Estimating taxonomic diversity, extinction rates, and speciation rates from fossil data using capture-recapture models

Methods currently used to estimate taxonomic extinction probabilities from fossil data generally assume that the probability of encountering a specimen in a particular stratum, given that the taxon was extant in the time period and location represented by the stratum, either equals 1.0 or else is a constant for all strata. Methods used to estimate taxonomic diversity (number of taxa) and speciation rate generally assume that encounter probabilities equal 1.0. We suspect that these assumptions are often false. Capture-recapture models were historically developed for estimation in the face of variable and unknown sampling probabilities. These models can thus be used to estimate parameters of interest from paleobiological data when encounter probabilities are unknown and variable over time. These models also permit estimation of sampling variances, and goodness-of-fit tests are available for assessing the fit of data to most models. Here we describe capture-recapture models which should be useful in paleobiological analyses and discuss the assumptions which underlie them. We illustrate these models with examples and discuss aspects of study design. We conclude that these models should prove useful in paleobiological analyses.