Critical assessment and ramifications of a purported marine trophic cascade

When identifying potential trophic cascades, it is important to clearly establish the trophic linkages between predators and prey with respect to temporal abundance, demographics, distribution, and diet. In the northwest Atlantic Ocean, the depletion of large coastal sharks was thought to trigger a trophic cascade whereby predation release resulted in increased cownose ray abundance, which then caused increased predation on and subsequent collapse of commercial bivalve stocks. These claims were used to justify the development of a predator-control fishery for cownose rays, the “Save the Bay, Eat a Ray” fishery, to reduce predation on commercial bivalves. A reexamination of data suggests declines in large coastal sharks did not coincide with purported rapid increases in cownose ray abundance. Likewise, the increase in cownose ray abundance did not coincide with declines in commercial bivalves. The lack of temporal correlations coupled with published diet data suggest the purported trophic cascade is lacking the empirical linkages required of a trophic cascade. Furthermore, the life history parameters of cownose rays suggest they have low reproductive potential and their populations are incapable of rapid increases. Hypothesized trophic cascades should be closely scrutinized as spurious conclusions may negatively influence conservation and management decision

The iterated minimum modulus and conjectures of Baker and Eremenko

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the minimum modulus, and obtain new results related to Eremenko's conjecture and Baker's conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function