ES 100 -- Fall 1998

Introduction to Environmental StudiesMid-term I: Population

Answer Key

1 (3 points total). Define, compare and contrast (1 point each):

r vs. R_0: r is the intrinsic rate of increase (or population growth rate), and is computed as births - deaths + immigration - emigration. is the net reproductive rate, or the average number of daughters per mother over her lifetime. R_0 can be used to calcluate r, and is related to r, but is not r.

exponential growth vs. logistic growth: A population growing exponentially increases in size without bounds, and at an increasingly rapid rate. A population growing logistically increases in size to an upper limit, and at a decreasing rate as it approaches its limit.

K vs. N_0: K is carrying capacity, or the limit to population size. N_0 is the starting population size, used in most calculations of future population size.

2 (5 points total). The population of the Cayman Islands in 1997 was 36,000 people. In that same year, the birth rate was 14 per 1000 individuals, the death rate was 5 per 1000 individuals, and the immigration rate was 33 per 1000 individuals.

(2 points) What was the 1997 rate of population growth on the Cayman Islands? (Show all calculations)? Calculate as births (14) - deaths (5) + immigrants (33) - emigrants (assume 0, since no information given) = 42 per 1000 individuals, or 4.2%, or r = 0.042 (per capita).

(2 point) What is the expected time to doubling of the population on the Cayman Islands (Show all calculations)? Using the 'back-of-the-envelope' formula (or 'rule of 70'), doubling time = 70/4.2 = 16.67 years. Using the more precise formula, doubling time = ln(2)/0.042, or 0.693/0.042 = 16.5 years. (Credit was given if you correctly used the answer you got in the first part)

(1 point) What is likely to limit population growth on the Cayman Islands? Why? Most likely, space and fresh water, since it's an island. Other answers were possible.

 

3 (2 points) What is the effect on population growth of increasing the age at which women have their first child?

It will slow down the rate of population growth, since most women will have fewer children if they begin having them later in life.

4 (5 points total). Consider this graph, which illustrates the so-called "demographic transition" that most developed countries have gone through in the last several hundred years. Answer the following questions using this graph as reference. Well, I messed this one up, by reversing the labels 'BIRTHS' and 'DEATHS' on the graph. So, I accepted either answers that matched the graph I drew, or answers that matched the graph I intended to draw. More details below.

a (2 points). Using the information shown on this graph, draw another graph on which the x-axis indicates years (just like on this one) and the y-axis illustrates population growth rate.

b (1 point). Describe in 1-2 sentences the main message of the graph that you have just drawn. Either way, the graph illustrates a change from no difference between birth and death rates (no change in population size) to a large difference in birth and death rates (either a large population growth rate for Fig. 2 or a negative population growth rate [shrinking population] in Fig. 1), and then back to no difference between birth and death rates (no change in population size). (An acceptable answer here had to correctly describe whatever graph you drew)

c (2 points). What transition do these two graphs (the printed one and the one you drew) illustrate? In other words, why do you think this phenomenon is called a "demographic transition"? It's a 'transition' from no change to some change and back to no change. Figure 2 illustrates the 'normal' trend, from high birth rate and high death rate to high births but low deaths (change in technology, medicine, hygiene, etc.) and then back to low growth as births decline (due to increasing standards of living, etc.). Figure 1 illustrates the opposite trend, and may in fact illustrate what will happen in many developing countries (such as Africa), if there is a resurgence in infectious diseases at the same time that birth rates are falling.

5. (1 Extra credit point). What two mountain ranges in the Continental United States (i.e., the lower 48 states) trend East-West? The Holyoke Range in Massachusetts, and the San Gabriels outside of Los Angeles.