Threshold Resource Redistribution in Spatially-Structured Kinship Networks

We present a model for a threshold-based resource redistribution process in a spatially-explicit population, characterizing the relation between kinship network structure, local interactions and persistence. We find that population survival becomes possible for lower resource densities, but leads to increased network heterogeneity and locally centralized clusters. We interpret this in relation to a feedback between the kinship network structure and reproduction ability. Agents receive stochastic resources and solicit additional resources from connected individuals when below a minimum, with each agent contributing a fraction of their excess based on relatedness. We first analyze a fully-connected population with uniform redistribution fraction and discuss mean field expectations as well as finite size corrections. We extend this model to a hub-and-spoke network, exploring the impact of network asymmetry or centrality on resource distribution. We then develop a spatially-limited population model with diffusion, local pairing, reproduction and mortality. Redistribution is introduced as a function of relatedness (generational distance through most-recent common ancestor) and distance. Redistribution-dependent populations exhibit a higher level of relational closeness with increased clustering for agents of highest node strength. These results highlight the interaction of resource density, cooperation and kinship in a spatially-limited regime.

💡 Research Summary

This paper introduces and systematically investigates a threshold‑based resource redistribution model in populations that differ in their interaction topology: a fully connected network, a hub‑and‑spoke (heterogeneous) network, and a spatially explicit kinship network. Each agent initially receives a stochastic amount of resource drawn from a Poisson distribution with mean μ. Agents require a minimum amount ϕ (set to 1 for most analyses). If an agent’s resource r_i is below ϕ, it has a deficit d_i = (ϕ – r_i)^+. Agents with excess s_j = (r_j – ϕ)^+ may transfer a fraction ρ of that excess to a deficit neighbor, but the transferred amount is capped at the recipient’s deficit.

Mean‑field analysis (fully connected case).
The authors derive closed‑form expressions for total demand D(μ) = N e^{‑μ} and total supply S(μ, ρ) = N ρ