ON THE FALLACY OF CONSTANT EXTINCTION RATES.

Van Valen's "new evolutionary law" (Van Valen, 1973) has provoked considerable discussion of taxonomic survivorship curves (for a review, see Van Valen, 1976; Hallam, 1976) and of the Red Queen hypothesis (Maynard Smith, 1976; Stensith, 1979). Despite allegations that the linearity of Van Valen's curves may be an artifact of his method of survivorship analysis (Foin et al., 1975; Salthe, 1975) and that many of the curves may not be linear (Sepkoski, 1975), "constant extinction rates" may have been admitted as evidence, or at least accepted as the empirical basis, for the Red Queen hypothesis (Lewontin, 1978; Stensith, 1979). My purpose here is to show that constant extinction rates cannot be deduced from Van Valen's survivorship curves even if we assume the curves are linear. Following this, I discuss several hypotheses, including the Red Queen, which would account for linearity of taxonomic survivorship curves. Van Valen originally set out to test his belief that the probability of extinction is correlated with the duration of a group. In order to isolate the effect of age-related factors on the probability of extinction, he graphed cumulative frequency distributions of durations of taxa within a larger group, for a variety of groups. The ordinate is the logarithm of the frequency of taxa. The abscissa is the duration of taxa, duration being the length of time that a taxon was extant. Each point on the graph represents the number of taxa which existed for a given length of time or longer. It is especially important to remember that the abscissa is not chronological time; durations of taxa within a group are graphed together without regard to their place in chronological time, as though they had all originated simultaneously. A logarithmic ordinate gives the property that the slope of the curve from duration x to x + 1 is proportional to the probability of extinction of a taxon over the same interval of lengths of durations. When the curve is a straight line the slopes over all intervals are equal, which means that the probability of extinction is constant with respect to the duration of taxa. A strict interpretation of linear taxonomic survivorship curves, that the probability of extinction is independent of duration, cannot be emphasized too strongly. Real time or geological age are not interchangeable with duration. Age is ambiguous because it could mean either geological age or duration. Discussions of constant extinction rates imply that the probability of extinction is constant with respect to time, not duration. These cautions against misinterpretations are not unwarranted because the curves are adorned frequently with meaning that they do not have such as (my italics) "Van Valen's discovery that individual higher taxa tend to have constant rates of extinction" (Stanley, 1974, p. 494), or "a straight survivorship curve of this type indicates that extinction probability is constant throughout the life of the subtaxon and that this rate is shared by other members of the larger taxonomic group" (Raup, 1975, p. 82), or "Van Valen's demonstration of nearly constant rates of extinction within higher taxa may reflect a large element of chance" (Lande, 1980, p. 236), or "there are some real and some spurious exceptions to constant extinction rates" (Van Valen, 1973, p. 7). While the Red Queen, in her ecological domain, does not depend on taxonomic survivorship curves, it hardly makes sense to derive theoretically the "empirical generalization . . . (of a) constant probability of extinction per unit time" (Maynard Smith, 1976, p. 325) when