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Human activities have elevated the extinction of natural populations as well as the invasion of new areas by non-native species. These dual processes of invasion and extinction may change the richness and similarity of communities, but the form these changes take is likely to depend on the manner in which invasions and extinctions occur and the spatial scale at which the changes are measured. Here, we explore the influence of differing patterns of extinction and invasion on the similarity and richness of a meta-community. In particular, we model simple stochastic processes analogous to realistic modes of human-mediated introduction of non-native species and range expansion by native species. We show that different modes of invasion and extinction can produce very different changes in diversity, and that the relative magnitude of these changes depends both on where in the meta-community diversity is measured and the degree of initial species aggregation. At any spatial scale of measurement, changes in the richness and similarity of communities following invasion and extinction are not necessarily strongly coupled: relatively large increases in richness may or may not also be associated with relatively large increases in similarity among communities. Thus, in real systems, the influence of human-induced invasions and extinctions on diversity will depend on both the precise mode of these processes (especially invasion), and how species populations are distributed across space.