  Adaptation often involves the acquisition of a large number of genomic
changes which arise as mutations in single individuals. In asexual populations,
combinations of mutations can fix only when they arise in the same lineage, but
for populations in which genetic information is exchanged, beneficial mutations
can arise in different individuals and be combined later. In large populations,
when the product of the population size N and the total beneficial mutation
rate U_b is large, many new beneficial alleles can be segregating in the
population simultaneously. We calculate the rate of adaptation, v, in several
models of such sexual populations and show that v is linear in NU_b only in
sufficiently small populations. In large populations, v increases much more
slowly as log NU_b. The prefactor of this logarithm, however, increases as the
square of the recombination rate. This acceleration of adaptation by
recombination implies a strong evolutionary advantage of sex.
