27.1 Student Matlab Project: Optimal Foraging Theory This project requires you t

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27.1 Student Matlab Project: Optimal Foraging Theory This project requires you to use the ideas of Chapter 25 regarding maximization of a function. Here we assume that evolution has acted to generate highly efficient foragers. By highly efficient here we mean that the animals searching for food which are able to more rapidly obtain a high food intake rate (food eaten per unit time), will be more likely to survive and reproduce. Thus, if the characteristics that lead to high food intake efficiency (which may depend upon speed, visual or hearing skills, size, etc.) are heritable, then the characteristics which lead to higher efficiency will become more prevalent (increase in frequency) in the population. This area of science is called optimal foraging theory. For a readable description of this theory see David Stephens and John Krebs book Foraging Theory [60]. One of the main areas of foraging theory deals with animals which move from

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The algorithmic steps are described below: Step 1—Initialization The following variables are initialized. 1) Number of bacteria (S) to be used in the search. 2) Number of parameters (p) to be optimized. 3) Swimming length Ns 4) Nc the number of iterations in a chemotactic loop (Nc > Ns). 5) Nrethe number of reproduction. 6) Ned the number of elimination and dispersal events. 7) Ped the probability of elimination and dispersal. 8) Location of each bacterium P(p, S, 1), i.e., random numbers on [0– 1]. 9) dattract, ?attract, hrepelent, and ?repelent are given of fixed values Step 2—Iterative algorithm for optimization This section models the bacterial population chemotaxis, swarming, reproduction, and elimination and dispersal (initially, j = k = l = 0). For the algorithm updating, ?i automatically results in updating of “P”. 1) Elimination-dispersal loop: l = l + 1 2) Reproduction loop: k = k + 1 3) Chemotaxis loop: j = j + 1 These steps have been applied as given in [6]. a) For i = 1, 2, . . . , S, calculate cost function value for each bacterium i as follows. • Compute value of cost function J(i, j, k, l). Let Jsw(i, j, k, l) = J(i, j, k, l) + Jcc(?i(j, k, l), P(j, k, l)) P(j, k, l) is the location of bacterium corresponding to the global minimum cost function out of all the generations and chemotactic loops until that point (i.e., add on the cell-to-cell attractant effect for swarming behavior). • Let Jlast = Jsw(i, j, k, l) to save this value since we may find a better cost via a run. • End of For loop b) For i = 1, 2, . . . , S, take the tumbling/swimming decision • Tumble: Generate a random vector ?(i) ? RP with each element number ?m(i) [where m = 1, 2, . . . , p,] a random number on [0, 1]. • Move: let ?i(j + 1, k, l)=?i(j, k, l) + C(i) ?(i) ?T (i)?(i) Fixed step size in the direction of tumble for bacterium i is considered. • Compute J(i, j + 1, k, l) and then let Jsw(i, j+1, k, l)=J(i, j+1, k, l)+Jcc(?i(j+1, k, l), P(j+1, k, l)) • Swim: (i) let m = 0; (counter for swim length) (ii) While m

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