Age effects in the extinction of Planktonic Foraminifera: A new look at Van Valen's Red Queen hypothesi

Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon duration (age) and the rate of extinction. Some of the more recent approaches to this problem using Planktonic Foraminifera (Foram) extinction data include Weibull and Exponential modeling (Parker and Arnold, 1997), and Cox proportional hazards modeling (Doran et al. 2004, 2006). I propose a general class of test statistics that can be used to test for the effect of age on extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead I control for covariate effects by pairing or grouping together similar species. I use simulated data sets to compare the power of the statistics. In applying the test statistics to the Foram data, I have found age to have a positive effect on extinction.