Evolutionary models

I have found a new hobby: simulating evolutionary models. Mostly I do it in the train on my way to and from work. Yes, you can do a lot in 1 hour a day! And it’s quite captivating.

When I tell people about this, they ask me how I make simulations. Here’s how.

Yes, I program them myself. I use Octave, a free and open-source environment similar to Matlab. Octave supports a large part of the Matlab syntax and library. It also has its own extensions, such as C-like operators. I like to use ++ and +=, but today’s example will be Matlab-compatible.

The example simulates the survival of the fittest, and is only 40-odd lines long.

Here we go:

worldCapacity = 100;
survivalScores = [1 1.2]; % of the 2 types
initNum = worldCapacity;
init2Ratio = 0.1; % The ratio of 2's initially
meanNumChildren = 1;
maxNumChildren = 3;

Our world has a limited capacity — more about that later. There will be two kinds of cells, type 1 and type 2. As you see, type 2 is slightly better at survival.

First, we create our population:

% init
population = [];
for i = 1 : initNum
  population(i) = (rand() < init2Ratio) + 1;

rand() returns a random number between 0 and 1. rand() < p is true with probability p. rand(i, j) returns an i x j matrix.

As you see, initially, only 10% of the cells are type 2.

generation = 0;

ratios = [];
while 1
  generation = generation + 1;

  % show
  ratios(generation) = length(find(population == 2)) / length(population);
  plot(1 : generation, ratios);

  if kbhit(1)

I use kbhit() because Octave doesn’t always handle Ctrl-C well.

  children = [];
  for cell = population
    for i = 1 : maxNumChildren
      if rand() < meanNumChildren / maxNumChildren
        children(end + 1) = cell;
  population = [population, children];

As you see, reproduction is asexual. With maxNumChildren large enough, the distribution becomes close to Gaussian, but that’s not today’s point.

  scores = survivalScores(population);
  prob = scores * (worldCapacity / length(population));
  survive = rand(1, length(population)) < prob;
  population = population(survive);

Our world has limited resources and can host only about worldCapacity cells.  So they have to compete for survival. There is no absolute survival in this model, i.e., if a cell is in the world alone, it won’t die. The reason a cell can die is that someone else is better at getting resources from the environment.

Most of the time I don’t use absolute survival at all. The reason to use competitive survival rather than (only) absolute survival is that with absolute survival, unless you calibrate the probabilities very well, you population will either die out or explode, making your simulation slow and eating up too much memory. The other reason of course is that in the real world, resources are indeed limited.

Competitive survival works like this: Each organism gets a survival score. They are then all multiplied by the same multiplier, such that their sum becomes worldCapacity. The products are survival probabilities. Of course, if a “probability” is greater than 1, the organism surely survives. This may be a little unnaturalistic and also gives the population a bias towards an underpopulated world.

What next? The next step is to download the whole program and run the simulation!


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3 Responses to “Evolutionary models”

  1. shlomi Says:

    These evolutionary models you are playing with are simple models of ALife. My Thesis is in the field of Evolutionary Robotics / Multi Objective Optimization / Competitive Coevolution. We can share some ideas if you want.

  2. Lev Says:

    Never knew about ALife, thanks. My inspiration was “The Selfish Gene”.
    Did you actually build any robots for the thesis?

  3. shlomix Says:

    Hi Lev,
    I just entered WorldPress.com for another blog I’m watching and saw that you left me a comment a long time ago.
    The answer is no. I don’t build phisical robots but my simulated robots subscribe to the laws of physics.

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