ESTIMATING NUMBERS OF WHOLE INDIVIDUALS FROM COLLECTIONS OF BODY PARTS - A TAPHONOMIC LIMITATION OF THE PALEONTOLOGICAL RECORD

Paleoecologists have long sought to obtain estimates of the sizes of e xtinct populations. However, even in ideal cases, accurate counts of i ndividuals have been hampered by the fact that many organisms disartic ulate after death and leave their remains in the form of multiple, sep arated parts. We here analyze the problem of estimating numbers of ind ividuals from collections of parts by developing a general counting th eory that elucidates the major contributing variables. We discover tha t the number of unique individuals of a particular species that are re presented in a fossil. collection can be described by an intricate set of relationships among (1) the number of body parts that were recover ed, (2) the number of body parts that were possessed by organisms belo nging to that species, and (3) the number of individuals of that speci es that served as the source of the parts from which the paleontologic al sample was obtained (the size of the ''sampling domain''). The ''mi nimum number of individuals'' and ''maximum number of individuals'' me thods currently used by paleontologists to count individuals emerge as end members in our more general, counting theory. The theory shows th at the numbers of individuals of a species that are represented in a s ample of body parts is fully tractable, at least in a theoretical sens e, 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 exact ly, thus placing a very real limit on our ability to count individuals rigorously. The good news is that one can often make a reasonable gue ss 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 nu mbers of individuals in paleontological samples, we are led to a bette r appreciation of the limits, and the possibilities, that are inherent in the fossil record.