Assume that the grouse play the same role as the rabbits.

Assume that food supply for both rabbits and grouse is

unlimited.

Assume that foxes do not prefer one prey over the other.

Fox population factors Fox birth rate:BRF (frac/fox/year) Fox death rate:DRF Fox growth rate:GRF = BRF-DRF

Rabbit population factors Rabbit birth rate:BRR Rabbit death rate:DRR Rabbit growth rate: GRF = BRR-DRR

g(t):population of grouse BRG,birth rate of grouse DRG,death rate of grouse EFG,effect of fox upon grouse EGF, effect of grouse upon fox

So,in MatLab what I am assuming is that the for loop I made either the dr, df or dg equation is incorrect because the parameters, initconds, timedata, and the output of the function is given so somewhere in the for loop is incorrect so I need help:

FUNCTION

function [ rvec,gvec,fvec ]= PredatorPrey_4_fcn(parameters,timedata,initconds)

% Copy and paste your code here

%Parameters 1-7

GRR=parameters(1);

EFR=parameters(2);

GRG=parameters(3);

ERG=parameters(4);

GRF=parameters(5);

ERF=parameters(6);

EGF=parameters(7);

%Initconds 1-3

rinit1=initconds(1);

finit1=initconds(2);

ginit1=initconds(3);

%timedata 1-3

tinit=timedata(1);

tfinal=timedata(2);

delt=timedata(3);

t=tinit:delt:tfinal;

%output

rvec=rinit1;

fvec=finit1;

gvec=ginit1;

%create for loop for fox/rabbit population (THIS PART I BELIEVE IS WRONG)

for i=1:length(t)-1

dr=(GRR*rvec(i)-((EFR*fvec(i))*rvec(i)));

df=(GRF*fvec(i)+((ERF*rvec(i))*fvec(i))+(EGF*gvec(i))*fvec(i));

dg=(GRG*gvec(i)-((ERG*fvec(i))*gvec(i)));

rvec(i+1)=rvec(i)+dr*delt;

fvec(i+1)=fvec(i)+df*delt;

gvec(i+1)=gvec(i)+dg*delt;

end

rvec=rvec'

fvec=fvec'

gvec=gvec'

end

CODE TO CALL YOUR FUNCTION

% Below is a script that will execute and plot your function for some given sample parameters.

% Try adjusting the parameters to see if the model behaves as you would predict

GRR4= 0.4;

EFR4= 0.032;

GRG4= 0.4;

EFG4= 0.032;

GRF4= -1.0;

ERF4= 0.02;

EGF4= 0.02;

tinit= 0.;

tfinal= 60.;

delt= 0.05;

rinit4= 35;

ginit4= 25;

finit4= 20;

parameters4= [GRR4,EFR4,GRG4,EFG4,GRF4,ERF4,EGF4];

initconds4= [rinit4,ginit4,finit4];

timedata4= [tinit,tfinal,delt];

[rvec,gvec,fvec]= PredatorPrey_4_fcn(parameters4,timedata4,initconds4);

hold on

plot(rvec)

plot(fvec,'r')

plot(gvec,'g')

xlabel('step #')

ylabel('population')

legend('rvec','fvec','gvec')

hold off

Below is the original correct code that only involved foxes and rabbits, not adding geese

FUNCTION

function [rvec,fvec]=PredatorPrey_1_fcn(parameters,initconds,timedata)

% Copy and paste your code here

%Parameters 1-4

GRR=parameters(1);

EFR=parameters(2);

GRF=parameters(3);

ERF=parameters(4);

%Initconds 1 & 2

rinit1=initconds(1);

finit1=initconds(2);

%timedata 1-3

tinit=timedata(1);

tfinal=timedata(2);

delt=timedata(3);

t=tinit:delt:tfinal;

%output

rvec=rinit1;

fvec=finit1;

%create for loop for fox/rabbit population

for i=1:length(t)-1

dr=(GRR*rvec(i)-((EFR*fvec(i))*rvec(i)));

df=(GRF*fvec(i)+((ERF*rvec(i))*fvec(i)));

rvec(i+1)=rvec(i)+dr*delt;

fvec(i+1)=fvec(i)+df*delt;

end

rvec=rvec'

fvec=fvec'

end

CODE TO CALL YOUR FUNCTION

% Below is a script that will execute and plot your function for some given sample parameters.

% Try adjusting the parameters to see if the model behaves as you would predict

GRR= 0.4;

EFR= 0.032;

GRF= -1.0;

ERF= 0.02;

tinit= 0.;

tfinal= 60.;

delt= 0.05;

rinit1= 30;

finit1= 20;

parameters1= [GRR,EFR,GRF,ERF];

timedata1= [tinit,tfinal,delt];

initconds1= [rinit1,finit1];

[rvec,fvec]= PredatorPrey_1_fcn(parameters1,initconds1,timedata1);

hold on

plot(rvec)

plot(fvec,'r')

xlabel('step #')

ylabel('population')

legend('rvec','fvec')

hold off

(Remember to be done in MATLAB language)