Large deviations for the Fleming–Viot process with neutral mutation and selection11Research supported by the Natural Science and Engineering Research Council of Canada.

Large deviation principles are established for the Fleming–Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele model, and then generalized, through the projective limit technique, to the infinite allele model. Explicit expressions are obtained for the rate functions.