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We analyze the interactions between division, mutation and selection in asimplified evolutionary model, assuming that the population observed can beclassified into fitness levels. The construction of our mathematical frameworkis motivated by the modeling of antibody affinity maturation of B-cells inGerminal Centers during an immune response. This is a key process in adaptiveimmunity leading to the production of high affinity antibodies against apresented antigen. Our aim is to understand how the different biologicalparameters affect the system's functionality. We identify the existence of anoptimal value of the selection rate, able to maximize the number of selectedB-cells for a given generation.

Multi-type Galton-Watson processes with affinity-dependent selection applied to antibody affinity maturation