Login

Create Account
+14156709189
info@expertsmind.com
Submit Homework/Assignment
Get quote & make Payment
Get Solution
Optimal foraging theory, MATLAB in Mathematics
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 “patch” to “patch” across a landscape, depleting the food in each patch the longer they stay there. Patches could be individual plants with nectar in the plants flowers that is eaten by bees, or individual plants with seeds that are eaten by birds. One question in foraging theory is to deduce the rules for when an individual will leave one patch to search for a new patch. Numerous complications arise in this, but we will consider only a very simple situation, in which we have the following assumptions:
(1) There are no interactions with other foragers, so depletion of food in a patch is due only to the single forager under consideration.
(2) There is no randomness in the environment, so that each patch is identical in terms of how much resource it has before foraging starts.
(3) Once the patch is depleted it stays depleted. (4) There are many patches available. (5) The traveltime of the forager between patches is constant.
(6) The food available in the patch decreases exponentially as the forager spends time there.
467
468 Unit 6 Derivatives
Let t be the time spent in a patch before leaving, M be the time it takes to move between two patches, and K be the amount of food in a patch before any food has been eaten. Then the total amount of food eaten in a patch is
K(1  ect) (27.1)
where c is the decay rate of available food in a patch once foraging starts. In Equation 27.1 ect represents the proportion of food left in the patch after the forager has eaten from the patch over time t. Thus, 1  ect represents the proportion of food eaten from the patch over time t. When we multiply this term by K (the total amount of food in the patch before any is eaten) we obtain the amount of food eaten from the patch after the foraging is complete.
We define the one foraging bout as the time spent moving to the patch plus the time spent foraging in that patch. Thus, the total time of one foraging bout is
M + T. The food intake rate is the amount of food consumed divided by the time spent
consuming the food, i.e.
K ??1  ecT ??
(27.2)
T+M Using the example from Section 25.6 as an example, complete the following.
1. Think of Equation 27.2 as a function of the time spent in a patch before leaving, t. Take the first derivative of this function with respect to t. Notice, that when the derivative is set equal to zero, you cannot explicitly solve for t. Write an equation, in terms of t, c, and M that can be graphed and used to find the critical points.
2. Use Matlab to estimate the critical point of the derivative of Equation 27.2, using c = 4 and M = 10. Based on the graph you produced to find the value of the critical point correct to two decimal places. Explain why you know that a local maximum occurs at this point.
3. The critical point found in part 2 is the optimal time a forager should spend foraging in one particular path. Explain why it makes sense biologically that this point is a local maximum.
4. Repeat part 2 but use M = 1, 5, 15, and 20. Does the graph in each case indicate that the critical point is still a maximum? How do the optimal foraging times in these cases compare to the optimal foraging time you found in part 2.
5. Repeat part 2 but use c = 0, 2, 4, 6, 8, 10. Does the graph in each case indicate that the critical point is till a maximum? How to the optimal foraging times in these cases compare to the optimal foraging time you found in part 2.
Chapter 27 Unit Projects 469
6. In Matlab, create the following mfile.
OptimalForaging.m 1 M = [1 5 10 15 20];
2 c = [0 2 4 6 8 10]; 3z= 4 5
6 7
surface(c,M,z); xlabel(’c’); ylabel(’M’);
For z, construct a matrix where each column corresponds to an M value, (1, 5, 10, 15, 20), each row corresponds to a c value, (0, 2, 4, 6, 8, 10), and the value of each entry in the matrix is the corresponding optimal foraging time. For example, the optimal foraging time found in part 2 would be the entry in row 3, column 3. You already have several of the values from parts 2, 4, and 5. You will need to use Matlab to determine the rest of the values. The resulting matrix z should be a 6 × 5 matrix.
Once you have constructed matrix z, run the mfile OptimalForaging.m. A plot
will be generated. Use the button to rotate the graph to look at the surface plot from different angles. Describe what this 3dimensional surface plot is showing you. What are the advantages and disadvantages of viewing a 3d plot such as this?
Posted Date: 11/5/2012 5:11:03 PM  Location : United States
Ask an Expert
Related Discussions:
Optimal foraging theory, Assignment Help, Ask Question on Optimal foraging theory, Get Answer, Expert's Help, Optimal foraging theory Discussions
Write discussion on Optimal foraging theory
Your posts are moderated
Write your message here..
Related Questions
Fprintf function  file function, fprintf function  File function: Th...
fprintf function  File function: The fprintf function really returns the number of bytes which was written to the file, therefore if you do not want to see that number, suppr
Illustration of a recursive function, Illustration of a recursive function:...
Illustration of a recursive function: illustration is of a recursive function which does not return anything, but simply prints. The below function prtwords receives a sentenc
Strvcat function  concatenation, strvcat function  concatenation: Th...
strvcat function  concatenation: The function strvcat will concatenate it vertically, that means that it will generate a column vector of the strings. >> strvcat(fir
Program of builtin factorial function, Program of builtin factorial funct...
Program of builtin factorial function: Calling this function yields similar result as the builtin factorial function: >> fact(5) ans = 120 >> factorial(
Strcat function  concatenation, Strcat function  Concatenation : The ...
Strcat function  Concatenation : The strcat function, though, will eliminate the trailing blanks from strings before concatenating. Note that in these illustrations, the trail
Symbolic expression, Symbolic Expression The solve function solves an e...
Symbolic Expression The solve function solves an equation and returns the solution(s) as symbolic expressions. The answer can be converted to numbers by using any numeric funct
Types of userdefined functions, Types of Userdefined Functions: We k...
Types of Userdefined Functions: We know how to write a userdefined function, stored in an Mfile, which computes and returns one value. This is merely one type of the functi
Use of logical vector, Use of logical vector: Determine how many eleme...
Use of logical vector: Determine how many elements in the vector vec were greater than 5, the sum function can be used on the resulting vector isg: >> sum(isg) ans =
Illustration of variance, Illustration of Variance For illustration, fo...
Illustration of Variance For illustration, for the vector [4, 6, 1, 5], there are n = 4 values therefore n  1 is 3. The mean of this data set is also 4. The variance will be
Plot types  plot functions, Plot types: Besides plot and bar, there a...
Plot types: Besides plot and bar, there are another plot types like stem plots, histograms, stem plots, area plots and pie charts, and also other functions which customize the
Assignment Help
Accounting Assignment Help
Economics Assignment Help
Finance Assignment Help
Statistics Assignment Help
Physics Assignment Help
Chemistry Assignment Help
Math Assignment Help
Biology Assignment Help
English Assignment Help
Management Assignment Help
Engineering Assignment Help
Programming Assignment Help
Computer Science Assignment Help
IT Courses and Help
ExpertsMind Services
Online Tutoring
Projects Assistance
Exam Preparation
Coursework Help
Programming Courses
Engineering Courses
Why Us ?
~Experienced Tutors
~24x7 hrs Support
~Plagiarism Free
~Quality of Work
~Time on Delivery
~Privacy of Work