4.1.5 Inner Loop: Building the Next Generation

The key part of the simulator is the inner loop that builds a new generation from the current generation . Recall that the current generation will be represented by an array named g, and the next generation by an array ng.

Let be the number of individuals in g. In the early stages of the simulation will be the same as , the carrying capacity, since all individuals in a new generation will survive. Toward the end of the simulation will be smaller than .

Recall also that on average each individual is able to reproduce times, where is reproductive factor, another one of the input parameters. A population of individuals will thus produce, on average, offspring.

To create the next generation, we need to simulate the creation of individuals, add new mutations to the individuals, and then select random survivors to form the new generation. If the number of survivors is less than , then all survivors go into the new generation. Extinction will occur when none of the new offspring survive.

is often very large compared to ; in the extreme cases is 2 and is . In these situations it does not make sense to create all potential offspring only to draw at random to fill up the new generation. Instead, we use a loop that iterates a maximum of times and exit the loop as soon as survivors are found. Note that during the meltdown phase fewer than offspring will survive to form the next generation and the loop will exit after generating all potential offspring.

The outline of the build_next_generation procedure is:

  limit = n * r;			/* max number of iterations */
  for (i = 0; i < limit; i++) {
    j = random() % n;			/* select a random parent */
    mom = g[j];
    kid = mom + poisson(mu);		/* kid is a clone of mom */
    if (survivor(kid)) {		/*   plus new mutations */
      ng[nkids] = kid;
      nkids = nkids + 1;
      if (nkids == k)			/* exit loop if the new gen */
        break;				/*   now has k individuals */
    }
  }