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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]

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]