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The rock–paper–scissors (RPS) game is known as one of the simplest cyclic dominance models. This game is key to understanding biodiversity. Three species, rock ( R ), paper ( P ) and scissors ( S ), can coexist in nature. In the present paper, we first present a metapopulation model for RPS game with mutation. Only mutation from R to S is allowed. The total population consists of spatially separated patches, and the mutation occurs in particular patches. We present reaction–diffusion equations which have two terms: reaction and migration terms. The former represents the RPS game with mutation, while the latter corresponds to random walk. The basic equations are solved analytically and numerically. It is found that the mutation induces one of three phases: the stable coexistence of three species, the stable phase of two species, and a single-species phase. The phase transitions among three phases occur by varying the mutation rate. We find the conditions for coexistence are largely changed depending on metapopulation models. We also find that the mutation induces different paradoxes in different patches. [ABSTRACT FROM AUTHOR]

This article is a preliminary attempt to understand the corporate social responsibility claims and impacts of Aracruz Celulose sa, Brazil's largest pulp and paper manufacturer. Aracruz locates its operations in the vulnerable biodiversity hotspot of the Atlantic Forest, having acquired 800 000 hectares of land in five states of Brazil for the planting of eucalyptus. It owns some of the largest pulp and paper mills in the country. Both its record of land acquisition and its impact on the environment have resulted in considerable social conflict with the indigenous inhabitants, former slave communities and other small farmers in the state of Espírito Santo, and with supportive activist ngos. The company's application of formal corporate social responsibility practices often flies in the face of its social and environmental impacts. This raises questions about the nature of corporate social responsibility and its claims in developing countries like Brazil and elsewhere. [ABSTRACT FROM AUTHOR]