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IN DEFENSE OF VERBAL ARGUMENTS BRUCE WALLACE* In an essay entitled "A Defense of Beanbag Genetics," Haldane [1] defended the role of mathematical geneticists (himself, Fisher, and Wright) and mathematical analyses against criticisms that had been leveled by Mayr [2] in questioning whether mathematical models had served any useful purpose in understanding evolutionary change. Haldane did not appeal to the analytical power of mathematics; rather, he stressed the precision with which verbal statements need be expressed if one attempts to fit them to a mathematical model. Otherwise, he pointed out, inconsistent (even contradictory) statements can be assembled in the guise of a logical argument; such inconsistencies were then illustrated with examples taken from Mayr's [2] article, itself. Most persons, I believe, are sympathetic to Haldane's thesis: If one cannot formulate a simple argument that lends itself to mathematical manipulations, how can one hope to construct a lengthy verbal argument that involves both numerous variables and their even more numerous interactions? Why, to cite an example, should a lengthy argument concerning the coadaptation of gene pools have credence if its proponent does not understand the roles of mutation, chance, and selection in modifying expectations based on the Hardy-Weinberg equilibrium? The later, it may be recalled, predicts that gene frequencies will remain constant from generation to generation; it also predicts that the distribution of genotypes in any one generation under random mating will be P2CAA), 2pq(Aa), and ^(aa) in the case of two alleles, A and a, whose frequencies are p and q. Citations of Haldane's defense have, in my opinion, exceeded his original intent. A recent book review alleges that Haldane once claimed that This paper was prepared while the author's research was supported by grant GM34576 from the National Institute of General Medical Science, U.S. Public Health Services, and while he was an Alexander von Humboldt Senior U.S. Scientist awardee at the University of Tübingen. Helpful suggestions by Professor D. Sperlich are gratefully acknowledged. ?Department of Biology, Virginia Polytechnic Institute and State University, Blacksburg , Virginia 24061.© 1988 by The University of Chicago. All rights reserved. 0031-5982/88/3 102-0561$01.00 Perspectives in Biology and Medicine, 31, 2 · Winter 1988 \ 201 no argument is worthwhile unless it can be expressed in mathematical terms. Such a claim seems rather extreme. In one of his children's books, Haldane notes that a truly invisible man would of necessity be blind. No mathematical argument accompanies this (obviously true) assertion. He also suggested that no husband should provide blood for his wife's transfusion ; this is sound advice with respect to possible mother-fetus immunological reactions during subsquent pregnancies. Similarly, without mathematical treatment, Haldane [3] refers to genes whose effects may be "touch and go" during embryonic development but which serve a useful purpose later in life; I provided a quantitative treatment of such alleles as an example of marginal overdominance [4]. More recently, Kimura [5] has cited Haldane's defense of beanbag genetics with (appropriate) approval, and has then proceeded to criticize various nonmathematical arguments: Waddington, for example, is dismissed for having introduced a "horde of neologisms," and Mayr's [2] views are said to be "entirely verbal and lacked any quantitative treatment ." Kimura also expresses surprise that Wright has failed to provide a quantitative study of Wright's shifting balance theory of evolution (see [6, pp. 454-455]). In general, according to Kimura, the period including the late 1950s and early 1960s "was a time of stagnation, rhetorical arguments dominating over meticulous scientific reasoning." One can sympathize with the emphasis Haldane and Kimura place on quantitative (mathematical) treatment without conceding that verbal arguments need be devoid of meticulous reasoning. In my own work, for example, I have attempted to be precise (even quantitative), although I have acquired only rudimentary mathematical skills. Nevertheless, in retrospect, I have a modicum of pride in my contributions to an understanding of the role that genetic loads play in natural populations, in my speculations on the role of reverse repeats in the control of gene action (speculations arising from population, not molecular, studies), and in my suggestion that the Tree Line gene arrangement in Drosophila pseudoobscura...


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