Significant advances were made in the study of biological [micro]evolution before its molecular basis was understood, in no small part through the use of simplified mathematical models, pioneered by Fisher (1930), Wright (1931), and J.B.S. Haldane (1932)...
Mathematical models such as [those for cultural evolution and gene-culture coevolution] are often treated with suspicion and even hostility by some social scientists, who consider them to be oversimplifications of reality... The alternatives..., however, are usually either analysis at a single (purely genetic or purely cultural) level or vague verbal accounts of “complex interactions,” neither of which we believe to be productive. Gene-culture analyses have repeatedly revealed circumstances under which the interactions between genetic and cultural processes lead populations to different equilibria than those predicted by single level models or anticipated in verbal accounts... as illustrated by the aforementioned examples of dairy farming and handedness.
Interestingly, fifty years ago the same reservations about simplifying assumptions were voiced about the use of population genetic models in biology by the prominent evolutionary biologist Ernst Mayr (1963). He argued that using such models was akin to treating genetics as pulling coloured beans from a bag (coining the phrase “beanbag genetics”), ignoring complex physiological and developmental processes that lead to interactions between genes.
In his classic article “A Defense ofBeanbag Genetics,” J. B. S. Haldane (1964) countered that the simplification of reality embodied in these models is the very reason for their usefulness. Such simplification can significantly aid our understanding of processes that are too complex to be considered through verbal arguments alone, because mathematical models force their authors to specify explicitly and exactly all of their assumptions, to focus on major factors, and to generate logically sound conclusions. Indeed, such conclusions are often counterintuitive to human minds relying solely on informal verbal reasoning.
Haldane (1964) provided several examples in which empirical facts follow the predictions of population genetic models in spite of their simplifying assumptions, and noted that models can often highlight the kind of data that need to be collected to evaluate a particular theory. Ultimately, Haldane won the argument, and population genetic modelling is now an established and invaluable tool in evolutionary biology (Crow 2001). We can only echo Haldane’s defence and argue that the same arguments apply to the use of similar mathematical models in the social sciences.
A more recent version of J.B. S. Haldane's argument is Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology Maria R. Servedio,Yaniv Brandvain, Sumit Dhole, Courtney L. Fitzpatrick, Emma E. Goldberg, Caitlin A. Stern, Jeremy Van Cleve, D. Justin Yeh
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