Human Population Growth

 

The biggest challenge facing conservation biologists is human population growth. Tonight’s exercises are designed to explore aspects of human population growth.

 

Exercise 1—historical population sizes

 

Below is a table listing human population sizes since 500 CE as estimated by the US Census Bureau.

 

year (CE)

population size

500

190,000,000

600

200,000,000

700

207,000,000

800

220,000,000

900

226,000,000

1000

254,000,000

1100

301,000,000

1200

360,000,000

1300

360,000,000

1400

350,000,000

1500

425,000,000

1600

545,000,000

1700

600,000,000

1800

813,000,000

1900

1,550,000,000

2000

6,080,000,000

 

Recall from Ecology that a population growing exponentially has a growth curve with the equation Nt = N0ert

The growth curve will be J-shaped on a graph of N vs. t and a straight line on a graph of ln(N) vs. t. On the graph of ln(N) vs. t, the slope of the line is r.

 

Open Excel and copy the table of dates and population sizes into two columns of a worksheet. Make a third column of ln(N) [use the =LN(cell address) function].

 

Make a graph of N vs. t using markers for the data points and no connecting lines.

 

Make a second graph of ln(N) vs. t using markers for the data points and no connecting lines. Note that from 500 to 1800 CE the plot is basically linear. Go back to the worksheet and find the equation for the line using years 500-1800 only. [use the =SLOPE(cell addresses) and =INTERCEPT(cell addresses) functions]. Use the equation for a line to make a column of the predicted ln(N) values for each year from 500-2000. Add this column as a second series to the ln(N) vs. t graph; format it as a line without markers. Print this graph and answer the following questions:

a.       What was the value for r for humans from 500-1800? Indicate the units.

slope of the line—0.0010 individuals/(individual·year)

b.      What has happened to value of r over the last 200 years?

r greatly increased [to 0.01 individuals/(individual·year)]—the slope is much steeper for the last 200 years

c.       Describe human population growth from 500-2000 in your own words.

the human population grew exponentially from 500-1800; it grew exponentially but a higher rate from 1800-2000

 

 

Exercise 2—demographic factors

 

Three important demographic factors determining the rate of human population growth are age structure, per-capita birth rate, and age at reproduction. We will model the effects of the last two factors.

 

Recall from Ecology that r can be determined from life tables with the equation r = ln(R0) / G where R0 is the net reproductive rate (number of daughters born to a female over her lifetime) and G is the generation time (average age of a female at the time of her daughters’ births).

 

Model the effect of increasing R0 on population growth. Make a column of R0 values: 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0. Make another column of G values all equal to 20. Make a column of r values. Let N0 = 100 and use the exponential growth equation  to project the population 40 years into the future (i.e., make a column of N40 values).

 

Model the effect of increasing G on population growth. Make a column of R0 values all equal to 1.5. Make another column of G values: 16, 20, 24, 28, 32, 36, 40. Make a column of r values. Let N0 = 100 and use the exponential growth equation to project the population 40 years into the future (i.e., make a column of N40 values).

 

Answer the following questions:

a.       What is the effect of increasing R0?

as R0 increases, N40 increases

b.      What is the effect of increasing G?

as G increases, N40 decreases

c.       Are the effects of changing R0 and G independent of each other?

the effects are independent of each other; changing R0 or G and holding the other constant still results in a change in N40; an important implication is the effect of delaying reproduction on population growth rate—if women delay childbearing, the population growth rate declines, even if the number of offspring does not change