## April 4, 2012

### Modeling population growth

Modeling Population Growth

We have progressed during the course of this activity from simpler to increasingly complexity models. First we started of by just calculating the population of sparrow for ten years using the spreadsheet. In part two, we incorporated another variable known as "rate of increase" to refine our original model. In part three, we took it to another level by inputting a carrying capacity to create a logistic model. By observing the progress of simple to complex models, we can conclude how living systems interact, and how biological factors place limitations on something so simple to make it more complex.

Effect of Deforestation on the Sparrow Population

Due to increasing settlement on the island, deforestation has increased termendously. Settlers are effectively utilizing their surrounding resources to build new homes and a major resource is wood made by trees. However, the problem is these large beautiful trees are homes for many sparrows. Therefore, deforestation will have a significant impact on the population growth of sparrows. To investigate the growth rate, I used a spreadsheet to model the effect. First I created a new formula that will account for the deforestation effect on the population. The new formula is shown below:

So basically what this equation says is the current generation is equal to the previous generation population times the rate of increase plus the previous generation's population. Then subtracted from that is the population of the previous generation times the rate of increase plus the previous generation's population times the death rate of sparrows due to deforestation.  The death rate and the rate of increase are fixed rates, which means that these numbers do not change as the population grows. The variable R signifies the rate of increase which was equal to .01 and the variable D represent the death rate which was equal to .02. The model below illustrates the Effect of Deforestation on the the sparrow population for 20 generations.

By analyzing the graph, it is apparent that deforestation influences the sparrow growth population to decrease as the years go on.

K. said...