1,721,094 research outputs found
Modelling Ecological Systems from a Niche Theory to Lotka-Volterra Equations
No full textThis paper is an attempt to analyze the notion of ecological niche as a community of different species and of ecosystem as a set of niches in order to formulate a dynamical model for an ecosystem. Our assumption is that the concept of fitness landscape allows to model the phenotype dynamics of an ensemble of species as a stochastic process. To take into account the interaction structure of different communities in the niches and the environment we introduce an ecological fitness potential to formulate a Lotka-Volterra system which describes the evolution of a mutual ecosystem in presence of finite resources. To explicitly consider the effect of fluctuations in the numerousness of the species, we associate a master equation to the average Lotka-Volterra system and we study the conditions of existence of a detailed balance equilibrium (i.e. a thermodynamic equilibrium) for the ecosystem. The explicit solution for the equilibrium probability distribution is a multinomial negative distribution and we discuss the relation between the detailed balance condition and relative species abundance distribution in the framework of Hubbell’s neutral theory. Moreover the theoretical distribution implies the existence of a correlation among the relative species distribution associated to the different communities. We use numerical simulations to illustrate the results on simple models
A PROBABILISTIC PHENOTYPE DYNAMICAL MODEL FOR SYMPATRIC SPECIATION: SOME PROPERTIES AND NUMERICAL RESULTS
No full textSympatric speciation is an important phenomenon in Evolution: A population being able to express two different phenotypes gives rise to a new species without a physical separation from the original population. In this paper, we describe a model that describes the sympatric speciation process using a population dynamics approach. Our aim is to point out some dynamical features that could be observed in a population where a sympatric speciation process is going on. Some interesting stochastic effects are discussed by means of numerical simulations
Master Equation and Relative Species Abundance Distribution for Lotka-Volterra Models of Interacting Ecological Communities
No full textThe understanding of the factors controlling the dynamics of interacting species is a fundamental problem in ecology. The nature of the interactions among different species is usually not completely understood, but it is assumed that the species interaction plays an important role in the ecosystems properties. However recent studies point out as a neutral
hypothesis of non-interacting species with an external source from the surrounding environment allows to explain the relative species abundance (RSA) distribution when the community has reached a stationary situation. In this paper we use a Lotka-Volterra model to derive the (RSA) distribution in the case of different communities which interact each other. We derive a Master equation to study the join RSA distribution of the communities near the stationary state and their correlation. These results suggest a possible explanation of the deviation from the neutral models of empirical RSA distributions
TOWARDS A STATISTICAL PHYSICS OF HUMAN MOBILITY
Full text linkIn this paper, we extend some ideas of statistical physics to describe the properties of human mobility. From a physical point of view, we consider the statistical empirical laws of private cars mobility, taking advantage of a GPS database which contains a sampling of the individual trajectories of 2% of the whole vehicle population in an Italian region. Our aim is to discover possible universal laws" that can be related to the dynamical cognitive features of individuals. Analyzing the empirical trip length distribution we study if the travel time can be used as universal cost function in a mesoscopic model of mobility. We discuss the implications of the elapsed times distribution between successive trips that shows an underlying Benford's law, and
we study the rank distribution of the average visitation frequency to understand how people organize their daily agenda. We also propose simple stochastic models to suggest possible explanations of the empirical observations and we compare our results with analogous results on statistical properties of human mobility presented in the literature
Random Walk Approximation for Stochastic Processes on Graphs
Full text linkWe introduce the Random Walk Approximation (RWA), a new method to approximate the stationary solution of master equations describing stochastic processes taking place on graphs. Our approximation can be used for all processes governed by non-linear master equations without long-range interactions and with a conserved number of entities, which are typical in biological systems, such as gene regulatory or chemical reaction networks, where no exact solution exists. For linear systems, the RWA becomes the exact result obtained from the maximum entropy principle. The RWA allows having a simple analytical, even though approximated, form of the solution, which is global and easier to deal with than the standard System Size Expansion (SSE). Here, we give some theoretically sufficient conditions for the validity of the RWA and estimate the order of error calculated by the approximation with respect to the number of particles. We compare RWA with SSE for two examples, a toy model and the more realistic dual phosphorylation cycle, governed by the same underlying process. Both approximations are compared with the exact integration of the master equation, showing for the RWA good performances of the same order or better than the SSE, even in regions where sufficient conditions are not met
Congestion Transition on Random Walks on Graphs
Full text linkThe formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Dynamical systems applied to economic science. A Sraffian supermultiplier model with the addition of inventory dynamics
Full text linkThe dynamic study of economic systems is an area of Economics that is now a century old, starting with the first economic growth models of Harrod-Domar. Through thework of economist Nicholas Kaldor and the eclectic Richard M. Goodwin, non-linear relationships have made their appearance in endogenous growth models, which are, we might say, the gateway to complex systems. In this work, we will study a series of models that
deal with the mathematisation of the business cycle and the study of its fluctuations.
In particular, the absolute protagonist will be the dynamic model of the Sraffian Supermultiplier, belonging precisely to the school of economic thought initiated by the work of Italian economist Piero Sraffa. Although the author will attempt to explain the differences
between the various schools of thought and introduce notions of economics, the central theme of the work will be the addition of inventory fluctuations to the Sraffian Supermultiplier model developed by Freitas and Serrano (2015). We firmly believe
that this topic deserves detailed investigation within the Sraffian School, not only for its mathematical content, but, above all, for the addition of an element of realism to the study of economic fluctuations and endogenous growth
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