1. There is inconsistency in the loop connecting food popn hare - food scarcity - disease.
2. The link between lynx and hare population is lacking. There should be a connection between popn of lynx to the death of rabbit and the popn of rabbit to the birth rate of lynx.


I. Background of the Problem

In the ecosystem, predation is one of the basic life cycle that make ups the food web. One of the most popular of this predator-prey cycle is the relationship between the rabbit and the lynx. Although the lynx feed on a wide range of animals, from reindeer to fishes, it is highly dependent on snowshoe hares, their main prey. The survival of the lynx population highly depends on the existence of snowshoe rabbits. Among all of its preys, Canadian lynx highly depends on snowshoe rabbits. As the snowshoe rabbits population peaks every 10 years, so does the lynx population. As the rabbit population continues to escalate, the source of food for the entire lynx population increases. However, it is considered as unstable because of the starvation patterns that occur when a predator has exterminated its prey.

II. Construction of the Problem


The graph above presented by Sylvia Mader shows that the predator's abundance curve is almost always lags behind that of the prey. This then tells us that the predators such as the lynx is always dependent on the prey which is the hare. To further see the behavior an additional graph is shown below which further illustrates the behavior of the population between the two.

Dynamic Problem:

The population of Canadian lynx and Snowshoe Rabbits shows an oscillating pattern from a time period of 40 years, which could lead to a poor predator-prey ecosystem.


As seen in the graph above, It illustrates the relationship between the size of the hare population and the size of the lynx population. Notice how each population has a boom (when there are too many lynxes or hares for the available resources) and a bust (when many hares or lynxes die and very few are left) pattern . Look at the pattern in the graph. Notice how the lynxes’ pattern closely follows the hares’ pattern, but that the lynxes’ peaks and valleys happen a bit after the hares’ peaks and valleys.The causes of the dynamic shift may be attributable to the following factors.
1. Hare Population Increases and eat vegetables2. Vegetation produces secondary defense compounds in response- less palatable and nutritious3. Triggers hare population crash- hares cannibalize end up dying in great numbers4. Lynx continue to feed on hares, but run out of prey eventually5. Plant growth slowly recovers and rejuvenate hare population
(Source Ecological Modeling 2002)

III. Results and Analysis

To be able to understand more on the behavior of the system, an initial causal loop is shown below to illustrate the cause of death rate of hare.


The death rate of hare was chosen since the lynx is dependent on the population of the hare. The graph above shows that the two main causes are the severity of the disease outbreak and the increasing population of the lynx which is its predators. This shows that when the disease outbreak is more sever it causes an increase in the death rate of the hare. The same applies for the variable population rate of the lynx wherein more predators means more preys being eaten.


Now seeing that the population rate of lynx affects the death rate of the hare, a casual loop interaction is shown above that shows how the two affect each other while considering the death rate and the birth rate of the two. As seen in the graph above as the population rate of the lynx increases the death rate of the hare increases as well. This emphasize the predator-prey relationship which was discussed previously. The casual loop above shows that if it is graphed, the population rate of lynx is dependent on the number of hare presently in the environment. And if graphed there is an oscillating pattern that would be present since once there is a point in time wherein the population of hare will peak but will eventually start to decline as population of lynx increases and when that happens a gradual decrease would occur as well with the lynx and until then hare would recover and its population would increase. The same pattern of behavior then repeats itself thus showing an oscillating pattern that supports the graphs in the problem statement.


Now as for the second main cause that directly affects the death rate of the hare would be the severity of the disease outbreak. This shows that as the number of hare increases food then becomes more scarce. Not only that but as what was discussed by the Ecological Modeling 2002 is when vegetation decreases, it in turn would produce secondary defense compounds in response wherein vegetations would be then less palatable and nutritious, this being said makes the condition of the hare be easily infected with different kinds of diseases since it is common knowledge that if one were to be lacking with the nutritional standards one would be prone to illness and diseases which can also be said with the hare. So in short the food is not only scarce but is also less nutritious which may cause the disease outbreak from happening this then triggers an increase in the death rate of the hare.

Now that the different causes and interactions have been discussed, a final overview of the whole causal loop can be generated which shows a balanced system. This then summarizes all the previous discussions made before.

IV. Conclusion

The balance of natural processes is extremely delicate. They are affected by any force placed upon them and reflect the concentric circles and chains of energy of the natural environment that are their foundation.In light of analyzing the case, factors such as growth rates and carrying capacity of the environment are usually considered. For a predator-prey ecosystem, predation produces direct effects on the dynamics of population for both the predators and preys.

VI. References

Ecological Modeling. Volume 152, Issue 1, June 15 2002. Pages 89-102.
Hassel, M.P. Vol. 95, Issue 18, 10661-10664, September 1, 1998.
Krebs, Charles J. Ecology. Vol 79, no.4. Pp. 1193-1208.
Launchbaugh. U of Idaho, Foraging Ecology. 2004.
MacLean, Stephen. June 9, 1980.
Madler, Sylvia. Biology 5th Edition. 1998.
Marty, Sid. Canadian Geographic Magazine, Sept./Oct. 1995.
Poole, Kim G. Cat News. Issue 20. Spring 1994.