Biology Reference
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factors of strength, namely, the size of population and causal relevance, are
independent from each other.
To sum up, on Millstein's view, the strength of natural selection depends on two
independent factors, namely, causal relevance and the effective population size. In
contrast, the strength of drift depends exclusively on the effective population size.
When the degree of causal relevance is higher and the effective population size
larger, the strength of natural selection increases. And the larger is the effective
population size, the smaller is the strength of drift.
Now, a problem with Millstein's account is that it would lead to a disagreement
with most biologists on how to determine the relative strength of natural selection to
drift. When natural selection and drift operate together, biologists are interested in
telling whether one of them predominates. And their judgment is based on a crucial
quantity, namely, 4Ns , where N is the effective population size and s is the selection
coefficient. If the quantity increases, then natural selection tends to dominate drift;
on the contrary, if the quantity decreases, then it is drift that tends to predominate. It
is noteworthy that interpreting “s” as “the degree of causal relevance” makes
perfect sense of Millstein's view that causal relevance and the effective population
size represent indeed two separate factors in determining the strength of natural
selection. In addition, since s is the selection coefficient, it also makes perfect sense
of Millstein's view that the effective population size is the only factor that affects
the strength of drift. Thus, when both s and N increase, the crucial quantity 4Ns
increases accordingly, and it turns out that natural selection tends to dominate drift,
because the strength of natural selection increases, whereas the strength of drift
decreases, and vice versa for decreasing s and decreasing N . So far so good for
Millstein's account.
However, recall that on Millstein's view, natural selection and drift, when they
operate together, are two separate sampling processes and that the effective popu-
lation size affects not merely the strength of natural selection but also the strength
of drift. In contrast, causal relevance affects only the strength of natural selection.
Now consider a case where N decreases but s increases in such a way that the crucial
quantity 4Ns increases. In such a case, because the crucial quantity increases,
biologists would predict that natural selection tends to dominate drift. However,
on Millstein's account, such a prediction would not be justified: when N decreases,
the strength of drift increases accordingly. As to the strength of natural selection, it
is hard to say whether it increases or not: on the one hand, the strength of natural
selection tends to diminish because N decreases. On the other hand, it tends to
increase because s increases. Since the two tendencies oppose each other, one might
wonder which one wins out. Even if the fact that the crucial quantity increases
suggests that the strength of natural selection ends up increasing, one might still
wonder whether it increases greatly enough to outcompete drift. Hence, this is a
case where it would be hard to say whether natural selection or drift tends to
predominate, even if the crucial quantity increases. To be sure, this is not the
only case where a disagreement arises between Millstein and the majority of
biologists. A similar argument can be provided in considering a second case
where N increases but s decreases in such a way that the crucial quantity 4Ns
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