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Spatial Altruism

altruism/altruism_model.py is a direct evolutionary altruism model rather than an ecological predator-prey system.

It models a patch-based population in which:

  • each grid cell is empty, selfish, or altruistic,
  • altruists provide a local benefit but pay a private cost,
  • selfish patches receive the local benefit without paying that cost,
  • the next occupant of each patch is chosen by a local weighted lottery.

Static Run Snapshot​

The figure below is generated from a fixed Python run of the current NumPy implementation. It shows the initial patch state, the patch state after 200 updates, and the population counts across time.

GitHub Module

Spatial altruism overview

Patch States​

Each patch has one of three states:

  • altruist: pink
  • selfish: green
  • empty: black

The model is spatial because each patch interacts only with its own plus-shaped neighborhood:

  • the focal patch itself,
  • the patch above,
  • the patch below,
  • the patch to the left,
  • the patch to the right.

So each local calculation uses exactly 5 patches.

Local Benefit Rule​

The altruism benefit at one patch is:

altruism_benefit = benefit_from_altruism × (benefit_out_self + sum_of_neighbor_benefit_out) / 5

Variable meanings:

  • altruism_benefit: total social benefit currently available at the focal patch
  • benefit_from_altruism: strength of the positive externality produced by altruists
  • benefit_out_self: 1 if the focal patch is altruist, otherwise 0
  • sum_of_neighbor_benefit_out: number of altruist contributors in the four-neighbor set
  • 5: the focal patch plus its four neighbors

This means altruists create a benefit that is local and shared.

Fitness Rule​

Fitness depends on patch type:

  • altruist patch: fitness = (1 - cost_of_altruism) + altruism_benefit
  • selfish patch: fitness = 1 + altruism_benefit
  • empty patch: fitness = harshness

Variable meanings:

  • fitness: the reproductive weight a patch contributes to nearby lotteries
  • cost_of_altruism: private cost paid only by altruist patches
  • harshness: baseline weight assigned to empty patches

This is the core social dilemma:

  • altruists help the neighborhood,
  • selfish patches enjoy that help too,
  • but only altruists pay the direct cost.

Neighborhood Lottery​

After each patch computes its fitness, the focal patch collects three local totals:

  • alt_fitness: summed fitness contributed by altruist patches in the focal plus-neighborhood
  • self_fitness: summed fitness contributed by selfish patches in the focal plus-neighborhood
  • harsh_fitness: summed fitness contributed by empty patches in the focal plus-neighborhood

The normalized lottery weights are:

  • alt_weight = alt_fitness / fitness_sum
  • self_weight = self_fitness / fitness_sum
  • harsh_weight = (harsh_fitness + disease) / fitness_sum

with:

fitness_sum = alt_fitness + self_fitness + harsh_fitness + disease

Variable meanings:

  • alt_weight: probability mass for the next patch becoming altruist
  • self_weight: probability mass for the next patch becoming selfish
  • harsh_weight: probability mass for the next patch becoming empty
  • disease: extra pressure toward emptiness, even when no empty neighbor strongly contributes

The next generation at each patch is then sampled from those weights:

  • altruist if the draw lands in alt_weight
  • selfish if the draw lands in self_weight
  • empty otherwise

Why This Belongs Under Evolved Cooperation​

This model is on equal footing with cooperative hunting because both models study cooperation through inherited variation and selection across generations.

The difference is the mechanism:

  • Spatial Altruism studies a direct altruism-versus-selfishness social dilemma in a patch lottery
  • Predator-Prey-Grass Cooperative Hunting studies selection on an inherited hunting-investment trait inside an ecological food web

So they are complementary examples of evolved cooperation at different levels of abstraction:

  • one minimal and spatial,
  • one ecological and agent-based

References​