'Residual diversity estimates' do not correct for sampling bias in palaeodiversity data

It is widely accepted that the fossil record suffers from various sampling biases - diversity signals through time may partly or largely reflect the rock record - and many methods have been devised to deal with this problem. One widely used method, the 'residual diversity' method, uses residuals from a modelled relationship between palaeodiversity and sampling (sampling-driven diversity model) as 'corrected' diversity estimates, but the unorthodox way in which these residuals are generated presents serious statistical problems; the response and predictor variables are decoupled through independent sorting, rendering the new bivariate relationship meaningless. Here, we use simple simulations to demonstrate the detrimental consequences of independent sorting, through assessing error rates and biases in regression model coefficients. Regression models based on independently sorted data result in unacceptably high rates of incorrect and systematically, directionally biased estimates, when the true parameter values are known. The large number of recent papers that used the method are likely to have produced misleading results and their implications should be reassessed. We note that the 'residuals' approach based on the sampling-driven diversity model cannot be used to 'correct' for sampling bias, and instead advocate the use of phylogenetic multiple regression models that can include various confounding factors, including sampling bias, while simultaneously accounting for statistical non-independence owing to shared ancestry. Evolutionary dynamics such as speciation are inherently a phylogenetic process, and only an explicitly phylogenetic approach will correctly model this process.