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.
Bibliography

Intro    Pred-Prey Graphs    Phase Plots    Equilibrium Points    Conclusion&Error

  

2000 -  Horowitz & Joshi