Non-Equilibrium Models

Sibani and co-workers have proposed a model of the extinction process, which they call the "reset model" (Sibani et al. 1995,1998), which differs from those discussed in the preceding chapters in a fundamental way; it allows for, and indeed relies upon, nonstationarity in the extinction process. That is, it acknowledges that the extinction record is not uniform in time, is not in any sense in equilibrium, as it is assumed to be in the other models we have considered. In fact, extinction intensity has declined on average over time from the beginning of the Phanerozoic until the Recent. Within the model of Sibani et al., the distributions of section 1.2 are all the result of this decline, and the challenge is then to explain the decline, rather than the distributions themselves. In figure 1.9 we showed the number of known families as a function of time over the last 600 My. On the logarithmic scale of the figure, this number appears to increase fairly steadily and although, as we pointed out, some of this increase can be accounted for by the bias known as the "pull of the recent," there is probably a real trend present as well. It is less clear that there is a similar trend in extinction intensity. The extinctions represented by the points in figure 1.1 certainly vary in intensity, but on average they appear fairly constant. Recall however, that figure 1.1 shows the number of families becoming extinct in each stage, and that the lengths of the stages are not uniform. In figure 6.1 we show the extinction intensity normalized by the lengths of the stages—the extinction rate in families per million years—and on this figure it is much clearer that there is an overall decline in extinction towards the Recent. In order to quantify the decline in extinction rate, we consider the cumulative extinction intensity c(t) as a function of time. The cumulative extinction at time t is defined to be the number of taxa which have become extinct up to that time.