A couple of comments on specific points (excerpted):

On 17-Jun-07 16:09:08, Paul Spicker wrote:
> [...]
> If, then, we take a statement that "height is 80% the result
> of inheritance, and 20% of environment", what would that mean?  
> Height is the result of inheritance-and-environment; neither
> means anything without the other.

I agree with this (see below).

> By the same token, the claim that "intelligence is 80% hereditable"
> has to be wrong; even if intelligence is something that exists and
> is capable of being inherited, the proportions make no sense.

In talking about "height is 80% the result of inheritance, and 20%
of environment", what this precisely means is that 80% of the
observed variance (in the statistical sense) of the characteristic
can be attributed to variation in heritable factors, and 20% of it
can be atteributed to variation in environmental factors. And the
environmental factors in question are those which obtain in the
population in question at the time in question.

Variation in inherited factors depends on the degree of inhomegeneity
in the gene pool and on the mating patterns in the population.
Variation in environmental factors means, well, variation in
environmental factors. Weight variation in (say) a "pure line"
of laboratory mice is going to be nearly 100% environmental -- there
is almost no heterogeneity in the gene pool to support variability
of heritable factors, so differences in weight at a given age are
likely to be mainly due to variations in how, and how much, they
were fed (and can be the subject of investigation by researchers
into "mouse nutrition" who will want to use "pure lines" in order
to shift the variation as much as possible onto the experimental
variation in diet). So, with widely varying experimental diets,
we can have 99.9% dependence of weight on environment, and 0.1%
dependence (perhaps) on genetic factors.

On the other hand, feed all the mice exactly the same, and keep
them all under exactly the same consitions. Then the variation
in weight (if any) is 100% due to genetic factors.

> [...]
> (I should also add a minor statistical footnote.  Life is
> lognormal, as a biology textbook of that title explains.  Hardly
> any biological distributions are normal, because they're
> developmental; lognormality, no normality, results when factors
> are randomly distributed forwards.

I do not understand "randomly distributed forwards", though I can
guess what it might mean (the accumulation of succesive random
variations over the course of time?).

This cannot account for the difference between normally and
lognormally distributed outcome.

If a quantity accumulates succesive additive increments, each
randomly say +/- 1 ("random walk"), then the distribution after
a sufficiently large number of steps will be close to normally
distributed.

What essentially makes the difference between normal and lognormal
is the way in which the "accumulation of random variations"
operates.

If it operates additively, then (other things being equal) the
result will be normally distributed.

If it accumulates multiplicatively, then the results will be
lognormally distributed.

Population sizes in the wild, for instance, might be better
described by lognormal than by normal distributions, since
the rate of growth of a population (other things being equal,
in particular the availability of environmental resources to
support the larger population) will be proportional to the
size of the population. So, in a given time increment, the
amount added to the population will be proportional to its
previous size. similarly, if conditions impose increasing
risk of death on individuals, then the number dying (hence
the decrement in population size) will be proportional to
the population size. either way, a multiplicative change.

On the other hand, even with multiplicative increments, the
sizes of the increments may be so small that the multiplicative
effect can be accurately described by linearising the relationship.
In that case the increment is, for practical purposes, additive.

It is basically the difference exemplified by a 20% random
increment X -> X*(1 + 0.2) or X/(1 + 0.2), and a 0.1% random
increment Y -> Y*(1 + 0.001) or Y/(1 + 0.001).

After only a few steps, X will (closely) have a lognormal
distribution. It will take an awful lot of steps for the
distribution of Y to be noticeably different from a normal
distribution (in simulations I'm looking at, over 2000 steps).

Another way of looking at it is that if the increment on X
is multiplicative, then the increment on log(X) is additive,
so log(X) tends to a normal distribution -- which is precisely
the definition of a lognormal distribution for X.

This difference has nothing whatever to do with "developmental"
issues, unless you are looking at developmental characteristics
which change, in the course of deveklopment, multiplicatively
rather than additively (and then by large enough amounts for
linearisation not to be valid).

> IQ was assumed to be normal, and the tests are geared to make
> it so. 

Indeed! More specifically to the point (for adults at least),
the scoring for an IQ Test is adjusted so that, in a reference
population, it is normally distributed with mean 100 and SD 15.
(similar things happen in University examinations, too -- which
has led me, in the past, to make a fuss about "normalising" the
marks in an exam set to a heterogenous collection of students
from several very different departments, the resulting distribution
of raw marks being clearly multimodal ... ).

So here, by definition, IQ score has to be normally distributed.
(It may be different in terms of the classical definition for
IQ of children, "Mental Age"/"Cronological Age").

> The idea of intelligence as something distributed on 
> a bell curve is inconsistent with the idea of intelligence as a
> developmental concept.)

For the reasons given above, I claim that this does not in the
least follow.

a) If your measure of IQ is by construction normally distributed,
   then it will be so, developmental or not.
b) Developmental characteristics can be normally, lognormally,
   or otherwise distributed. There is nothing in "development"
   which forces any particular distribution, unless the mechanism
   of change of that particular characteristic is such as to
   induce a particular distribution.

Best wishes to all,
Ted.

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Date: 17-Jun-07                                       Time: 18:51:33
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