Conference Agenda

Studying relations, effects and properties of modified genes or organisms is an important topic in biology with implications in evolution, drug resistance and targeting, and much more. Biological data can many times be represented in digital form, a mutation has occurred or not, a species is present in an ecological system, or not. A fitness landscape is a function from such bit strings to some measured quality.
A property of fitness landscapes is epistasis, which is a phenomenon describing dependency relations among effects of combinations of modified genes. Polyhedral decompositions, such as cube triangulations induced by fitness landscapes, provide a systematic approach to epistasis.
In this session, we aim at bringing researches of various areas of science together to discuss contact points between applied polyhedral geometry, statistics and biology, and present recent developments in the field.

How are fitness landscapes used in biology? What type of data is analyzed? Which methods are applicable to this theory?

These are some of the issues we will touch upon in this introductory talk and elaborate further throughout the session. The starting point of this presentation will be given by reviewing the geometric framework to study epistasis proposed by Beerenwinkel et al.(2007). In particular, we will define various forms of genetic interactions of current interest in evolutionary biology and demonstrate their utility. Computational limitations of these approaches will also be discussed.

Beerenwinkel et al.(2007) suggested studying fitness landscapes via regular subdivisions of convex polytopes.Building on their approach we propose cluster partitions and cluster filtrations of fitness landscapes as a new mathematical tool. In this way, we provide a concise combinatorial way of processing metric information from epistatic interactions. Using existing Drosophila microbiome data, we demonstrate similarities with and differences to the previous approach. As one outcome we locate interesting epistatic information where the previous approach is less conclusive.

An important goal for biologists is construction of quantitative, predictive models relating the genome sequence of an organism (its genotype) to its observed traits (its phenotype). This is a challenging problem. If mutations behave independently, the difference in phenotype between two genotypes that differ at L positions can be described as the sum of the individual effects of all L mutations. Mutations, however, rarely act independently: the effect of a mutation can change depending on the presence or absence of another mutation. We, and others, have even documented extensive three-way and even higher-ordered interactions between mutations. In my talk, I will discuss the evidence for these multi-way interactions, as well as how such interactions undermine models that sum the effects of mutations to predict phenotype from genotype. I will then discuss an alternative, mechanistically informed model, and describe experimental work done in my lab testing predictions of this model. Our work demonstrates a powerful, workable alternative to linear models and points to other classes of models that may be better suited for describing the map between genotype and phenotype.

We use tools from complex adaptive systems theory to describe, model and interpret macro-economic dynamics. We apply Kauffman's fitness landscape ideas with (intrinsic) location parameters, (extrinsic) intensity parameters and epistasis. We focus on a pricing state space ("pricescape"), study the system's macro topology and use geometric insights to understand pathways and dynamics.

We apply this general concept to understand the makeup and dynamics of a set of commercially relevant antibiotics. This is finally interpreted as a landscape of different economic configurations, allowing to study the commercial fate of competing products in well-described terms of clusters such as market leaders, niche players and competing generic products. These clusters do not exist in a simple equilibrium or in utter chaos, but rather as a periodic order of evolutionary progress.