Remote Oceania was colonized initially in three migratory phases: the western archipelagos of Micronesia plus eastern Melanesia out to west Polynesia in the period 3500–2800 cal BP (all dates hereafter are cal BP), central and eastern Micronesia 2200–2000 BP and east and south Polynesia 1100–700 BP. The early and late migration phases are best-known archaeologically. During these phases a number of plants and animals were introduced. Of the latter, the pig (Sus scrofa), dog (Canis familiaris), fowl or chicken (Gallus gallus) and rats (Rattus spp., especially R. exulans) were most deliberately associated with human settlement. The pattern of introductions appears to be only partly in agreement with an implication of widespread early distribution derived from the orthodox colonisation model of ‘transported landscape’ coupled with sophisticated seafaring. Within the two main migrations the pattern of introductions is similar. Excepting in the movement to West Micronesia, all four taxa were transported into the islands nearest their proximate sources at, or soon after, the beginning of migration, but their introduction to more remote islands was partial and patchy. Evaluation of invasibility, invasiveness and transportability characteristics amongst the four taxa suggest that island size and complexity, propagule pressure and seafaring capability were important factors in differential distribution and survival. Seafaring capability was especially important because it determined the extent of accessibility to islands near and far and the degree of propagule or introduction pressure that was exerted. Framing the archaeological data within a model of invasion biology offers a richer and more systematic approach to the complexities of introduction than adopting a culture-historical perspective.