefinitely, covering matters that
Willis neglected, discussing overdominance at the MHC, gene complexes
that are associated with antibody formation and the functioning of the
immune system, and how these relate to the loss of heterozygosity
arising from inbreeding. The effect of inbreeding on the reduction of
the effective population size, Ne, is relevant, especially when
discussing the inevitable rate of increase over time of the breed
average COI, which Willis treats casually as of concern only to
"scientists who ...deal with small population genetics." But this is
already too long.

Jim Seltzer
Willowind Dalmatians
jseltzer@nbn.net
http://users.nbn.net/~jseltzer

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