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A ratio-dependent diffusion predator-prey system with free boundary is investigated to understand the impact of free boundary on spreading-vanishing dichotomy and a long time behavior of species. The existence and uniqueness of solutions are verified and the behavior of positive solutions is considered for this system. Moreover, the criteria for spreading-vanishing dichotomy are also derived. The results show that if the length of the initial occupying area is longer than a critical size for the predators or the length of the initial occupying area is shorter than a critical size, but the moving coefficient of free boundary is relatively big, then the spreading of predators always happens under relatively small rate of death for the predator. On the other hand, it is found that if the initial value of free boundary is smaller than a threshold value and the moving coefficient of free boundary is relatively small depending on initial size of predator or the rate of death is relatively big, the predators fail in spreading to new environment. [ABSTRACT FROM AUTHOR]

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It is well known that Darwin and Wallace came to discover the phenomenon of evolution through a historical approach to the geographical distribution of organisms. Before Darwin, evolution was a mere speculation that could be invoked to explain some facts. Darwin’s biogeographical argument for evolution is based largely on three main explanatory hypotheses. The first is that the geographical distribution of organisms is historically informative. The second hypothesis is that long-distance dispersal over barriers is one main force (extinction is the other) that modifies the distribution of organisms. The third of Darwin’s biogeographical hypotheses is that the factors that shape the distribution of organisms are mainly historical (large, often global and long temporal scales) rather than ecological (small spatial and short temporal scales). From the time of Darwin until now, a wide spectrum of biogeographical schools have provided new insights that challenge the central role of space, dispersal and history as the main explanatory hypotheses for the distribution of organisms, generating three binary opposites: (1) the spatial dimension of evolution: geographical distribution of organisms as historically informative vs. historically uninformative; (2) the processes that modify the geographical distribution of organisms: dispersal vs. vicariance; and (3) the explanation of geographical distribution: history vs. ecology. We analyse these three binary opposites to show that the components of each are complementary rather than antagonistic approaches to the study of biogeography. [ABSTRACT FROM AUTHOR]

Ecology, though poor in philosophical scrutiny, is full of foundational controversies. The holism-reductionism debate is one associated with ontological, methodological and epistemological premises. During the beginning of the twentieth century, ecology appeared highly holistic mainly due to Frederic Clements's organismic approach. Influential criticism gathered, however, and by the middle of the century ecology seemed divided in two conflicting camps, reductionists and holists. Yet for the majority of ecologists eclecticism was the only choice since both doctrines were a poor description of the reality they faced in the field. Thus, by the beginning of the 1980s, ecologists searched for more pluralistic approaches which seemed more adequate to deal with nature's complexity. Evolutionary geneticist and ecologist Richard Levins was one such pioneer against closed systems of thought, such as holism and reductionism, proposing instead a dialectical approach. His view served both as a salve to the fallacies committed by vulgar reductionism and as a response to the rise of systems ecology. We consider Levins's arguments as a breakthrough to a challenging heuristic, a constant reminder of the limitations faced by scientists and an homage to self-consciousness [ABSTRACT FROM AUTHOR]