Mobility census for monitoring rapid urban development.

Monitoring urban structure and development requires high-quality data at high spatio-temporal resolution. While traditional censuses have provided foundational insights into demographic and socio-economic aspects of urban life, their pace may not always align with the pace of urban development. To complement these traditional methods, we explore the potential of analysing alternative big-data sources, such as human mobility data. However, these often noisy and unstructured big data pose new challenges. Here, we propose a method to extract meaningful explanatory variables and classifications from such data. Using movement data from Beijing, which are produced as a by-product of mobile communication, we show that meaningful features can be extracted, revealing, for example, the emergence and absorption of subcentres. This method allows the analysis of urban dynamics at a high-spatial resolution (here 500 m) and near real-time frequency, and high computational efficiency, which is especially suitable for tracing event-driven mobility changes and their impact on urban structures.

Critical Drift in a Neuro-Inspired Adaptive Network.

It has been postulated that the brain operates in a self-organized critical state that brings multiple benefits, such as optimal sensitivity to input. Thus far, self-organized criticality has typically been depicted as a one-dimensional process, where one parameter is tuned to a critical value. However, the number of adjustable parameters in the brain is vast, and hence critical states can be expected to occupy a high-dimensional manifold inside a high-dimensional parameter space. Here, we show that adaptation rules inspired by homeostatic plasticity drive a neuro-inspired network to drift on a critical manifold, where the system is poised between inactivity and persistent activity. During the drift, global network parameters continue to change while the system remains at criticality.

Quantification of metabolic niche occupancy dynamics in a Baltic Sea bacterial community.

Progress in molecular methods has enabled the monitoring of bacterial populations in time. Nevertheless, understanding community dynamics and its links with ecosystem functioning remains challenging due to the tremendous diversity of microorganisms. Conceptual frameworks that make sense of time series of taxonomically rich bacterial communities, regarding their potential ecological function, are needed. A key concept for organizing ecological functions is the niche, the set of strategies that enable a population to persist and define its impacts on the surroundings. Here we present a framework based on manifold learning to organize genomic information into potentially occupied bacterial metabolic niches over time. Manifold learning tries to uncover low-dimensional data structures in high-dimensional data sets that can be used to describe the data in reduced dimensions. We apply the method to re-construct the dynamics of putatively occupied metabolic niches using a long-term bacterial time series from the Baltic Sea, the Linnaeus Microbial Observatory (LMO). The results reveal a relatively low-dimensional space of occupied metabolic niches comprising groups of taxa with similar functional capabilities. Time patterns of occupied niches were strongly driven by seasonality. Some metabolic niches were dominated by one bacterial taxon, whereas others were occupied by multiple taxa, depending on the season. These results illustrate the power of manifold learning approaches to advance our understanding of the links between community composition and functioning in microbial systems. IMPORTANCE The increase in data availability of bacterial communities highlights the need for conceptual frameworks to advance our understanding of these complex and diverse communities alongside the production of such data. To understand the dynamics of these tremendously diverse communities, we need tools to identify overarching strategies and describe their role and function in the ecosystem in a comprehensive way. Here, we show that a manifold learning approach can coarse grain bacterial communities in terms of their metabolic strategies and that we can thereby quantitatively organize genomic information in terms of potentially occupied niches over time. This approach, therefore, advances our understanding of how fluctuations in bacterial abundances and species composition can relate to ecosystem functions and it can facilitate the analysis, monitoring, and future predictions of the development of microbial communities.

Estimation of functional diversity and species traits from ecological monitoring data.

The twin crises of climate change and biodiversity loss define a strong need for functional diversity monitoring. While the availability of high-quality ecological monitoring data is increasing, the quantification of functional diversity so far requires the identification of species traits, for which data are harder to obtain. However, the traits that are relevant for the ecological function of a species also shape its performance in the environment and hence, should be reflected indirectly in its spatiotemporal distribution. Thus, it may be possible to reconstruct these traits from a sufficiently extensive monitoring dataset. Here, we use diffusion maps, a deterministic and de facto parameter-free analysis method, to reconstruct a proxy representation of the species' traits directly from monitoring data and use it to estimate functional diversity. We demonstrate this approach with both simulated data and real-world phytoplankton monitoring data from the Baltic Sea. We anticipate that wider application of this approach to existing data could greatly advance the analysis of changes in functional biodiversity.

Sharp thresholds limit the benefit of defector avoidance in cooperation on networks.

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.

Master stability functions for metacommunities with two types of habitats.

Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the master stability function formalism to inhomogeneous biregular networks having two types of spatial nodes. Notably, this class of systems also allows the investigation of certain types of dynamics on higher-order networks. Combined with the generalized modeling approach to study the linear stability of steady states, this is a powerful tool to numerically asses the stability of large ensembles of systems. We analyze the stability of ecological metacommunities with two distinct types of habitats analytically and numerically in order to identify several sets of conditions under which the dynamics can become stabilized by dispersal. Our analytical approach allows general insights into stabilizing and destabilizing effects in metapopulations. Specifically, we identify self-regulation and negative feedback loops between source and sink populations as stabilizing mechanisms and we show that maladaptive dispersal may be stable under certain conditions.

Generalized Structural Kinetic Modeling: A Survey and Guide.

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.

Not One, but Many Critical States: A Dynamical Systems Perspective.

The past decade has seen growing support for the critical brain hypothesis, i.e., the possibility that the brain could operate at or very near a critical state between two different dynamical regimes. Such critical states are well-studied in different disciplines, therefore there is potential for a continued transfer of knowledge. Here, I revisit foundations of bifurcation theory, the mathematical theory of transitions. While the mathematics is well-known it's transfer to neural dynamics leads to new insights and hypothesis.

Revealing environmentally driven population dynamics of an Arctic diatom using a novel microsatellite PoolSeq barcoding approach.

Ecological stability under environmental change is determined by both interspecific and intraspecific processes. Particularly for planktonic microorganisms, it is challenging to follow intraspecific dynamics over space and time. We propose a new method, microsatellite PoolSeq barcoding (MPB), for tracing allele frequency changes in protist populations. We successfully applied this method to experimental community incubations and field samples of the diatom Thalassiosira hyalina from the Arctic, a rapidly changing ecosystem. Validation of the method found compelling accuracy in comparison with established genotyping approaches within different diversity contexts. In experimental and environmental samples, we show that MPB can detect meaningful patterns of population dynamics, resolving allelic stability and shifts within a key diatom species in response to experimental treatments as well as different bloom phases and years. Through our novel MPB approach, we produced a large dataset of populations at different time-points and locations with comparably little effort. Results like this can add insights into the roles of selection and plasticity in natural protist populations under stable experimental but also variable field conditions. Especially for organisms where genotype sampling remains challenging, MPB holds great potential to efficiently resolve eco-evolutionary dynamics and to assess the mechanisms and limits of resilience to environmental stressors.

A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics.

The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system's Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.

Wireless localization with diffusion maps.

In the Wireless Localization Matching Problem (WLMP) the challenge is to match pieces of equipment with a set of candidate locations based on wireless signal measurements taken by the pieces of equipment. This challenge is complicated by the noise that is inherent in wireless signal measurements. Here we propose the use of diffusion maps, a manifold learning technique, to obtain an embedding of positions and equipment coordinates in a space that enables coordinate comparison and reliable evaluation of assignment quality at very low computational cost. We show that the mapping is robust to noise and using diffusion maps allows for accurate matching in a realistic setting. This suggests that the diffusion-map-based approach could significantly increase the accuracy of wireless localization in applications.

Modern models of trophic meta-communities.

Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

Mapping the bacterial metabolic niche space.

The rise in the availability of bacterial genomes defines a need for synthesis: abstracting from individual taxa, to see larger patterns of bacterial lifestyles across systems. A key concept for such synthesis in ecology is the niche, the set of capabilities that enables a population's persistence and defines its impact on the environment. The set of possible niches forms the niche space, a conceptual space delineating ways in which persistence in a system is possible. Here we use manifold learning to map the space of metabolic networks representing thousands of bacterial genera. The results suggest a metabolic niche space comprising a collection of discrete clusters and branching manifolds, which constitute strategies spanning life in different habitats and hosts. We further demonstrate that communities from similar ecosystem types map to characteristic regions of this functional coordinate system, permitting coarse-graining of microbiomes in terms of ecological niches that may be filled.

Diverse interactions and ecosystem engineering can stabilize community assembly.

The complexity of an ecological community can be distilled into a network, where diverse interactions connect species in a web of dependencies. Species interact directly with each other and indirectly through environmental effects, however to our knowledge the role of these ecosystem engineers has not been considered in ecological network models. Here we explore the dynamics of ecosystem assembly, where species colonization and extinction depends on the constraints imposed by trophic, service, and engineering dependencies. We show that our assembly model reproduces many key features of ecological systems, such as the role of generalists during assembly, realistic maximum trophic levels, and increased nestedness with mutualistic interactions. We find that ecosystem engineering has large and nonlinear effects on extinction rates. While small numbers of engineers reduce stability by increasing primary extinctions, larger numbers of engineers increase stability by reducing primary extinctions and extinction cascade magnitude. Our results suggest that ecological engineers may enhance community diversity while increasing persistence by facilitating colonization and limiting competitive exclusion.

Far-ranging generalist top predators enhance the stability of meta-foodwebs.

Identifying stabilizing factors in foodwebs is a long standing challenge with wide implications for community ecology and conservation. Here, we investigate the stability of spatially resolved meta-foodwebs with far-ranging super-predators for whom the whole meta-foodwebs appears to be a single habitat. By using a combination of generalized modeling with a master stability function approach, we are able to efficiently explore the asymptotic stability of large classes of realistic many-patch meta-foodwebs. We show that meta-foodwebs with far-ranging top predators are more stable than those with localized top predators. Moreover, adding far-ranging generalist top predators to a system can have a net stabilizing effect. These results highlight the importance of top predator conservation.

Manifold cities: social variables of urban areas in the UK.

In the twenty-first century, ongoing rapid urbanization highlights the need to gain deeper insights into the social structure of cities. While work on this challenge can profit from abundant data sources, the complexity of this data itself proves to be a challenge. In this paper, we use diffusion maps, a manifold learning method, to discover hidden manifolds in the UK 2011 census dataset. The census key statistics and quick statistics report 1450 different statistical features for each census output area. Here, we focus primarily on the city of Bristol and the surrounding countryside, comprising 3490 of these output areas. Our analysis finds the main variables that span the census responses, highlighting that university student density and poverty are the most important explanatory variables of variation in census responses.

Introduction to dynamics of manufacturing supply networks.

Manufacturing supply networks are complex dynamic networks that play a crucial role in the economy. Nevertheless, there are so far only few studies that apply modern tools of network science and dynamical system theory to the analysis of these networks. Here, we provide a brief introduction to these types of networks highlighting their basic organization, current challenges, and selected previous work. This paper serves as an introduction to a focus topic consisting of five papers by experts on supply network dynamics.

Impact of cyber-invasive species on a large ecological network.

As impacts of introduced species cascade through trophic levels, they can cause indirect and counter-intuitive effects. To investigate the impact of invasive species at the network scale, we use a generalized food web model, capable of propagating changes through networks with a series of ecologically realistic criteria. Using data from a small British offshore island, we quantify the impacts of four virtual invasive species (an insectivore, a herbivore, a carnivore and an omnivore whose diet is based on a rat) and explore which clusters of species react in similar ways. We find that the predictions for the impacts of invasive species are ecologically plausible, even in large networks. Species in the same taxonomic group are similarly impacted by a virtual invasive species. However, interesting differences within a given taxonomic group can occur. The results suggest that some native species may be at risk from a wider range of invasives than previously believed. The implications of these results for ecologists and land managers are discussed.

Revealing instabilities in a generalized triadic supply network: A bifurcation analysis.

Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.

Master stability functions reveal diffusion-driven pattern formation in networks.

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.