FURTHER REVISITING THE BIVALVE AND BRACHIOPOD SAGA; BEYOND PAIRWISE ANALYSIS

We use a type of statistical process modelling as a tool to explore the nature of biotic time series and the interactions between them. The process models family known as linear stochastic differential equations allow for distinguishing between causal and purely correlative connections. Hidden processes that causally affect the measured ones can also be detected, in which case the system of processes is called multi-layered. After performing pairwise analysis of bivalve and brachiopod extinction and origination rate time series, we now move on to study all four time series at the same time. Thus we correct for the effect of one time series on another, when studying other connections. This allows us to sort out pairwise connections that are explained by other connections as well as detecting connections that were previously hidden because of the lack of correction. Some unforeseen problems emerged when we did not use our knowledge of hidden processes from single time series analysis. But when hidden processes were taken into account, we arrived at a picture that was subtly different from the one from pairwise analysis. While the pairwise analysis suggests brachiopod rates are simply reacting to bivalve rates, the new analysis revealed a causal interaction going the other way also.