In his theory of evolution, Darwin recognized that the conditions of life play a role in the generation of hereditary variations, as well as in their selection. However, as evolutionary theory was developed further, heredity became identified with genetics, and variation was seen in terms of combinations of randomly generated gene mutations. We argue that this view is now changing, because it is clear that a notion of hereditary variation that is based solely on randomly varying genes that are unaffected by developmental conditions is an inadequate basis for evolutionary theories. Such a view not only fails to provide satisfying explanations of many evolutionary phenomena, it also makes assumptions that are not consistent with the data that are emerging from disciplines ranging from molecular biology to cultural studies. These data show that the genome is far more responsive to the environment than previously thought, and that not all transmissible variation is underlain by genetic differences. In Evolution in Four Dimensions (2005) we identify four types of inheritance (genetic, epigenetic, behavioral, and symbol-based), each of which can provide variations on which natural selection will act. Some of these variations arise in response to developmental conditions, so there are Lamarckian aspects to evolution. We argue that a better insight into evolutionary processes will result from recognizing that transmitted variations that are not based on DNA differences have played a role. This is particularly true for understanding the evolution of human behavior, where all four dimensions of heredity have been important.

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p0 = e–m; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.