Plate tectonic processes can cause metacommunities to grow or shrink, as well as cause them to merge or divide, potentially changing diversity. Early predictions of these effects were based on seemingly straightforward applications of species-area relationships, but it is now possible to use dynamical models of neutral metacommunities to test these predictions. The models used here are based on those of the Neutral Theory of Biodiversity and Biogeography, but differ in that they allow for the number of communities in a metacommunity to increase or decrease over time, and they also allow for the merging of two isolated metacommunities into a single metacommunity and the division of a single metacommunity into two isolated metacommunities. Intuitively, when metacommunities grow by the addition of communities, their diversity increases, and their diversity declines when they shrink by losing communities. In contrast, the diversity response for metacommunity merging and division is unexpected: neither has any response on global diversity, but they do affect diversity within metacommunities and the beta diversity among them. Furthermore, these effects are intensified for smaller metacommunities. Because land area changes little when continents rift or collide, global terrestrial diversity should be largely unchanged by these plate tectonic processes, although individual regions may experience substantial changes in diversity, consistent with previous observations. In contrast, the area of shallow-marine regions is markedly affected by rifting and collision, such that global shallow-marine diversity should vary strongly as a result of plate-tectonic processes, also consistent with previous observations. The response time of metacommunities to these plate-tectonic events is controlled mainly by the size of the metacommunity (slower responses in larger metacommunities), but also by the probability of death of individuals (slower responses for longer-lived individuals). For metacommunities of up to 10^7 individuals, simulated response times were geologically undetectable (<100 kyr). Some marine metacommunities are much larger, and their response times to plate-tectonic events might be geologically measurable.