Structural asymmetry in biotic interactions as a tool to understand and predict ecological persistence.

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.

Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities.

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.

The non-random assembly of network motifs in plant-pollinator networks.

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.

CropPol: A dynamic, open and global database on crop pollination.

Seventy five percent of the world's food crops benefit from insect pollination. Hence, there has been increased interest in how global change drivers impact this critical ecosystem service. Because standardized data on crop pollination are rarely available, we are limited in our capacity to understand the variation in pollination benefits to crop yield, as well as to anticipate changes in this service, develop predictions, and inform management actions. Here, we present CropPol, a dynamic, open, and global database on crop pollination. It contains measurements recorded from 202 crop studies, covering 3,394 field observations, 2,552 yield measurements (i.e., berry mass, number of fruits, and fruit density [kg/ha], among others), and 47,752 insect records from 48 commercial crops distributed around the globe. CropPol comprises 32 of the 87 leading global crops and commodities that are pollinator dependent. Malus domestica is the most represented crop (32 studies), followed by Brassica napus (22 studies), Vaccinium corymbosum (13 studies), and Citrullus lanatus (12 studies). The most abundant pollinator guilds recorded are honey bees (34.22% counts), bumblebees (19.19%), flies other than Syrphidae and Bombyliidae (13.18%), other wild bees (13.13%), beetles (10.97%), Syrphidae (4.87%), and Bombyliidae (0.05%). Locations comprise 34 countries distributed among Europe (76 studies), North America (60), Latin America and the Caribbean (29), Asia (20), Oceania (10), and Africa (7). Sampling spans three decades and is concentrated on 2001-2005 (21 studies), 2006-2010 (40), 2011-2015 (88), and 2016-2020 (50). This is the most comprehensive open global data set on measurements of crop flower visitors, crop pollinators and pollination to date, and we encourage researchers to add more datasets to this database in the future. This data set is released for non-commercial use only. Credits should be given to this paper (i.e., proper citation), and the products generated with this database should be shared under the same license terms (CC BY-NC-SA).

Approach to the inverse problem of superdiffusion on finite systems based on time-dependent long-range navigation.

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.

Mathematical modelling for sustainable aphid control in agriculture via intercropping.

Agricultural losses to pests represent an important challenge in a global warming scenario. Intercropping is an alternative farming practice that promotes pest control without the use of chemical pesticides. Here, we develop a mathematical model to study epidemic spreading and control in intercropped agricultural fields as a sustainable pest management tool for agriculture. The model combines the movement of aphids transmitting a virus in an agricultural field, the spatial distribution of plants in the intercropped field and the presence of 'trap crops' in an epidemiological susceptible-infected-removed model. Using this model, we study several intercropping arrangements without and with trap crops and find a new intercropping arrangement that may improve significantly pest management in agricultural fields with respect to the commonly used intercrop systems.

Relaxation time of the global order parameter on multiplex networks: The role of interlayer coupling in Kuramoto oscillators.

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.

Inducing self-organized criticality in a network toy model by neighborhood assortativity.

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 Erdos-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.