Peter Smith

Both biologists and philosophers often make use of simple verbal formulations of necessary and sufficient conditions for evolution by natural selection (ENS). Such summaries go back to Darwin's Origin of Species (especially the "Recapitulation"), but recent ones are more compact.1 Perhaps the most commonly cited formulation is due to Lewontin.2 These summaries tend to have three or four conditions, where the core requirement is a combination of variation, heredity, and fitness differences. The summaries are employed in several ways. First, they are often used in pedagogical contexts, and in showing the coherence of evolutionary theory in response to attacks from outside biology. Second, they are important in discussions of extensions of evolutionary principles to new domains, such as cultural change. The summaries also have intrinsic scientific and philosophical interest as attempts to capture some core principles of evolutionary theory in a highly concise way. Despite their prominence, both the proper formulation and status of these summaries are unclear. Standard formulations are subject to counterexamples, and their relations to formal models of evolutionary change are not straightforward. Here I look closely at these verbal summaries, and at how they relate to formal models. Are the summaries merely rough approximations that have no theoretical role of their own? Perhaps they could operate as theoretical statements in Darwin's time, but have now been superseded by more exact treatments.

We present a dynamic model of the evolution of communication in a Lewis signaling game while systematically varying the degree of common interest between sender and receiver. We show that the level of common interest between sender and receiver is strongly predictive of the amount of information transferred between them. We also discuss a set of rare but interesting cases in which common interest is almost entirely absent, yet substantial information transfer persists in a *cheap talk* regime, and offer a diagnosis of how this may arise.

The commentaries by Dennett, Sterelny, and Queller on Darwinian Populations and Natural Selection (DPNS) are so constructive that they make it possible to extend and improve the book’s framework in several ways. My replies will focus on points of disagreement, and I will pick a small number of themes and develop them in detail. The three replies below are mostly self-contained, except that all my comments about genes, discussed by all three critics, are in the reply to Queller. Agential views of evolution, discussed by Queller and Dennett, are addressed in my reply to Dennett

Recent years have seen a renewed debate over the importance of groupselection, especially as it relates to the evolution of altruism. Onefeature of this debate has been disagreement over which kinds ofprocesses should be described in terms of selection at multiple levels,within and between groups. Adapting some earlier discussions, we presenta mathematical framework that can be used to explore the exactrelationships between evolutionary models that do, and those that donot, explicitly recognize biological groups as fitness-bearing entities.We show a fundamental set of mathematical equivalences between these twokinds of models, one of which applies a form of multi-level selectiontheory and the other being a form of ``individualism.'' However, we alsoargue that each type of model can have heuristic advantages over theother. Indeed, it can be positively useful to engage in a kind ofback-and-forth switching between two different perspectives on theevolutionary role of groups. So the position we defend is a``gestalt-switching pluralism.''.

One version of pluralism was defended in a well-known paper by Sterelny and Kitcher. In this sense, pluralism is the view that any given selective process can be described at a variety of different levels in the biological hierarchy. On Sterelny and Kitcher’s view, one can explain giraffe necks in terms of competition among longer-necked and shorter-necked giraffes, and one can also explain them in terms of competition among the genes that lead to these differences in neck size. Although these descriptions might have different heuristic virtues, neither description has a special explanatory status that the other lacks.

A number of recent discussions have argued that George Price's equationfor representing evolutionary change is a powerful and illuminatingtool, especially in the context of debates about multiple levels ofselection. Our paper dissects Price's equation in detail, and comparesit to another statistical tool: the calculation and comparison ofaverage fitnesses. The relations between Price's equation and equationsfor evolutionary change using average fitness are closer than issometimes supposed. The two approaches achieve a similar kind ofstatistical summary of one generation of change, and they achieve thisvia a similar loss of information about the underlying fitnessstructure.