Questions on Sibly et al. (2005)

1. The logistic equation, dN/dt = r N (1 - N/K), is composed of two functional forms, N, and r (1 - N/K).  Graph the latter.  You may want to assume that r = 1.0 and that K = 100.



2. What is figure 1 illustrating? What is the difference between the left hand and right hand panels? How many data points are there on the left and right panels of figure 1? Are they the same? Why or why not?


3. Explain in biological terms what happens to the effective value of r as N increases from 0 to K.  (Note: The authors call the effective growth rate pgr).  What are the consequences of this change for population growth?

4. The theta-logistic is very similar to the more familiar logistic equation.  Notice that if theta = 1.0 then we recover the familiar logistic equation.  Graph the effective growth rate of the theta-logistic for theta = 2, and theta = 0.5.  List the values of r (1 - (N/K)^theta) in a table.  Assume that N = 0, 10 , 20 , 30, 40, 50, 60, 70, 80, 90, 100.  Again assume that r = 1.0 and that K = 100.  You may want to use a spread sheet, although a calculator will work too.  In biological terms explain the effect that theta has on the effective growth rate.

5. Sibly et al say, "Mechanistically, the value of theta must depend on the ways that animals interact at different densities."  What are the authors trying to say?

6. The authors say that theta was significantly different from 1 in 613 of the 1780 cases examined, and was less han 1 in 581 cases and greater than 1 in 32 cases. How does this relate to Fig 3? Which cases on these graphs are most likely to be significantly different from 0?

7. Figure 3 shows estimated values of theta for mammals, birds, fish, and insects.  From what you have learned in the previous questions, and from reading the paper, what can you say about how the effective growth rate of species in these major taxonomic groups respond to population density?  Compare the responses.  Is it what you would expect?

8. The authors argue that there are broad implications from their conclusion that the most common relationships between growth rate and density are concave. How does their logic work? Draw a diagram to illustrate your explanation.