Re: Heritability of fitness
- From: "Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
- Date: Sun, 1 Jan 2006 01:19:24 -0500 (EST)
"John Edser" <edser@xxxxxxxxxx> wrote in message news:dp6luj$1q5c$1@xxxxxxxxxxxxxxxxxxxxxx
> "Perplexed in Peoria" jimmenegay@xxxxxxxxxxxxx wrote:-
>
> > Some empirical studies report that total fitness heritability was
> > undetectable "as expected". Apparently I don't understand evolutionary
> > theory as well as I thought I did. The following abstract seems to
> > summarize the conventional thinking (and also points out that heritability
> > is probably not EXACTLY zero):
> > Mayo, O., Bürger, R., Leach, C.R.:
> > The heritability of fitness: some single gene models.
> > Theoret. Appl. Genetics 79, 278-284 (1990).
> >
> > Summary Because directional selection exhausts additive-genetic
> > variance,
> > it is frequently claimed that the heritability of fitness should be very
> > close to zero. However, mutation-selection balance generates a certain
> > amount of additive-genetic variance, so that even parent-offspring
> > measures of heritability may be greater than zero at equilibrium.
> > Intra-generation heritability may also be non-zero, providing the
> > potentials for genetic change following environmental change.
> >
> > So my current understanding of this is that the heritability of fitness
> > in the wild is near zero at most times and places for most species.
> > But occasionally, due to environmental change or the freak appearance
> > of a rare beneficial mutation, the heritability of fitness in a population
> > rises to a level high enough to actually DO something.
>
> JE:-
> Firstly, you need to define fitness in an entirely unambiguous way that is
> biologically and not just mathematically, meaningful. The gene centric Neo
> Darwinists who dominate evolutionary theory today with
> simplified/oversimplified mathematically based models appear to be claiming
> that the key fitness concept is just mathematical putty in THEIR hands, i.e.
> fitness can mean just about anything they want it to, e.g. "inclusive
> fitness", "expected fitness" etc. While I do not agree with many of Gould's
> views his review of Darwin's theory gets to the heart of this matter.
>
> http://www.stephenjaygould.org/ctrl/gould_tautology.html
>
> Here are some quotes:
> "Natural selection is the central concept of Darwinian theory?the fittest
> survive and spread their favored traits through populations. Natural
> selection is defined by Spencer's phrase "survival of the fittest," but what
> does this famous bit of jargon really mean? Who are the fittest? And how is
> "fitness" defined? We often read that fitness involves no more than
> "differential reproductive success"?the production of more surviving
> offspring than other competing members of the population. Whoa! cries
> Bethell, as many others have before him. This formulation defines fitness in
> terms of survival only. The crucial phrase of natural selection means no
> more than "the survival of those who survive"?a vacuous tautology. (A
> tautology is a phrase?like "my father is a man"?contain no information in
> the predicate ("a man") not inherent in the subject my ("my father").
> Tautologies are fine as definitions, but not as testable scientific
> statements?there can be nothing to test in a statement true by definition.)"
>
> "It is beginning to look as though what Darwin really discovered was nothing
> more than the Victorian propensity to believe in progress."
>
> "I believe that Darwin was right and that Bethell and his colleagues are
> mistaken: criteria of fitness independent of survival can be applied to
> nature.."
>
> "My defense of Darwin is neither startling, novel, nor profound. I merely
> assert that Darwin was justified in analogizing natural selection with
> animal breeding."
>
> JE:-
> Animal breeding is essentially a simple process which has been going on for
> many 1000's of years without the benefit of Darwinian evolutionary theory,
> Mendel's genetics or population genetics. What you end up doing is
> increasing the total number of fertile forms that a series of fitness
> independent but related parents reproduce into the one, same population. In
> this process you and not the natural environment act as the major selector
> on each parent over many organism generations. The aim is to breed in the
> desired traits and breed out the undesirable ones using artificial selective
> mating and artificial selection based entirely on reproductive success.
> Since these processes can _very clearly_ provide heritable results then
> natural selection must also be able to provide a heritable Total Darwinian
> Fitness (TDF) which can only be empirically defined to be: the total number
> of fertile forms each parent reproduces into one population. Because an
> artificial total fitness has been demonstrated to be heritable, total
> Darwinian fitness must be considered to be heritable to some degree ...
[break inserted by JM for emphasis]
> ...despite
> the claims of Neo Darwinists using gene centric models which delete gene
> fitness epistasis entirely and/or incorrectly convert one level of fitness
> into another, e.g. Hamilton's Rule.
Well, to respond to the last bit first, I think that your claims about
neo-Darwinist claims are a distortion.
But before that, you give an interesting argument suggesting (as Darwin did)
that whatever is possible with artificial selection must also be possible
with natural selection. That is not quite true, since the successes of
selective breeding are due only partly to artificial selection. The breeder
engages in not only culling (artificial selection) but also in a control
over mating patterns - matching like with like usually, but also trying some
carefully designed crosses.
To analyze this, it is useful to start with the textbook definition of
heritability. Of course, since these definitions were produced by statisticians,
they are interested not in heritibility of a trait, but rather the heritability
of variation in a character. Here are some definitions, as I recall them:
V is the total variance in a character.
It is broken into four components V = V_a + V_d + V_i + V_e
V_a is the 'additive genetic variance'
V_d is the 'dominance variance' due to interactions between the two gene
copies on different chromosomes at a single locus
V_i is the 'interaction variance' due to epistatic interactions between
genes at different loci
V_e is the 'environmental variance' due to the fact that no two organisms
experience exactly the same environment. For example, one individual
may be hit by lightening, while his twin brother is not.
For convenience, V_g is the 'total genetic variance': V_g = V_a + V_d + V_i
H^2 is the 'broad-sense heritability' and is defined as V_g / V
That is, it is the fraction of the total variance (in fitness, say)
which can be attributed to the organisms genes.
h^2 is the 'narrow sense heritability' and is defined as V_a / V
It is important because (whether you like it or not) V_a is the only
component of the variance which responds to selection in a sexually
reproducing population. By contrast, if the population were to
reproduce by cloning, then H^2 would be the appropriate notion of
heritability since reproduction would not break up the non-additive
'dominance' and 'epistasis' features of the parent's genome.
I hope I have these definitions right.
Now, your argument seems to be that artificial selection and breeding can
purify and concentrate effects in the V_d and V_i components of variance,
so the neo-Darwinists must be wrong in their insistence that V_d and V_i
don't respond in a situation of *natural* selection. So H^2 is the right
definition of heritibility, not h^2, according to you.
Hmmm. I see your point and I am not completely sure I see the flaw in your
argument. But here goes my attempt to understand you. First, I think that
you and the neo-Darwinists would agree that H^2 would apply if the species
reproduced asexually, by a process of cloning. But the neo-Darwinists
insist that their math (under the assumption of random mating) proves that
h^2 gives the true response to selection. Double hmmmm. 'Under the
assumption of random mating'. ...
Sewall Wright, who was an expert on selective breeding, argued that natural
selection 'works best' when the total population is divided into fairly
small sub-populations which are mostly inbred, but allow just enough
gene flow between subpopulations to remain a single species. His scheme
also allows for a kind of group selection in which a particularly fit
sub-population can completely replace another less fit subpopulation.
(My knowlege of Wright's theories comes from secondary sources, so I may
be seriously distorting here.)
Under these conditions, a sexual population takes on some of the characteristics
of an asexual, clonally reproducing, population - in particular, it can
respond to selection using V_g and H^2, rather than V_a and h^2.
So, if I am understanding you correctly, and if I am understanding Wright
correctly, and if Wright is right, then just maybe Edser is not completely
wrong.
Happy New Year, John.
.
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