Starting from the early decades of the twentieth century, evolutionary biology began to acquire mathematical overtones. This took place via the development of a set of models in which the Darwinian picture of evolution was shown to be consistent with the laws of heredity discovered by Mendel. The models, which came to be elaborated over the years, define a field of study known as population genetics. Population genetics is generally looked upon as an essential component of modern evolutionary theory. This (...) article deals with a famous dispute between J. B. S. Haldane, one of the founders of population genetics, and Ernst Mayr, a major contributor to the way we understand evolution. The philosophical undercurrents of the dispute remain relevant today. Mayr and Haldane agreed that genetics provided a broad explanatory framework for explaining how evolution took place but differed over the relevance of the mathematical models that sought to underpin that framework. The dispute began with a fundamental issue raised by Mayr in 1959: in terms of understanding evolution, did population genetics contribute anything beyond the obvious? Haldane's response came just before his death in 1964. It contained a spirited defense, not just of population genetics, but also of the motivations that lie behind mathematical modelling in biology. While the difference of opinion persisted and was not glossed over, the two continued to maintain cordial personal relations. (shrink)

We discuss N. I. Vavilov’s 1922 landmark publication, “The Law of Homologous Series in Variation,” and highlight its salient points. Vavilov drew upon his considerable experience in the field with wild and cultivated crop plants and summarized what he noticed in the form of a law. The law stated that comparable variant forms tended to appear in different varieties of the same species, different species of the same genus, different genera of the same family, and so on. His survey of (...) the older literature suggested that the law applied to multicellular animals as well. Vavilov acknowledged that such “parallel” series might be the outcome of convergent evolution (as conventionally understood). At the same time, by way of an alternative hypothesis, he posed a question that continues to engage evolutionary biology to this day. Namely, does the existence of such parallelisms reflect underlying structural and developmental principles (based on the laws of physics and chemistry) which constrain the range of possible plant and animal forms? Vavilov’s original 1922 paper from the _Journal of Genetics_ (12:47–89) is available as supplementary material in the online version of this article. (shrink)

Different types of explanations coexist in present-day biology. Functional explanations describe mechanisms, whereas evolutionary explanations provide answers to the question “why?” mostly by appealing to the past and present action of natural selection. But the relations between these two types of explanations, as well as the relative insights they offer, vary from one domain of research to another. We will illustrate this complex landscape of biological explanations with three examples involving aging, the sex ratio, and the phenomenon of genomic imprinting. (...) We will show that the two types of explanations have recently often progressed towards each other. In consequence, they cease to be “pure” functional or evolutionary explanations and become explanations that may be alternatively considered as functional or evolutionary. (shrink)