Biology 570

Discussion of Constantino, Desharnais, Cushing and Dennis 1997

Discussion Sept 18, 2007

Try not to be overwhelmed by the math, but rather look at how it relates to the biology. 

Bring typed answers to class, with room to make annotations during the discussion.

1.      What do you know about the organism in this study?  Is it similar to one you have read about before? 

2.      What general kinds of methods did the authors use in this study?  What are they trying to show in this paper?

3.      The authors say (Equation 1) that larvae in the future (L_t+1) are dependent upon the number of adults alive today (A_t).  Crudely from Equation 1, one could describe maximum population growth as L_t+1=bA_t .  From the references and notes at the end of the paper, find out what value the authors used for b.  Does this value make sense, based on what you have read before in Birch and May?  Why or why not?

4.      The authors say (Equation 3) that adult survival from one time step to the next is described by: A_t+1 = A_t (1-m_a) .  From the notes at the end of the paper, what is the value of m_a (adult mortality rate)?  Calculate an adult survival distribution l_x by the following method (from the crude version of adult survival above):

l₁ = 1.00 (1-m_a)

l₂ = l₁ (1-m_a)

l₃ = l₂ (1-m_a)

l₄ = l₃ (1-m_a)

How does this compare to the lx distribution in Birch’s paper, which was based on Tribolium?  In the experiments the authors used m_a=0.96 (p 390 left column); does this make sense, given the value for m_a measured in the control cultures, that you used in your calculations above?

5.      Briefly describe           i. Stable equilibria         

ii. Periodic cycles

iii. Quasi-periodic cycles

iv. Chaos

            Are these ideas any different from what you encountered in May’s paper?

6.      What is a “dynamical transition?”  Is there anything you read in May that sounds similar?  In the Constantino paper, what life history feature of the organism causes a dynamical transition?

7.      What life stages do the authors follow in the LPA model?  What life stage of the organism is omitted?  Does this omission make the model more or less convincing?  Why do you think they ignored this life stage?

8.      Describe the dynamics of the control culture.  Do you think it was a proper control?  Does it differ from the other experimental treatments?  Why or why not?

9.      Does the dynamical behavior of the experimental cultures change in the different experimental treatments?  What info in the paper led you to your conclusion?

10.  Describe the initial conditions in the experiment.  Describe the habitat in the experiment.

11.  How did the authors manipulate mortality and cannibalism? (look at the 1^st and 2^nd columns of p 390 and the last paragraph of the paper) If the authors had run the identical experiment with 3 kinds of poker chips in jars rather than live organisms, do you think they would they have obtained the same dynamic behavior?  Why or why not?