How do social animals make effective decisions in the absence of a leader? While coordination can improve accuracy, it also introduces delays as information propagates through the group. In changing environments, these delays can outweigh the benefits of globally coordinated decisions, even when local interactions remain tightly organized. This raises a key question: how can groups implement efficient collective decision-making without central coordination? We address this question using a collective foraging model in which individuals share information and rewards, but each must choose whether to bear the cost of exploring or to remain idle. We show that decentralized collectives can match the performance of centrally controlled groups through a division of labor: a small, heterogeneous subset explores even when expected rewards are negative, acquiring information to enable future foraging, while a coordinated majority forages only when expected rewards are positive. Information redundancy causes the optimal number of explorers to grow sublinearly with group size, so that larger groups need proportionally fewer explorers. The heterogeneity of the group is maximized at intermediate ecological pressures, but optimal groups are homogeneous when costs or fluctuations are extreme. Crucially, these group-level policies do not require central coordination, emerging instead from agents following simple threshold-based decision rules. We thus demonstrate a mechanism through which leaderless collectives can make effective decisions under uncertainty and show how ecological pressures can drive changes in the distribution of strategies employed by the group.
How animal groups balance individual exploration costs and collective information gains remains a central question in understanding ecological decision-making [1][2][3][4]. Individual foragers bear energetic and survival costs when venturing into uncertain environments [5,6], yet the information about the environmental state resulting from these forays can outweigh any immediate rewards [2,7,8]. This tension raises a fundamental question: How should groups be organized to balance these costs and benefits?
One solution to this problem is centralized leadership, in which a small number of individuals guide collective action. In many wild wolf packs, for example, the breeding pair tends to initiate movements and coordinates traveling, resting, and hunting [9]. Human history offers parallel examples. Admiral Zheng He commanded fleets across the Indian Ocean in the early fifteenth century on imperial orders, spurring Chinese emigration and trade throughout Southeast Asia [10]. A century later, royal sponsorship supported Magellan’s circumnavigation, opening the first western sea route to the Spice Islands and accelerated global trade and contact between distant regions [11]. In each case, a small number of designated explorers, acting under a central authority, bore enormous personal risk, while the societies that sent them reaped lasting rewards. However, most social animals, including honeybees, ants, and fish schools, lack fixed leaders and coordinate through local interactions [2,3,7,[12][13][14]. Despite extensive empirical study of decentralized animal groups [3,12,15,16], it remains unclear how closely decentralized coordination can match centralized control, how performance depends on diversity in individual strategies, and under what conditions heterogeneous strategies offer an advantage in leaderless groups.
To address these questions, we develop and analyze a stochastic foraging model [17][18][19][20][21][22][23][24] to understand how collectives can achieve efficient exploration. We show that well-calibrated collectives exhibit two characteristic behavioral regimes: during times of plenty, risk-averse individuals venture out together, amplifying collective gains. When resources are scarce, most individuals refrain from foraging, but a small subset of risk-tolerant explorers continues foraging to rapidly detect environmental improvements. Composition is critical as populations dominated by cautious individuals fail to discover new resources, whereas those dominated by risk-tolerant foragers exhaust shared reserves. The number of risk-tolerant individuals grows sublinearly with population size, making a balanced division of labor between exploration and exploitation essential for efficient foraging [14,25]. Remarkably, collectives with a well-calibrated mixture of cautious and bold individuals can perform as well as groups governed by a central decisionmaker. The most heterogeneous compositions emerge under intermediate ecological pressures, when exploration costs and environmental variability are balanced. We thus show how simple individual decision rules lead to optimal collective performance and predict when ecological pressures favor heterogeneous versus uniform group composition.
Collective decisions about foraging in large, decentralized collectives face a fundamental challenge: how do groups balance individual risk and collective benefit in changing environments without central coordination? To address this question, we consider a minimal model designed to examine whether decentralized decision-making mechanisms can yield optimal collective long-term returns, even when individual expected returns are negative. Here we provide an overview of the model; mathematical details can be found in SI Appendix, Section 1.
We consider a collective of 𝑁 agents who forage for resources. Time is discrete, and on each time step an agent chooses either to leave the “hive” and forage, or to stay. Each foraging attempt is either successful, resulting in a positive reward, or unsuccessful, resulting in no reward. The environment alternates between a highand low-rewarding state, so that in the high (low) state a foraging attempt is successful with probability 𝛾 + (𝛾 -). To model energetic expenditure and environmental risk, we assume that each foraging attempt incurs a fixed cost, 𝜆, and that the expected return from an attempt is positive in the high-reward state and negative in the low-reward state. Transitions between the states are memoryless, so the environmental state evolves
Maximizing returns requires optimizing forager number: too many foragers when conditions are poor wastes effort; too few when conditions are good misses opportunities. To establish an upper bound on collective performance, we derive a theoretical benchmark based on a centralized planner that optimally determines foraging effort required to maximize long-term collective returns (Fig. 1D). Under this centralized policy, all individuals
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