Hyperspace geography: Visualizing fitness landscapes beyond 4D

Human perception is finely tuned to extract structure about the 4D world of time and space as well as properties such as color and texture. Developing intuitions about spatial structure beyond 4D requires exploiting other perceptual and cognitive abilities. One of the most natural ways to explore complex spaces is for a user to actively navigate through them, using local explorations and global summaries to develop intuitions about structure, and then testing the developing ideas by further exploration. This article provides a brief overview of a technique for visualizing surfaces defined over moderate-dimensional binary spaces, by recursively unfolding them onto a 2D hypergraph. We briefly summarize the uses of a freely available Web-based visualization tool, Hyperspace Graph Paper (HSGP), for exploring fitness landscapes and search algorithms in evolutionary computation. HSGP provides a way for a user to actively explore a landscape, from simple tasks such as mapping the neighborhood structure of different points, to seeing global properties such as the size and distribution of basins of attraction or how different search algorithms interact with landscape structure. It has been most useful for exploring recursive and repetitive landscapes, and its strength is that it allows intuitions to be developed through active navigation by the user, and exploits the visual system's ability to detect pattern and texture. The technique is most effective when applied to continuous functions over Boolean variables using 4 to 16 dimensions.

Investigating ontogenetic space with developmental cell lineages

Development plays a significant role in biological evolution, and is likely to prove an effective route to overcoming the limitations of direct genotype-phenotype mappings in artificial evolution. Nonetheless, the relationship between development and evolution is complex and still poorly understood. One question of current interest concerns the possible role that developmental processes may play in orienting evolution. A first step towards exploring this issue from a theoretical perspective is understanding the structure of ontogenetic space: the space of possible genotype-phenotype mappings. Using a quantitative model of development that enables ontogenetic space to be characterised in terms of complexity, we show that ontogenetic landscapes have a characteristic structure that varies with genotypic properties.