Role Differentiation in a Coupled Resource Ecology under Multi-Level Selection

Abstract

A group of non-cooperating agents can succumb to the \emph{tragedy-of-the-commons} if all of them seek to maximize the same resource channel to improve their viability. In nature, however, groups often avoid such collapses by differentiating into distinct roles that exploit different resource channels. It remains unclear how such coordination can emerge under continual individual-level selection alone. To address this, we introduce a computational model of multi-level selection, in which group-level selection shapes a common substrate and mutation operator shared by all group members undergoing individual-level selection. We also place this process in an embodied ecology where distinct resource channels are not segregated, but coupled through the same behavioral primitives. These channels are classified as a positive-sum intake channel and a zero-sum redistribution channel. We investigate whether such a setting can give rise to role differentiation under turnover driven by birth and death. We find that in a learned ecology, both channels remain occupied at the colony level, and the collapse into a single acquisition mode is avoided. Zero-sum channel usage increases over generations despite not being directly optimized by group-level selection. Channel occupancy also fluctuates over the lifetime of a boid. Ablation studies suggest that most baseline performance is carried by the inherited behavioral basis, while the learned variation process provides a smaller but systematic improvement prior to saturation. Together, the results suggest that multi-level selection can enable groups in a common-pool setting to circumvent tragedy-of-the-commons through differentiated use of coupled channels under continual turnover.

Figures (6)

• Figure 1: Simulation sample scenario. Boids $2$ and $3$ are detected by the rays emitted from boid $1$, while boid $4$ lies in the blind-spot of $1$. Boid $2$ occludes boid $5$ from $1$. Boids $6$ and $7$ overlap, thus exchange resources. Boid $8$ moves faster, thus incurs more metabolic-cost, while boid $9$ is slower, thus gains from grazing.
• Figure 2: Mutation process. The mutation-operator $g_\alpha(\cdot)$ acts on each element $J_i^{(x)(y)}$ of the parent boid's $J_i$ using the input $\mathbf{o}_i^{(x)(y)}$. The resulting perturbation, together with stochastic noise, is added to $J_i^{(x)(y)}$ to produce the corresponding element $J_j^{(x)(y)}$ of the progeny boid's $J_j$.
• Figure 3: Birth-death process. When boid $i$ spends time $t_2-t_1 > t_{\text{birth}}$ above the resource threshold for birth ($e_{\text{birth}}$), it produces a progeny $j$ with half the resource at that step $e(t_2)/2$. In the process, its own resource depot is halved. When boid $i$ spends time $t_4-t_3>t_{\text{death}}$ below the resource threshold for death $e_{\text{death}}$, it is eliminated from the simulation.
• Figure 4: Group-level fitness trends: (a) The resource fitness, age-mass fitness, and net fitness rise and saturate across generations. (b) The average positive resources received via exchange by boids also increases with generations. Trends in (a) and (b) are averaged across $3$ training seeds and smoothed using a filter of $5$ bins.
• Figure 5: Inference analysis: (a) Different roles observed in boids during a long inference rollout. (b) A zoomed-in view of the role heat map for the same rollout between the time steps $25{,}000$ and $30{,}000$. (c) Cartesian plane boid trajectories in the first $100$ time steps of the rollout. (d) Cartesian plane boid trajectories between time steps $20{,}000$ and $20{,}100$. (e) Proportion of active boids in different roles between time steps $20{,}000$ and $30{,}000$.