Bio 481 - Problem Set 2 - Life History

1. Implement Schaffer's (1974) simple model of the evolution of reproductive effort. Assume that the total amount of enery available (E) is constant and allocated either to reproduction (B) or to maintenance and growth (influences P, survival), such that B and P are negatively related, i.e. exhibit a phenotypic tradeoff. Derive and plot different kinds of functions for B and P vs. E with biological explanations for the shape of your functions. (Try exponential shaped, saturating, and sigmoidal curves.) Assuming lambda= B(E) + P(E), plot lambda vs. E and determine the optimum E (that maximizes lambda).
   


2. Modify the model to compare optimal reproductive effort in environments that differ in overall favorability. What aspects of the model could be changed and how.
   


3. Choose your favorite organism and describe the steps to test the model you developed in questions 1+2 - what kinds of data are needed and how would you analyze them.
   


4. Implement the Smith-Fretwell model of offspring size-number tradeoffs and use it to ask how the optimal balance between number and size of offspring should change when the environment becomes more favorable (this could effect either the toal resources available for reproduction (Ep) and/or the offspring fitness function (Wy vs. Ey).
   

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