Barrier Trees for Continuous Fitness Landscapes

Local minima of a fitness landscape are separated by barriers. A barrier tree (Flamm et al., 2002) is a representation of a fitness landscape as a binary tree, where each leaf represents a local minimum; the barriers connecting the local minima are represented as the internal horizontal nodes of the barrier tree. To reflect the fitness values of barriers and minima, each node in the barrier tree is positioned relative to the height of the represented point in the fitness landscape. Until now, barrier trees have been applied to discrete fitness landscapes. This contribution extends the concept to multidimensional continuous landscapes; a generalization that allows the use of the approach in various areas of life sciences. Methods for generating barrier trees for continuous fitness landscapes will be presented, ranging from a coarse grained view of the landscapes by converting them to discrete ones, to the use of heuristic approaches, where local minima are found via the Nelder-Mead simplex method, and the minima are then connected via biased random walks. Advantages and disadvantages of the approaches will be demonstrated and methods to compare generated trees will be explained. In order to exemplify the power of the approach, the real-life problem of molecular docking will be treated. In molecular