Forage (aka carrying capacity) feeds the deer; deer feed the wolves; wolves keep the deer herd in balance with the forage. It's a nice model, but things don't always work that smoothly. Two previous posts discuss a mathematical model written in Excel that interactively explores some of the possible outcomes given initial conditions of deer herd size, number of wolves, intrinsic growth rates of deer and wolves, and the carrying capacity and carrying capacity variance factor. This latter is a random card designed to incorporate the unpredictable effects of climatic variation, forage decline, or other things that can change the amount of forage but are not predictable from one year to the next.

Previous posts on this topic are at:

http://misterkenblog.blogspot.com/2012/01/predator-vs-prey-mathematical-model.html

http://misterkenblog.blogspot.com/2011/12/predator-vs-prey-will-wolves-dominate.html

Ready to try you hand at creating your own scenarios? A simplified interactive model programmed in an Excel spreadsheet is available for the curious in Google Docs at

https://docs.google.com/spreadsheet/ccc?key=0AixHzIqC4EIYdGJ6VFgyLUl3UERKUEF4RUw1Z0dVMkE

There are eight variables in the model you can work with shown in the diagram below.

The population size of the deer herd (here it is 5000), deer growth rate, carrying capacity for the deer herd, variance in carrying capacity (K), wolf population (here it is 10), wolf pack growth rate, predator efficiency, and number of deer required for wolf survival. You can change any and all of these starting numbers to see what happens. For example, to evaluate the effect of dramatic swings in climate try changing the variance in K (now at 2000) to a higher or lower number. A higher number would represent greater unpredictability and a lower number a more stable environment.

Have fun.

## Friday, February 10, 2012

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