Diagram 1.
Flowchart of the model dynamics.
Table 1.
Overview of the model parameters and their values.
Fig 1.
Equilibrium state for populations in an abundant environment (e = 4.5) when varying the mortality rate for selfish risk-seeking agents and the community cost.
The color shade represents the population size at equilibrium, while the percentages represent the proportion of generous risk-averse agents in the population at equilibrium. White tiles represent the conditions in which the population reached extinction by the 104 generation. While most populations survive and are mostly composed of selfish risk-seekers when the mortality rate is greater than zero, populations reach extinction if no mortality rate is imposed on selfish risk-seeking agents.
Fig 2.
Average evolution of the combined reproduction rates φS,S, φG,G over generations in an abundant environment (e = 4.5).
: φS,S,
: φG,G. φG,G = 1(0)/φS,S = 1(0) means that a generous risk-averse/selfish risk-seeking agent has a 100(0)% chance of reproducing generous risk-averse/selfish risk-seeking offspring.
Fig 3.
Average evolution of the separate parameters (ω, γ and ϕ) regulating the reproduction mechanism over generations in an abundant environment (e = 4.5).
: γ, contribution of selfish risk-seeking parent to the probability of reproducing selfish risk-seeking offspring,
: ω, contribution of generous risk-averse parent to the probability of reproducing generous risk-averse offspring, Black line: ϕ, population baseline contribution to the probability that agents will reproduce selfish risk-seeking offspring (independent of parental phenotype).
Fig 4.
Equilibrium state for populations in an abundant environment (e = 4.5), when generous agents behave as conditional cooperators.
The color shade represents the population size at equilibrium, while the percentages represent the proportion of generous risk-averse agents in the population at equilibrium. Populations do not reach extinction regardless of mortality rate or community cost. At 0% or to 50% mortality rate the majority of the population comprises generous risk-averse agents, while the opposite happens at 25% mortality rate.
Fig 5.
Average evolution of the combined reproduction rates φS,S, φG,G over generations when generous agents behave as conditional cooperators and the environment is abundant (e = 4.5).
: φS,S,
: φG,G. φG,G = 1(0)/φS,S = 1(0) means that a generous risk-averse/selfish risk-seeking agent has a 100(0)% chance of reproducing a generous risk-averse/selfish risk-seeking offspring. At 0% mortality rate, both selfish and generous agents have a 50% chance of passing on their own phenotype to their offspring. At 50% mortality rate, generous agents have a high probability of passing on their own phenotype to their offspring (φG,G ~ 65%), while less than half of selfish agents reproduce selfish offspring.
Fig 6.
Equilibrium state for populations in (a) a scarce (e = 1.2) and (b) an abundant (e = 4.5) environment, when generous risk-averse agents act as conditional cooperators and selfish risk-seekers bear individual costs.
The color shade represents the population size at equilibrium, while the percentages represent the proportion of generous risk-averse agents in the population at equilibrium. White tiles represent the conditions in which the population reached extinction by the 104 generation. At 25% mortality rate, populations reach a stable equilibrium and the majority of the community is composed of selfish agents unless the community cost is set to 0. At 50% mortality rate, population reaches extinction before the 104 generation when a community cost is present (λ = 50, 100) but survives in its absence (λ = 0) and 70% of the population expresses generous risk-averse attitudes.
Fig 7.
Average evolution of the combined reproduction rates φS,S, φG,G over generations, in an abundant environment, when generous risk-averse agents act as conditional cooperators and selfish risk-seekers bear individual costs.
: φS,S,
: φG,G. φG,G = 1(0)/φS,S = 1(0) means that a generous risk-averse/selfish risk-seeking agent has a 100(0)% chance of reproducing a generous risk-averse/selfish risk-seeking offspring. At 25% mortality rate, selfish risk-seeking agents are more likely to be reproduced, while generous risk-averse behaviours are favoured when the mortality is high mS = 50%.