ESTIMATING THE SIZE OF THE SAMPLING DOMAIN FROM THE NUMBER OF UNIQUE BIVALVED INDIVIDUALS IN A PALEONTOLOGICAL SAMPLE

A common problem in paleoecological studies involves estimating the number of whole organisms represented in a disarticulated assemblage of fossils. A particular case of this general problem involves estimating the total number of unique individuals represented in a collection of disarticulated skeletal parts. Gilinsky and Bennington (Paleobiology 20(2):245-258, 1994) showed that if one knows the number of discrete skeletal elements per individual organism and the total number of skeletal elements in a sample, the total number of unique individuals represented in the sample can be estimated using the rarefaction equation. Unfortunately, to solve the rarefaction equation, one needs an estimate of the size of the sampling domain, the total number of individuals in the population that the sample was drawn from. The size of the sampling domain is related to several variables inherent in the formation of the fossil assemblage, including the size of the living population, the amount of time averaging, and the degree of post-mortem transport and mixing. Gilinsky and Bennington concluded that the size of the sampling domain was essentially unknowable and a reliable estimate of the number of unique individuals forever out of reach. However, we demonstrate that by estimating the number of unique bivalved individuals in a paleontological sample, the rarefaction equation can be solved in reverse to provide an estimate of the size of the sampling domain. Estimating the number of unique bivalved individuals in a sample is a tractable problem because many bivalved organisms have valves that articulate uniquely or are otherwise equal in length and width, allowing the identification of potentially matching valves. We provide a solution for the rarefaction equation solving for sampling domain given the number of unique bivalved individuals in a sample and apply this to estimate the size of the sampling domain for a bulk sample of the pelecypod Hiatella arctica from the Pleistocene Champlain Sea deposits at St. Nicholas, Quebec. Estimates of the size of the sampling domain might prove useful for quantifying the amount of time averaging and post-mortem disturbance in different fossil assemblages.