Fig 1.
Schematic representation of our model’s processes and evolving traits.
For the sake of illustration, only a single consumer is shown. (A) Consumers harvest the resource in their neighborhoods at a rate that declines with the distance from their locations. (B) When the local resource density falls below a threshold, consumers disperse to other locations at distances randomly drawn from a normal distribution. (C) Once consumers have dispersed, the resource densities around their original location can rebound.
Table 1.
Model parameters.
Fig 2.
Sedentary and mobile resource-consumption strategies emerge spontaneously.
Changes over time (measured in units of the reciprocal of the imitation rate) of the population distributions of (A) harvesting rates, (B) dispersal radii, and (C) per capita resource extraction rates, shown alongside the time-averaged population distributions of these quantities (averaged over the last 1,000 time units so as to exclude the initial transient, with the frequencies in the separate bins adding up to the number N of consumers). Brighter colors indicate higher frequencies, using a nonlinear color scale. The population starts with all consumers having identical strategies. As time progresses, social learning leads to the spontaneous emergence of two distinct strategies: a frugal sedentary strategy (labeled ‘S’) with a low harvesting rate and near-zero dispersal radius, and an overexploitative mobile strategy (labeled ‘M’) with a high harvesting rate and large dispersal radius. Parameter values are as shown in Table 1.
Fig 3.
Increasing consumption density leads to social inequality.
(A, B) When the density of consumers is low (expressed as the ratio of harvested area to total area), all of them evolve to harvest at high rates and disperse far, without overexploiting the resource. As consumption density increases, such a resource-consumption strategy becomes unsustainable, leading to a diversification of strategies into frugal sedentary consumers with low harvesting rates and near-zero dispersal radii, and overexploitative mobile consumers with high harvesting rates and large dispersal radii. (C) The resultant per capita resource extraction rates (expressed as fractions of the system’s carrying capacity extracted per unit time) decrease with consumption density. Population averages are indicated by white lines, yield-maximizing resource-consumption strategies and resultant resource extraction rates by green lines, and profit-maximizing resource-consumption strategies and resultant resource extraction rates by magenta lines. The green and magenta lines are exponential fits to numerically estimated strategy values, as in S2F Fig. The average harvesting rates exceed the corresponding yield-maximizing and profit-maximizing harvesting rates, implying overexploitation of the resource and suboptimal per capita resource extraction rates. Parameter values are as shown in Table 1.
Fig 4.
Strategy regimes for different unit benefits and costs of harvesting.
Effects of the unit benefit bH and cost cH of harvesting on the (A) difference between harvesting rates of sedentary and mobile consumers, (B) population average of harvesting rates, (C) difference between dispersal distances of sedentary and mobile consumers, and (D) population average of dispersal distances. In panels A and B, the sedentary and mobile yield-maximizing harvesting rates (S2 Appendix) are indicated, respectively, by the unlabeled tick marks in the blue and green ranges of the color bars. In panel C, grey areas indicate where a difference in dispersal distances could not be reliably detect, due to insufficient numerical resolution. We find three strategy regimes, delimited by cyan and blue lines: in the region labeled ‘S,’ all consumers are prudent and sedentary, in the region labeled ‘M,’ all consumers are overexploitative and mobile, and in the region labeled ‘S & M,’ frugal sedentary consumers are coexisting with overexploitative mobile consumers. For the latter regime, outsets in panels B and D show average values separately for sedentary and mobile consumers. Parameter values are as shown in Table 1.
Fig 5.
Maximum sustainable resource extraction occurs for mobile consumers at the ‘edge of inequality’.
(A) Average per capita resource extraction rate (expressed as a fraction of the yield-maximizing extraction rate) and (B) amount of resource left in the environment (expressed as a fraction of the system’s carrying capacity), depending on the unit benefit bH and cost cH of harvesting. The sedentary regime, labeled ‘S,’ is equitable, but inefficient: the resource extraction is far less than optimal, despite the ample amounts of resource left in the environment. The mobile regime, labeled ‘M,’ is both equitable and efficient: the total resource extraction rate resulting from the evolved resource-consumption strategies reaches its maximum in this regime. However, for high unit benefits and costs of harvesting (or equivalently, for low unit costs of dispersal), the tragedy of the commons can occur also in this regime. The coexistence regime, labeled ‘S & M,’ is neither equitable nor efficient: the resource extraction rate is far less than optimal, and overexploitation by mobile consumers results in the tragedy of the commons. Parameter values are as in Fig 4.
Fig 6.
Strategy regimes for different spatio-temporal scales of imitation.
Effects of the imitation radius σI and imitation rate rI on the (A) difference between harvesting rates of sedentary and mobile consumers, (B) population average of harvesting rates, (C) difference between dispersal distances of sedentary and mobile consumers, and (D) population average of dispersal distances. In panels A and B, the sedentary and mobile yield-maximizing harvesting rates (S2 Appendix) are indicated, respectively, by the unlabeled tick marks in the blue and green ranges of the color bars. We find four strategy regimes, delimited by cyan, blue, black, and white lines. In the region labeled ‘M,’ characterized by relatively low imitation rates and not too small imitation radii, the population’s strategy distribution is unimodal, featuring an efficient mobile resource-consumption strategy. Increasing the imitation rate is taking the population into the coexistence region, labeled ‘S & M,’ in which strategies diversify, and sedentary and mobile consumers coexist. For the latter regime, outsets in panels B and D show average values separately for sedentary and mobile consumers. We further divide the region labeled ‘S & M’ into three regions. In the region labeled ‘I,’ characterized by global information, both sedentary and mobile consumers have high harvesting rates, resulting in the tragedy of the commons. Decreasing the imitation radius is taking the population into the region labeled ‘II,’ in which the mobile cheating consumers are becoming less common but more overexploitative, while sedentary cooperative consumers are harvesting at rates close to the sedentary profit-maximizing rate. Decreasing the imitation radius even further is taking the population into the region labeled ‘III,’ in which the mobile cheating consumers are becoming even less common but extremely overexploitative. S5 Fig provides additional information on the regions labeled ‘I’ to ‘III.’ Parameter values are as shown in Table 1, except for bH = 0.02 and cH = 0.8.
Fig 7.
Consumer impatience and myopia aggravate social inequality.
Effects of the imitation radius σI and imitation rate rI on the (A) average per capita resource extraction rate (expressed as a fraction of the yield-maximizing extraction rate) and (B) amount of resource left in the environment (expressed as a fraction of the system’s carrying capacity). The average per capita resource extraction rate decreases as the imitation rate is increased. In the region labeled ‘III,’ this is because a small fraction of mobile cheating consumers is exploiting the resource at a very high harvesting rate, while sedentary cooperative consumers, which form the vast majority of the population, adopt a frugal harvesting rate and receive hardly any resource. In the region labeled ‘I,’ sedentary and mobile consumers are present in roughly similar proportions, both harvesting aggressively and overexploiting the resource. In the region labeled ‘II,’ a smaller, but still substantial, proportion of cheating consumers is enabled to coexist with the cooperative consumers. S5 Fig provides additional information on the regions labeled ‘I’ to ‘III.’ Parameter values are as in Fig 6.
Fig 8.
Overview of harvesting and dispersal regimes and their ranges in equality-efficiency space.
The sedentary regime (labelled ‘S’) is equitable but inefficient, the mobile regime (labelled ‘M’) is equitable and efficient at high dispersal costs but inefficient at low dispersal costs, while the coexistence regime (labelled ‘S & M’) is neither equitable nor efficient.