1. Population Simulation Using MatLab Jie Ma EPS 109 Professor. Militzer

2. Fox vs. Rabbit 1. Predator-prey Function: (Lab3) Predator: Fox Prey: Rabbit 2. Solve Differential Equation (Lab 13) Runge Kutta Method Stable when dx/dt = 0; dr/ dt = 0;

3. Population changes How to visualize ? Red: Fox Blue: rabbit Reference the Random walk Lab5: 1.Generate a white matrix to represent the total population 2.Using Red grad to represent fox population and blue grad to represent the rabbit population 3.Use random number to generate a random location of Fox or Rabbit.

4. Red for Fox and Blue for rabbit When the rabbit population increase, the fox population increase, and rabbit population decrease. for j = 1:numFox %calculte the index of the location while 1 randloc = round(rand()*maxPoP); rand_row = round(mod(randloc,sn))+1; rand_col = round(randloc/sn)+1; %if the poistion has already be not been taken, reject to move if(A(rand_row,rand_col,2) == 255) A(rand_row,rand_col,1) = 255; A(rand_row,rand_col,2) = 0; A(rand_row,rand_col,3) = 0; break end

5. Peppered Moth evolution X for bird: dx/dt = (-d +e * y+ et *z) * x; Y for White Moth: dy/dt = (kr*( m –y )- c * x) *y; Z for Blue moth: dz/dt = (kt*(mt- z)-ct* x )* z; C > Ct

6. Background color : gray Yellow: white peppered moth Black: black peppered moth Their dark color blend them in the polluted trees and makes it difficult to find by their predators. As a result they are more likely to survive and reproduce. As a result, the black moth population increase.