April 4, 2012

Population Growth Model

Creating models that show simulated environments is a typical way of representing projected data. By not having to actually collect real data and do field studies, mathematical models help us see what would happen in nature without us spending so many resources and so much time.

I decided to model a sparrow population with a carrying capa
city (K) starting at 10,000. Each year, due to dwindling resources, this carrying capacity decreases by .2%. At the same time, this population has a steady growth rate of .1% a year.
Here's our original population growth equation:

Our N values represent population size, R represents the rate of growth, and K represents our carrying capacity.

As many years in my model passed, eventually the population reached this diminishing carrying capacity. Our equation for this bit is here:

The population even kept going above the carrying capacity and although the population now decreased steadily alongside the carrying capacity, it was always a little higher than what the environment could handle. In year 198, however, suddenly the simulated environment changes. Now, there's a new abundance of resources that increases our carrying capacity by .5% every year. This caused the carrying capacity to shoot upward, and the population to increase along with it.
Like this:
But, in year 299, the carrying capacity regresses to its original patterns and steadily decreases at a rate of .2% a year once more.

Here's a graph of the data:

1 comment:

K. said...

Very cool simulation. I like the use of multiple equations for multiple parts of the process. NIce work.