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Puzzles for ZFEL, McShea and Brandon’s zero force evolutionary law

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Abstract

In their 2010 book, Biology’s First Law, D. McShea and R. Brandon present a principle that they call “ZFEL,” the zero force evolutionary law. ZFEL says (roughly) that when there are no evolutionary forces acting on a population, the population’s complexity (i.e., how diverse its member organisms are) will increase. Here we develop criticisms of ZFEL and describe a different law of evolution; it says that diversity and complexity do not change when there are no evolutionary causes.

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Notes

  1. All such numbers refer to pages in McShea and Brandon (2010).

  2. Without this “per trait” rider, ZFEL faces the problem of having to measure how diverse and complex a set of objects is overall, rather than just having to make sense of how diverse and complex they are with respect to this or that trait. This difficulty resembles a standard problem faced by pheneticism in its discussion of overall similarity.

  3. Could this problem be solved by distinguishing the level at which at which variation exists and the level at which the forces act? This won’t help with the present example, since McShea and Brandon correctly describe the variation at the level of allelic frequencies and the force of mutation as acting on allelic frequencies.

  4. When there are more than two allelic types in the population, it is natural to use the entropy, −∑pi(log pi), of the probability distribution as a measure of variability. For n alleles, the entropy is maximal when all alleles have the same probability.

  5. See Sober (1984, pp. 97–102) for discussion of the difference between selection-of and selection-for.

  6. A similar scenario can be described for mutation. Again, imagine 1,000 identical populations but let each population’s mutation probabilities be drawn from a flat distribution. The forces of mutation at work in these different populations are then “random with respect to each other” and the populations can be expected to diverge. McShea and Brandon intend this process to be an instance of ZFEL, even though there is no selection and the process isn’t one of pure drift, either. This mutation process resembles McShea and Brandon’s example of the “evolution” of a picket fence (2–4); the pickets start in the same state and random insults then cause them to diverge.

  7. Our argument can also be applied to cases in which optima for populations are drawn from a normal distribution. This distribution can run from negative to positive infinity on a log scale. Whether optima drawn from a given normal distribution will cause the populations to converge or diverge depends on the variance in the normal distribution and on how much variance there is among the populations’ starting trait values.

  8. A defender of the gene’s eye view of evolution might insist that evolutionary forces must be defined solely in terms of their impact on gene frequencies, not in terms of their impact on genotype frequencies. McShea and Brandon do not take this position, which is no surprise, given that Brandon has been a strong proponent of the need to look beyond gene frequencies and genic fitnesses, and to include genotype frequencies and genotypic fitnesses, as well as other “higher-level” descriptors, in adequate models of the evolutionary process; see, for example, Brandon and Nijhout (2006) and Weinberger’s (2011) reply.

  9. Beatty (1995) develops this point more fully and Sober (1997) replies.

  10. This third formulation of Hardy–Weinberg is perhaps a good place to answer McShea and Brandon’s question about how the law applies to real populations. The law is often applied in population genetics by using its contrapositive form: if a population deviates (significantly) from Hardy–Weinberg frequencies, biologists conclude that an evolutionary cause or force is present. We also want to emphasize that Hardy–Weinberg describes a sufficient condition for a population to have expected genotype frequencies of p2, 2pq, and q2. The conditions described are not necessary; for example, a population can exhibit these frequencies when there is stabilizing selection.

  11. The definition of evolution as change in the genetic composition of populations is defective for the same reason (Sober 1993, p. 5).

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Acknowledgments

We are grateful to Dan McShea and Robert Brandon for their helpful comments on an earlier draft, and to the anonymous referees of this journal for theirs.

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Correspondence to Elliott Sober.

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Barrett, M., Clatterbuck, H., Goldsby, M. et al. Puzzles for ZFEL, McShea and Brandon’s zero force evolutionary law. Biol Philos 27, 723–735 (2012). https://doi.org/10.1007/s10539-012-9321-7

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