Implementation notes

• Structure to represent an individual

  struct individual {
    int allele;
    int phenotype;
    double fitness;
  };
  

  • Strucure member allele represents the genotype of a haploid. The value can be one of the followings:
    

    ALT	Altruist allele (=2)
    SELFISH	Selfish allele (=1)
    EMP	Empty, the site is not occupied by any individuals (=0)

  • In the haploid model, phenotype is same as its genotype allele. But the model can be easily modified for a diploid model.

• Dynamic allocation of arrays to represent the population spreading over 1 dimensional space.
  Each element of the array is struct individual

   
    popB=calloc(popSize, sizeof(struct individual));
  

• Fitness
  • DeterminePhenotypeHap(nextPop, popSize);
    Goes through each individual, and put the phenotypic values to the member phenotype of each struct individual.
  • AssignFitness(nextPop, popSize);
    Similarly, assign values to the member fitness of each struct individual.

  Fitness of an individual

  Altruist	1 + gBenefit * p - gCost
  Selfish	1 + gBenefit * p
  Empty	gColonizationDifficulty

  p is the frequencies of altruist in the neighbor (defined by gNeighborSize).

  Actually, all of the fitness was divided by 1 + gBenefit - gCost (the maximum possible fitness when gBenefit > gCost) to make it between 0 and 1.

• Stochastic population disturbance.
  • Some stochastic events (fire, a teen-ager decided to play with chain-saw, localized disease epidemic) could destroy some portion of the population. Then the population may gradually grow back
  • Every generation, there is a probability of destruction (gTragedyFreq). And a contiguous region with size DAMAGE_FRAC * (population size) get destroyed. The location of destruction is uniformly distributed (Not an appropriate model for the destruction by Godzilla).
  • An empty site surrounded by dense population is likely to be occupied immediately. An empty site in a low density area is likely to be empty in the next generation.
  • To emulate this gradual grow back, we assign ``fitness'' to empty site.
    
  • If the ``fitness'' of an empty site gColonizationDifficulty is large, the population can't recover from the damage (eventual extinction).

Results

Basic settings: Panmictic, global interaction for altruism

population size	200
Initial Frequency	0.5
neighbor size for altruistic behaviors	100
Maximal dispersal of offspring	100
Benefit (b)	0.6
Cost (c)	0.2
``Fitness'' of empty site	0.95
Probability of population disturbance	0
Damage (fraction of population size)	0.1

• Set the cost to 0, and start from various initial frequencies. After consideing the fitnesses of the two alleles, do you think that the simulation is behaving in the way you expect?

• Set the initial frequency to 0.5, and raise the cost to 0.1. What happens?

• Make the NeighborSize smaller. Can Altruist win? If so, why?

  Hint: Set NeighborSize to 1, varies the cost from 0.1 to 0.3. 50:50 chance of winning when cost is around 0.2.

• Let's make the population viscous by making gDispersal smaller.
  Set the cost to 0.2.
  Does it make any differences? Why?

  To plot, how spatial distribution changes,

  R
  
  > source("/home/progClass/src/altruism/altruism.r")
  > plot.altruism("altruism.spatial.out")
  

  altruism.spatial.out is the output of the program which shows the changes of alleles at each site. This output is only from the first repetition.

  

  Low dispersal distance:

  • Clumping of genotypes. Altruists have high fitness.
  • Local competition. Only the fitness of neighbors matter.

• The Altruists patches with high productivity can't export more individuals to the next generation.

• Let's make the disturbance. Set to the default values, except the following parameters
  

  neighbor Size = 1
  disperal = 4
  gTragedyFreq = 0.1

  Wow!! Take a look at the changes in allele distribution. Think why this make such a big differences.

  Even with higher cost (0.22), Altruist can win.