BIOND LAB

The robustness of complex networks was one of the first phenomena studied after the inception of network science. However, many contemporary presentations of this theory do not go beyond the original papers. Here we revisit this topic with the aim of providing a deep but didactic introduction. We pay attention to some complications in the computation of giant component sizes that are commonly ignored. Following an intuitive procedure, we derive simple formulas that capture the effect of common attack scenarios on arbitrary (configuration model) networks. We hope that this easy introduction will help new researchers discover this beautiful area of network science.

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.

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.

The concept of ecosystem services (ES), first introduced in 1970’s, gained mainstream attention in 2005, when the Millennium Ecosystem Assessment formally proposed a definition for it. In spite of this attention, many aspects about the ES concept have remained controversial to date, i.e., their classification, value, generation, link to human well-being, and supportive role as management tool. This review explores the knowledge status of ecosystem services, focusing on those services generated in coastal and marine environments (CMES). A knowledge gap and an underdevelopment of tools to assess CMES is evident in the literature, especially when compared to the progress done in the assessment of land ES. Possible explanations reside on the yet small proportion that the research done on CMES represents for the ecosystem service framework (ESF), in part due to the intrinsic challenges of researching the marine environment, also due to the limited availability of spatial data on marine ecosystems. Nevertheless, the ES concept is getting more attention toward policy-makers and stakeholders, leading to the implementation of an ecosystem services approach (ESA) to the management and protection of CMES. Six lessons are rescued from the literature to improve the ESA: (1) integration of the ESA in a science-policy process; (2) more simplicity for the CMES prediction models; (3) move toward empowering of stakeholders; (4) integration of the value pluralism of CMES with less focus on money; (5) the link of ES to Human Well-being must not been forgotten; and (6) communication of results and social literacy are key.

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.