# Program

**Cailin O'Connor** (University of California, Irvine, United States)

Evolutionary modeling is used widely in biology and the social sciences. In recent years, this practice has spread in philosophy, and philosophy of biology in particular. Given the increasing use of evolutionary modeling in philosophy of biology, it is appropriate to ask: what are the limits of this sort of modeling? In what ways does it go wrong? In what ways can evolutionary models be misleading? At the same time, how can this be a useful methodology? How does it provide insight and explanation? This session will explore this methodology focusing of questions related to fitness and inclusive fitness.

##### Quantitative and population genetics methodologies in the inclusive fitness debate

**Hannah Rubin** (University of California, Irvine, United States)

The mathematical framework of inclusive fitness has come under intense debate, following an article by Nowak et al. (2010) which launches several criticisms against the generality and usefulness of the framework. Here I will look at two of their criticisms in detail, namely that inclusive fitness calculations require weak selection and are insufficient to completely analyze dynamics. Inclusive fitness calculations can be seen as fundamentally within the tradition of quantitative genetics, a tradition which emphasizes simplicity and measurability (Queller 1992). As such, recent defenses of the framework, and of kin selection results associated with the framework, are often stated within this tradition. The connections to kin selection are also clear within this framework as ‘relatedness’ can be estimated by various methods intuitively connected to kinship, for example by using pedigrees. However, inclusive fitness as a mathematical framework is not limited to use within quantitative genetics. I will look at how inclusive fitness models using replicator dynamics fit in within a unified framework of natural selection (Page and Nowak 2002). I will look at how these models are connected to common inclusive fitness calculations in quantitative genetics, where the need for weak selection may arise, and when the claim of dynamic insufficiency may be appropriate. I will also see whether any intuitive notions of ‘relatedness’ can be recovered from the population genetics models in which the relatedness parameter is not necessarily intuitively connected to kinship.

##### How game-theoretic models of social behavior (should) track fitness

**Patrick Forber** (Tufts University, United States)

Evolutionary game theory provides a set of formal tools for exploring the evolution of social behaviors. The biological interpretation of this framework presumes evolutionary fitness is the currency of interactions between behavioral strategies. Based (at least in part) on the payoffs of such interactions, various evolutionary dynamics model how the frequencies of strategies change over time. A crucial challenge for applying these idealized evolutionary models of social behavior to real evolving systems is determining what fitness properties the models track and how to measure such properties. One standard response to the challenge is to insist that models track the lifetime statistical average effect on fitness of different behavioral strategies (e.g., West and Gardner 2010). This paper will argue that the standard response is problematic, for it must measure fitness consequences over a rigid and too long a time frame (with the exception of a few notable cases, such as sex ratios; see, e.g., Ariew and Lewontin 2004). Based on the critical argument, a set of constraints on how game-theoretic models of social behavior should track fitness will be proposed and defended. Some connections to old puzzles about fitness and concerns about adaptationism will be explored.

##### Invariance and symmetry in evolutionary dynamics

**Simon Huttegger** (University of California, Irvine, United States)

In both evolutionary game theory and population genetics the basic dynamical systems describing evolutionary change are based on quantitative measures of fitness. For instance, the replicator dynamics, the canonical selection equation, or Wright's selection equation assert that evolutionary change is driven by how a type's fitness compares to the average fitness in a population. Because of the role fitness plays in these models, the mathematical form of dynamical equations constrains concepts of fitness in various ways. In this paper I explain how the scale type of a measure of fitness (such as ratio, interval or ordinal scale) is determined by the type of invariance one considers to be important. If the trajectories of a deterministic evolutionary dynamics should be invariant under admissible transformations of the fitness measure, this measure is a ratio scale. However, if only certain topological properties of trajectories should be preserved, fitness may be an interval scale. Finally, for concepts like that of an evolutionarily stable strategy, only the order relations between fitnesses play a role. This paper is an application of the theory of measurement as developed in Krantz et al. (1971) and subsequent volumes to questions in biology. It takes as it's point of departure Wagner's measurement theory of fitness introduced in Wagner (2010) and discusses the differences and commonalities of the other concepts of fitness mentioned above to Wagner's measure.