From individual-based models to partial differential equations

Gómez-Mourelo, Pablo

doi:10.1016/j.ecolmodel.2005.05.014

Cited by 19 publications

(14 citation statements)

References 31 publications

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“…Consequently, a third route is to formally connect an IBM with a PDE model via some scaling-based approach: by drawing clear lines between the data-friendly IBM and the terms and parameters of a macroscopic model, their distinct advantages can be exploited. We refer to [20,21] for recent reviews with regards to biological movement; in the context of the present article, we particularly mention [22,23].…”

Section: Modelling Movement In Ecologymentioning

confidence: 99%

Navigating the flow: individual and continuum models for homing in flowing environments

Painter

Hillen

2015

J. R. Soc. Interface.

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Navigation for aquatic and airborne species often takes place in the face of complicated flows, from persistent currents to highly unpredictable storms. Hydrodynamic models are capable of simulating flow dynamics and provide the impetus for much individual-based modelling, in which particlesized individuals are immersed into a flowing medium. These models yield insights on the impact of currents on population distributions from fish eggs to large organisms, yet their computational demands and intractability reduce their capacity to generate the broader, less parameter-specific, insights allowed by traditional continuous approaches. In this paper, we formulate an individual-based model for navigation within a flowing field and apply scaling to derive its corresponding macroscopic and continuous model. We apply it to various movement classes, from drifters that simply go with the flow to navigators that respond to environmental orienteering cues. The utility of the model is demonstrated via its application to 'homing' problems and, in particular, the navigation of the marine green turtle Chelonia mydas to Ascension Island.

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Section: Modelling Movement In Ecologymentioning

confidence: 99%

Navigating the flow: individual and continuum models for homing in flowing environments

Painter

Hillen

2015

J. R. Soc. Interface.

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“…This work is extended to higher dimensions and to more general kinematic rules in Ref. [40,41]. However, our model is based on dynamic rules and the corresponding continuum limit is much more difficult to rigorously justify.…”

Section: Continuum Modelmentioning

confidence: 99%

State transitions and the continuum limit for a 2D interacting, self-propelled particle system

Chuang

D’Orsogna²,

Marthaler

et al. 2007

Physica D: Nonlinear Phenomena

265

312

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We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the selfpropulsion and interaction potential parameters. In this paper, we utilize a procedure which, in a definitive way, connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one.

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“…In this line, two previous studies in the area of biology can be cited to illustrate quantitative results in the comparison of IBMs and PDEs, comparisons of the observed macroscopic and microscopic behaviour of an IBM with the corresponding differential equation counterpart of this IBM were shown. The first study is about an application to the upstream movement of elvers [52] and the second is a study on yeast populations [47] . These types of works provide a further insight into the possibilities of both modelling tools and their connections.…”

Section: Discussionmentioning

confidence: 99%

A connection between discrete individual-based and continuous population-based models: A forest modelling case study

Gómez-Mourelo

Gisbert

2013

AIR

Self Cite

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Modelling is perceived as a way of dealing with real life activities. The aim of this work is to compare two approaches to study forest dynamics, namely discrete individual-based and continuous population-based models, in order to contribute to an improvement in their use among researchers. An analysis of the strengths, weaknesses, opportunities and threats of the two different approaches, jointly with a mention of the state-of-the-art, allows us to illustrate this discussion. We will also provide a bridge or connection between these two modelling methodologies. This link will be developed in detail in a particular study case. Firstly, an individual-tree based model to deal with dynamics of forests is presented. Secondly, this model is scaled up to a system of partial differential equations, which represents the limiting behaviour of the individualbased model.

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From individual-based models to partial differential equations

Cited by 19 publications

References 31 publications

Navigating the flow: individual and continuum models for homing in flowing environments

Navigating the flow: individual and continuum models for homing in flowing environments

State transitions and the continuum limit for a 2D interacting, self-propelled particle system

A connection between discrete individual-based and continuous population-based models: A forest modelling case study

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