The trade-off between the need to obtain new knowledge and the need to use that knowledge to improve performance is one of the most basic trade-offs in nature, and optimal performance usually requires some balance between exploratory and exploitative behaviors. Researchers in many disciplines have been searching for the optimal solution to this dilemma. Here we present a novel model in which the exploration strategy itself is dynamic and varies with time in order to optimize a definite goal, such as the acquisition of energy, money, or prestige. Our model produced four very distinct phases: Knowledge establishment, Knowledge accumulation, Knowledge maintenance, and Knowledge exploitation, giving rise to a multidisciplinary framework that applies equally to humans, animals, and organizations. The framework can be used to explain a multitude of phenomena in various disciplines, such as the movement of animals in novel landscapes, the most efficient resource allocation for a start-up company, or the effects of old age on knowledge acquisition in humans.

Two major forms of vegetation patterns have been observed in drylands: nearly periodic patterns with characteristic length scales, and amorphous, scale-free patterns with wide patch-size distributions. The emergence of scale-free patterns has been attributed to global competition over a limiting resource, but the physical and ecological origin of this phenomenon is not understood. Using a spatially explicit mathematical model for vegetation dynamics in water-limited systems, we unravel a general mechanism for global competition: fast spatial distribution of the water resource relative to processes that exploit or absorb it. We study two possible realizations of this mechanism and identify physical and ecological conditions for scale-free patterns. We conclude by discussing the implications of this study for interpreting signals of imminent desertification.

Summary Functional diversity (FD) has become a principal concept for revealing mechanisms driving community assembly and ecosystem function. Multiple assembly processes, including abiotic filtering, competition and multi‐trophic relationships, operate simultaneously to structure FD. In water‐limited plant communities, FD is likely to reflect trade‐offs between drought resistance vs. disturbance resistance and competitive ability. We propose a mathematical mechanistic model for understanding the organization and function of water‐limited plant communities. The approach captures the interplay between abiotic filtering, below‐ and above‐ground competition and disturbance. We exploit this powerful model to uncover mechanisms underlying changes in functional diversity along stress gradients. Our approach links biomass production and FD to environmental conditions through plant resource capture ability. Functional groups are defined along a single trade‐off axis according to investment in capturing light (shoot) vs. water (root). Species growth rate is determined dynamically by the species traits, water availability and grazing stress. We derive biomass production, functional diversity and composition along precipitation and grazing gradients. Model's results revealed several regimes structuring FD along the precipitation gradient: ‘Struggle for water’ at low precipitation, ‘competition for water’ at intermediate precipitation and ‘competition for light’ at high precipitation. We observed a shift in grazing effect on FD from negative at very low precipitation, to positive at higher precipitation. Unimodal FD–grazing intensity relationship was observed under high precipitation, while under low precipitation, FD decreased moderately with increasing grazing intensity. Synthesis. Our model showcases how fundamental tradeoffs in plant traits may drive functional diversity and ecosystem function along environmental gradients. It offers a mechanism through which novel understandings can be obtained regarding the interplay between water stress, below‐ and above‐ground competition and disturbance intensity and history. We discuss further model testing possibilities as well as required empirical work.

No abstract

No abstract