Laws of macroevolutionary expansion

Van Valen’s law of constant extinction postulates that in comparable ecological contexts, the probability for a taxon to survive to the next time interval is independent of how long it has already existed. The law implies that species do not age, that is, the survival probability from one time step to the next does not decrease with species’ age. While the original law describes survivorship over time, here we show that there is a counterpart to the law describing species dynamics in space. Indeed, the probability for a taxon to expand a step further in its range size does not depend on how large of a range the taxon already occupies. We show that such patterns of stochastically constant expansion are common in the global mammalian fossil record throughout the Cenozoic and are consistent with the mammalian species distribution in the present-day world. Intriguing is that the law in space holds best for the linear dimension of the range rather than for the range area. We interpret this as suggesting that species primarily expand via the frontier of their range; this process is known as leading-edge expansion in ecology. And while the difficulty of expanding in linear steps remains constant, the area gains diminish. In line with evolutionary theory collectively known as the Red Queen’s hypothesis, this suggests that the effectiveness of expansion saturates, even if species longevity does not. When interpreted in reverse, this explains from the macroevolutionary perspective why larger species ranges are associated with lower extinction risks.