Formal spaces have become commonplace conceptual and computational tools in a large array of scientific disciplines, including both the natural and the social sciences. Morphological spaces are spaces describing and relating organismal phenotypes. They play a central role in morphometrics, the statistical description of biological forms, but also underlie the notion of adaptive landscapes that drives many theoretical considerations in evolutionary biology. We briefly review the topological and geometrical properties of the most common morphospaces in the biological literature. In contemporary (...) geometric morphometrics, the notion of a morphospace is based on the Euclidean tangent space to Kendall’s shape space, which is a Riemannian manifold. Many more classical morphospaces, such as Raup’s space of coiled shells, lack these metric properties, e.g., due to incommensurably scaled variables, so that these morphospaces typically are affine vector spaces. Other notions of a morphospace, like Thomas and Reif’s skeleton space, may not give rise to a quantitative measure of similarity at all. Such spaces can often be characterized in terms of topological or pretopological spaces. (shrink)

The concepts of adaptation and fitness have such an appeal that they have been used in other scientific domains, including the social sciences. One particular aspect of this theory transfer concerns the so-called fitness landscape models. At first sight, fitness landscapes visualize how an agent, of any kind, relates to its environment, how its position is conditional because of the mutual interaction with other agents, and the potential routes towards improved fitness. The allure of fitness landscapes is first and foremost (...) that it represents a complex story about adaptation and fitness in one coherent image. Different accounts of fitness landscapes in different domains in the social sciences suggest that the properties and functions of fitness landscapes are attributed rather freely. These differences are testimony of the model’s versatility. At the same time, one will notice that the different approaches can also create ambiguity about the exact meaning and role of fitness landscapes in the social sciences. This article presents an extensive literature survey of the diverging interpretations and uses of fitness landscapes in the social sciences and discusses the implications in terms of how these models inform scientific inquiry. (shrink)