We tackle three components of evolutionary modelling: payoffs, dynamic
al systems and equilibrium concepts, Firstly, we merely require that f
itness functions are continuous, Secondly, we examine very general cla
sses of dynamics. Thirdly, we give useful parallels to the Nash equili
brium and the evolutionarily stable strategy. Under (weakly) sign-comp
atible dynamics the change in population share of every (at least one)
subgroup present in the population corresponds in sign with its relat
ive fitness. At a saturated equilibrium, each subgroup with positive p
opulation share has highest fitness. We examine two evolutionary stabi
lity concepts: the evolutionarily stable equilibrium and the generaliz
ed evolutionarily stable state.