% island1.m
% Markov chain model for colonization-extinction
%                       2/22/03     SG
clear all
close all

% PARAMETERS

T = 500;        % number of generations to run
p_col = 0.2;    % probability of colonization
p_ext = 0.1;    % probability of extinction

% INITIAL CONDITIONS

X(1) = 0;       % island is empty initially

% MAIN PROGRAMM

for t = 1:T
    
    if X(t)==0             % if island is empty       
        if rand < p_col    % colonization with probability p10
            X(t+1)=1; 
        else               % no change otherwise
            X(t+1)=0;
        end          
    else                   % if island is colonized
        if rand < p_ext    % extinction with probability p01
            X(t+1)=0; 
        else               % no change otherwize
            X(t+1)=1;
        end   
    end
end

% GRAPHICS

plot(X,'o')
xlabel('year')
ylabel('island state X')
axis([0 T -.1 1.1])

% ADDITIONAL STATISTICS

X_mean = mean(X)           % overall frequency of being occupied