Chapter 2
Exploring Dynamic Biological Systems
Art may be said. . .to overcome, and advance nature, as in these
Mechanicall disciplines.
(Wilkins, Mathematical Magick, 1648)
2.1 Simple Population Dynamics
In this chapter we will return to the concepts and ideas presented above, and explore
in more detail the dynamics of seemingly simple dynamic population models. In the
process of developing and exploring these models you will learn more about
the features of the STELLA software. The findings of this exploration should
sensitize your perception of dynamic processes and help you develop your dynamic
modeling skills.
Let us begin with a simple model of a population N in a given ecosystem with
carrying capacity K. The initial size of the population is N(t ¼ 0) ¼ 10, and the
carrying capacity is K ¼ 100 ¼ constant. For population sizes below the carrying
capacity, N will increase. Above the carrying capacity, N will decrease. The
maximum rate of increase of N is R ¼ 0.1, measured in individuals per individual
in N per time period. A convenient specification for the change in the population
size is the logistic function
ΔN ¼ R Ã N Ã 1 À
N
k
ð2:1Þ
To set up the STELLA model for our investigation of the dynamics of this
population, use the reservoir icon for the stock N, the flow symbol for ΔN, and
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_2,
© Springer International Publishing Switzerland 2014
29
Exploring Dynamic Biological Systems
Art may be said. . .to overcome, and advance nature, as in these
Mechanicall disciplines.
(Wilkins, Mathematical Magick, 1648)
2.1 Simple Population Dynamics
In this chapter we will return to the concepts and ideas presented above, and explore
in more detail the dynamics of seemingly simple dynamic population models. In the
process of developing and exploring these models you will learn more about
the features of the STELLA software. The findings of this exploration should
sensitize your perception of dynamic processes and help you develop your dynamic
modeling skills.
Let us begin with a simple model of a population N in a given ecosystem with
carrying capacity K. The initial size of the population is N(t ¼ 0) ¼ 10, and the
carrying capacity is K ¼ 100 ¼ constant. For population sizes below the carrying
capacity, N will increase. Above the carrying capacity, N will decrease. The
maximum rate of increase of N is R ¼ 0.1, measured in individuals per individual
in N per time period. A convenient specification for the change in the population
size is the logistic function
ΔN ¼ R Ã N Ã 1 À
N
k
ð2:1Þ
To set up the STELLA model for our investigation of the dynamics of this
population, use the reservoir icon for the stock N, the flow symbol for ΔN, and
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_2,
© Springer International Publishing Switzerland 2014
29