TITLE: Mutation and Adaptation in Non-Monotonic Landscapes
SPEAKER: Roman Belavkin (Middlesex University)

ABSTRACT:

Classical theories of adaptation and beneficial mutation are based on a representation of organisms by points in some metric space (e.g. Euclidean space of traits, Hamming space of DNA sequences), and adaptation is viewed as a motion in this space towards some target point (an optimal organism).  In such formulation, maximisation of biological fitness corresponds to a minimisation of distance to the target, and geometry of the metric space allows one to solve the optimisation problem precisely.  In particular, this way one can derive probability of beneficial mutation and obtain a function for optimal control of mutation rate.  There is currently a lot of interest in the topic of variable mutation rates, but there is limited understanding of how such perfect geometric models of adaptation can be related to real biological fitness landscapes that can be rugged.  I will discuss a theory of mutation rate control that is based on fitness feedback from general landscapes.  The theory considers a landscape as a noisy communication channel between fitness and distance, and their monotonic relationship is exploited to analyse probability of beneficial mutation and its control.  Because all landscapes are at least weakly monotonic in some small, but non-trivial neighbourhood of the global optimum, the optimal mutation rate control function in this neighbourhood coincides with that obtained using idealised geometric models.  As an illustration, we consider 115 landscapes of binding scores between DNA and transcription factors, which are not monotonic in general.  The mutation rates for optimal evolution on these landscapes have common properties.  Generally, optimal mutation rates increase when fitness decreases, and the increase of mutation rate is more rapid in landscapes that are less monotonic (i.e. more rugged).  We shall discuss the relevance of these findings to living organisms, including the phenomenon of stress-induced mutagenesis.