1. General Model Information



Main medium: terrestrial
Main subject: populationdynamics, forestry
Organization level: biocoenosis, ecosystem
Type of model: difference equations, individual-based, cellular autmat
Main application:
Keywords: sequential predation, predator-prey systems, insects,comparison of implementations, scarlet oak, white oak, fall cankerworm, quercus coccinea, quercus alba, alsophila pometaria


Jan D. van der Laan
Theoretical Biology Group
University of Utrecht
Pandualaan 8
3584CH Utrecht, The Netrherlands
Phone: +31 30 2533692
Fax: +31 30 2513655
email: P.Hogeweg@biol.ruu.nl


Jan D. van der Laan, Ladislav Lhotka and Pauline Hogeweg


In a simulation study by van der Laan et al. (1995) three different modelling methodologies were applied to an ecosystem characterized by two competing prey species both of which are consumed by a common predator species. The modelled system is based on a field study (Futuyma and Wasserman 1980) on the interactions between foliage feeding larvae of fall cankerworm (Alsophila pometaria) and the competing tree species scarlet oak (Quercus coccinea) and white oak (Quercus alba) . Both oak species are asyncronically available to the predator due to a shift in timing of budbreak and decreasing palatability of maturing leaves. The two tree species interact indirectly via the predator ( apparent competition) and the predation occurs sequentially, although overlapping.

Phenology of the system:

Scarlet oak breaks bud approximately ten days before white oak. Larvae of the fall cankerworm hatch about the time that scarlet oak comes into leaf . Since they can only survive two or three days without food, they are entirely dependent on scarlet oak during early stages. As leaves mature, they become unpalatable and the larvae have to migrate to white oak to complete their development. So at the end of their ontogenesis larvae depend on white oak.
An important feature of the system is that migration radii of A. pometaria are small, because females are wingless.

The following differences in the larvae-tree relations were considered:

  • Whereas after hatching all larvae immediately have to find an early tree (scarlet oak), the transition to the late trees is gradual.
  • Because there is only one generation of larvae per season, the number of larvae feeding on early trees is greater
  • Since the per capita consumption of the larvae increases with their weight, the late tree may suffer more extensively from the presence of larvae
  • The early tree may benefit from earlier start of photosynthesis.

    Alternative model formalisms:

  • First, the model was formulated as a discrete dynamical system (DDS) consisting of a system of three difference equations (DFE) describing the compartments scarlet oak, white oak and larvae
  • Second , the system was described as an individual-oriented two dimensional Hobo model. The ´Forest´ is represented by a lattice of square patches that are regarded as stand for a single tree and retain specific parameter values. Several age classes of trees and weight classes of larvae are considered. An important aspect of this model is the state of the seedling banks that are filled by annual seed production and dispersed to adjactent patches. The state of the seedling bank in a patch influences the (transition) probability for a defoliated or dead tree to be replaced by a tree of the other species. Larvae are represented by a population of individual insects that reside in the tree-patches and perform actions such as feeding, growing, passive migration, active migration, reproduction etc.
  • Third, the model was formulated as a cellular automaton (CA).

    Author of the Abstract: T. Gabele
    Abstract Reference:
    Laan, J.D. van der, Lhotka, L. and Hogeweg. P 1995 Sequential predation: a multi model study. J. Theor Biol. 174:149-167

    II. Technical Information

    II.1 Executables:

    Operating System(s):

    II.2 Source-code:

    Programming Language(s):

    II.3 Manuals:

    II.4 Data:

    III. Mathematical Information

    III.1 Mathematics

    III.2 Quantities

    III.2.1 Input

    III.2.2 Output

    IV. References

    Laan, J.D. van der, Lhotka, L. and Hogeweg. P 1995 Sequential predation: a multi model study. J. Theor Biol. 174:149-167
    Laan, J.D. van der, Hogeweg. P 1995 Predator-prey coevolution: interactions among different time scales. Proc. R. Soc. Lond. B. 259: 35-42
    Futuyma D.J. and Wasserman S.S . 1980: Resource concentration and herbivory in oak forests. Science, 210, 920-922.

    V. Further information in the World-Wide-Web

    VI. Additional remarks

    Last review of this document by: T. Gabele: Jan 19 1998
    Status of the document:
    last modified by Tobias Gabele Wed Aug 21 21:44:49 CEST 2002

    Go back to Register of Ecological Models (R E M)