A General Class of Test Statistics for Van Valen's Red Queen Hypothesis.

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 age and the rate of extinction. We propose a general class of test statistics that can be used to test for the effect of age on the rate of 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 we control for covariate effects by pairing or grouping together similar species. Simulations are used to compare the power of the statistics. We apply the test statistics to data on Foram extinctions and find that age has a positive effect on the rate of extinction. A derivation of the null distribution of one of the test statistics is provided in the supplementary material.

Clustering with exclusion zones: genomic applications.

Methods for formally evaluating the clustering of events in space or time, notably the scan statistic, have been richly developed and widely applied. In order to utilize the scan statistic and related approaches, it is necessary to know the extent of the spatial or temporal domains wherein the events arise. Implicit in their usage is that these domains have no "holes"-hereafter "exclusion zones"-regions in which events a priori cannot occur. However, in many contexts, this requirement is not met. When the exclusion zones are known, it is straightforward to correct the scan statistic for their occurrence by simply adjusting the extent of the domain. Here, we tackle the more ambitious objective of formally evaluating clustering in the presence of "unknown" exclusion zones. We develop an algorithm for estimating total exclusion zone extent, the quantity needed to correct scan statistic-based inference, using distributional properties of "spacings," and show how bias correction for this estimator can be effected. Performance of the algorithm is assessed via simulation study. We showcase applications to genomic settings for differing marker (event) types-binding sites, housekeeping genes, and microRNAs-wherein exclusion zones can arise through a variety of mechanisms. In several instances, dramatic changes to unadjusted inference that does not accommodate exclusions are evidenced.