Question

I am new to Matlab. I was reading this code snippet, but in some parts (marked with asterisks) I don’t understand what it means, so if anybody could help would be very much appreciated

function [A1nmb] = moran(initsize, popsize) 
% MORAN generates a trajectory of a Moran type process 
%  which gives the number of genes of allelic type A1 in a population 
%  of haploid individuals that can exist in either type A1 or type A2.
%  The population size is popsize and the initial number of type A1 
%  individuals os initsize. 
%  Inputs: initsize - initial number of A1 genes
%          popsize - the total population size (preserved)

if (nargin==0)
  initsize=10;
  popsize=30;
end

A1nmb=zeros(1,popsize);
A1nmb(1)=initsize;

**lambda = inline('(x-1).*(1-(x-1)./N)', 'x', 'N');
mu = inline('(x-1).*(1-(x-1)./N)', 'x', 'N');**

x=initsize;
i=1;
while  (x>1 & x<popsize+1)
  if (lambda(x,popsize)/(lambda(x,popsize)+mu(x,popsize))>rand)
   x=x+1;
   A1nmb(i)=x;
  else
   x=x-1;
   A1nmb(i)=x;
  end;
  i=i+1;
end;
nmbsteps=length(A1nmb);
***rate = lambda(A1nmb(1:nmbsteps-1),popsize) ...
        +mu(A1nmb(1:nmbsteps-1),popsize);***  

**jumptimes=cumsum(-log(rand(1,nmbsteps-1))./rate);**
jumptimes=[0 jumptimes];

stairs(jumptimes,A1nmb);
axis([0 jumptimes(nmbsteps) 0 popsize+1]);

Answer 1

The first line you marked

lambda = inline('(x-1).*(1-(x-1)./N)', 'x', 'N');

creates something called an inline function. It is equivalent to defining a mathematical function. Example:

y = inline('x^2')

would allow you to do

>> y(2)
4

This immediately explains the second line you marked.

rate = lambda(A1nmb(1:nmbsteps-1),popsize) ...
    +mu(A1nmb(1:nmbsteps-1),popsize);

will compute the value of the function lambda(x,N) at x = A1nmb(1:nmbsteps-1) and N = popsize.

I will say immediately here that you should take a look at anonymous functions, a different format used to accomplish the same as inline. Only, anonymous functions are generally better supported, and usually a lot faster than inline functions.

Then, for the final line,

jumptimes = cumsum(-log(rand(1,nmbsteps-1))./rate);

is a nested command. rand will create a matrix containing pseudorandom numbers, log is the natural logarithm ("ln"), and cumsum creates a new matrix, where all the elements in the new matrix are the cumulative sum of the elements in the input matrix.

You will find the commands doc and help very useful. Try typing

doc cumsum 

or

help inline

on the Matlab command prompt. Try that again with the commands forming the previous statement.

As a general word of advice: spend an insane lot of time reading through the documentation. Really, for each new command you encounter, read about it and play with it in a sandbox until you feel you understand it. Matlab only becomes powerful if you know all its commands, and there are a lot to get to know.