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Lévy Processes in Animal Movement and Dispersal

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Universitat de Barcelona. Departament d'Ecologia

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[eng]  The general aim of this thesis was to develop a theoretical framework in order to study large-scale animal movements and/or dispersal processes as random search strategies. The framework was based on statistical physics methods and concepts related to a class of stochastic processes based on the Lévy-stable distribution (the so-called Lévy processes). In particular, we modeled animal movement and dispersal processes by means of a new class of random walks based on the Lévy-stable distribution (the so-called Lévy flights). Lévy flight models introduce two relevant long-term statistical properties: super-diffusion and scale invariance. Both phenomena have been observed in large-scale animal movement and dispersal data, and impinge directly into organisms' encounter probabilities at both individual (e.g., search strategies) and population (e.g., colonization of new habitats) organizational levels. The approach is novel not only because of the methodology used (based on the statistical physics related to Lévy processes), but also because it is founded on statistical principles usually understated in animal ecology. To achieve this general objective we carried out three main studies, which define the main parts of the thesis. First, we quantified the variations in encounter rates due to the statistical properties provided by Lévy walking particles in spatially explicit systems. We carried out a series of numerical simulations in spatially explicit systems (1D, 2D, and 3D) where randomly moving particles (Lévy random walkers) must find each other. The simulations were meant to represent different encounter scenarios and different encounter dynamics: destructive and non-destructive. We showed that in certain scenarios encounter rate variation was shaped by the nature of the statistical properties of movement rather than by physical aspects of the particles (organisms) such as size or velocity. In particular, super-diffusion and scale invariance were relevant at low resource densities and/or when the search processes involve low spatial dimensionality. We also showed how the movement trajectories of the searching particles could be optimized depending on the type of encounter dynamics (destructive or not), and the mobility of the target particles (i.e., both velocity and super-diffusive properties). Second, we studied how and why Lévy flight properties (i.e., scale invariance, and super-diffusion) should be sustained by specific animal movement mechanisms. We showed an organism capable to adjust its search statistics as a function of resource concentration. As resource decreased the marine heteroflagellate Oxhyrris marina changed from a Brownian to a Lévy search statistics. Changes in the helical component of the animal movement were also tracked and interpreted. The biological mechanism allowing the main statistical change was also identified: the transient arrests of the longitudinal flagellum provided scale invariant intermittence to the movement. Assuming random walk models as a necessary tool to understand how animals face environmental uncertainty, we also analyzed the statistical differences between Lévy walks and another type of random walk models commonly used to fit animal movement data, the correlated random walks. This analysis allowed us to understand better why we should expect Lévy flight statistical properties to be behaviorally adaptive in living organisms. Third, we establish a link between the individual and the population level of organization by modeling "population dispersal strategies" as Lévy processes. A Lévy-dispersal kernel is the one based on a Lévy-stable distribution. We modeled (meta) population dispersal strategies by means of Lévy-dispersal kernels. In particular, we studied how different Lévy flight dispersal strategies are optimized depending on the underlying landscape architecture (e.g., spatial correlation, fragmentation, etc.). Finally, as a first step towards the introduction of Lévy-dispersal kernels in the context of metapopulation theory, we developed a model (both numerical and analytic) to study the role of dispersal range in the persistence and dynamics of metapopulations living in fragmented habitats.

# metadata.dc.description.abstract[].value
[cat] L'objectiu principal d'aquesta tesi va ser desenvolupar un marc teòric basat en mètodes i conceptes de física estadística per tal d'estudiar el moviment animal i els fenòmens de dispersió. A escales espacio-temporals grans, el moviment dels animals i els fenòmens de dispersió poden ésser entesos com a processos de cerca a l'atzar. Concretament, nosaltres hem modelat el moviment animal i els processos de dispersió en base a una classe de passeigs a l'atzar coneguts com a vols de Lévy que es fonamenten en la distribució estable de Lévy. Els vols de Lévy s'inclouen en una classe més àmplia de processos estocàstics tots ells basats en la distribució estable de Lévy i que reben el nom genèric de processos de Lévy. Els vols de Lévy introdueixen en el món dels passeigs a l'atzar dues propietats estadístiques rellevants: la super-difusió i la invariànça d'escala. Tots dos fenòmens han estat descrits en relació al moviment dels animals a gran escala i/o en relació a certs processos de dispersió. Tots dos fenòmens tenen implicacions directes sobre les probabilitats d'encontre tant a nivell individual (processos de cerca de recursos) com a nivell poblacional (processos de colonització d'habitats fragmentats). L'aproximació al problema del moviment animal i la dispersió proposada en aquesta tesi, no només és novedosa en el sentit estrictament metodològic (i.e., aplicació de la física estadística i dels processos de Lévy al moviment animal), sinó també perquè es basa en una sèrie de principis estadístics que fins ara no han estat considerats en l'estudi del moviment animal. Les principals conclusions que es poden extreure del treball realitzat són: 1) les propietats estadístiques lligades als processos de tipus Lévy (i.e., super-difusió i invariànça d'escala) incrementen les taxes d'encontre en situacions de cerca a l'atzar, 2) existeixen organismes capaços de provocar l'emergència d'aquestes propietats estadístiques en una situació de cerca a l'atzar, 3) a nivell poblacional, fenòmens de dispersió de tipus Lévy incrementen la taxa de colonització en hàbitats molt fragmentats, i 4) la dispersió de llarg abast facilita l'existència de metapoblacions en hàbitats fragmentats.

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Tesis Doctorals - Departament - Ecologia

# metadata.dc.title[].value
Lévy Processes in Animal Movement and Dispersal