GSA Annual Meeting in Seattle, Washington, USA - 2017

Paper No. 272-29
Presentation Time: 9:00 AM-6:30 PM


HANDLEY, John C., Paleontological Research Institution, 1259 Trumansburg Road, Ithaca, NY 14850, SMITH, Jansen A., Earth and Atmospheric Sciences, Cornell University, Ithaca, NY 14853 and DIETL, Gregory P., Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY 14853,

In the paleoecological literature, drilling frequencies on prey taxa are commonly taken to indicate a predator’s preference. Those taxon-specific drilling frequencies are often compared with one another and related to underlying prey characteristics such as cost: benefit ratio or body size. Although this approach can demonstrate a predator’s relative preference for one prey type over another, it fails to consider whether predation on any prey type is greater than would be expected by a predator without preference. Manly’s alpha, which is a well-established model in the ecological literature, provides a means to test the null model of no prey preference against an alternative of preference for one or more taxa and also identify which taxa deviate from the null.

Given a sample of specimens of m taxa, some with and some without drill holes, the probability model of the drill hole counts per taxon is a multinomial distribution where the probability of selection is parameterized by a vector of m alphas that are greater than or equal to zero and sum to 1. The null hypothesis is that each alpha is equal to 1/m.

Statistical tests can be derived to test the null hypothesis. There is a closed-form maximum likelihood estimate that can be used to form a likelihood ratio test (LRT). The literature on alpha suggests that, owing to a high proportion of undrilled taxa and low specimen counts, a classical LRT is not appropriate. The accepted alternative is a randomization test. In addition, a Bayesian formulation enables a true probability assessment of the alpha for each taxon by assessing the probability of being less than or equal to 1/m for the estimated posterior distribution of each alpha. This approach provides a less cumbersome interpretation of drilling data and can be computed in a few lines of code.

Here, we describe Manly’s alpha probability model and the estimation approaches. We demonstrate the application of this approach on several data sets.