In 1991 he was awarded the Balzan Prize for genetics and evolution "for his powerful analysis of evolutionary theory and of the role of sexual reproduction as a critical factor in evolution and in the survival of species; for his mathematical models applying the theory of games to evolutionary problems" (motivation of the Balzan General Prize Committee). In 1995 he was awarded the Linnean Medal by the Linnean Society and in 1999 he was awarded the Crafoord Prize jointly with Ernst Mayr and George C. Williams. In 2001 he was awarded the Kyoto Prize.