Emergence of social inequality in a spatial-ecological public goods game

Spatial ecological public goods, such as forests, grasslands, and fish stocks risk being overexploited by selfish consumers, a phenomenon called “the tragedy of commons”. The spatial and ecological dimensions introduce new features absent in non spatio-ecological contexts, such as consumer mobility, incomplete information availability, and rapid evolution by social learning. It is unclear how these different processes interact to influence the harvesting and dispersal strategies of consumers. To answer these questions, we develop and analyze an individual-based, spatially-structured evolutionary model with explicit resource dynamics. We find that, 1) When harvesting efficiency is low, consumers evolve a sedentary harvesting strategy, with which resources are harvested sustainably, but harvesting rates remain far below their maximum sustainable value. 2) As harvesting efficiency increases, consumers adopt a mobile ‘consume-and-disperse’ strategy, which is sustainable, equitable, and allows for maximum sustainable yield. 3) Further increase in harvesting efficiency leads to large-scale overexploitation. 4) If costs of dispersal are significant, increased harvesting efficiency also leads to social inequality between frugal sedentary consumers and overexploitative mobile consumers. Whereas overexploitation can occur without social inequality, social inequality always leads to overexploitation. Thus, we identify four conditions, which are characteristic (and as such positive) features of modern societies resulting from technological progress, but also risk promoting social inequality and unsustainable resource use: high harvesting efficiency, moderately low costs of dispersal, high consumer density, and consumers’ tendency to rapidly adopt new strategies. We also show that access to global information, which is also a feature of modern societies, may help mitigate these risks.


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Most real socio-ecological systems are spatially structured. With some exceptions [e.g., 24 32], spatial structure is thought to promote cooperation as it both exposes defectors 25 to the consequences of their own selfish acts and allows local clusters of cooperators 26 to form, enabling multilevel selection for cooperation [33][34][35]. However, space also 27 allows mobility. Mobility can hinder cooperation allowing defectors to escape the con-28 sequences of their own acts [36]. Indeed, several studies have considered the effect 29 of fixed mobility and found that cooperation can be sustained when mobility is either 30 low [37] or dependent on local conditions [38,39]. If mobility incurs no cost, then defec-31 tors may invariably evolve high mobility and undermine cooperation. When dispersal 32 is costly, an evolutionary interplay between mobility and cooperation may occur, but 33 thus far only a handful of studies have considered the joint evolution of costly mobility 34 and cooperation [40][41][42][43][44]. A recent study by Mullon et al. [45] found that when disper-35 sal and cooperation coevolve, two coexisting strategies can spontaneously emerge: one 36 benevolent and sessile, the other self-serving and dispersing.

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In socio-ecological settings, the ecological dynamics of the resource plays a crucial 38 role in the evolutionary dynamics. First, interactions between individuals are often 39 mediated through the resource, i.e., individuals do not directly interact with other 40 individuals, but respond to changes in the resource caused by others. Second, limited 41 resource availability may lead to the evolution of density-dependent strategies, since ecological or even faster timescales. Evolutionary outcomes may be dramatically different depending on whether evolution is slow or fast [46]. Furthermore, spatial extent 48 may prevent consumers from having full information about other consumers and the 49 environment, because information may not reach far-off consumers. Such local infor-50 mation may lead to local selection, which is typically expected to benefit defectors. 51 Despite these important gaps, only a few studies have so far considered ecological pub- 52 lic goods [2,47,48], and even fewer studies explicitly model a renewable resource [e.g., 53 49]. 54 Here, we move beyond the aforementioned studies, in particular the work by Parvi-  We model consumers and resources on a continuous two-dimensional space. We assume 62 that resource growth is logistic with intrinsic growth rate r and carrying capacity K. and imitation radius, on the evolved strategies. We present our key findings below.

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To investigate the robustness of this result under more realistic assumptions of intel-110 ligent consumers, we allow consumers to 'explore' random strategies at a low rate.
SI- Fig. 2 shows that with low strategy exploration rates, the system evolves to the 112 same evolutionary endpoints as in Fig. 1 At all consumer densities, the average evolved harvesting rates (white line in Fig. 2) are 127 higher than the corresponding optimal rates, i.e., the yield-maximizing rate (green) or 128 the profit-maximizing rate (magenta). Consequently, the average resource extraction 129 rate is less than the optimal values. Thus, when left to themselves, consumers over-  with very high harvesting rates. However, the proportion of cheaters is low (SI- Fig. 7).

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Therefore this regime is marked by stark social divide, with a handful of cheaters 200 driving extraction rates of the majority of consumers to zero. Resource extraction 201 is acutely inefficient, with much of the resource being left unharvested (Fig. 6) (Fig. 6, SI-Fig. 7). In other words, this region is most favourable for cheaters.     Table 1. Figure 2: Increasing consumer density leads to social inequality. When consumer density is low, all consumers harvest at high rates and disperse, because available resources suffice for everyone. As consumer density increases, everyone harvesting at high rates becomes unsustainable, leading to diversification of strategies into prudent sedentary consumers and overexploitative mobile consumers (A-B). Average per capita resource extraction rate (% of total carrying capacity of the system) decreases with density (C). However, the average harvesting rate (white line) is higher than the corresponding yield-maximizing (green line) and profit-maximizing (magenta line) rates, leading to overexploitation of resource and suboptimal per capita resource extraction. Parameters: b = 0.059, c = 0.68, r I = 0.1, σ I → ∞. Other parameters are as in Table 1. Each consumer is assumed to 'occupy' the space within its exploitation radius, and consumer density is the percentage of total area occupied by all consumers without overlap).  Per capita average resource extraction rate as a fraction of the yieldmaximizing rate (A) and the resource left in the environment as a fraction of the carrying capacity (B). The sedentary regime is equitable, but inefficient, because the resource extraction is less than optimal even though there are ample resources in the environment. The mobile regime is both equitable as well as efficient, and the total resource extraction rate reaches its maximum evolved value in this regime. However, for very low dispersal costs, the tragedy of the commons occurs in this regime. The coexistence regime is neither equitable nor efficient. In this regime, the resource extraction rate is suboptimal, and overexploitation by mobile consumers results in the tragedy of the commons.  Table 1. Figure 6: Impatience and myopia among consumers aggravate social inequality. Average resource extraction rate decreases with increasing imitation rate. In region III, this is because only a small fraction of cheaters exploit resource at a high rate, while cooperators, which form a vast majority of the population, get zero resource. In region I, both cooperators and cheaters harvest aggressively and overexploit the resource. Region II allows a substantial number of cheaters to coexist with cooperators. See SI- Fig. 7 for additional analysis of regions I-III.