The Mathematical Structure of an Aquatic Ecosystem Model

Abstract

As ecological models become more complex, the question of whether they are stable becomes more difficult to answer. Some ecologists believe that a complex system is more stable than a simple system because it is less dependent on any single path through it. Mathematicians, on the other hand, have shown that systems of equations are more likely to become unstable as the number of equations increases. Neither tendency may apply to ecological systems that include time-varying components and in which the number of significant interactions does not depend strongly on the number of components.American Association for the Advancement of Science. This equation is the version of the model MS. CLEANER that we will analyze in the sections that follow.Multiplying (4) by (K. + S.) gives J J where at PENNSYLVANIA STATE UNIV on March 16, 2015 sim.sagepub.com Downloaded from = W'kSk' The graph of J J J J J J this function is a rectangular hyperbola. The limiting value of f under eutrophic conditions is W*k and the function is essentially linear in S. under oligotrophic conditions. Under eutrophic or oligotrophic conditions the nonlinear function (2) becomes constant or linear, respectively. These changes explain why behavior under these conditions differs from behavior under mesotrophic conditions, in which the function f(s) is nonlinear. Albanesel has demonstrated the existence of more than one stable solution under mesotropic conditions by conducting three-year simulations of a benthic estuarine community. He found that perturbing the model by increasing silt loadings abruptly (to reat PENNSYLVANIA STATE UNIV on March 16, 2015 sim.sagepub.com Downloaded from