## April 4, 2012

### Population Growth

The graph below compares the effect of the r value doubling half way through the experiment to r values that remain constant.  The r value is the rate of increase during a generation.  The green line on the graph shows the number of sparrows after 100 years ending at 1,315 with an r value of .05.  The pink line shows the number of sparrows after 100 years ending at 137,806 with an r value of .1. The purple lines r value doubles after 50 years, changing from .05 to .1, ending with a population of 13,462 sparrows.  The double in the r value was caused because the weather got warmer and more food was produced.  They didn't need to go and search for their food which allowed them to produce more offspring therefore leading to an increase in the rate of increase in the population.  This number is significantly lower than the population with an r value of .1 and not significantly higher than the population with an r value of .05.  I did not expect this to occur, but it is cool because something like this can really happen.  With all the weather changes that have occurred lately, this is a possibility.

Throughout this activity the complexity of the graphs increased.  First, we modeled the population growth if each pair produced 10 offspring. Then, we looked at the change on the population when an r value was present.  Then, a new factor was added like a carrying capacity. This showed us more accurate data as to what can occur and what happens.

Formula used
$N_t = (N_t_-_1 \cdot r) + N_t_-_1$
This formula takes the number of individuals from the previous year and multiplies it by the rate of increase.  Then the previous years population is added to get the new total population.