arXiv subjects

Thilo Gross

Publications and source records attributed to Thilo Gross.

At least 37 records · Page 2Linked to original sources

arXiv2021

Generalized 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 to formulating dynamical models. 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.

q-bio.PE↗

arXiv2020

Mathematical construction of a low-bias high-resolution deprivation index for the United States

The construction of deprivation indices is complicated by the inherent ambiguity in defining deprivation as well as the potential for partisan manipulation. Nevertheless, deprivation indices provide an essential tool for mitigating the effects of deprivation and reducing it through policy interventions. Here we demonstrate the construction of a deprivation index using diffusion maps, a manifold learning technique capable of finding the variables that optimally describe the variations in a dataset in the sense of preserving pairwise relationships among the data points. The method is applied to the 2010 US decennial census. In contrast to other methods the proposed procedure does not select particular columns from the census, but rather constructs an indicator of deprivation from the complete dataset. Due to its construction the proposed index does not introduce biases except those already present in the source data, does not require normative judgment regarding the desirability of certain life styles, and is highly resilient against attempts of partisan manipulation. We demonstrate that the new index aligns well with established income-based deprivation indices but deviates in aspects that are perceived as problematic in some of the existing indices. The proposed procedure provides an efficient way for constructing accurate, high resolution indices. These indices can thus have the potential to become powerful tools for the academic study of social structure as well as political decision making.

physics.soc-ph↗

arXiv2020

Mapping the bacterial ways of life

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 reveal a metabolic niche space with a complex branching geometry, whose branches constitute major strategies spanning life in different habitats and hosts. We further demonstrate that communities from similar ecosystem types map to characteristic regions of this new functional coordinate system, permitting ecological descriptions of microbiomes in terms of large scale metabolic roles that may be filled.

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arXiv2019

A closed form for Jacobian reconstruction from timeseries 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. Here we present a closed form analytical solution for the calculation of a system's Jacobian from a timeseries. Being able to access a system's Jacobian enables us to perform 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 transition. 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.

nlin.CD↗

arXiv2019

Diverse interactions and ecosystem engineering 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 not only with each other but indirectly through environmental effects, however the role of these ecosystem engineers has not yet been considered in models of ecological networks. Here we explore the dynamics of ecosystem assembly, where the colonization and extinction of species within a community 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 higher frequencies of mutualisms. We find that ecosystem engineering has large and nonlinear effects on extinction rates, facilitating robustness by creating niche space, but at the same time increasing the magnitude of extinction cascades. We emphasize the importance of redundancies in engineered effects and show that such redundancy lowers the barriers to colonization, promoting community diversity. Together, our results suggest that ecological engineers may enhance community diversity while increasing persistence by facilitating colonization and limiting competitive exclusion.

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arXiv2019

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.

eess.SP↗

arXiv2019

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 generalised 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, despite increasing the food web size. These results highlight the importance of top predator conservation.

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arXiv2019

Manifold Cities: Social variables of urban areas in the UK

In the 21st 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 data set. 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.

physics.soc-ph↗

arXiv2018

Quantitative analysis of approaches to group marking

Group work, where students work on projects to overcome challenges together, has numerous advantages, including learning of important transferable skills, better learning experience and increased motivation. However, in many academic systems the advantages of group projects clash with the need to assign individualised marks to students. A number of different schemes have been proposed to individualise group project marks, these include marking of individual reflexive accounts of the group work and peer assessment. Here we explore a number of these schemes in computational experiments with an artificial student population. Our analysis highlights the advantages and disadvantages of each scheme and particularly reveals the power of a new scheme proposed here that we call pseudoinverse marking.

cs.CY↗

arXiv2018

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 for large networks robust predictions for the impacts of invasive species can be obtained. 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.

q-bio.PE↗

arXiv2018

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-foodwebs. 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.

physics.soc-ph↗

arXiv2017

Spatial effects in meta-food-webs

In ecology it is widely recognised that many landscapes comprise a network of discrete patches of habitat. The species that inhabit the patches interact with each other through a foodweb, the network of feeding interactions. The meta-foodweb model proposed by Pillai et al. combines the feeding relationships at each patch with the dispersal of species between patches, such that the whole system is represented by a network of networks. Previous work on meta-foodwebs has focussed on landscape networks that do not have an explicit spatial embedding, but in real landscapes the patches are usually distributed in space. Here we compare the dispersal of a meta-foodweb on \ER networks, that do not have a spatial embedding, and random geometric networks, that do have a spatial embedding. We found that local structure and large network distances in spatially embedded networks, lead to meso-scale patterns of patch occupation by both specialist and omnivorous species. In particular, we found that spatial separations make the coexistence of competing species more likely. Our results highlight the effects of spatial embeddings for meta-foodweb models, and the need for new analytical approaches to them.

q-bio.PE↗

arXiv2016

Network Inoculation: Heteroclinics and phase transitions in an epidemic model

In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity in the individuals with adaptive rewiring of the network structure in response to a disease. We show that in this model qualitative changes in the dynamics occur in two phase transitions. In a macroscopic description one of these corresponds to a local bifurcation whereas the other one corresponds to a non-local heteroclinic bifurcation. This model thus provides a rare example of a system where a phase transition is caused by a non-local bifurcation, while both micro- and macro-level dynamics are accessible to mathematical analysis. The bifurcation points mark the onset of a behaviour that we call network inoculation. In the respective parameter region exposure of the system to a pathogen will lead to an outbreak that collapses, but leaves the network in a configuration where the disease cannot reinvade, despite every agent returning to the susceptible class. We argue that this behaviour and the associated phase transitions can be expected to occur in a wide class of models of sufficient complexity.

physics.soc-ph↗

arXiv2016

Temporal and structural heterogeneities emerging in adaptive temporal networks

We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a homogeneous initial configuration, we show that temporal and structural heterogeneities, characteristic of real-world networks, spontaneously emerge. This theoretically tractable model thus contributes to the understanding of the dynamics of human activity and interaction networks.

physics.soc-ph↗

arXiv2016

The influence of dispersal on a predator-prey system with two habitats

Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with migration rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.

physics.bio-ph↗

arXiv2016

Meta-food-chains as a many-layer epidemic process on networks

Notable recent works have focused on the multi-layer properties of coevolving diseases. We point out that very similar systems play an important role in population ecology. Specifically we study a meta food-web model that was recently proposed by Pillai et al. This model describes a network of species connected by feeding interactions, which spread over a network of spatial patches. Focusing on the essential case, where the network of feeding interactions is a chain, we develop an analytical approach for the computation of the degree distributions of colonized spatial patches for the different species in the chain. This framework allows us to address ecologically relevant questions. Considering configuration model ensembles of spatial networks, we find that there is an upper bound for the fraction of patches that a given species can occupy, which depends only on the networks mean degree. For a given mean degree there is then an optimal degree distribution that comes closest to the upper bound. Notably scale-free degree distributions perform worse than more homogeneous degree distributions if the mean degree is sufficiently high. Because species experience the underlying network differently the optimal degree distribution for one particular species is generally not the optimal distribution for the other species in the same food web. These results are of interest for conservation ecology, where, for instance, the task of selecting areas of old-growth forest to preserve in an agricultural landscape, amounts to the design of a patch network.

physics.soc-ph↗

arXiv2016

Impact of dispersal on the stability of metapopulations

Dispersal is a key ecological process, that enables local populations to form spatially extended systems called metapopulations. In the present study, we investigate how dispersal affects the linear stability of a general single-species metapopulation model. We discuss both the influence of local within-patch dynamics and the effects of various dispersal behaviors on stability. We find that positive density-dependent dispersal and positive density-dependent settlement are destabilizing dispersal behaviors while negative density-dependent dispersal and negative density-dependent settlement are stabilizing. It is also shown that dispersal has a stabilizing impact on heterogeneous metapopulations that correlates positively with the number of patches and the connectance of metapopulation networks.

q-bio.PE↗

arXiv2015

Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes

One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been shown that heterogeneity can lower the epidemic threshold at which epidemics can invade the system. Network heterogeneity can thus allow diseases with lower transmission probabilities to persist and spread. Here, we point out that for real world applications, this result should not be regarded independently of the intra-individual heterogeneity between people. Our results show that, if heterogeneity among people is taken into account, networks that are more heterogeneous in connectivity can be more resistant to epidemic spreading. We study a susceptible-infected-susceptible model with adaptive disease avoidance. Results from this model suggest that this reversal of the effect of network heterogeneity is likely to occur in populations in which the individuals are aware of their subjective disease risk. For epidemiology, this implies that network heterogeneity should not be studied in isolation.

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