Predation: Watts

SC-IPM Processes (Predator-Prey)

Overview

Watts predation is a generalization of Ivlev predation, analogous to the Generalized-Gauss generalization of Holling type I (ie, Lotka-Volterra) predation.

Formulas

In this model, the predators (ie, G, grazers) are Zooplankton and the prey (ie, P, producers) are Phytoplankton. This Generic Process uses a single algebraic equation, based on:

  • G.conc - Carbon concentration of grazers
  • G.gmax - maximum grazing rate of grazers
  • P.conc - Carbon concentration of producers
  • delta - ???
  • m - ???

As SC-IPM evaluates each candidate model structure against the training data, it estimates appropriate values for all numeric values:

    t1 & = & P.conc / G.conc^m\t2 & = & e^{- delta * t1}\G.grazing\_rate & = & G.gmax * (1 - t2) \

Data Structures

:description
  "Watts Predation"

:name      :watts

:constants {
  ;; higher value increases grazing rate
  :delta                [   0.01,      0.5    ]

  ;; higher value retards grazing rate
  :m                    [   0.0001,    0.9999 ]
}

:entity-roles {
  :G { :types [ :grazer   ] }
  :P { :types [ :producer ] }
}

:equations {
  ;; predation (ie, grazing) rate
  ;; (eg, of phytoplankton by zooplankton)
  :G.grazing_rate {
    :type     :ALG
    :infix
      "G.gmax * (1 -
         exp(-1 * delta * P.conc / expt(G.conc, m)"
    :prefix
      "(* G.gmax (- 1 (exp (* -1 delta (/ P.conc 
         (expt G.conc m))))))"
  }
}

See Data Structures for details.

References

  • C. Jost & S. Ellner. 2000.
    Testing for predator dependence in predator-prey dynamics:
    a nonparametric approach.
    Proc. Roy. Soc. Lond. B 267: 1611-1620.
    (See also Christian Jost's home page)

See Also


This wiki page is maintained by Rich Morin, an independent consultant specializing in software design, development, and documentation. Please feel free to email comments, inquiries, suggestions, etc!

Topic revision: r10 - 22 Jul 2013, RichMorin
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