How structurally stable are global socioeconomic systems?

The stability analysis of socioeconomic systems has been centered on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. Therefore, a key stability question that has been under-investigated is how strong the conditions of a system itself can change before the system moves to a qualitatively different behavior, i.e., how structurally stable the systems is. Here, we introduce a framework to investigate the structural stability of socioeconomic systems formed by the network of interactions among agents competing for resources. We measure the structural stability of the system as the range of conditions in the distribution and availability of resources compatible with the qualitative behavior in which all the constituent agents can be self-sustained across time. To illustrate our framework, we study an empirical representation of the global socioeconomic system formed by countries sharing and competing for multinational companies used as proxy for resources. We demonstrate that the structural stability of the system is inversely associated with the level of competition and the level of heterogeneity in the distribution of resources. Importantly, we show that the qualitative behavior of the observed global socioeconomic system is highly sensitive to changes in the distribution of resources. We believe this work provides a methodological basis to develop sustainable strategies for socioeconomic systems subject to constantly changing conditions

The role of asymmetric interactions on the effect of habitat destruction in mutualistic networks

Plant-pollinator mutualistic networks are asymmetric in their interactions: specialist plants are pollinated by generalist animals, while generalist plants are pollinated by a broad involving specialists and generalists. It has been suggested that this asymmetric ---or disassortative--- assemblage could play an important role in determining the equal susceptibility of specialist and generalist plants under habitat destruction. At the core of the argument lies the observation that specialist plants, otherwise candidates to extinction, could cope with the disruption thanks to their interaction with generalist pollinators. We present a theoretical framework that supports this thesis. We analyze a dynamical model of a system of mutualistic plants and pollinators, subject to the destruction of their habitat. We analyze and compare two families of interaction topologies, ranging from highly assortative to highly disassortative ones, as well as real pollination networks. We found that several features observed in natural systems are predicted by the mathematical model. First, there is a tendency to increase the asymmetry of the network as a result of the extinctions. Second, an entropy measure of the differential susceptibility to extinction of specialist and generalist species show that they tend to balance when the network is disassortative. Finally, the disappearance of links in the network, as a result of extinctions, shows that specialist plants preserve more connections than the corresponding plants in an assortative system, enabling them to resist the disruption.Comment: 14 pages, 7 figure

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches

Food web cohesion

Both dynamic and topologic approaches in food webs have shown how structure alters conditions for stability. However, while most studies concerning the structure of food webs have shown a nonrandom pattern, it still remains unclear how this structure is related to compartmentalization and to responses to perturbations. Here we build a bridge between connectance, food web structure, and compartmentalization by studying how links are distributed within and between subwebs. A ‘‘k subweb’’ is defined as a subset of species that are connected to at least k species from the same subset. We study the k subweb frequency distribution (i.e., the number of k subwebs in each food web). This distribution is highly skewed, decaying in all cases as a power law. The most dense subweb has the most interactions, despite containing a small number of species, and shows connectivity values independent of species richness. The removal of the most dense subweb implies multiple fragmentation. Our results show a cohesive organization, that is, a high number of small subwebs highly connected among themselves through the most dense subweb. We discuss the implications of this organization in relation to different types of disturbancesPeer reviewe

Frugivore species maintain their structural role in the trophic and spatial networks of seed dispersal interactions

1. Trophic relationships have inherent spatial dimensions associated with the sites where species interactions, or their delayed effects, occur. Trophic networks among interacting species may thus be coupled with spatial networks linking species and habitats whereby animals connect patches across the landscape thanks to their high mobility. This trophic and spatial duality is especially inherent in processes like seed dispersal by animals, where frugivores consume fruit species and deposit seeds across habitats. 2. We analysed the frugivore–plant interactions and seed deposition patterns of a diverse assemblage of frugivores in a heterogeneous landscape in order to determine whether the roles of frugivores in network topology are correlated across trophic and spatial networks of seed dispersal. 3. We recorded fruit consumption and seed deposition by birds and mammals during 2 years in the Cantabrian Range (N Spain). We then constructed two networks of trophic (i.e. frugivore–plant) and spatial (i.e. frugivore–seed deposition habitat) interactions and estimated the contributions of each frugivore species to the network structure in terms of nestedness, modularity and complementary specialization. We tested whether the structural role of frugivore species was correlated across the trophic and spatial networks, and evaluated the influence of each frugivore abundance and body mass in that relationship. 4. Both the trophic and the spatial networks were modular and specialized. Trophic modules matched medium-sized birds with fleshy-fruited trees, and small bird and mammals with small-fruit trees and shrubs. Spatial modules associated birds with woody canopies, and mammals with open habitats. Frugivore species maintained their structural role across the trophic and spatial networks of seed dispersal, even after accounting for frugivore abundance and body mass. 5. The modularity found in our system points to complementarity between birds and mammals in the seed dispersal process, a fact that may trigger landscape-scale secondary succession. Our results open up the possibility of predicting the consumption pattern of a diverse frugivore community, and its ecological consequences, from the uneven distribution of fleshy-fruit resources in the landscape

A keystone gene underlies the persistence of an experimental food web

Genes encode information that determines an organism’s fitness. Yet we know little about whether genes of one species influence the persistence of interacting species in an ecological community. Here, we experimentally tested the effect of three plant defense genes on the persistence of an insect food web and found that a single allele at a single gene promoted coexistence by increasing plant growth rate, which in turn increased the intrinsic growth rates of species across multiple trophic levels. Our discovery of a “keystone gene” illustrates the need to bridge between biological scales, from genes to ecosystems, to understand community persistence

How structurally stable are global socioeconomic systems?

The stability analysis of socioeconomic systems has been centred on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. Therefore, a key stability question that has been under-investigated is how strongly the conditions of a system itself can change before the system moves to a qualitatively different behaviour, i.e. how structurally stable the systems is. Here, we introduce a framework to investigate the structural stability of socioeconomic systems formed by a network of interactions among agents competing for resources. We measure the structural stability of the system as the range of conditions in the distribution and availability of resources compatible with the qualitative behaviour in which all the constituent agents can be self-sustained across time. To illustrate our framework, we study an empirical representation of the global socioeconomic system formed by countries sharing and competing for multinational companies used as proxy for resources. We demonstrate that the structural stability of the system is inversely associated with the level of competition and the level of heterogeneity in the distribution of resources. Importantly, we show that the qualitative behaviour of the observed global socioeconomic system is highly sensitive to changes in the distribution of resources. We believe that this work provides a methodological basis to develop sustainable strategies for socioeconomic systems subject to constantly changing conditions

Statistical mechanics of ecosystem assembly

We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the endstate of the process), which is therefore resistant to invasions. This also shows that the endstate is independent on the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner.Comment: Accepted for publication in Physical Review Letter

Five fundamental ways in which complex food webs may spiral out of control

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these ‘delayed negative feedbacks’ may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large‐scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food‐web patterns are sufficient to prevent abrupt, large‐scale transitions under global environmental change

Mutually-Antagonistic Interactions in Baseball Networks

We formulate the head-to-head matchups between Major League Baseball pitchers and batters from 1954 to 2008 as a bipartite network of mutually-antagonistic interactions. We consider both the full network and single-season networks, which exhibit interesting structural changes over time. We find interesting structure in the network and examine their sensitivity to baseball's rule changes. We then study a biased random walk on the matchup networks as a simple and transparent way to compare the performance of players who competed under different conditions and to include information about which particular players a given player has faced. We find that a player's position in the network does not correlate with his success in the random walker ranking but instead has a substantial effect on its sensitivity to changes in his own aggregate performance.Comment: A few clarifications added 14 pages, 2 tables, 6 figures. Submitte