Question

Explain the marginal value theorem and its key assumptions. How might incorporating (a) constraints on spatial memory; and (b) variation in the discounting parameter, k, change those assumptions? ii. How do (a) cognitive constraints and (b) competing for resources affect the key assumptions of the ideal free distribution model?

Answer 1

The marginal value theorem is an optimal theory. It states that all animals must forage to obtain food. In this process a lot of energy is utilized. All animals use up the most optimal method for doing the above job. Optimal value means that they choose a method in which maximum work/output is reached by utilization of minimum energy. For this animals forage in patches.

Spatial memory is the memory of an animal which gives it the information regarding its location in space. With the help of this memory, the animal locates its food in its environment. For doing so, a cognitive map is spontaneously placed in the memory of the animal. If there are constraints on spatial memory, then the exact location of anything would not be traced properly. Then "maximum work/output would not be reached by utilization of minimum energy." So, ideal value of marginal value theorem would not be obtained.

The mathematical statement for this theorem is dE/dh = I (rate of energy acquisition in a patch).

Where, E = energy gain; h= time spent for foraging in one patch;

Please note that value of "h" further depends on how much resource is present in a patch, and "k". “k” is a parameter that determines initial slope of gain function in a patch; h is inversely proportional to k.

Now, if "k" decreases, then "h" will increase, and "I" will decrease. So, less energy will be gained from a single patch. Again the ideality of marginal value theorem will not be achieved.

*** Please post part II separately.