This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.

This paper deals with the study of a predator–prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator–prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka–Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator–prey model, which is shown to be a Lotka–Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator–prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.

Sediment and water can potentially be altered, chemically, physically and biologically as they are sampled at the seafloor, brought to the surface, processed and analysed. As a result, in situ observations of relatively undisturbed systems have become the goal of a growing body of scientists. Our understanding of sediment biogeochemistry and exchange fluxes was revolutionized by the introduction of benthic chambers and in situ micro-electrode profilers that allow for the direct measurement of chemical fluxes between sediment and water at the sea floor and for porewater composition. Since then, rapid progress in the technology of in situ sensors and benthic chambers (such as the introduction of gel probes, voltammetric electrodes or one- and two-dimensional optodes) have yielded major breakthroughs in the scientific understanding of benthic biogeochemistry. This paper is a synthesis of discussions held during the workshop on sediment biogeochemistry at the “Benthic Dynamics: in situ surveillance of the sediment–water interface” international conference (Aberdeen, UK—March 25–29, 2002). We present a review of existing in situ technologies for the study of benthic biogeochemistry dynamics and related scientific applications. Limitations and possible improvement (e.g., technology coupling) of these technologies and future development of new sensors are discussed. There are countless important scientific and technical issues that lend themselves to investigation using in situ benthic biogeochemical assessment. While the increasing availability of these tools will lead research in yet unanticipated directions, a few emerging issues include greater insight into the controls on organic matter (OM) mineralization, better models for the understanding of benthic fluxes to reconcile microelectrode and larger-scale chamber measurements, insight into the impacts of redox changes on trace metal behavior, new insights into geochemical reaction pathways in surface sediments, and a better understanding of contaminant fate in nearshore sediments.