Some Nonlinear Problems in Plankton Ecology.
MASSACHUSETTS INST OF TECH CAMBRIDGE
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In marine ecology, the variability of the physical environment is often considered a main determinant of biological pattern. A common approach to identifying key environmental forcings is to match scales of variability fluctuations of a biological variable at a particular frequency are attributed to forcing by the physical environment at a similar frequency. In nonlinear systems, however, different scales of variability interact and forcing at one scale can produce variability at a different scale. The general theme of this dissertation regards the interplay of scales in nonlinear ecological systems, with an emphasis on the mismatch of scales between biological variables and environmental forcings in the plankton. I use simple models to identify conditions leading to such a mismatch. The models focus on one ubiquitous nonlinear ecological interaction, that between a consumer and a resource. I consider first, the interaction between a phytoplankton population and a limiting nutrient resource second, the interaction of a predator and a prey that diffuse along an environmental gradient. I demonstrate two novel scenarios leading to scales of plankton variability different from those of the environment. I end by considering another consequence of the transfer of variability in nonlinear systems the lack of a dominant scale.