Modeling the Rise and Fall of Species by Using a Mixed Effects Model. A New Way of Looking at Species Persistence In the Fossil Record

Species arise and establish themselves before eventually declining to extinction and this process is manifested in the fossil record as a change in the frequency of recorded detections of a given species or group of species. We model this as a “hat” trajectory, where the probability of being recorded is an amalgamation of two logistic functions (one for the rise and one for the fall) multiplied by a parameter controlling the maximal level attained during the existence of the species. We fit this “hat” function to occurrence data of microfossil species from the online database, Neptune, using a mixed effects model where each of the four microfossil groups (nannoplankton, planktic foraminifers, diatoms, radiolarians) can each assume a characteristic occurrence trajectory (group effects) but individual species can also assume specific values in the model (random effects, allowing species specific hat trajectories). We discuss the observation that the inference of first and last appearance records (often interpreted as time of speciation and extinction) of fossil species is highly model dependent. We suggest a new way of looking at species persistence in the fossil record, where the absolute times of the estimated exponential rise and exponential decline in our “hat” model can be interpreted as a period of ecological dominance.