GUSTAVE MAL ~ COT AND THE TRANSITION FROM CLASSICAL TO MODERN POPULATION GENETICS

The contributions of Gustave Malkcot to theoretical population genetics are described, discussed, and put into perspective relative to earlier and later work. In this context, certain aspects of the theory of inbreeding, the correlation between relatives, the volution of finite panmictic populations, and (in more depth) spatial variation are reviewed. A brief biographical sketch of Malkcot is also presented. S ELDOM does a doctoral dissertation substantially advance its field. Nevertheless, just such a rare dissertation, Thiorie mathimatique de 1 hiriditi mendilienne generalisie, was submitted fifty years ago, to the Faculty of Sciences of the University of Paris, by GUSTAVE MAL~COT (1939a). Despite the breadth, depth, originality, power, and elegance of the contributions of this great French theoretical population geneticist, much of his work is known even now only to a small minority of researchers in his area. Therefore, it seems appropriate on this semicentennial to delineate and discuss MAL~COT’S contributions and to place them into perspective relative to earlier and later work, especially that of FISHER, WRIGHT, and KIMURA. It is also of interest to inquire why his contributions have not diffused more rapidly and widely. MAL~COT has written articles on the philosophy of science, on statistics, and on the theory of stochastic processes and its application to economics and physics. These will not be discussed here. About 45 of his papers fully or partly concern population genetics. They include brief research announcements; some items, such as lecture notes, whose aim is primarily didactic, but which often contain important new results and approaches; and long, detailed, powerful original papers. It is interesting to note, and an indication of MAL~COT’S intellectual independence and of the relative isolation in which he worked, that he is This paper is dedicated to the memory of CHARLES W. COTTERMAN (1914-1989), one of the most lucid, rigorous, and original thinkers in mathematical genetics, who was always exceeding generous with his deep understanding and extensive unpublished research. Genetics 122: 253-268 (June, 1989) the sole author of every one of his papers in genetics. MAL~COT’S work focuses on stochastic processes in population genetics. His doctoral research on the correlation between relatives (MAL~COT 1939a) led him to the gradual discovery of one of the most basic and fruitful concepts in population genetics: identity by descent (MAL~COT 1941, 1942, 1946, 1948). He used this idea to prove and interpret probabilistically WRIGHT’S formulas for the genotypic frequencies under inbreeding (which he generalized to multiple alleles) and for the inbreeding coefficient of an individual with an arbitrary pedigree (MAL~COT 194 1, 1942, 1948), to derive the correlation between relatives for traits without epistasis (MAL~COT 1948), to examine the evolution of finite panmictic populations (MAL& COT 1946, 1948, 195 l), and to investigate his original models for the genetic structure of populations distributed discretely or continuously in space (MAL~COT 1948, 1949, 1950, 1951, 1965, 1967, 1975). Before molecular genetics might have motivated him, MAL ~ C O T (1946, 1948, 195 1) introduced mutation by proposing that every allele mutates at the same rate and no mutant is identical by descent to any preexisting allele, and he employed this beautifully simple hypothesis in many of his studies. He deduced the asymptotic distribution of the gene frequency for pure random genetic drift (MAL~COT 1944), the complete time-dependent diffusion approximation for the genefrequency distribution with reversible mutation (MAL ~ C O T 1948), and the probability of ultimate fixation for selection without dominance (MAL~COT 1952). MALECOT’S 1948 classic, Les mathimatiques de 1 ’hiridit i , is one of the most original, elegant, concise, and