A general review of the patterns of species richness of insular mammals (Lomolino, 1984a) indicated that richness is determined by interactive as well as additive effects of factors affecting immigration and extinction. The present paper reports that species composition of insular mammals is also influenced by such additive and interactive effects. Therefore, insular incidence should be high for those species whose (or on those islands where) (immigration rates) are high relative to extinction rates. The model presented in this paper predicts that species have high incidence on islands if low immigration rates (poor immigrators and/or distant islands) are compensated by low extinction rates (good survivors and/or large islands), or high extinction rates are compensated for by high immigration rates. Therefore, poor immigrators may be frequent inhabitants of distant islands if their extinction rates are compensatorily low (large islands and/or low resource requirements). Conversely, extinction‐prone species (large, specialist carnivores) may be frequent inhabitants of small islands if their immigration rates are compensatorily high (near islands and/or good immigrators). These ‘compensatory effects’ were well evidenced by the mammalian faunas of the islands in the Thousand Islands Region, New York, and Lake Michigan (U.S.A.). ‘Compensatory effects’ are also evidenced by mammals of other archipelagos, as well as by birds inhabiting real and habitat islands. These results are consistent with the fundamental assumption of the equilibrium theory of island biogeography, i.e. insular community structure is the result of recurrent (rather than unique) immigrations and extinctions. Accordingly, I suggest that the concept of a fixed critical minimum area for isolated populations may be meaningless unless immigrations are unimportant with respect to the fauna under study. Finally, apparently anomalous or stochastic distribution patterns of insular species may readily be explained by the deterministic model presented here which incorporates the interactive as well as additive effects of immigration and extinctions on insular community