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Pollinator choices when selecting flowers for nectar or pollen collection are crucial in determining the effectiveness of pollination services provided to plants. From the plant's perspective, this effectiveness is a phenomenon shaped by factors at both the species‐ (e.g. pollinator density and flower morphology) and community‐level, including pollinator diversity and plant competition for pollinators. At the species level, individual pollinator effectiveness is influenced by foraging choices, plant identity, and the resulting pollen flow within and between plant species. In natural ecosystems, these species coexist within a complex community, where various interactions can modify foraging choices and alter pollen flows, giving rise to community‐level effectiveness, a less explored aspect of pollinator effectiveness. This study investigates the drivers of individual pollinator foraging choices across two study areas and two flowering seasons. It also assesses the community‐level effectiveness of pollination services received by different plant species, considering indirect interactions between plants through shared pollinators and evaluating their impact on plant reproductive success. Our results show that the determinants of pollinator foraging choices are consistent across different habitats, with floral constancy and flower abundance playing pivotal roles across all species and sites. Foraging choices can shift throughout the flowering season as plant and pollinator composition changes, significantly impacting pollination effectiveness. The overlap in pollination service use by individuals of the same plant species decreases their fruit set, whereas sharing pollinator services with individuals of other plant species increases fruit set. Our results support significant, positive biodiversity–ecosystem functioning associations driven by both plant and pollinator species richness, suggesting that the overlap in pollination service use by different plant species fosters facilitative interactions rather than competition. This is likely influenced by more stable pollination supplies under high plant species diversity conditions and the existence of mechanisms to mitigate the negative impacts of heterospecific pollen deposition. [ABSTRACT FROM AUTHOR]

Interaction networks are a widely used tool to understand the dynamics of plant–pollinator ecological communities. However, while most mutualistic networks have been defined at the species level, ecological processes such as pollination take place at different scales, including the individual or patch levels. Yet, current approaches studying fine‐grain sub‐specific plant–pollinator networks only account for interactions among nodes belonging to a single plant species due to the conceptual and mathematical limitations of modeling simultaneously several plant species each composed of several nodes. Here, we introduce a multilayer diffusion network framework that allows modeling simple diffusion processes between nodes pertaining to the same or different layers (i.e. species). It is designed to depict from the network structure the potential conspecific and heterospecific pollen flows among plant individuals or patches. This potential pollen flow is modeled as a transport‐like system, in which pollen grain movements are represented as random‐walkers that diffuse on an ensemble of bipartite layers of conspecific plants and their shared pollinators. We exemplify this physical conceptualization using a dataset of nine fine‐grain sub‐specific plant–pollinator networks from a Mediterranean grassland of annual plants, where plant nodes represent groups of conspecifics within patches of 1 m2. The diffusion networks show pollinators effectively connecting sets of patches of the same and different plant species, forming a modular structure. Interestingly, different properties of the network structure, such as the conspecific pollen arrival probability and the number of conspecific subgraphs in which plants are embedded, are critical for the seed production of different plant species. We provide a simple but robust set of metrics to calculate potential pollen flow and scale down network ecology to functioning properties at the individual or patch level, where most ecological processes take place, hence moving forward the description and interpretation of species‐rich communities across scales. [ABSTRACT FROM AUTHOR]

Aim: Most of the world's food crops are dependent on pollinators. However, there is a great deal of uncertainty in the strength of this relationship, especially regarding the relative contributions of the honey bee (often a managed species) and wild insects to crop yields on a global scale. Previous data syntheses have likewise reached differing conclusions on whether pollinator species diversity, or only the number of pollinator visits to flowers, is important to crop yield. This study quantifies the current state of these relationships and links to a dynamic version of our analyses that updates automatically as studies become available. Location: Global. Time Period: Present. Taxa studied: Insect pollinators of global crops. Methods: Using a newly created database of 93 crop pollination studies across six continents that roughly triples the number of studies previously available, we analysed the relationship between insect visit rates, pollinator diversity, and crop yields in a series of mixed‐effects models. Results: We found that honey bees and wild insects contribute roughly equal amounts to crop yields worldwide, having similar average flower visitation rates and producing similar increases in yield per visit. We also found that pollinator species diversity was positively associated with increased crop yields even when total visits from all species are accounted for, though it was less explanatory than the total number of visits itself. Main conclusions: Our analysis suggests a middle ground where honey bees are not responsible for the vast majority of crop pollination as has often been assumed in the agricultural literature, and likewise wild insects are not vastly more important than honey bees, as recent global analyses have reported. We also conclude that while pollinator diversity is less important than the number of pollinator visits, these typically involve many species, underscoring the importance of conserving a diversity of wild pollinators. [ABSTRACT FROM AUTHOR]

A universal feature of ecological systems is that species do not interact with others with the same sign and strength. Yet, the consequences of this asymmetry in biotic interactions for the short‐ and long‐term persistence of individual species and entire communities remains unclear. Here, we develop a set of metrics to evaluate how asymmetric interactions among species translate to asymmetries in their individual vulnerability to extinction under changing environmental conditions. These metrics, which solve previous limitations of how to independently quantify the size from the shape of the so‐called feasibility domain, provide rigorous advances to understand simultaneously why some species and communities present more opportunities to persist than others. We further demonstrate that our shape‐related metrics are useful to predict short‐term changes in species' relative abundances during 7 years in a Mediterranean grassland. Our approach is designed to be applied to any ecological system regardless of the number of species and type of interactions. With it, we show that is possible to obtain both mechanistic and predictive information on ecological persistence for individual species and entire communities, paving the way for a stronger integration of theoretical and empirical research. [ABSTRACT FROM AUTHOR]

Ecological intensification has been embraced with great interest by the academic sector but is still rarely taken up by farmers because monitoring the state of different ecological functions is not straightforward. Modelling tools can represent a more accessible alternative of measuring ecological functions, which could help promote their use amongst farmers and other decision-makers. In the case of crop pollination, modelling has traditionally followed either a mechanistic or a data-driven approach. Mechanistic models simulate the habitat preferences and foraging behaviour of pollinators, while data-driven models associate georeferenced variables with real observations. Here, we test these two approaches to predict pollination supply and validate these predictions using data from a newly released global dataset on pollinator visitation rates to different crops. We use one of the most extensively used models for the mechanistic approach, while for the data-driven approach, we select from among a comprehensive set of state-of-the-art machine-learning models. Moreover, we explore a mixed approach, where data-derived inputs, rather than expert assessment, inform the mechanistic model. We find that, at a global scale, machine-learning models work best, offering a rank correlation coefficient between predictions and observations of pollinator visitation rates of 0.56. In turn, the mechanistic model works moderately well at a global scale for wild bees other than bumblebees. Biomes characterized by temperate or Mediterranean forests show a better agreement between mechanistic model predictions and observations, probably due to more comprehensive ecological knowledge and therefore better parameterization of input variables for these biomes. This study highlights the challenges of transferring input variables across multiple biomes, as expected given the different composition of species in different biomes. Our results provide clear guidance on which pollination supply models perform best at different spatial scales – the first step towards bridging the stakeholder–academia gap in modelling ecosystem service delivery under ecological intensification. [ABSTRACT FROM AUTHOR]

Theory posits that the persistence of species in ecological communities is shaped by their interactions within and across trophic guilds. However, we lack empirical evaluations of how the structure, strength and sign of biotic interactions drive the potential to coexist in diverse multi‐trophic communities. Here, we model community feasibility domains, a theoretically informed measure of multi‐species coexistence probability, from grassland communities comprising more than 45 species on average from three trophic guilds (plants, pollinators and herbivores). Contrary to our hypothesis, increasing community complexity, measured either as the number of guilds or community richness, did not decrease community feasibility. Rather, we observed that high degrees of species self‐regulation and niche partitioning allow for maintaining larger levels of community feasibility and higher species persistence in more diverse communities. Our results show that biotic interactions within and across guilds are not random in nature and both structures significantly contribute to maintaining multi‐trophic diversity. [ABSTRACT FROM AUTHOR]

Ecological processes leave distinct structural imprints on the species interactions that shape the topology of animal–plant mutualistic networks. Detecting how direct and indirect interactions between animals and plants are organised is not trivial since they go beyond pairwise interactions, but may get blurred when considering global network descriptors.Recent work has shown that the meso‐scale, the intermediate level of network complexity between the species and the global network, can capture this important information. The meso‐scale describes network subgraphs representing patterns of direct and indirect interactions between a small number of species, and when these network subgraphs differ statistically from a benchmark, they are often referred to as 'network motifs'. Although motifs can capture relevant ecological information of species interactions, they remain overlooked in natural plant–pollinator networks.By exploring 60 empirical plant–pollinator networks from 18 different studies with wide geographical coverage, we show that some network subgraphs are consistently under‐ or over‐represented, suggesting the presence of worldwide network motifs in plant–pollinator networks. In addition, we found a higher proportion of densely connected network subgraphs that, based on previous findings, could reflect that species relative abundances are the main driver shaping the structure of the meso‐scale on plant–pollinator communities. Moreover, we found that distinct subgraph positions describing species ecological roles (e.g. generalisation and number of indirect interactions) are occupied by different groups of animal and plant species representing their main life‐history strategies (i.e. functional groups). For instance, we found that the functional group of 'bees' was over‐represented in subgraph positions with a lower number of indirect interactions in contrast to the rest of floral visitors groups. Finally, we show that the observed functional group combinations within a subgraph cannot be retrieved from their expected probabilities (i.e. joint probability distributions), indicating that plant and floral visitor associations within subgraphs are not random either.Our results highlight the presence of common network motifs in plant–pollinator communities that are formed by a non‐random association of plants and floral visitors functional groups. [ABSTRACT FROM AUTHOR]

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This work resumes the investigation on discrete-time super-diffusive in Lévy random walks defined on networks by using a inverse problem approach, with a focus on 2D-tori. Imposing that the mean square displacement of the walker should be proportional to t γ , we use a Markov Chain formalism to evaluate a fine tuned time-dependent probability distribution of long-distance jumps the walker should use to meet this dependency. Despite its wide applicability, calculations are time-intensive, with a computing time proportional to the number of nodes in the graph to a power > 3. 4. Here it is shown that, by using the circulant property satisfied by the adjacency matrices of a class of tori, it is possible to significantly speed up the calculations. For the purpose of comparison, the inverse super-diffusion problem is solved for two tori based on finite patches of the two-dimensional square lattice, namely the usual (non-circulant) and the helical (circulant) ones. The results of the latter, based on derived new expressions to compute the mean square displacement valid for circulant tori, are in complete agreement with those derived using general expressions, even if the computing time increases with respect to the number of nodes with a significantly smaller exponent ≳ 2. 1. Numerical simulations in both tori types also reproduce super-diffusion when using the time-dependent probability distributions obtained for the helical one. The results suggest that this time efficient approach can be extended to model super-diffusion on cubic and hyper-cubic lattices. • Markovian formulation for diffusion of discrete Lévy random walkers on circulant tori. • Analytical solutions based on the eigenvalues and eigenvectors of circulant matrices. • Evaluation of power law distribution of long jumps with a time dependent exponent. • Numerically computed exponents lead to exact superdiffusive walks before saturation. • Circulant property enables using large lattice sizes with small computing time. [ABSTRACT FROM AUTHOR]

This work addresses the superdiffusive motion of a random walker on a discrete finite-size substrate. It is shown that, with the inclusion of suitably tuned time-dependent probability of large distance jumps over the substrate, the mean square displacement (MSD) of the walker has a power-law dependence on time with a previously chosen exponent γ>1. The developed framework provides an exact solution to the inverse problem, i.e., an adequate jump probability function leading to a preestablished solution is evaluated. Using the Markov Chain (MC) formalism, an exact map for the time dependence of the probability function is derived, which depends on the topology of the substrate and on the chosen value of γ. While the formalism imposes no restriction on the substrate, being applicable from ordered Euclidean lattices to complex networks, results for the cycle graph and two-dimensional torus are highlighted. It is also shown that, based on the previously derived probability function, MSD values resulting from direct numerical simulations agree quite well with those solely obtained within the MC framework. [ABSTRACT FROM AUTHOR]

This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a (d-1) sphere with radius r in a d-dimensional Euclidean space, instead of on a unit hypercube [0,1]d. Then, two vertices are connected by a link if their great circle distance is at most s. In the case of d=3, the topological properties of the random spherical graphs (RSGs) generated by this model are studied as a function of s. We obtain analytical expressions for the average degree, degree distribution, connectivity, average path length, diameter, and clustering coefficient for RSGs. By setting r=√π/(2π), we also show the differences between the topological properties of RSGs and those of two-dimensional RGGs and random rectangular graphs. Surprisingly, in terms of the average clustering coefficient, RSGs look more similar to the analytical estimation for RGGs than RGGs themselves, when their boundary effects are considered. We support all our findings by computer simulations that corroborate the accuracy of the theoretical models proposed for RSGs. [ABSTRACT FROM AUTHOR]

This work considers the time scales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For two-layer multiplexes with an initially high degree of synchronization in each layer, the difference between the average phases in each layer is analyzed from two different perspectives: the spectral analysis and the nonlinear Kuramoto model. Both viewpoints confirm that the prior time scales are inversely proportional to the interlayer coupling strength. Thus, increasing the interlayer coupling always shortens the transient regimes of both the global order parameter and the interlayer synchronization. Surprisingly, the analytical results show that the convergence of the global order parameter is faster than the interlayer synchronization, and the latter is generally faster than the global synchronization of the multiplex. The formalism also outlines the effects of frequencies on the difference between the average phases of each layer, and it identifies the conditions for an oscillatory behavior. Computer simulations are in fairly good agreement with the analytical findings, and they reveal that the time scale of the global order parameter is half the size of the time scale of the multiplex, if not smaller. [ABSTRACT FROM AUTHOR]

Complex networks are a recent type of framework used to study complex systems with many interacting elements, such as self-organized criticality (SOC). The network nodes' tendency to link to other nodes of similar type is characterized by assortative mixing. Real networks exhibit assortative mixing by vertex degree, however, typical random network models, such as the Erdős-Rényi or the Barabási-Albert model, show no assortative arrangements. In this paper we introduce the notion of neighborhood assortativity as the tendency of a node to belong to a community (its neighborhood) showing an average property similar to its own. Imposing neighborhood assortative mixing by degree in a network toy model, SOC dynamics can be found. These dynamics are driven only by the network topology. The long-range correlations resulting from criticality have been characterized by means of fluctuation analysis and show an anticorrelation in the node's activity. The model contains only one parameter and its statistics plots for different values of the parameter can be collapsed into a single curve. The simplicity of the model allows us to perform numerical simulations and also to study analytically the statistics for a specific value of the parameter, making use of the Markov chains. [ABSTRACT FROM AUTHOR]