Mathematics and 21st Century Biology (2005) / Chapter Skim
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7 Understanding Communities and Ecosystems
7 Understanding Communities and Ecosystems
Pages 110-126
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From page 110... ...
. In the beginning of community ecology, questions focused on community structure, population dynamics, and, in the case of plant communities, on succession (Grinnell, 1917; Clements et al., 1929)
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resource competition model led the way from phenomenological to mechanistic competition models. Like the Lotka-Volterra models, mechanistic competition models are also based on systems of differential equations and continue to form the conceptual basis for understanding competition among multiple species.
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This has led to the insight that biotic interactions alone can generate spatial patterns. Stochastic models are rarely employed in theoretical ecological studies owing to the difficulties in analyzing them, even though both environmental and demographic stochasticity play an important role in the dynamics of ecological communities.
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These models were originally developed for problems in statistical physics, but it soon became clear that local interactions are important in other fields as well, including community ecology. The study of interacting particle systems and their discrete-time analogs, discrete-time cellular automata, has greatly advanced our understanding of the role of space and local interactions in the dynamics of ecological communities.
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. The connections among the four major modeling frameworks (ordinary differential equation, partial differential equation, integrodifferential equation, and interacting particle system)
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Looking at this another way, if one needs to include the effects of fluctuations, correlations, and spatial heterogeneities, the simple framework of ordinary differential equations no longer suffices. Instead, the much more complicated framework of interacting particle systems (or similar processes)
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Most field experiments are studied over only short timescales, even if the dynamics are slow, thus probably describing dynamics that are not in equilibrium. COMPUTATION Multispecies interactions across trophic levels, including ecosystem processes, provide statistical and modeling challenges for community ecologists.
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Spatial heterogeneity and demographic and environmental stochasticity are often key driving factors. Spatial control, a mathematically sophisticated and computationally intensive tool, appears to be a promising methodology (Hof and Bevers, 1998, 2002)
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illustrates this approach: Recognizing that detailed bookkeeping of the calorie consumption of the members of a food web could explain food web structure and, ultimately, the diversity of a local community, Paine manipulated food webs through removal (or addition) experiments so as to assess the importance of each link.
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(2004) attempted to unify the relationships between species richness and spatial scaling and between species richness and trophic interactions to extend the spatial scale at which food web theory applies.
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(2004) , using shotgun sequencing of microbes in the ocean, have given us a static glimpse into the enormous diversity of largely unknown organ isms that are responsible for biogeochemical cycles.
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For instance, invasive species or the assembly of novel communities can alter ecological interactions and impose strong selection on all members of a community (Reznick et al., 1997, 2001; Davis and Shaw, 2001)
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Understanding carbon and nutrient cycles at global and regional scales is a very active area of ecology that integrates across community ecology and ecosystem ecology. As an example, predicting an increase in temperature as a function of an increase in carbon dioxide at the spatial scale of the whole earth was already accomplished by Arrhenius (1896)
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2004. Network structure and robustness of marine food webs.
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1994. Partial differential equations in ecology: Spatial interactions and population dynamics.
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1992. Ergodic theorems for the multitype contact process.
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Nature 367: 363-365. van der Heijden, M.G.A., and J.H.C.
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