Modelling pelagic biogeography

Abstract

Various combinations of physical and biological models are used to explore factors that determine the distribution of organisms in the world's oceans. The physical models examined include simple box models with parameterized inter-box exchanges that take into account variable box geometries, and specified continuous flows either in the Eulerian frame as stream-functions or as Lagrangian trajectories. A 1-dimensional mixed-layer model and a primitive equation channel model are introduced as examples of dynamical models depicting ocean physics. Biological models are discussed starting with a simple nitrogen (N), phytoplankton (P), zooplankton (Z) and detritus (D), NPZD formulation. The equilibria of this model is explored analytically as an example of computing steady state solutions, and then considering where in parameter space extinction occurs. Nonlinearities and expansion of NPZD to multi-species models are also treated. This is followed by the introduction of a nonlinear three-component food chain model, multi-species Lotka-Voltera competition models, and finally a discussion of structured population models including a derivation of a genetics model written in terms of genotypes. The physical models are then coupled with the biological ones in a series of examples. Both the box model with Lotka-Voltera multi-species population dynamics, and the 1-dimensional mixed-layer model with NPZD are used to demonstrate how the existence of spatial and temporal niches can allow a large number of species to coexist within biogeographic domains even though conditions at most sites and times are not conducive to supporting such diversity. These models recreate the basic diversity patterns observed in the pelagic ecosystem at various latitudes. The box model simulations also demonstrate the tendency for diffusive models to overestimate the dispersion of a species. In order to explore the dynamics of the edges of biogeographic domains a three species food chain model is combined with a Lagrangian trajectory calculation that specifies the dynamics of populations in a meandering jet environment. This model shows that the interaction of biological and physical dynamics can produce complex species distribution patterns that would be difficult to interpret from field observations of species abundance alone. Finally, results from a population genetics box model show that even when there is significant exchange of organisms between domains and natural selection affects allele and genotype proportions, genotype frequencies are in approximate Hardy-Weinberg equilibrium. This demonstrates the overly restrictive nature of some of the Hardy-Weinberg assumptions and provides a means for exploring population dynamics in a biogeographic context.