Chapter 34
Two-Species Colonization Model
Thou eternal fugitive, Hovering over all that live.
(1847 Emerson Poems, Ode to Beauty)
34.1 Basic Colonization Model
In Chap. 5 we have modeled spatial dynamics in a rather abstract way. Let us take
up the issue of spatial dynamics in this chapter and deal specifically with the
competition between two species for space. We will begin this chapter with a
simple version of this model, then introduce disturbances on the physical landscape
and observe the implications for population dynamics.
Assume you are the manager of forestland on which two species of trees can
grow [1]. Both species are able to colonize open patches of land. The colonization
coefficient C is different for each of the species. One of the species has a higher
ability to colonize, but after colonization took place it is easily outcompeted by the
other species. Call the species that loses in competition the INFERIOR or “fugitive”
species, and the other one the SUPERIOR species. Both species have an extinction
rate, E, which we assume—only to keep things simple—to be the same for each
species. The constant E is multiplied by the number of patches occupied by a
species, to obtain the extinction rate of that species. Once extinction from a patch on
the landscape takes place, the area that was previously covered by a particular
species is converted into an open patch.
There are three state variables of this system: One state variable for the amount
of open land that can be colonized, and one each for the land occupied by a Superior
and Inferior species. In the model we normalize the total habitable forest area
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_34,
© Springer International Publishing Switzerland 2014
283
Two-Species Colonization Model
Thou eternal fugitive, Hovering over all that live.
(1847 Emerson Poems, Ode to Beauty)
34.1 Basic Colonization Model
In Chap. 5 we have modeled spatial dynamics in a rather abstract way. Let us take
up the issue of spatial dynamics in this chapter and deal specifically with the
competition between two species for space. We will begin this chapter with a
simple version of this model, then introduce disturbances on the physical landscape
and observe the implications for population dynamics.
Assume you are the manager of forestland on which two species of trees can
grow [1]. Both species are able to colonize open patches of land. The colonization
coefficient C is different for each of the species. One of the species has a higher
ability to colonize, but after colonization took place it is easily outcompeted by the
other species. Call the species that loses in competition the INFERIOR or “fugitive”
species, and the other one the SUPERIOR species. Both species have an extinction
rate, E, which we assume—only to keep things simple—to be the same for each
species. The constant E is multiplied by the number of patches occupied by a
species, to obtain the extinction rate of that species. Once extinction from a patch on
the landscape takes place, the area that was previously covered by a particular
species is converted into an open patch.
There are three state variables of this system: One state variable for the amount
of open land that can be colonized, and one each for the land occupied by a Superior
and Inferior species. In the model we normalize the total habitable forest area
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_34,
© Springer International Publishing Switzerland 2014
283