Sustainability and Bifurcations of Positive Attractors

In this paper we show how sustainability can be rigorously defined by making reference to the positivity of the attractors of a dynamical system. Consistently, the sustainability analysis with respect to various system and policy parameters can be performed by using specialized software for the study of the bifurcations of nonlinear dynamical systems. By means of an example concerning the tourism industry, we show how the analysis can be systematically organized and how easy it is to interpret the results of the numerical bifurcation analysis

The time varying network of urban space uses in Milan

Abstract In a metropolis, people movements design intricate patterns that change on very short temporal scales. Population mobility obviously is not random, but driven by the land uses of the city. Such an urban ecosystem can interestingly be explored by integrating the spatial analysis of land uses (through ecological indicators commonly used to characterize natural environments) with the temporal analysis of human mobility (reconstructed from anonymized mobile phone data). Considering the city of Milan (Italy) as a case study, here we aimed to identify the complex relations occurring between the land-use composition of its neighborhoods and the spatio-temporal patterns of occupation made by citizens. We generated two spatially explicit networks, one static and the other temporal, based on the analysis of land uses and mobile phone data, respectively. The comparison between the results of community detection performed on both networks revealed that neighborhoods that are similar in terms of land-use composition are not necessarily characterized by analogous temporal fluctuations of human activities. In particular, the historical concentric urban structure of Milan is still under play. Our big data driven approach to characterize urban diversity provides outcomes that could be important (i) to better understand how and when urban spaces are actually used, and (ii) to allow policy makers improving strategic development plans that account for the needs of metropolis-like permanently changing cities

The temporal patterns of disease severity and prevalence in schistosomiasis

Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra-and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility. (C) 2015 AIP Publishing LLC

Conditions for transient epidemics of waterborne disease in spatially explicit systems

Waterborne diseases are a diverse family of infections transmitted through ingestion of-or contact with-water infested with pathogens. Outbreaks of waterborne infections often show well-defined spatial signatures that are typically linked to local eco-epidemiological conditions, water-mediated pathogen transport and human mobility. In this work, we apply a spatially explicit network model describing the transmission cycle of waterborne pathogens to determine invasion conditions in metacommunities endowed with a realistic spatial structure. Specifically, we aim to define conditions under which pathogens can temporarily colonize a set of human communities, thus triggering a transient epidemic outbreak. To that end, we apply generalized reactivity analysis, a recently developed methodological framework for the study of transient dynamics in ecological systems subject to external perturbations. The study of pathogen invasion is complemented by the detection of the spatial signatures associated with the perturbations to a disease-free system that are expected to be amplified the most over different time scales. Understanding the drivers of waterborne disease dynamics over time scales that are relevant to epidemic and/or endemic transmission is a crucial, cross-disciplinary challenge, as large portions of the developing world still struggle to cope with the burden of these infections

Movement Strategies of Seed Predators as Determinants of Plant Recruitment Patterns

Plant recruitment in nature exhibits several distinctive patterns ranging from hump shaped to monotonically decreasing with distance from the seed source. We investigate the role of post-dispersal seed predation in shaping these patterns, introducing a new mechanistic model that explicitly accounts for the movement strategy used by seed eaters. The model consists of two partial differential equations describing the spatiotemporal dynamics of both seed and predator densities. The movement strategy is defined by how predators move in response to the different cues they can use to search for seeds. These cues may be seed density, seed intake, distance from the plant, density of conspecific foragers, or a mixture of these four.The model is able to reproduce all the basic plant recruitment pat-terns found in the field. We compare the results to those of the ideal free distribution (IFD) theory and show that hump-shaped plant recruitment patterns cannot be generated by IFD predators and, in general, by foragers that respond exclusively to seed density. These foragers can produce only non increasing patterns, the shapes of which are determined by the foragers’ navigation capacities. In contrast, hump-shaped patterns can be produced by distance-responsive predators or by foragers that use conspecifics as a cue for seed abundanc

A theoretical approach to tourism sustainability

This paper shows that it is difficult, if not impossible, to formulate policies that guarantee that tourism can be maintained for a long time without severely impacting on the environment. The analysis is purely theoretical and is based on very simple and general assumptions about the interactions between the three main components of the system: the tourists, the environment, and the capital. These assumptions are encapsulated in a so-called minimal model, used to predict the economic and environmental impact of any given policy. This paper is of value for three reasons. First, it introduces the approach of minimal descriptive models in the context of tourism, which has traditionally been dominated by the use of black-box econometric models. Second, the specific results are quite interesting. We show, in fact, that tourism sustainability can be achieved, provided agents are prudent about reinvesting their profits and are willing to protect the environment, but that sustainability is very often at risk, because unforeseen shocks can easily trigger a switch from a profitable and compatible behavior to an unprofitable or incompatible one. These results are in line with conventional wisdom and observations, but the interesting fact is that here they are theoretically derived from a few very simple and abstract premises. Third, although not directly related to the problem of tourism but rather to the general topic of sustainability, this is one of the first times that the notion of sustainability, which is more and more pervasive in the field of resource management, is interpreted strictly in terms of the structural properties of the attractors of a dynamic system. This creates an important and promising bridge between sustainability and bifurcation theory, one of the most important areas of systems analysis

Modelling carbon export mediated by biofouled microplastics in the Mediterranean Sea

Marine microplastics can be colonized by biofouling microbial organisms, leading to a decrease in microplastics' buoyancy. The sinking of biofouled microplastics could therefore represent a novel carbon export pathway within the ocean carbon cycle. Here, we model how microplastics are biofouled by diatoms, their consequent vertical motion due to buoyancy changes, and the interactions between particle-attached diatoms and carbon pools within the water column. We initialize our Lagrangian framework with biogeochemical data from NEMO-MEDUSA-2.0 and estimate the amount of organic carbon exported below 100 m depth starting from different surface concentrations of 1-mm microplastics. We focus on the Mediterranean Sea that is characterized by some of the world's highest microplastics concentrations and is a hotspot for biogeochemical changes induced by rising atmospheric carbon dioxide levels. Our results show that the carbon export caused by sinking biofouled microplastics is proportional to the concentration of microplastics in the sea surface layer, at least at modeled concentrations. We estimate that, while current concentrations of microplastics can modify the natural biological carbon export by < 1%, future concentrations projected under business-as-usual pollution scenarios may lead to carbon exports up to 5% larger than the baseline (1998–2012) by 2050. Areas characterized by high primary productivity, that is, the Western and Central Mediterranean, are those where microplastics-mediated carbon export results to be the highest. While highlighting the potential and quantitatively limited occurrence of this phenomenon in the Mediterranean Sea, our results call for further investigation of a microplastics-related carbon export pathway in the global ocean