Ecological theory predicts an inverse association between population size and extinction risk, but most previous paleontological studies have failed to confirm this relationship. The reasons for this discrepancy between theory and observation remain poorly understood. In this study, we compiled a global database of gastropod occurrences and collection-level abundances spanning the Early Permian through Early Jurassic (Pliensbachian). Globally, the database contains 5469 occurrences of 496 genera and 2156 species from 839 localities. Within the database, 30 collections distributed across seven stages contain at least 75 specimens and ten genera-our minimum criteria for within-collection analysis of extinction selectivity. We use logistic regression analysis, based on global and local measures of population size and stage-level extinction patterns in Early Permian through Early Jurassic marine gastropods, to assess the relationship between abundance and extinction risk. We find that global genus occurrence frequency is inversely associated with extinction risk (i.e., positively associated with survival) in 15 of 16 stages examined, statistically significantly so in five stages. Although correlation between geographic range and occurrence frequency may account for some of this association, results from multivariable regression analysis suggest that the association between occurrence frequency and extinction risk is largely independent of geographic range. Within local assemblages, abundance (number of individuals) is also inversely associated with extinction risk. The strength of association is consistent across time and modes of fossil preservation. Effect strength is poorly constrained, particularly in analyses of local collections. In addition to limited power due to small sample size, this poor constraint may result from confounding by ecological variables not controlled for in the analyses, by taphonomic or collection biases, or from non-monotonic relationships between abundance and extinction risk. Two factors are likely to account for the difference between our results and those of most previous studies. First, many previous studies focused on the end-Cretaceous mass extinction event; the extent to which these results can be generalized to other intervals remains unclear. Second, previous findings of nonselective extinction could result from insufficient statistical power rather than the absence of an underlying effect, because nonselective extinction is generally used as the null hypothesis for statistical convenience. Survivorship patterns in late Paleozoic and early Mesozoic gastropods suggest that abundance has been a more important influence on extinction risk through the Phanerozoic than previously appreciated.

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