This population begins with 10 individual sparrows. From years zero to fifty, the carrying capacity for this population is two thousand. After one generation produces offspring, they die off. In year fifty, a drought occurred which limited resources and the carrying capacity decreased to one thousand. In the graph below, the two carrying capacities are shown, as well as the number of individuals within in the population throughout the years. Also the rate of increase is kept constant at .2. We can illustrate the relationship between the rate of increase, the carrying capacity and the number of individuals by this equation:
The current population is equal to the the population of the previous generation multiplied by the rate of increase, multiplied by the carrying capacity minus the population of the previous generation divided by the carrying capacity, plus the current population.
This activity has enabled us to model different scenarios on different populations. Rather than spending massive amounts of time trying to figure out the effect of certain factors when they change, with the formulas in the spreadsheets, just by changing the number, all results will change with it as well. This helps us with a visual representation of what’s going on and what is being affected, as well as saving us time. Within science, several changes occur, whether they are expected or not. Being that there are so many changes, modeling scenarios in this manner help us express the changes better and in a short period of time.