In the fossil record, taxa exhibit a regular pattern of waxing and waning of occupancy, range or diversity between their origin and extinction. This pattern appears to contradict the law of constant extinction(1), which states that the probability of extinction in a given taxon is independent of that taxon's age. It is nevertheless well established for species, genera and higher taxa of terrestrial mammals(2-4), marine invertebrates(5-7), marine microorganisms(8), and recent Hawaiian clades of animals and plants(9). Here we show that the apparent contradiction between a stochastically constant extinction rate and the seemingly deterministic waxing and waning pattern of taxa disappears when we consider their peak of expansion rather than their final extinction. To a first approximation, we find that biotic drivers of evolution pertain mainly to the peak of taxon expansion, whereas abiotic drivers mainly apply to taxon extinction. The Red Queen's hypothesis(1), which emphasizes biotic interactions, was originally proposed as an explanation of the law of constant extinction. Much effort has since been devoted to determining how this hypothesis, emphasizing competition for resources, relates to the effects of environmental change. One proposed resolution is that biotic and abiotic processes operate at different scales(10). By focusing attention on taxon expansion rather than survival, we resolve an apparent contradiction between the seemingly deterministic waxing and waning patterns over time and the randomness of extinction that the Red Queen's hypothesis implies.