These problems are intended to give you practice with some of the graphical models and equations that we have been discussing. The answers are now posted. - Judie Bronstein

Exponential Growth Use Figure 1 in answering the questions below.

1. Write out the exponential equation and make sure you know the definition of each term.

2. Is the population growth rate (dN/dt) higher at time B or time C, or is it the same at both points?

3. Show how this curve would be different if the average death rate suddenly increased at time B (but stayed lower than the average birth rate)

4. Show how this curve would be different if the average birth rate suddenly fell at time C, so that it equalled the average death rate.

5. Imagine that at time B the population was suddenly reduced down to the size shown at time A. Draw a curve showing how population would resume growing (assume there are no lasting effects from whatever reduced their numbers).

Logistic Growth Use Figure 2 in answering the next questions.

6. Write out the logistic equation and make sure you know the definition of each term.

7. What is Òzero population growthÓ? Be able to explain this concept using the terms in the logistic equation.

8. At what time (D, E, or F) has the population reached its carrying capacity? What is the value of dN/dt at that time?

9. During which interval is the population growing exponentially: D to E, E to F, D to F, or none of these?

10. Imagine that at time E the population was suddenly reduced down to the size shown at time D. Draw a curve showing how population would resume growing. Now do the same, imagining that at time F it was suddenly reduced to the level it was at time E.

11. Show how the population would grow if carrying capacity of the population were G individuals.

Survivorship Curves Use Figure 3 in answering the next questions.

12. For which of these curves is the likelihood of survival low at young ages but fairly high at older ages?

13. Describe in words the difference in timing of mortality between curves A and B.

14. Try to sketch a survivorship curve for a species that experiences highest mortality halfway through its lifespan (a midlife crisis?)

15. Below is a list of AGES AT DEATH in (A) a lizard population and (B) an acanthocephalan population. Which of the survivorship curves in Figure 3 best matches these data? Be able to explain your answer.

• (A) Ages at death: 1, 3, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8.
• (B) Ages of death: 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 5, 9.

16. Compare the two survivorship curves below. What biological explanation could account for the difference in shape between them?

Population Estimation

17. In June 1996 you mark 30 coyotes in the Tucson Mountains. In September you go back and catch 100 individuals, of which 10 are marked. How large do you estimate the population is? What assumptions have you made, in making this estimation?

18. Why is mark/recapture an ineffective method for estimating plant population sizes? What are some better measures of estimation, for plants?

19. What are some alternate ways of measuring the human population of the US? What are their benefits and drawbacks?