We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions d ≥ 3. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins [8] and the second confirms a conjecture of Ohtsuki et al [38] in the context of certain infinite graphs. An important feature of our general results is that they do not require the process to be attractive.

Toxicogenomics, the genome-wide analysis of gene expression to study the effect of toxicants, has great potential for use in environmental toxicology. Applied to standard test organisms, it has possible applications in aquatic toxicology as a sensitive monitoring tool to detect the presence of contaminants while providing information on the mechanisms of action of these pollutants. We describe the use of a complementary DNA (cDNA) microarray of the fathead minnow (Pimephales promelas) a standard sentinel organism in aquatic toxicology, to better understand the mechanisms of toxicity of 2,4-dinitrotoluene (2,4-DNT) which is released in the environment through military and industrial use. We have constructed a fathead minnow microarray containing 5000 randomly picked anonymous cDNAs from a whole fish cDNA library. Expression profiles were analyzed in fish exposed to 2,4-DNT for 10 days at three concentrations (11, 22, and 44 microM, respectively) below the measured median lethal concentration (58 microM). Sequence analysis of cDNAs corresponding to differentially expressed genes affected by exposure revealed that lipid metabolism and oxygen transport genes were prominently affected in a dose-specific manner. We measured liver lipids and demonstrate that lipid metabolism is indeed perturbed following exposure. These observations correlate well with available toxicological data on 2,4-DNT. We present possible modes of action of 2,4-DNT toxicity and suggest that fathead minnow cDNA microarrays can be useful to identify mechanisms of toxicity in fish and as a predictive tool for toxicity in mammals.

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