A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

Monkey-based Research on Human Disease: The Implications of Genetic Differences

Assertions that the use of monkeys to investigate human diseases is valid scientifically are frequently based on a reported 90–93% genetic similarity between the species. Critical analyses of the relevance of monkey studies to human biology, however, indicate that this genetic similarity does not result in sufficient physiological similarity for monkeys to constitute good models for research, and that monkey data do not translate well to progress in clinical practice for humans. Salient examples include the failure of new drugs in clinical trials, the highly different infectivity and pathology of SIV/HIV, and poor extrapolation of research on Alzheimer’s disease, Parkinson’s disease and stroke. The major molecular differences underlying these inter-species phenotypic disparities have been revealed by comparative genomics and molecular biology — there are key differences in all aspects of gene expression and protein function, from chromosome and chromatin structure to post-translational modification. The collective effects of these differences are striking, extensive and widespread, and they show that the superficial similarity between human and monkey genetic sequences is of little benefit for biomedical research. The extrapolation of biomedical data from monkeys to humans is therefore highly unreliable, and the use of monkeys must be considered of questionable value, particularly given the breadth and potential of alternative methods of enquiry that are currently available to scientists