A model with environmental stochasticity and alternative stable states reproduces variability in the human gut microbiome.
In ATM systems, the massive number of interacting entities makes it difficult to predict the system-wide effects that innovations might have. Here, we present the approach proposed by the project Domino to assess and identify the impact that innovations might bring for the different stakeholders, based on agent-based modelling and complex network science. By investigating a dataset of US flights, we first show that existing centrality and causality metrics are not suited in characterising the effect of delays in the system. We then propose generalisations of such metrics that we prove suited to ATM applications. Then, we introduce the Agent Based Model used in Domino to model scenarios mirroring different system innovations which change the agents' actions and behaviour. We focus on a specific innovation related to flight arrival coordination and we show the insights on its effects at the network level obtained by applying the proposed new metrics.
Scaling laws in ecology, intended both as functional relationships among ecologically relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances, and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked has been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply, and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations.macroecology | species-area relation | Kleiber's law | allometry | power law A prototypical example of the ecological scaling law is the species-area relationship (SAR) on which island biogeography is based (1). It states that the number of species S inhabiting disjoint ecosystems increases as a power of their area; i.e., S ∝ A z , where z is the SAR scaling exponent. The widespread interest in scaling laws (2-8) lies in their intrinsic predictive power, e.g., the use of SAR to forecast how many species might go extinct if the available habitat shrinks or is fragmented into smaller unconnected parts. Precise estimates of the scaling exponents' values are thus crucial. Empirical evidence, however, shows that they vary considerably across ecosystems (9-11), suggesting that exponents of scaling ecological laws are far from universal, although the power-law form proves remarkably robust (Fig. 1).Scaling patterns in ecology have mostly been studied within independent ecosystems, leading to canonical estimates of scaling exponents which may not be simultaneously achievable in a single ecosystem due to extant and consistency constraints. Although ecological scaling laws have historically been treated as disconnected, it is instructive to show by a simple example that they are functionally related. Consider a community hosted within a resource-limited ecosystem of area A whose ith species is characterized by abundance ni and typical body mass mi . Empirical evidence suggests that the following patterns can be described at least approximately by power laws, disregarding possible cutoffs at large sizes: (i) the...
Kleiber’s law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber’s law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber’s law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber’s law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.
In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the walks that can be travelled according to the network temporal structure, i.e. “trips”, while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports’ centrality losses due to delays in the flight network.
Betweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of $$\sim 20$$ ∼ 20 k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.
The most fundamental questions in microbial ecology concern the diversity and variability of communities. Their composition varies widely across space and time, as it is determined by a non-trivial combination of stochastic and deterministic processes. The interplay between non-linear community dynamics and environmental fluctuations determines the rich statistical structure of community variability, with both rapid temporal dynamics fluctuations and non-trivial correlations across habitats. Here we analyze long time-series of gut microbiome and compare intra- and inter-community dissimilarity. Under a macroecological framework we characterize their statistical properties. We show that most taxa have large but stationary fluctuations over time, while a minority is characterized by quick changes of average abundance which cluster in time, suggesting the presence of alternative stable states. We disentangle inter-individual variability in a major stochastic component and a deterministic one, the latter recapitulated by differences in the carrying capacities of taxa. Finally, we develop a model which includes environmental fluctuations and alternative stable states. This model quantitatively predicts the statistical properties of both intra- and inter-individual community variability, therefore summarizing variation in a unique macroecological framework.
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