12-Cell ecological model

Whitmore H, Pawlowski C, Cabezas H. Integration of an economy under imperfect competition with a twelve-cell ecological model. Technical report EPA/600/R-06/046. 2006. 

Zonneveld C. (1998). A cell-based model for the chlorophyll a to carbon ratio in phytoplankton. Ecological Modelling, 113(1-3), 55-70. 

Droop, M.R. (1973) Some thoughts on nutrient limitation in algae. Journal of Phycology, 9, 264—272. Droop, M.R. (1979) On the definition of X and of Q in the Cell Quota model. Journal of Experimental Marine Biology and Ecology, 39, 203. 

In this chapter we present an individual-based population model (Metapopulation model for Assessing Spatial and Temporal Effects of Pesticides [MASTEP]). M ASTEP describes the effects on, and recovery of, populations of the water louse Asellus aqua-ticus following exposure to a fast-acting, nonpersistent insecticide caused by spray drift for pond, ditch, and stream scenarios. The model used the spatial and temporal distribution of the exposure in different treatment conditions as an input parameter. A dose-response relation derived from a hypothetical mesocosm study was used to link the exposure with the effects. The modeled landscape was represented as a lattice of 1 x 1 m cells. The model included processes of mortality of A. aquaticus, life history, random walk between cells, density-dependent population regulation, and in the case of the stream scenario, medium-distance drift of A. aquaticus due to flow. All parameter estimates were based on the results of a thorough review of published information on the ecology of A. aquaticus and expert judgment. 

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

As indicated above, theoretical models for biological rhythms were first used in ecology to study the oscillations resulting from interactions between populations of predators and preys [6]. Neural rhythms represent another field where such models were used at an early stage The formalism developed by Hodgkin and Huxley [7] stiU forms the core of most models for oscillations of the membrane potential in nerve and cardiac cells [33-35]. Models were subsequently proposed for oscillations that arise at the cellular level from regulation of enzyme, receptor, or gene activity (see Ref. 31 for a detailed fist of references). 

Fig. 5 Results of a mesocososm study on Phaeocystis globosa bloom dynamics and the ecological role of viruses. The measured data are represented by the symbols and the modeled results are represented by the lines, (a) measured and modeled biomass of P. globosa colonies (solid line and open symbol) and single cells (outline of grey area and...

Equation (8.2) can be shown to apply equivalently to either a continuous concentration field or the position probability density of a single particle undergoing Brownian motion [174], This equation is used to model transport processes in a wide range of natural phenomena from population distribution in ecology [146] to pollutant distribution in groundwater [30], One of the earliest (and still important) applications to transport within cells and tissues is to describe the transport of oxygen from microvessels to the sites of oxidative metabolism in cells. 

Fuerst J. A. (1995) The planctomycetes emerging models for microbial ecology, evolution, and cell biology. Microbiology 141, 1493-1506. 

---