Paleoecologists have long sought to obtain estimates of the sizes of extinct populations. However, even in ideal cases, accurate counts of individuals have been hampered by the fact that many organisms disarticulate after death and leave their remains in the form of multiple, separated parts. We here analyze the problem of estimating numbers of individuals from collections of parts by developing a general counting theory that elucidates the major contributing variables. We discover that the number of unique individuals of a particular species that are represented in a fossil collection can be described by an intricate set of relationships among (1) the number of body parts that were recovered, (2) the number of body parts that were possessed by organisms belonging to that species, and (3) the number of individuals of that species that served as the source of the parts from which the paleontological sample was obtained (the size of the “sampling domain”). The “minimum number of individuals” and “maximum number of individuals” methods currently used by paleontologists to count individuals emerge as end members in our more general counting theory. The theory shows that the numbers of individuals of a species that are represented in a sample of body parts is fully tractable, at least in a theoretical sense, in terms of the variables just mentioned. The bad news is that the size of the “sampling domain” for a species can never be known exactly, thus placing a very real limit on our ability to count individuals rigorously. The good news is that one can often make a reasonable guess regarding the size of the sampling domain, and can therefore make a more thoroughly informed choice regarding how to estimate numbers of individuals. By isolating the variables involved in determining the numbers of individuals in paleontological samples, we are led to a better appreciation of the limits, and the possibilities, that are inherent in the fossil record.
