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Mendel's research, rediscovered at the turn of the century, demonstrated what Darwin himself had at one time dimly glimpsed, that heredity is particulate, not blending. Whether or not offspring are bodily intermediate between their two parents, they inherit, and pass on, discrete hereditary particles—nowadays we call them genes. An individual either definitely inherits a particular gene from a particular parent or it definitely does not. Since the same can be said of its parents, it follows that an individual either inherits a particular gene from a particular grandparent or it does not. This argument can be applied repeatedly for an indefinite number of generations. Discrete single genes are shuffled independently through the generations like cards in a pack, rather than being mixed like the ingredients of a pudding.
This makes all the difference to the mathematical plausibility of the theory of natural selection. If heredity is particulate, natural selection really can work. As was first realized by the British mathematician G. H. Hardy and the German scientist W. Weinberg, there is no inherent tendency for genes to disappear from the gene pool. If they do disappear, it will be due to chance processes, or due to natural selection—because something about those genes influences the probability that individuals possessing them will survive and reproduce. The modern version of Darwinism, often called Neo-Darwinism, is based upon this insight. It was worked out in the 1920s and 1930s by the population geneticists R. A. Fisher, J. B. S. Haldane, and Sewall Wright, and was later consolidated in the 1940s as Neo-Darwinism. The recent revolution in molecular biology, beginning in the 1950s, has reinforced and confirmed, rather than changed, the theory of the 1930s and 1940s.