ERROR AND CONCLUSIONS
For any predator-prey model constructed there will always be an
element of error due to the extreme variability of nature. To eliminate as
much of this error, it is always important to take as careful measurements
as possible. Also, when reviewing results from a model, one must remember
that 0.58 does not equal one animal, nor does it equal zero animals.
Determining which of those two values - zero or one - that you choose will
indisputably skew your results. There are extensive statistical analyses
that we will not cover here that can be used to test the accuracy of any
given model but it is suffice to say that mathematical
modeling is an approximation that will always involve a certain amount of
error.
Another
major problem with the previous graphs, and for that matter the models
themselves, is that the time units were in years. Many interactions
between the predator and prey go unseen because the models are sampling
only once each year. For more accuracy the time units are decreased
so that more samples per year (or whatever time interval you are looking
at) are taken. This property of a 'slide show' effect is an inherent
characteristic of the discrete model.
In a closed system with two populations will
- unless the initial interactions between predator and prey lead to early
extinction - find an equilibrium point to fluctuate
between over the years. They reach a steady state that allows both
species to continue. Recall that in the phase plot, where the
predator population was plotted against the prey population, they cycled
around the equilibrium point.
There are ways to improve the predator-prey model to
make it better fit the real world. The most obvious place to start
would be to include more variables to create a non-closed system.
Realistically, immigration and emigration do exist. Animals do leave
an area of interaction through other methods besides death and
birth. It is also rare that only two species interact. Rabbits
are preyed on by wolves, foxes and other animals. Wolves also prey
on animals besides rabbits. Creating equations that take these
factors into account would be more realistic. Although adding
variables would be easy, figuring out how they relate to the other
variables is complicated. Eventually there will be newer, better
models, but the Lotka-Volterra model is decently helpful in predicting the
future trends, which is what population models are needed to do.
As we have explained, the predator - prey model is a very useful tool
in helping to describe and thus predict the behavior of population
interactions in the wild. The usefulness of this modeling technique goes
far beyond animal interactions in the wild though. Ranging from modeling
chemo therapy versus the cancerous cells to describing the fermentation of
yeast, various forms of predator - prey models can be and are used in a
wide variety of ways to lend a scientific hand to everyday life's
complications.
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