Hybridization may influence evolution in a variety of ways. If hybrids are
less fit, the geographical range of ecologically divergent populations may
be limited, and prezygotic reproductive isolation may be reinforced. If som
e hybrid genotypes are fitter than one or both parents, at least in some en
vironments, then hybridization could make a positive contribution. Single a
lleles that are at an advantage in the alternative environment and genetic
background will introgress readily, although such introgression may be hard
to detect. 'Hybrid speciation', in which fit combinations of alleles are e
stablished, is more problematic; its likelihood depends on how divergent po
pulations meet, and on the structure of epistasis. These issues are illustr
ated using Fisher's model of stabilizing selection on multiple traits, unde
r which reproductive isolation evolves as a side-effect of adaptation in al
lopatry. This confirms a priori arguments that while recombinant hybrids ar
e less fit on average, some gene combinations may be fitter than the parent
s, even in the parental environment. Fisher's model does predict heterosis
in diploid F(1)s, asymmetric incompatibility in reciprocal backcrosses, and
(when dominance is included) Haldane's Rule. However, heterosis arises onl
y when traits are additive, whereas the latter two patterns require dominan
ce. Moreover because adaptation is via substitutions of small effect, Fishe
r's model does not generate the strong effects of single chromosome regions
often observed in species crosses.