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A DEFENSE OF BEANBAG GENETICS J. B. S. HALDANE* My friend Professor Ernst Mayr, of Harvard University, in his recent book Animal Species and Evolution [i], which I find admirable, though I disagree with quite a lot ofit, has the following sentences on page 263. The Mendelian was apt to compare the genetic contents ofa population to a bag full ofcolored beans. Mutation was uie exchange ofone kind ofbean for another. This conceptualization has been referred to as "beanbag genetics." Work in population and developmental genetics has shown, however, diat the thinking ofbeanbag genetics is in many ways quite misleading. To consider genes as independent units is meaningless from the physiological as well as the evolutionary viewpoint. Any kind ofthinking whatever is misleading out ofits context. Thus ethical thinking involves the concept of duty, or some equivalent, such as righteousness or dharma. Without such a concept one is lost in the present world, and, according to the religions, in the next also. Joule, in his classical papers on the mechanical equivalent of heat, wrote of the duty ofa steam engine. We now write ofits horsepower. It is ofcourse possible that ethical conceptions will in future be applied to electronic calculators, which may be given built-in consciences! In another place [2] Mayr made a more specific challenge. He stated that Fisher, Wright, and I "have worked out an impressive mathematical theory ofgenetical variation and evolutionary change. But what, precisely , has been the contribution ofthis mathematical school to evolutionary theory, ifI may be permitted to ask such a provocative question?" "However ," he continued in the next paragraph, "I should perhaps leave it to Fisher, Wright, and Haldane to point out what they consider their major contributions." While Mayr may certainly ask this question, I may not answer it at Cold Spring Harbor, as I have been officially informed that * Address: Genetics and Biometry Laboratory, Government of Orissa, Bhubaneswar-3, Orissa, India. 343 I am ineligible for a visa for entering the United States.1 Fisher is dead, but when alive preferred attack to defense. Wright is one ofthe gentlest men I have ever met, and if he defends himself, will not counterattack. This leaves me to hold the fort, and that by writing rather than speech. Now, in the first place I deny that the mathematical theory ofpopulation genetics is at all impressive, at least to a mathematician. On the contrary , Wright, Fisher, and I all made simplifying assumptions which allowed us to pose problems soluble by the elementary mathematics at our disposal, and even then did not always fully solve the simple problems we set ourselves. Our mathematics may impress zoologists but do not greatly impress mathematicians. Let me give a simple example. We want to know how the frequency ofa gene in a population changes under natural selection. I made the following simplifying assumptions [3]: 1)The population is infinite, so the frequency in each generation is exactly that calculated, notjust somewhere near it. 2)Generations are separate. This is true for a minority only ofanimal and plant species. Thus even in so-called annual plants a few seeds can survive for several years. 3)Mating is at random. In fact, it was not hard to allow for inbreeding once Wright had given a quantitative measure ofit. 4)The gene is completely recessive as regards fitness. Again it is not hard to allow for incomplete dominance. Only two alleles at one locus are considered. 5)Mendelian segregation is perfect. There is no mutation, non-disjunction , gametic selection, or similar complications. 6)Selection acts so that the fraction ofrécessives breeding per dominant is constant from one generation to another. This fraction is the same in the two sexes. With all these assumptions, we get a fairly simple equation. If^n is the frequency ofthe recessive gene, and a fraction k ofrécessives is killed off when the corresponding dominants survive, then Qn- kqn* * In spite ofthis ineligibility I have, since writing this article, been granted an American visa, for which I must thank the federal government. However, I am not permitted to lecture in North Carolina, and perhaps in other states, without answering a question which I refuse to...


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