  Using data drawn from large-scale databases, a number of interesting trends
in the fossil record have been observed in recent years. These include the
average decline in extinction rates throughout the Phanerozoic, the average
increase in standing diversity, correlations between rates of origination and
extinction, and simple laws governing the form of survivorship curves and the
distribution of the lifetimes of taxa. In this paper we derive mathematically a
number of relations between these quantities and show how these different
trends are inter-related. We also derive a variety of constraints on the
possible forms of these trends, such as limits on the rate at which extinction
may decline and limits on the allowed difference between extinction and
origination rates at any given time.
