Questions for Robert May
article
Biological Populations with non-overlapping
generations. Science 186: 645-647.
Due Sept 11, 2007
Write several sentence answers to the following questions. Bring your typed answers to class and be prepared to discuss them. Note that these are questions to think about - there is not necessarily a single answer to them.
Try not to get bogged down in the mathematical aspects of this paper - May is trying to explain to non-mathematicians that ecological systems may have very interesting behaviors.
Make notes on your typed answers during the discussion and hand in
your annotated answers at the end of class.
What kinds of populations are best modeled with (a) differential equations, and (b) difference equations. What might be some real world examples of such populations?
What does May consider to be the simplest equation for a single species? Draw a graph of numbers versus time for the differential equation version of this.
How does May's equation 2 compare to the logistic equation? What is similar and what is different?
What behavior did May observe in Equation 2? What "numerical experiments" did he do in his analysis?
Look at Table 1 and Figure 1. What does May mean by the terms (a) stable equilibrium, (b) 2-point cycle, (c) 4-point cycle?
May says on p 645 "For population biology in general and for temperate zone insects in particular, the implication is that even if the natural world were 100 percent predictable, the dynamics of populations with 'density dependent' regulation could nonetheless in some circumstances be indistinguishable from chaos, if the intrinsic growth rate r were large enough." What is May trying to say here, and why do you think ecologists were interested?
From your reading of Birch's paper, is it reasonable to expect natural populations to have a value of r large enough to cause the interesting behavior discussed by May?
Do you think May's 'r' is the same as Birch's 'r' or 'R0', and does it make a difference to your previous answer? When you were reading Birch, did the 'r' or 'R0' values seem large or small? (On p 16 Birch talks about Nt+1/Nt = er = lambda. For these Non-overlapping generation populations discussed by May, perhaps lambda is really what is meant by "r". See if er for Birch's Calandra is large enough to cause the interesting behavior.)
What point is May trying to make in Figure 1 parts d, e ,and f? Look carefully at the figure legend. See also the 2nd paragraph in the center column of p 646.