Abstract
Resource distribution networks are the infrastructure facilitating the flow of resources in both biotic and abiotic systems. Both theoretical and empirical arguments have proposed that physical systems self-organise to maximise power production, but how this trajectory is related to network development, especially regarding the heterogeneity of resource distribution in explicitly spatial networks, is less understood. Quantifying the heterogeneity of resource distribution is necessary for understanding how phenomena such as economic inequality or energetic niches emerge across socio-ecological and environmental systems. Although qualitative discussions have been put forward on this topic, to date there has not been a quantitative analysis of the relationship between network development, maximum power, and inequality. This paper introduces a theoretical framework and applies it to simulate the power consumption and inequality in generalised, spatially explicit resource distribution networks. The networks illustrate how increasing resource flows amplify inequality in power consumption at network end points, due to the spatial heterogeneity of the distribution architecture. As increasing resource flows and the development of hierarchical branching can both be strategies for increasing power consumption, this raises important questions about the different outcomes of heterogeneous distribution in natural versus human-engineered networks, and how to prioritise equity of distribution in the latter.
Highlights
Both biotic and abiotic systems require energy for maintenance and growth, necessitating the relocation of energetic resources from points of supply to points of consumption and end use
This work has explored the characteristics of complex networks evolving toward maximum power production, and the relationship between the development and dynamics of these networks and the inequality of resource distribution through them
The derived equations and illustrative simulations related the potential, resource flow, power, and resistance across a network of resources and consumers, and illustrated how those relationships changed as the network evolved toward maximum power, through adaptation in network state, architecture, or both
Summary
Both biotic and abiotic systems require energy for maintenance and growth, necessitating the relocation of energetic resources from points of supply to points of consumption and end use. The ‘evolved branching’ simulations showed lower total power consumption and no inequality present in the final stage of network evolution, as the consumers were all placed equal path distances from the resource, despite being at slightly differing Euclidean distances This demonstrates that the self-similar branching architecture itself does not lead to inequality, but rather the hierarchical or otherwise heterogeneous distribution of consumers. Branching is still only energetically advantageous to the overall system, and those positioned close to the resource within the network architecture These optimally located and connected consumers experience increased final power even after the total network final power begins to decrease (Fig 7), due to the larger frictional losses experienced by the more distant consumers along the bottom level of the network, who have higher effective resistance (Fig 4A).
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