How many named species are valid?

Estimates of biodiversity in both living and fossil groups depend on raw counts of currently recognized named species, but many of these names eventually will prove to be synonyms or otherwise invalid. This difficult bias can be resolved with a simple ''flux ratio'' equation that compares historical rates of invalidation and revalidation. Flux ratio analysis of a taxonomic data set of unrivalled completeness for 4,861 North American fossil mammal species shows that 24-31% of currently accepted names eventually will prove invalid, so diversity estimates are inflated by 32-44%. The estimate is conservative compared with one obtained by using an older, more basic method. Although the degree of inflation varies through both historical and evolutionary time, it has a minor impact on previously published background origination and extinction rates. Several lines of evidence suggest that the same bias probably affects more poorly studied, hyperdiverse living groups such as fungi and insects. If so, then current estimates of total global diversity could be revised downwards to as low as 3.5-10.5 million species.