We used two agent-based simulation models to investigate the concepts of “cooperate for the spread” and “pay for the escape,” both were net logo models created by Dr. Susan Hanisch.
Afterward, we modified the first model to represent the concept of sharing the dispersal costs. We used the second model without modifications. Instead, we assigned definite values of some parameters that highlight the pay for the escape strategy.
First model
The original model was entitled “Evolution and patchy resource”18. She first developed it for educational purposes. It illustrates the concepts of cooperator-cheater competition, natural selection, spatial structure mechanisms, multilevel selection, and founder effects.
Changeable variables
Distance-resource-areas: the distance between the centers of the resource areas.
Size-resource areas: the size of resource areas as a radius in the number of patches.
Living costs: the costs that each agent has to deduct from energy per iteration for basic survival.
Mutation rate: The probability that offspring agents have different traits than their parents.
Evolution: the ability of agents to produce offspring.
Constant variables
The number of patches is 112 × 112 patches.
Carrying capacity per patch: Resource = 10, Agents = 1
The growth rate of the resource = 0.2
The resources on a patch regrow by a logistic growth function up to the carrying capacity: New resource level = current resource level + (Growth-Rate × current resource level) × (1 – (Current resource level/carrying capacity)).
The cost for producing offspring is ten subtracted units of energy.
The initial level of energy of agents is set at living costs.
Role of randomness
Agents are distributed randomly in resource areas at the beginning of a simulation.
Sustainable behavior is distributed randomly with a probability of percent sustainables among the initial agent population.
The order in which agents move and harvest within one iteration is random.
Agents move to a randomly selected patch if several patches fulfill the objectives.
The order in which agents produce offspring within one iteration is random.
Agents reproduce offspring with a probability of (0.0005 × Energy).
Agents place offspring on a randomly selected unoccupied neighboring patch.
Offspring mutate with a potential mutation rate.
Model processes
In each iteration, each agent moves around in random order. There are three likelihoods:
If there are no unoccupied patches in a two-patch radius, they stay on the current patch.
If there are unoccupied patches with resources amounting to more than living costs, the agents move to them.
If the resource amount is less than the living costs, the agents move randomly to other unoccupied patches.
The agents harvest the resources from separated patches to gain energy for metabolism and proliferation. If the energy level of any agent falls to zero, it dies. The cooperator type harvests half of the resource, while the greedy type consumes 99%.
The living costs are deducted from the energy amount of the agent constantly everywhere all the time. This process occurs whether an agent moves within the patch, between the patches, or even not. Therefore, the model does not consider dispersal cost explicitly.
If there is an unoccupied neighbor patch, the agent can reproduce with a probability of 0.0005 of his energy, place the offspring on the unoccupied neighbor patch, and then transfer ten units of the energy to his offspring.
Resources regrow only on resource patches. When the resource amount is more than or equal to 0.1, then it regrows. When the resource is less than 0.1, its value is set to 0.1.
Output diagrams and monitors
The average energy of agents: average energy levels of sustainable and greedy agents, resulting from resource harvest minus living costs and reproduction.
Trait frequencies: the relative frequencies of sustainable and greedy agents in the total population, resulting from mutations, different reproduction rates, and death.
Agent population: the absolute number of the total population size resulting from reproduction and death.
Modifications
In the first modification, we added a different type of cost that agents only incur when they disperse from one patch to another (in-between the patches). It is the slider entitled “dispersal costs”.
In the second modification, we added another sharing dispersal costs tool to reduce them by dividing their value by the number of included agents (flock-mates) in the identified range from the same type. It is the slider entitled “group-dispersal-range.” which is the flock mate’s areas as a radius in the number of patches. Therefore, changing the value of the group dispersal range will change the area around every agent. Accordingly, the number of its flock mates who share the dispersal costs also adjusts.
The group dispersal range is not confined to greedy agents but applies to all agents. Therefore, it represents the case of the wild-type cooperators who can also cooperate for the spread. The group dispersal range also does not only target the agents in between patches. However, it counts the agents inside and outside the patches. For example, once an agent starts its dispersion with a determined range containing ten agents, four from another type, three non-dispersal agents from the same type that existed inside a patch, and three dispersal agents from the same type outside the patches. The dispersal costs for this agent will be divided by 6.
Our assumption that non-dispersal agents at the pre-departure stage share dispersion costs with dispersal agents; seems justified because they reap mutual benefits by reducing kin competition inside patches if they promote the migrators. However, can agents remotely pay the dispersion costs? Yes. For instance, some bacterial species can trigger the migration of other species if located in their vicinity, even if the two bacterial colonies are separated by a barrier19,20 or if they are non-motile21. On the other hand, dispersion is an extended process with many factors, including escape from predators, suppression of host defense mechanisms, and production of biosurfactants to reduce surface tension to facilitate motility. Therefore, the agent’s contribution (inside/outside the patches) to support such factors is considered a shared dispersal cost.
Finally, cheaters can arise within cooperator patches by mutation or immigration. Therefore, to investigate the efficacy of migration, the mutation rate value should be 0 to cancel its effect in the meta-population dynamics.
Second model
The model is entitled “Evolution, resources, monitoring, and punishment.”22 is a simulation of a population with four types of agents competing for the same resource. It demonstrates many concepts, such as kin selection, cooperation, selfishness, public good, monitoring, punishment, sharing the costs, positive/negative frequency-dependent selection, and multilevel selection. The four agent colors and types: (1) Red: greedy, non-punishing. (2) Orange: greedy, punishing. (3) Turquoise: sustainable, non-punishing. (4) Green: sustainable, punishing.
Punishing agents can perceive other agents in their environment to some degree (perception accuracy) and react to their behavior. There are three kinds of punishment: Punishers can kill agents with greedy harvesting behavior, stop them from harvesting in the next iteration, or have them pay a penalty fee to their neighbors.
Agents have a cost (energy) to pay for, both detection and punishment, so this behavior is altruistic. Punisher agents of one type share punishment costs equally.
Changeable variables
Death rate: the probability that agents die independent of their energy level.
Carrying capacity: the maximum amount of resource units on a patch from 1 to 100.
Growth rate: the rate at which resources on patches regrow. The maximum sustainable yield is calculated based on the carrying capacity and growth rate.
Harvest-sustainable: the number of resource units harvested by sustainable agents.
Harvest-greedy: the number of resource units harvested by sustainable agents.
Perception accuracy: the probability with which punishing agents notice greedy agents.
Costs-perception: the costs in units of energy, punishing agents have to pay for perceiving other agents.
Costs-punishment: the costs as units of energy that punishing agents have to pay in each iteration to punish other agents. All punishing agents of an agent divide the costs of punishment.
Punishment: the kinds of punishing behavior that punishing agents perform.
Fine: if the kind of punishment is “pay fine”, the fine in energy units that punished agents have to pay (shared between all their neighbors).
Living costs and mutation rate: see the first model.
Constant variables
The number of patches: There are 60 × 60 patches in the world.
The initial energy level of agents is set at living costs + 1.
The initial number of resource units on a patch is set to the carrying capacity.
The resources on a patch regrow: see the first model.
Role of randomness
* In addition to items in the first model.
Agents take on their traits (harvest preference and ability to notice and punish) randomly based on the probability of percent-sustainable and percent-punishers.
The order in which punishing agents notice greedy agents within one iteration is random.
Greedy agents are noticed by punishing agents with a probability of perception accuracy.
The order in which detected greedy agents are punished within one iteration is random.
Agents produce offspring with a probability of (0.001 × Energy).
Agents die with a probability of (death-rate).
Model processes
In each iteration, each agent attempts to harvest resources from the patches it is on and the eight neighboring patches until the harvest preference level is reached, except for the punished agent with the sanction (suspend harvest once), its harvest amount = 0 in the current iteration. If the amount of resources available is lower than the amount that the unpunished agent attempts to harvest. Then, the agent moves to a neighboring unoccupied patch with the most resources after losing one energy unit as a move cost.
Punishers pay the costs of perceiving the greedy agents. The greedy neighbors have been noticed with the probability of perception accuracy. The agent lost an amount of energy as living costs. The agent dies with the likelihood of death rate or if the energy level falls to zero.
If there is an unoccupied neighbor patch, the agent can reproduce with a probability of 0.001 of its energy, place the offspring on the unoccupied neighbor patch, and then transfer half of its energy to its offspring that mutate according to the probability of the mutation rate.
Resources regrow on all patches. When the resource amount is more than or equal to 0.1, then it regrows. When the resource is less than 0.1, its value is set to 0.1.
Output diagrams and monitors
Populations (% of carrying capacity): the state of the resource and the agent population in the world as a percentage of total carrying capacity resulting from resource harvesting behavior and resource regrowth, agent reproduction, and death.
Average harvest per iteration: the average harvested amounts of agents per iteration by trait, resulting from harvested resource units, minus costs for monitoring and punishing (for punishing agents), minus fines (for punished agents in case of punishment “Pay fine”)
The average energy of agents and trait frequencies: see the first model.
How does the model represent a conditional defector strategy?
The model aims to highlight the role of kin selection and punishment mechanisms in supporting cooperation evolution against cheats. We did not need to modify the model but just thought about what the conditional defector should do to upside down the game. The answer was to pay for the escape.
For instance, if the standard Harvest-greedy of a cheater (greedy, non-punishing) was 13 and the Perception-accuracy of its actual punishers was 75%. Now suppose this cheater faces troubles, and it cannot dominate. However, if it gives up some of its profit to become 12, to escape punishment, and to reduce the perception accuracy to 60%, it could dominate and take over the population.
The conditional cheater can pay something and reduce its profit to escape punishment by reducing perception accuracy if there is a positive correlation between these two variables. Therefore, this model is appropriate if it can support/deny such a correlation.
Source: Ecology - nature.com
