Experimentally testing the accuracy of an extinction estimator: Solow's optimal linear estimation model

Abstract

Mathematical methods for inferring time to extinction have been widely applied but poorly tested. Optimal linear estimation (also called the 'Weibull' or 'Weibull extreme value' model) infers time to extinction from a temporal distribution of species sightings. Previous studies have suggested optimal linear estimation provides accurate estimates of extinction time for some species; however, an in-depth test of the technique is lacking. The use of data from wild populations to gauge the error associated with estimations is often limited by very approximate estimates of the actual extinction date and poor sighting records. Microcosms provide a system in which the accuracy of estimations can be tested against known extinction dates, whilst incorporating a variety of extinction rates created by changing environmental conditions, species identity and species richness. We present the first use of experimental microcosm data to exhaustively test the accuracy of one sighting-based method of inferring time of extinction under a range of search efforts, search regimes, sighting frequencies and extinction rates. Our results show that the accuracy of optimal linear estimation can be affected by both observer-controlled parameters, such as change in search effort, and inherent features of the system, such as species identity. Whilst optimal linear estimation provides generally accurate and precise estimates, the technique is susceptible to both overestimation and underestimation of extinction date. Microcosm experiments provide a framework within which the accuracy of extinction predictors can be clearly gauged. Variables such as search effort, search regularity and species identity can significantly affect the accuracy of estimates and should be taken into account when testing extinction predictors in the future.