ISAT 420 First Modeling Assignment
Gregory Baker & Sean McArdle
9/17/2015
This report will analyze a model of a predator/prey system of grass consumed by deer which are
in turn consumed by wolves. We are modeling a common simple food chain within a meadow or forest
ecosystem. The boundaries of our system are limited to the grass, deer, and wolves. No other organisms’
effect on the system will be taken into account for this report. The scope of this system is to identify and
observe the relationship between the wolves, deer, and grass and how fluctuations in their various
populations affect the other members of the system. The flux of this system includes carrying capacity
which is the number of deer/wolves the environment can maintain. The deer carrying capacity (K) is
limited by the amount of grass and the wolf capacity is in turn limited by the deer population. The grass is
only limited by the amount of sunlight and water available which is assumed in this system to be
unlimited so it reproduces simply based on its reproduction rate. We also assume no density dependence.
Another important flux in this system is the deer death rate which is attributed to the amount of deer
killed by wolves (Dd). This system could be observed over the course of a year because there would be
significant enough trends to see after a year. The temporal resolution would be in days so the changes
could be seen on a precise enough scale to be able to observe changes in the system and how all the
components and fluxes affect each other. With a daily resolution we can see the change in population of
wolves and deer every day which would help us find a clear trend in the data.
We started by researching models of similar systems to get an idea of their structure and which
components were important to the system. We then used STELLA modeling software to build a visual
interpretation of our model with its various stocks and fluxes. Our model for this system can be seen
below as well as a chart of the variables used and their values.
In this system there are the three stocks represented by the labelled boxes in the diagram which
represent the grass, deer, and wolves of this system. There are also many different fluxes that affect this
system. The deer death is represented by Dd and is a function of the wolf population because of the deer
killed by wolves. Wolf birth rate is represented by Wb which is a function of the deer population because
the wolves need deer to eat to reproduce. The wolves are also affected by the value of Wd which is the
decline of the wolf population due to lack of available prey. The reproduction ratio of the deer is
represented by r and shows the inflow of the deer stock based on available grass. Kd represents the
carrying capacity of the population which we have set to zero. We set this carrying capacity to zero
because it would simplify the system to allow the relationship of the animals to be seen more easily. Our
third stock we added to the initial system was the grass which had one factor affecting its inflow and one
affecting its outflow representing reproduction rate (rg) and death rate (gd) respectively.
We gave the fluxes values for replacement and depletion of the various organisms in order to try
to get our system at equilibrium. The units for these values was the number of animals added or removed
from the system over time. When we tried running our system it would run for a short time and then all
stocks would drop to zero meaning they had all died off. Our goal was to achieve a system at equilibrium
so we could see the stocks of each species fluctuate over time and chart their increases and decreases. For
a future test like this we would need to research and adjust our ratios to achieve system that would
function more similarly to a real system like this. We would need to adjust the fluxes as our independent
variables to see the result we want in our stock of organisms or dependent variables. To correct this issue
of the species dying we could look at data actually taken from a system like this to more accurately
simulate it.