Wolves

Fox	Coyote

Small mammals	Deer	Elk

	Vegetation

My modeling situation was designed to demonstrate the subtle effects of the wolf introductions on the fox and coyote populations.  The coyotes and foxes must compete with each other for prey while the wolves and coyotes also interact. Observations in the park and other areas have shown that wolves may kill coyotes that share territories. (Klinghammer, 1979) I hoped that my model would reflect these interactions.

The many food items of the various carnivores were grouped into the small mammals category for simplicity. The challenge of the initial model design was to get all of the species included in the model to persist in proportion to the data collected at Yellowstone before the 1995 wolf introductions.

The initial model included only vegetation and small mammals. Species were systematically introduced into the model, and the model restabilized in order to maintain the population numbers in proportion to each other. For instance, the small rodents are by far the most numerous, coyotes outnumber the foxes, and the deer population is much smaller than the elk population.

As each species was introduced, adjustments had to be made to factors such as immigration and reproduction rates. Feeding strategies and relative values of the various foods that could be eaten by each animal had to be adjusted to better reflect the "real" situation. I found that as the number of species in the model increased, the stability of the model decreased. Slight changes in feeding ratios of the newly introduced animals at the upper levels of the food web resulted in radical changes to the number of small rodents available for the upper level carnivores. This was still without the wolves.

After finally stabilizing all populations, I had to introduce the wolves. My prediction was that the wolves would affect the food balance such that the coyote population would decrease, and the fox population would increase. The first introduction of the wolves failed. There were not enough individuals introduced to sustain the population. The second try with lightly different parameters resulted in the extinction of the elk, deer and small mammals....oops! Like a house of cards, the whole model collapsed.

The third try at setting more appropriate parameters was more successful. The wolf population increased to a sustainable size, then leveled off. The population of the wolves' preferred food item, elk, dropped, but stayed within sustainable numbers, as did the deer and small mammals, both secondary food items. As designed, the coyote population decreased, and more importantly, the fox population increased as the wolves decreased the number of their direct competitors, the coyotes.
 

This is a graph of the relative population levels of the competing predators in the model. Note the change in the relative abundance of the fox and coyote after the introduction of the wolves at time step 150.

The model seems to work fairly well at showing carnivore relationships. Of course, the actual situation is much more complex with differing preferred habitats for the animals, and much more complex carnivore-herbivore-plant interactions. This model, however, does seem to be useful for illustrating some of the complex interactions that exist in the Yellowstone area, and has applications  in teaching about the results of small perturbations in complex ecosystems.

As I worked on the models, I learned that it was far easier to adjust the population levels of the whole system by manipulating the predators' parameters than by changing things at the base of the web.
 
 

Main Page

Introduction

Situation 1

Situation 2

Resources: Wolves

Resources: Modeling

 

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The Woodrow Wilson National Fellowship Foundation CN 5281, Princeton NJ 08543-5281 - Tel:(609)452-7007 - Fax:(609)452-0066 Technical contact: lpt@woodrow.org