% island2.m
% Markov chain model for colonization-extinction
%                       2/22/03     SG


clear all
close all
tic
% PARAMETERS

T = 100;        % number of generations to run
p_col = 0.2;      % probability of colonization
p_ext = 0.1;      % probability of extinction

% TRANSITION MATRIX

P = [1-p_col p_col;...
     p_ext 1-p_ext];

% INITIAL CONDITIONS

x(1,:) = [1  0];       % island is empty initially with probability 1

% MAIN PROGRAMM

for t = 2:T
    
    x(t,:) = x(1,:)* P^t;
    
end

% GRAPHICS

plot(1:T,x(:,1),'d',1:T,x(:,2),'o')            % plot probability of being occupied
legend('Pr(empty)','Pr(occupied)')
xlabel('year')
ylabel('probabilities')
axis([0 T 0 1])
toc
% ADDITIONAL STATISTICS

asym_prob_occupied = x(T,2)            % asymptotic frequency of being occupied