Scaling as a key conceptual tool for the interpretation of empirical and experimental patterns in ecology and biology

This thesis is concerned with regular patterns found in ecology and biology, their linkages and the statistical description of their fluctuations around average trends. Among such patterns, often conforming to power laws, well-known examples include the Species-Area relationship (SAR), quantifying the increase of the number of species S inhabiting an ecosystem with ecosystem area, and the scale-invariant body size spectrum, routinely observed, e.g., in aquatic ecosystems. In biology, Kleiber's law is an allometric relationship describing how metabolic rates scale with an organism's body size. While ecological laws have often been studied independently, simple heuristic reasonings show that they are linked. The need for a unifying effort in ecology, coherently synthesizing the vast and diverse set of empirical observations across scales, has been often voiced. However, a theoretical framework answering this need was still lacking. Furthermore, ecological variables are the result of the interplay between several stochastic ecological processes, and are therefore stochastic variables fluctuating around average values. Ecological and biological scaling laws typically make predictions for such averages, but the issue of fluctuations received scarce attention in the literature. Similarly, biological fluctuations have been typically neglected in the study of the size-scaling of metabolic rates, even though body sizes and metabolic rates may have a significant variability within a species. Fluctuations may be relevant to interpret empirical observations, judge the reliability of predictions and understand ecosystem dynamics. An hypothesis for the distribution of abundances and body sizes of species inhabiting an ecosystem of finite area is proposed here. The hypothesis is inspired by finite-size scaling and is used to derive macroecological patterns and their linkages within a coherent theoretical framework. Stochastic models of community dynamics are used to support the hypothesis, and the derived linkages are tested on empirical datasets. Several stochastic models of community dynamics are also used here to study the fluctuations of S and how they scale with the average S. The intra-specific variability of metabolic rates and body sizes is investigated experimentally using freshwater phytoplankton species by nanoscale secondary ion mass spectrometry (NanoSIMS). The linkages among ecological scaling laws predicted by the theoretical framework are verified in several empirical datasets. Theoretical generalizations including deviations from pure power-law behavior and heavy-tailed intra-specific size distributions are also addressed. The theoretical study of the relative scaling of the fluctuations of S with the mean $\langle S \rangle$ in various community dynamics models shows that different ecological processes predict radically different fluctuations scalings, highlighting the need of empirical investigations to sort out which scenario applies to real ecosystems. Experiments on phytoplankton metabolic rate scaling with body size suggest that intra-specific metabolic rate distributions are described by a universal scaling form across different taxa and over three orders of magnitude in body size. This thesis, along with previous works, suggests that scaling concepts derived for inanimate systems can provide new insights into the dynamics of ecosystems and help unraveling regularities across scales of biological complexity

Betweenness centrality for temporal multiplexes

Betweenness centrality quantifies the importance of a vertex for the information flow in a network. We propose a flexible definition of betweenness for temporal multiplexes, where geodesics are determined accounting for the topological and temporal structure and the duration of paths. We propose an algorithm to compute the new metric via a mapping to a static graph. We show the importance of considering the temporal multiplex structure and an appropriate distance metric comparing the results with those obtained with static or single-layer metrics on a dataset of $\sim 20$k European flights

Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time

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. \u201ctrips\u201d, 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\u2019 centrality losses due to delays in the flight network

Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time

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 paths 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

Network-wide assessment of ATM mechanisms using an agent-based model

This paper presents results from the SESAR ER3 Domino project. Three mechanisms are assessed at the ECAC-wide level: 4D trajectory adjustments (a combination of actively waiting for connecting passengers and dynamic cost indexing), flight prioritisation (enabling ATFM slot swapping at arrival regulations), and flight arrival coordination (where flights are sequenced in extended arrival managers based on an advanced cost-driven optimisation). Classical and new metrics, designed to capture network effects, are used to analyse the results of a micro-level agent-based model. A scenario with congestion at three hubs is used to assess the 4D trajectory adjustment and the flight prioritisation mechanisms. Two different scopes for the extended arrival manager are modelled to analyse the impact of the flight arrival coordination mechanism. Results show that the 4D trajectory adjustments mechanism succeeds in reducing costs and delays for connecting passengers. A trade-off between the interests of the airlines in reducing costs and those of non-connecting passengers emerges, although passengers benefit overall from the mechanism. Flight prioritisation is found to have no significant effects at the network level, as it is applied to a small number of flights. Advanced flight arrival coordination, as implemented, increases delays and costs in the system. The arrival manager optimises the arrival sequence of all flights within its scope but does not consider flight uncertainties, thus leading to sub-optimal actions.Comment: 20 pages, 6 figures, Journal of Air Transport Managemen

On the probabilistic nature of the species-area relation

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR. (C) 2018 The Authors. Published by Elsevier Ltd

Phenomenological Modeling of the Motility of Self-Propelled Microorganisms

The motility of microorganisms in liquid media is an important issue in active matter, and it is not yet fully understood. Previous theoretical approaches dealing with the microscopic description of microbial movement have modeled the propelling force exerted by the organism as a gaussian white noise term in the equation of motion. We present experimental results for ciliates of the genus "Colpidium", which do not agree with the white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion

Community Detection for Air Traffic Networks and Its Application in Strategic Flight Planning

An environmentally and economically sustainable air traffic management system must rely on fast models to assess and compare various alternatives and decisions at the different flight planning levels. Due to the numerous interactions between flights, mathematical models to manage the traffic can be computationally time-consuming when considering a large number of flights to be optimised at the same time. Focusing on demand\u2013capacity imbalances, this paper proposes an approach that permits to quickly obtain an approximate but acceptable solution of this problem. The approach consists in partitioning flights into subgroups that influence each other only weakly, solving the problem independently in each subgroup, and then aggregating the solutions. The core of the approach is a method to build a network representing the interactions among flights, and several options for the definition of an interaction are tested. The network is then partitioned with existing community detection algorithms. The results show that applying a strategic flight planning optimisation algorithm on each subgroup independently reduces significantly the computational time with respect to its application on the entire European air traffic network, at the cost of few and small violations of sector capacity constraints, much smaller than those actually observed on the day of operations