BEFORE YOU BEGIN: make sure you have 6 different pages of questions. Put your name of the first page and your social security number on each other page.

BRIEF ANSWER: for multiple choice, circle the one best answer.  Fill-in answers should not require more than about 9 words at most.  If asked to draw a graph, be sure the axes are labeled (if they're not labeled, then label them correctly.)

1. The model of population growth that models the density dependent effect of intraspecific competition is called:

2. The model of population growth that assumes that per capita birthrates and per capita deathrates remain constant over time is called:

3. A population is evolving according to logistic growth with a time lag.  Write the formula for logistic growth with a time lag (note: BE COMPLETELY CLEAR in your writing if you show subscripts or exponents; if I can't tell whether something is in a subscript or exponent or not, I will assume it is NOT correct.)

 dN/dt =

4. A population is growing according to the equation for logistic growth with a time lag, and shows stable limit cycles. Draw this on the axes provided.

5.  Suppose the environment in which the previous population lived changed so that resources respond more quickly to changes in the population size, decreasing the length of the time lag.  The result of this change is predicted to be:
a. the population will show damped oscillations instead of stable limit cycles
b. the population will continue to show stable limit cycles, but the length of the cycle will become shorter
c. the population will show unstable oscillations instead of stable limit cycles
d. the population will continue to show stable limit cycles, but will not reach as large population sizes at the peaks of the cycles

6.  State the ecological meaning of the symbol r_m in the logistic growth equation.
 

7.-9. Two populations are growing with a maximum per capita growth rate of 0.8.  One is growing exponentially, the other logistically. The carrying capacity of the population growing logistically is 450.  On the following axes, showing per capita growth rate versus population size, plot one line that represents the population growing exponentially and one line that represents the population growing logistically.  Put the numerical values you are given in the appropriate places on the appropriate axes. Label the lines E for exponential growth and L for logistic growth.

10.  You have censused a population once a year for 8 years.  The population has been increasing in size and you suspect that it is growing exponentially.  You want to test whether it is growing exponentially, and to estimate the per capita population growth rate.  On the axes provided, draw a graph with the appropriate axes to best test for exponential growth and estimate the per capita growth rate. LABEL THE AXES to indicate what you are graphing, and draw the expected shape of the graph if population growth is exponential.

11.  Briefly state how you would estimate the per capita population growth rate from the graph you drew in the previous question.

12.-13.  Briefly state the two reasons discussed in lecture that an individual living in a foraging group could have higher food intake than a solitary individual would:

 12.
 

 13.

 Use the following information to answer questions 14 - 15.

You have a cohort life table for a species with columns x, a_x, l_x, d_x, q_x, k_x, m_x, Sl_xm_x, and S_xl_xm_x. x is measured in years, and you have information for each year, from newborns to five year olds.  All individuals died before reaching age six.  The age of first reproduction was found to be 2 years; 2, 3, and 4 year olds reproduced, 5 year olds did not.

14. You are interested in comparing the chance of mortality for newborn individuals during the years before they reproduce with the mortality of individuals who have survived to reproductive age during their reproductive period.  Which of the following is a measure of mortality that would be most appropriate to use to make this comparison?
a. l_x
b. d_x
c. q_x
d. k_x
e.Sl_xm_x

15. You calculate r for this species as Sl_xm_x/T.  The general assumption you need to make for this calculation is that:
a. the population is stationary
b. growth is exponential
c. growth is positive
d. growth is logistic
e. growth is negative

16. For a different population, you make a static life table.  For the static life table to be accurate, is assumed that:
a. the population is stationary
b. growth is exponential
c. growth is positive
d. growth is logistic
e. growth is negative

17. On the axes provided, draw a type II survivorship curve.  CORRECTLY LABEL THE AXES.

 18.  The curve you just drew indicates that:
a. the probability of mortality is highest early in life and decreases steadily throughout life
b. the probability of mortality is lowest early in life and decreases steadily throughout life
c. there is highest probability of mortality early in life; after that time, probability of mortality is much lower and remains fairly constant
d. there is low probability of mortality throughout life until old ages, when the probability of mortality increases dramatically
e. the probability of mortality remains constant throughout life.

LONGER ANSWER: Answer in the space provided.  For essay questions, provide all logical steps so that your answer would fully explain the topic to someone who did not know the answer.  For mathematical problems, show equations and work. Point value given in parentheses.

19. (6) (a) A population is growing according to the basic model of logistic growth (with no time lags and no non-linearity).  The carrying capacity is 140 and the maximum instantaneous per capita growth rate is 0.2.  At what population size is population growth maximum?  Show how you obtained your value (the formula you used).  Explain why this population size has the maximum population growth rate; you may give either a verbal or a mathematical explanation.

For parts b-c of this question, suppose that the impact of intraspecific competition on per capita population growth is non-linear in the logistic growth model, so that the population grows according to the equation dN/dt=r_mN(1-(N/K)^q)

(b) (6) For most populations that grow with a non-linear impact of intraspecific competition on population growth, would theta be greater than one or less than one?  Explain why.  For the value you determine to be more likely (greater or less than one), describe a possible scenario that would cause this form of non-linear logistic growth.

(c) (3) For the value of theta you determined to be more likely in part (b) (greater or less than one), suppose a population is growing with the same carrying capacity (140) and maximum per capita growth rate (0.2) as the population in part (a) of this question.  The number of individuals for which population growth is maximum would be:
a. less than the number for the population in part (a)
b. the same as the number for the population in part (a)
c. greater than the number for the population in part (a)

20. The following data are for two hypothetical species of toad:

	Warty Toad	Bumpy Toad
Average offspring produced per reproductive effort	20	2
Egg Size	small	large
Number of reproductive bouts during life	1	many

(a) (7) Assuming the differences between the two species result from r-K selection, how is the environment predicted to differ between the warty toad and the bumpy toad? Clearly explain why this environmental difference is expected to cause each of the three factors (offspring produced, egg size, and number of reproductive bouts per life) to differ in the way shown, based on r-K selection.

(b) (6) Suppose you have published a paper concluding that the difference between the toads is based on r-K selection.  Someone criticizes you by saying you have not considered phenotypic plasticity.  What do they mean?  Describe a way to test for phenotypic plasticity; be sure to indicate what results of this test would support a hypothesis of phenotypic plasticity and what results would not.

(c) (3) Suppose they are not subject to r-K selection OR phenotypic plasticity, but rather that one species is bet-hedging.  Which species (warty toad or bumpy toad) would be bet-hedging?

 (d) (5) Six warty toads are introduced to a new area where resources are abundance.  The population grows exponentially, and three years later there are eighty toads.  Estimate r. (Do not use any information from the table above, just the information in this part of the question.)

Answer questions e-g based on the following information.
You follow a cohort of eighty bumpy toads through their life and obtain the following life table data the following cohort life table.  NOTE: READ THE QUESTIONS below BEFORE you start to answer this question; include ONLY the columns required!
 

x	ax	mx
0	80	0
1	75	0
2	60	1
3	40	2
4	10	3
5	0

(e) (3) Calculate R0; include any required column(s) in the life table above.

(f) (4) Explain what R0 means, and state what the calculated value tells you about whether the population is increasing, staying the same size, or decreasing.

(g) (3) How long is a generation for this population? To determine this, make any required column(s) in the life table above and show your work.