Towards the marriage of theory and data.

Theoretical biology is a subject with a rich history, tracing back certainly to demographers such as Graunt [1], and also drawing inspiration from perhaps the most important biological theoretician of all, Darwin [2]. Although Darwin did not deal in mathematics, his use of deductive reasoning to provide a conceptual framework for an otherwise confusing body of observations, and to make testable predictions, is the model for what theoretical biology should be. Quantitative approaches to biological problems have been around for a while, among demographers such as Graunt, as well as among others such as Verhulst [3] and Quetelet [4,5], who addressed Malthus’s [6] challenges of population regulation. However, in the first part of the twentieth century, the subject was elevated to a new level: in ecological systems by the sophisticated mathematical contributions of Volterra [7] and Lotka [8]; in population genetics by Wright [9–11], Fisher [12,13] and Haldane [14,15]; and in epidemiology by Ross [16] and by Kermack & McKendrick [17] No course in ecology is complete without a discussion of the equations of Volterra and Lotka, describing the dynamics of interacting species; despite their reliance on mathematical techniques that may be unfamiliar to some ecologists, their essential elements can be translated into terms that all can understand, and led early on to close links to experimental work, such as the studies of Gause [18], Park [19] and Utida [20]. The legacy of Volterra and Lotka has not been universally positive, although this is certainly not their fault. The attractive simplicity of the model equations proved irresistible to mathematicians eager to add bells and whistles, with little concern for biological relevance, and to explore their tortured implications in painful detail. This has produced a large literature, harmless except for its effect on perceptions of the field of mathematical biology, and its obfuscation of the cryptic nuggets that sometimes lie within. I was influenced early in my career by the distinguished probabilist Mark Kac [21], who wrote that the great contributions of physicists to biology had been carried out by physicists who had become biologists; that perceptive insight would be even more valid today. In interdisciplinary work, the standards for