Though the first attempts to introduce game theory into evolutionary biology failed, new formalism by Maynard Smith and Price in 1973 had almost instant success. We use information supplied by early workers to analyse how and why evolutionary game theory (EGT) spread so rapidly in its earliest years. EGT was a major tool for the rapidly expanding discipline of behavioural ecology in the 1970s; each catalysed the other. The first models were applied to animal contests, and early workers sought to improve their biological reality to compare predictions with observations. Furthermore, it was quickly realized that EGT provided a general evolutionary modelling method; not only was it swiftly applied to diverse phenotypic adaptations in evolutionary biology, it also attracted researchers from other disciplines such as mathematics and economics, for which game theory was first devised. Lastly, we pay attention to exchanges with population geneticists, considering tensions between the two modelling methods, as well as efforts to bring them closer. This article is part of the theme issue ‘Half a century of evolutionary games: a synthesis of theory, application and future directions’.

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: "our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection" (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this "obsession", by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura's and Richard Lewontin's works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.

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