The theoretical framework developed here delineates the biological and paleontological circumstances under which the observed durations and diversities of fossil taxa will be significantly affected by three time-dependent sampling biases. The pull of the Recent and the loss of fossiliferous sediments shorten the observed durations of ancient taxa, as compared to the observed durations of Recent taxa. By contrast, the duration truncation mechanism lengthens the observed durations of ancient, as compared to more recent, taxa. Both the pull of the Recent and loss of fossiliferous sediments decrease the observed diversity of ancient, as compared to contemporary, communities.
This theoretical framework is built on four parameters: the extinction and origination rates q and p; the fossilization rate, v; and the fossil loss rate, h. I derive formulas for the observed durations and diversities of fossil taxa in terms of these parameters and develop a method of estimating these parameters. The estimation procedure is applied to the bivalve families, and I provide statistical evidence for the conclusion that q – p < 0 for bivalve families, and hence that bivalve diversity has been increasing through time. The theory predicts that a certain fraction of an extinct fauna will be represented by only one fossil, and hence will have an observed duration of zero. As the record becomes poorer, this fraction increases. For bivalves I assume that families known from only one stage have an observed duration of zero, and exploit this assumption to estimate h and v/p.
To evaluate the errors made in applying the model to the bivalves, I estimate several parameters in two different ways and find the estimates to be consistent. Additionally, I argue that the errors caused by the simplifying assumptions of the model are less than the sampling errors inherent in estimating p, q, h, and v.