By Charles Hall, Dr. John W. Day
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Extra resources for Ecosystem Modeling in Theory and Practice: An Introduction With Case Histories
105a) we see that (108) Substituting Eq. 108 for the last term in Eq. 107, we obtain (109) where (110) Equations 109 and 110 are the fundamental equations of dynamic programming. Let V (Qk) be the value of the decision variable which maximizes the right side of Eq. 109. html (1 of 2)9/3/2008 8:46:56 AM page_109 Notice that although Rk(Qk,vk)is a specified function and its value therefore known, the values of the functions, Hk and Hk+1, are not known. Thus Eq. 109 < previous page page_109 next page > If you like this book, buy it!
In policy 3 nothing is harvested until the last stage, when the entire population is removed. Similarly, in policy 4 nothing is harvested until the last stage. a Policy 1 Q(t) Time 0 h(t) 100 100 Q(t) Policy 3 h(t) Q(t) Policy 4 h(t) Q(t) h(t) 100 10 100 0 100 0 1 10 10 100 10 110 0 110 0 2 1 1 100 10 121 0 121 0 3 0 0 100 10 133 133 133 46 4 0 Total harvested Net income Policy 2 100 111 $1110 13 40 $400 100 133 $1330 46 $460 Calculations are based on Eqs. 81 to 84, which are explained in the text.
Obviously, this realistic orientation is by no means an unalloyed blessing. By striving for a faithful representation of many factors, and particularly the many distinct decision-making components which cause energy use patterns to be what they are, we abandon the comforts of more usual modeling assumptions that substantially but arbitrarily eliminate the need to consider decision-making behavior. Instead, we are forced to employ our best, although admittedly very rough, notions or observations of how the system's many decision makers act.