Abstract Boundary-defining events influence the evolutionary behaviour of post-extinction survivors. The Cox proportional hazards model takes into account the varying background extinction rates characteristic of boundaries and enables survivorship analysis of post-boundary behaviour. Survivorship results from the Middle Cretaceous to recent planktonic foraminifera reveal two intriguing observations. First, they indicate significantly age-dependent extinction probabilities in populations of species following two boundaries: Cenomanian-Turonian (C-T) and Cretaceous-Tertiary (K-T); the survivors are short lived and show rapid turnover. Characteristics that might mediate this macroevolutionary behaviour are clearly distinct from those that precede the extinction. We hypothesize that the rapid taxonomic turnover during post-extinction macroevolutionary recovery is driven by the lingering expression of ‘passport’ characteristics, where the primary adaptive value was during the preceding extinction. Second, age-dependency of extinction oscillates through time. Many survivorship curves averaging long-term data have exponential or near-exponential form: suggesting a lack of age-dependence consistent with the Red Queen hypothesis. The boundary events discussed here, analysed in higher-resolution 15 Ma subsets, demonstrate perturbation of some post-extinction populations toward positive age-dependence, and are followed by long intervals suggestive of recovery. Red Queen behaviour, when measured over very long time-spans, appears to be the time-averaged result of these boundary-generated oscillations between short-term positive age-dependence and longer-term return to nearly age-independent Red Queen behaviour.
Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon age and the rate of extinction. We propose a general class of test statistics that can be used to test for the effect of age on the rate of extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead we control for covariate effects by pairing or grouping together similar species. Simulations are used to compare the power of the statistics. We apply the test statistics to data on Foram extinctions and find that age has a positive effect on the rate of extinction. A derivation of the null distribution of one of the test statistics is provided in the supplementary material.
Abstract Age-dependent extinction is an observation with important biological implications. Van Valen's Red Queen hypothesis triggered three decades of research testing its primary implication: that age is independent of extinction. In contrast to this, later studies with species-level data have indicated the possible presence of age dependence. Since the formulation of the Red Queen hypothesis, more powerful tests of survivorship models have been developed. This is the first report of the application of the Cox Proportional Hazards model to paleontological data. Planktonic foraminiferal morphospecies allow the taxonomic and precise stratigraphic resolution necessary for the Cox model. As a whole, planktonic foraminiferal morphospecies clearly show age-dependent extinction. In particular, the effect is attributable to the presence of shorter-ranged species (range < 4 myr) following extinction events. These shorter-ranged species also possess tests with unique morphological architecture. The morphological ...
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