Modeling Population Growth in Sparrows

This graph from year 0 to 100 show the change in population of a species of Sparrow. In the beginning of time (year 0), the population of the sparrows is at 40.  The sparrow population grows at a constant rate (r) of 0.25 with the death of 5 sparrows each generation.   At year 25, however, a natural disaster occurs and half of the Sparrow population is wiped out with the growth rate (r)  changing to 1.2. The carrying capacity (K) of the environment is 50,000 sparrows which keeps the population limited. 

Equations: 

1. Original Growth Rate Equation:

2. New Equation:

N= Population Size, t= generation, r= rate of increase, K= carrying capacity

Conclusion: Despite the great fall due to the natural disaster, the Sparrow population was able to expand greatly and seems to be leveled off due to the carrying capacity.

By using a spreadsheet to express the population of the sparrows, we're introduced to a new, easier, scientific way of graphing things. This can be used for future experiments dealing with rapid growth or exponential factors.

Sparrow Population

The formula i created shows the sparrow population fluctuating constantly; it increases and then decreases, then increases and decreases. This is because at certain points the birth/immigration rate is greater than the death/emigration rat, and vice versa. And as the years progress it continues to cycle, until it finally comes to a stop at the 99th year, and the population levels off and remains the same. The population equilibrium could be a result of many factors; the most reasonable factor could be that the birth/immigration rate became equal with the death/emigration rate. This would be an extremely ideal circumstance because this means that a decent amount of birds (2,632) could be sustained in this environment without running out of resources or exceeding the carrying capacity. 

The way we progressed during the course of this activity from simpler to increasingly complex models really made it easy to understand how to work spreadsheets very efficiently. It was a good learning process. Spreadsheets are also a good way to do business from a science standpoint because spreadsheets perform any type of calculation you type in, and everything stays organized and clear, and it processes the information quickly. It is also very easy to go back and make any corrections to your mistakes.

Modeling Population Growth

The first model simply graphed the population of sparrows without any external factors. The number of individuals just grew exponentially due to a constant birth rate (10 offspring for each pair). However this model is not an accurate representation of populations in nature. Therefore, the next model introduced birth rates, death rates, and migration. By having a rate of increase (r) to account for the number of individuals entering and leaving a population, the growth model becomes more specific and accurate. Also, by adding a carrying capacity, the population model becomes even more complex and accurate. By observing nature from simple to complex, we can get a better understanding of how systems overlap or come together to work the way it does.

The first line on my graph (red) demonstrates a population of sparrows with a carrying capacity of 10,000 individuals. The second line demonstrates the population after the carrying capacity decreased to 7,000 after year 60. A probable cause for the decrease in carrying capacity is habitat destruction. Since this is a common environmental issue faces many habitats, I thought it would be interesting to see the effect on a population. The population reached its carrying capacity 10 years earlier in the second population. The formula used to determine the population after each year is:

N represents the number of individuals, t is the time in years, r is the rate of increase, and K is the carrying capacity. The rate of increase (r) accounts for births, deaths, and migration in the population and K demonstrates the maximum amount of individuals that a given environment can sustain. The graph shows an exponential growth, however after about 85 years, growth seems to slow down and remain almost constant as it approaches the carrying capacity.