The Aquatic Ecosystem Model Ms. Cleaner

Park, Richard A.; Collins, Carol D.; Leung, Donna K.; Boylen, Charles W.; Albanese, James R.; deCaprariis, Pascal; Forstner, H.

doi:10.1016/b978-0-08-023443-4.50028-2

Cited by 11 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(12) is stable only for R2 > 4bW kSk , that is, when the growth term exceeds the prediction term. When a(t), b(t), and Sk are allowed to vary, the solution of (11) will oscillate between fixed bounds determined by (13) that are independent of the initial conditions.…”

Section: Eutrophic Zakesmentioning

confidence: 99%

“…Using (12) and (13) for eutrophic conditions and (19) and (20) for oligotrophic conditions shows that realvalued, stable solutions occur only when the growth terms exceed the predation terms. We may generalize this analysis to systems of coupled equations by noting that when the number of nonzero elements in an interaction matrix is large, the predation terms in (12), (13), (19), and (20) are more likely to exceed the growth terms. When the interaction matrix is sparse, these stability conditions are more likely to be satisfied.…”

Section: Ozigotrophic Lakesmentioning

confidence: 99%

See 1 more Smart Citation

The Mathematical Structure of an Aquatic Ecosystem Model

Caprariis

1981

SIMULATION

View full text Add to dashboard Cite

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

show abstract

Section: Eutrophic Zakesmentioning

confidence: 99%

Section: Ozigotrophic Lakesmentioning

confidence: 99%

The Mathematical Structure of an Aquatic Ecosystem Model

Caprariis

1981

SIMULATION

View full text Add to dashboard Cite

show abstract

“…The use of generalized ecosystem models for predictive research for freshwater and grassland ecosystems are well documented (Park et al 1979;Parton et a\. 1987Parton et a\.…”

Section: Introductionmentioning

confidence: 99%

Export coefficients for total phosphorus, total nitrogen and total suspended solids in the southern Alberta region : a review of literature /

Jeje¹

2006

View full text Add to dashboard Cite

The contents of this document have been prepared with funds from Alberta Environment but do not necessarily reflect the Ministry's views or policies. Any mention of trade names or commercial products does not constitute an endorsement or recommendation for use. Any comments, questions or suggestions on the content of this document may be directed to: Regional Environmental Management Alberta Environment 3rd Floor, Deerfoot Square 2938-11 Street N. E.

show abstract

Lake Eutrophication Models

Straten¹

1986

Modeling and Managing Shallow Lake Eutrophication

View full text Add to dashboard Cite

The Aquatic Ecosystem Model Ms. Cleaner

Cited by 11 publications

References 24 publications

The Mathematical Structure of an Aquatic Ecosystem Model

The Mathematical Structure of an Aquatic Ecosystem Model

Export coefficients for total phosphorus, total nitrogen and total suspended solids in the southern Alberta region : a review of literature /

Lake Eutrophication Models

Contact Info

Product

Resources

About