Extinction, diversity and survivorship of taxa in the fossil record
  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. 
M. E. J. Newman (Santa Fe Institute), Paolo Sibani (Odense University)