Social learning moderates the tradeoffs between efficiency, stability, and equity in group foraging

TL;DR

The paper addresses how the range of social information sharing, parameterized by $\rho$, shapes collective foraging under exploration–exploitation trade-offs. It introduces a minimal model combining Lévy-walk exploration ($\mu=1.1$), area-restricted search exploitation ($\mu=3$), and socially guided targeted movement, with $\rho$ governing signal reach. Key findings show that mean efficiency $\eta$ is maximal at an intermediate $\rho$, while larger $\rho$ increases equity but induces bursty, unstable intake and redundant exploitation; when penalties are present, the optimal $\rho$ shifts upward to prioritize hazard avoidance, and even random negative cues can improve efficiency by pruning exploration. Mechanistically, these effects correlate with an emergent proximity network whose intermediate connectivity supports transient diversity, suggesting design principles for resilient biological and engineered collectives in patchy, risky environments.

Abstract

Collective foragers, from animals to robotic swarms, must balance exploration and exploitation to locate sparse resources efficiently. While social learning is known to facilitate this balance, how the range of information sharing shapes group-level outcomes remains unclear. Here, we develop a minimal collective foraging model in which individuals combine independent exploration, local exploitation, and socially guided movement. We show that foraging efficiency is maximized at an intermediate social learning range, where groups exploit discovered resources without suppressing independent discovery. This optimal regime also minimizes temporal burstiness in resource intake, reducing starvation risk. Increasing social learning range further improves equity among individuals but degrades efficiency through redundant exploitation. Introducing risky (negative) targets shifts the optimal range upward; in contrast, when penalties are ignored, randomly distributed negative cues can further enhance efficiency by constraining unproductive exploration. Together, these results reveal how local information rules regulate a fundamental trade-off between efficiency, stability, and equity, providing design principles for biological foraging systems and engineered collectives.

Figures (10)

• Figure 1: A schematic of the collective search model. Agents begin by performing independent Lèvy walks with $\mu = 1.1$ (exploration, shown in purple) until they detect a target. Upon detection, the agent ceases social learning and switches to a Lèvy walk with $\mu = 3$ (exploitation, shown in blue) within a circular region of radius $R$ centered at the detected target, which is updated over time. Meanwhile, a social signal emitted by this agent attracts other agents within a region of radius $\rho$ to perform targeted walk towards the detected target (shown in orange). Agents outside this region do not receive the social signal and maintain their search mode.
• Figure 1: $\beta$ controls the clustering of targets within a patch (A)(B)(C) The target distributions feature 10 patches of 600 targets each, with varying degrees of clustering controlled by $\beta=1.1$, $\beta=2$, and $\beta=3$.
• Figure 2: Optimal $\rho$ mediates the tradeoff between exploration and exploitation. (A) Efficiency versus $\rho$ for a fixed number of agents ($N_A=50$) and three numbers of positive patches ($N_+=10;20;50$). The total number of targets is fixed at 6000 with $\beta=2$. Error bars denote 95% confidence intervals but are too small to be visible. The inset shows that efficiency increases monotonically with the $f_{\mu=3}$. (B) Average time fractions spent in three behaviors for the $N_+=10$ case in (A); the optimal $\rho$ aligns with the social-learning regime where agents spend the largest fraction of time exploiting targets ($\mu=3$). (C) Counts of targeted walks, normalized by total time (benefit), plotted against their average length (cost). (D) Slope of the curve in (C) as a function of targeted-walk length, showing that the highest benefit-to-cost ratio coincides with the optimal $\rho$.
• Figure 2: Sparsely distributed targets per patch lowers the efficiency and time ratio of exploitation (A) Plots of efficiency as a function of $\rho$ with a fixed number of agents $N_A$ = 50 and a series of number of patches, $N_+$ = 10, $N_+$ = 20, and $N_+$ = 50, while the total number of targets within the domain is fixed at 6000. The controlling parameter of the target distribution is $\beta=1.1$. Error bars indicating 95% confidence interval are too short to show on the figure. The inset shows that efficiency is positively correlated with $f_{\mu=3}$, time ratio of exploitation. (B) Averaged time ratios spending on three behaviors for the case of $N_+=20$ in (A) with 50 agents.
• Figure 3: Collective search characteristics induced by $\rho$: burstiness, equity, and network connectivity. (A) Time variation of instantaneous efficiency $\eta_i$ with $\rho=0.01$, $\rho = 0.15$, and $\rho = 0.7$ (showing one case). $\eta_i$ represents the number of collected targets per time step. (B) Probability density function (PDF) of $\eta_i$ indicating that low $\rho\leq 0.2$ limits $\eta_i$ due to less social learning, while higher $\rho$ ($0.2<\rho<0.5$) allows $\eta_i$ to reach greater values with an exponential distribution. For $\rho\geq 0.5$, the proportion of medium $\eta_i$ values decreases, though $\eta_i$ can achieve higher values with a heavy-tail distribution. (C) PDF of inter-event time, defining an event as when the instantaneous efficiency $\eta_i\geq 1$. The inset figure illustrates the variation of the burstiness parameter $B$ with $\rho$. The optimal $\rho$ corresponds to the lowest B, indicating a steady intake of resources and, consequently, a minimal starvation time. (D) PDF of number of collected targets by each agent, with an inset indicating that the standard deviation (representing equity) decreases as $\rho$ increases. (E) PDF of the average component size in each case $S$. The PDF of $S$ shifts to the right as $\rho$ increases, indicating that the case-averaged component size $\left\langle S \right\rangle$ increases with $\rho$, as shown in the inset. (F) PDF of average number of components in each case $N_C$. The PDF of $N_C$ shifts to the left as $\rho$ increases, indicating the case-averaged number of components $\left\langle N_C \right\rangle$ decreases with increasing $\rho$, as shown in the inset. All data is based on a scenario with 50 agents and $N_+=10$.