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.

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