Statistical analysis indicates that the fossil exctinction record is compatible with a distribution of extinction events whose frequency is related to their size by a power law with exponent tau approx. = 2. This result is in agreement with preductions based on self-organized critical models of extinction, and might well be taken as evidence for self-organizing behavior in terrestrial evolution. We argue however that there is a much simpler explanation for the appearance of a power law in terms of extinctions caused by stresses (either biotic or abiotic) to which species are subjected by their environment. We give an explicit model of this process and discussits properties and implications for the interpretation of the fossil record.