Assignment 8

If vital rates remain constant, what will happen to population numbers over time? This question is investigated in the following exercises. Keep in mind that although we are working with a human population model, the same principles will apply for any population of plants or animals.


1 .		Working within DemographyLab, set the number of years to 300 and simulate the population growth of each of the seven nations. Examine the Time Series graphs on both the linear and logarithmic scales. What happens to each population over the long-term? These simulations assume that current fertility and mortality rates remain unchanged. Is this possible? Why or why not?

2 .		Exponential growth is described by the following exponential equation: N(t) = N(0)exp^rt equation (1) where N(0) is the total population size at some arbitrary initial time, N(t) is the population size t years in the future, and r is the intrinsic growth rate of the population.

3 .		Exponential growth is described by the following exponential equation: N(t) = N(0)exp^rt equation (1) where N(0) is the total population size at some arbitrary initial time, N(t) is the population size t years in the future, and r is the intrinsic growth rate of the population. If we take the logarithm of both sides of the exponential growth equation, we get: log N(t) = log N(0) + rt equation (2) What would you expect from a plot of the logarithm of population size over time? How the case for r > 0 differ from r < 0? Examine the Time Series plots of population size versus time for each of the seven nations with the Logarithmic Scale option selected. Do the logarithmic plots of the long-term population values agree with your predictions?

4 .		Let's use equation (1) to predict population size. Choose any nation and simulate population growth for 300 years. Using the Intrinsic Growth Rate parameter, try predicting the 2298 population size using the population sizes for 1998, 2098, and 2198. (Set r equal to the intrinsic growth rate, set N(0) to the population size for 1998, 2098, or 2198, and use t = 100, 200, or 300 years.) Since the intrinsic rate is displayed to three significant figures, your predictions will be limited to three significant figures of precision. How well does the exponential growth model do with the three predictions? Which predictions are most accurate? Can you explain why this might be the case? Try another nation to see if you get similar results.

5 .		Another measure of population growth is the doubling time, if r>0 or half-life, if r<0. The doubling time is the number of years it takes the population to double in numbers. The half-life is the amount of time it takes the population to decrease by 50%. The doubling time or half-life is given by the equation: T=0.6931/(r( equation (3) where (r( refers to the absolute value of the intrinsic growth rate. If r>0, T is a doubling time; if r<0, T is a half-life. Compute the doubling times or half-lives for each of the seven nations. What are the political and social implications of these values?

6 .		Choose any country, alter its 1998 population size, and simulate the population for 300 years. What effect, if any, does this have on the long-term population growth rates? Repeat the procedure for alterations in the population structure, fertility rates, and female and male mortality rates. Come up with a hypothesis for how changes in each of these factors affect the long-term population growth rates. Design and carry out simulations to test your hypotheses.

7 .		Choose any country, alter its 1998 population size, and simulate the population for 300 years. Try deriving equation (3) from equation (1). [Hint: Set N(t) equal to 2N(0) or N(0)/2.]