Optimizing Evolution Under Cyclic Selection: the Case of B Cells

Rapid evolutionary adaptation may be necessary for organisms facing strong environmental pressures. Although selection often acts continuously, in the case of B cells evolving high affinity antibodies in germinal centers, selection can take place after multiple rounds of division. To study how the number of divisions between selection events affects adaptation, we develop a minimal computational model of cyclic selection. We find that the optimal average mutation rate per division and the corresponding adaptation velocity are nearly invariant across number of divisions between selections, and we quantitatively explain this behavior with a theory based on the dynamics of the "nose", i.e. the fittest individuals in the population. We also find that when the number of divisions between selection events is large, then mutating every division results in slower adaptation than mutating only at the last division before selection (as is the case for B cells). Our model provides a framework for understanding adaptation in natural and experimental systems subject to cyclic selection.