Chapter 3
Risky Population
I know that history at all times draws strangest consequence
from remotest cause.
(T.S. Eliot, Murder in the Cathedral, Part I, 1935)
3.1 Risky Population Model
In the previous chapter we have seen how to model simple deterministic and
random processes that influence population dynamics. We emphasized the need
to thoroughly test your models before you move on and expand them. This chapter
provides a novel expansion to the traditional model of population dynamics. Other
expansions follow in the next chapters. Each of those expansions is kept to a
minimum complexity yet the resulting dynamics can be rather surprising. A central
utility of this model is that it produces what could be called a carrying capacity of an
environment as reflected in the birth, death, and behavioral characteristics of the
population, as determined by that environment. Simple population model that claim
to represent resource limits often do it by simply specifying the carrying capacity as
a model input parameter [such as K in Eq. (2.1) of Chap. 2]. Here the carrying
capacity is derived.
For the following model assume that a population grows exponentially by virtue
of a birth rate and dies according to a death rate. If the birth rate is 7 % and the death
rate is 4 %, then the population grows exponentially at the rate of 3 %. That is a
simple matter and we have addressed this model in our most elementary examples
of the previous chapters.
But we all know that, as the population size (or density) grows and no migration
can take place, the chance of a sudden unanticipated rise in the death rate increases.
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_3,
© Springer International Publishing Switzerland 2014
41
Risky Population
I know that history at all times draws strangest consequence
from remotest cause.
(T.S. Eliot, Murder in the Cathedral, Part I, 1935)
3.1 Risky Population Model
In the previous chapter we have seen how to model simple deterministic and
random processes that influence population dynamics. We emphasized the need
to thoroughly test your models before you move on and expand them. This chapter
provides a novel expansion to the traditional model of population dynamics. Other
expansions follow in the next chapters. Each of those expansions is kept to a
minimum complexity yet the resulting dynamics can be rather surprising. A central
utility of this model is that it produces what could be called a carrying capacity of an
environment as reflected in the birth, death, and behavioral characteristics of the
population, as determined by that environment. Simple population model that claim
to represent resource limits often do it by simply specifying the carrying capacity as
a model input parameter [such as K in Eq. (2.1) of Chap. 2]. Here the carrying
capacity is derived.
For the following model assume that a population grows exponentially by virtue
of a birth rate and dies according to a death rate. If the birth rate is 7 % and the death
rate is 4 %, then the population grows exponentially at the rate of 3 %. That is a
simple matter and we have addressed this model in our most elementary examples
of the previous chapters.
But we all know that, as the population size (or density) grows and no migration
can take place, the chance of a sudden unanticipated rise in the death rate increases.
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_3,
© Springer International Publishing Switzerland 2014
41