MATHEMATICAL MODELING AND BAYESIAN ANALYSIS OF PALEOCOMMUNITY COLLAPSE DURING MASS EXTINCTIONS

The current biodiversity crisis requires an understanding of the history of biodiversity and extinction. Preliminary analyses of the relationships among mass extinction, the shutdown of primary production, and the collapse of ecosystems, show that perturbations to primary production can lead to catastrophic extinctions. We extend these findings by developing mathematical methods for partitioning primary and secondary extinction. The abiotic factors underlying mass extinctions could cause the loss of species through two different pathways. First, factors may have a direct effect on species. An example is the elimination of a species by the blast effects of an asteroid impact. We refer to such extinctions as primary extinctions. Second, there are indirect effects mediated by the biotic interactions among species. For example, the shutdown of photosynthesis, caused by the ejection of particles into the upper atmosphere, could result in the decline and extinction of consumers. Such secondary extinctions could be propagated throughout an ecosystem via its network of interactions.

We model communities probabilistically as complex networks of trophic relationships, focusing on Neogene shallow marine tropical American communities. Understanding the partitioning of primary and secondary extinction is approached in two ways: First, given that food web structure varies with species composition, we use simulations to evaluate the sensitivity of webs to perturbations of primary production. We predict that sensitivity will decline during intervals of mass extinction and recovery. Second, we estimate secondary extinction using Bayesian models and extinction data from the fossil record of specific communities. We then estimate the levels of primary production disruption that could yield observed levels of extinction. We predict such levels to increase during intervals of mass extinction, if disruption of photosynthesis and secondary extinction were indeed important in ecosystem collapse.