Re: Hamilton's Rule In The Mirror


"Guy Hoelzer" <hoelzer@xxxxxxx> wrote in message news:d4sdhj$iu4$1@xxxxxxxxxxxxxxxxxxxxxx
> in article d4pr82$2pa0$1@xxxxxxxxxxxxxxxxxxx, Perplexed in Peoria at
> jimmenegay@xxxxxxxxxxxxx wrote on 4/27/05 10:10 PM:

[snip my complaints about Guy's question and Guy's responses. But in response
to Guy's query, I don't believe that NS optimizes the time scale. In fact,
I don't think that there is an objective time scale in any evolutionary
situation. Time scale is arbitrarily chosen by the investigator, as
described below.]

> > Natural selection works at ALL time scales. Choose any time scale you like,
> > measure fitnesses at that time scale (by counting descendents or gene copies
> > after that amount of time). Then check to see whether the fittest type has
> > increased in frequency within the population over that time scale. It has.
>
> This appears to confound pattern with process. I presumed above that
> natural selection is a legitimate process. I would never argue that
> heritable factors observed to increase in frequency were by definition
> favored by selection. It is possible, for example, that deleterious factors
> drifted to higher frequency.

I am not familiar with the "pattern vs process" language, so I may be missing
the point here. But, based on my guess as to what is meant, my response is:
I see fitness as something which is measured by observing the pattern. It
is a parameter which serves to summarize the pattern. You apparently see
fitness as a parameter modulating the process. As such, it is not directly
observable. In fact, it can only be estimated by using my "pattern"
measurement, or perhaps by inferring it from other measurements of the
pattern.

> > That the original type has increased in frequency over a time scale of
> > one generation is a tautology. That it has increased in frequency over
> > multiple generations is not a tautology, since the direction of selection
> > may change between generations. That is, a fit individual in our original
> > population may have many descendents, but those descendents are all very
> > different from their ancestor because in the later portion of the time scale,
> > the traits of the ancestor became maladaptive.
>
> Implicit in this argument is that you think natural selection has a
> particular time scale of effect that is reflected in a time lag of some
> length in the adaptation of organisms to a novel environment.

I'm not even considering adaptation by individual organisms (and I hope
you didn't intend to raise this issue). As for the response time of the
population to a change in the environment, that is entirely determined
by the inheritance mechanisms and the measured fitnesses.

> This appears
> to me to contradict your premise that selection acts at all time scales
> equally.

I didn't say "equally" - in fact, I think that the effects of selection at
different time scales are incomparable.

> If you think there is a meaningful mean duration of such a time
> lag, or perhaps several modes of time lag duration, then you would have
> answered my question.

Ah! I begin to understand that you are equating time scales with time
lags. Well, as I understand it, the lag for a trait is proportional
to the selection coefficient times the heritability.

> > Consider a trait which is adaptive in one environment and maladaptive in
> > another. Consider an environment that changes periodically back and forth.
> > Choose a time scale equal to this period. We would expect the frequency
> > of this trait to oscillate.
>
> Not necessarily. It would only oscillate if the period of the oscillation
> was greater than the time scale of the effects of selection.

Actually, I would say exactly the opposite. If the period of oscillation
is much greater than the time scale of effects (aka lag time, aka response
time), then the trait which is favored first goes to fixation and there
is no response to the swing of the environment in the other direction. Or,
rather, the response will be novel - not a return to the status quo.

> Consider the
> minimum time scale at which conventional Darwinian selection can manifest
> adaptive effects while maintaining the potential for adapting (oscillating)
> back to the original environmental conditions. Without being precise, it
> must be several generations.

I would prefer to be precise. It is one generation in a non-overlapping
generation model. It is less than a generation in a model with overlapping
generations. I am assuming here that by "adaptive effects" you mean a change
in gene frequencies which increases the mean fitness of the population.

> It is clearly the case that if the
> environmental oscillation is too fast, then natural selection cannot respond
> to it by dragging the population along in match-step with the environment.

If organisms die and are born during the oscillation, and if the death
rate and birth rate depend on genotype in that environment, then the population
is dragged.

> In fact, there are empirical (e.g., Zeh's research on pseudoscorpions) and
> theoretical results indicating that when the environment oscillates too fast
> selection can promote long-term intraspecific polymorphism instead of
> evolutionary oscillations by the population.

Right. So now you are defining "response to selection" to mean genes going
to fixation. Your time scale needs another factor which depends on the
population size. So now I claim it is fitness of the trait times heritability
of the trait times the square root of the population size.

[snip remainder]


.

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