Safarzynska (2013) The coevolution of culture and environment

Safarzynska, K. (2013). The coevolution of culture and environment. Journal of Theoretical Biology, 322, 46-57. 

The model:

• Individuals are organized into groups, each with access to a renewable resource.
• Cooperators and punishers employ a low-harvesting strategy.
• Defectors employ a high-harvesting strategy.
• Imitation:
• Individuals imitate strategies which generate above-average payoffs.
• Sustainability requires that the total harvest is less than the resource growth rate.
• Weather shocks accelerate resource depression and eliminate groups with many defectors.
• Two types of between-group interaction
• Resource conflict: A share of the resource from the losing group is transferred to the winning group. The probability of winning is related to the group's total resources (returns to scale). 
• Harvest sharing: A group is matched with another group for a long-term friendship. With a certain probability, a fraction of harvests is transferred from the group with more to the one with less.

Details

• The amount of harvesting (high vs. low) is a percentage of the total resources available to a group.
• Resources replenish according to a logistic function, plus a weather shock variable drawn from a normal distribution with some probability. Weather shocks are always negative.
• If a group runs out of resource, they collapse.
• The empty spot is populated by a replica of a random group from the population, and the resource level is reset to its initial value (group-level replication!). 

There is a lot of mathematical analysis that is pretty dry, and not particularly revelatory. There is also a bunch of simulation studies. These also aren’t particularly enlightening, but I will highlight the major results.

Major results

• Weather shocks basically kill off groups with lots of defectors.
• The frequency (and the size) of weather shocks increases the frequency of low-harvesting individuals (cooperators and punishers), and also increases the number of cases of resource exhaustion.
• Resource conflict leads to the highest frequencies of low-harvesters, followed by baseline (no inter-group interactions), followed by harvest sharing.
• Low-harvesters also increase with group size. This is because the larger the group, the more harvesters there are. This increases the chances that the total harvest in a group will exceed the resource growth rate.