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Seasonal spatial distributions of amphibians and Gibbs measures: a new approach inspired by Hamiltonian mechanics.

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Title: Seasonal spatial distributions of amphibians and Gibbs measures: a new approach inspired by Hamiltonian mechanics.
Authors: Ballesteros, Miguel1 (AUTHOR) miguel.ballesteros@iimas.unam.mx, Iniesta, Diego1 (AUTHOR), Morales, Luis B.1 (AUTHOR), Garro, Guillermo1 (AUTHOR), Hernández, Omar2 (AUTHOR), Aguilar, Daniel2 (AUTHOR), Guillén, Fedro1 (AUTHOR)
Source: Environmental & Ecological Statistics. Jun2026, Vol. 33 Issue 2, p699-735. 37p.
Subject Terms: *Hamiltonian mechanics, *Markov random fields, *Habitat selection, *Amphibians, *Population dynamics, *Spatial analysis (Statistics), *Dispersal (Ecology)
Abstract: We introduce a model that describes the population dynamics of species in ecology. Our model employs a Hamiltonian framework from physics, where the balance between species dispersal and environmental attraction is governed by two competing energy terms: a kinetic-like term driving homogeneous spatial spread, and a potential-like term generating attraction to key landscape features such as rivers, with a coupling constant modulating their seasonal balance. An innovative aspect that we address in this paper is a dynamical picture in ecology in which we model the different distributions of individuals throughout the year (four seasons). Our main contribution is focused on applied mathematics and statistics. Our model presents a new perspective on how Markov random fields (Gibbs measures) can be used to describe spatial statistics in the context of ecology. We present a case study of our model using Plectrohyla sagorum, a vulnerable species of amphibians. Our model indicates that Plectrohyla sagorum concentrates near the river in the dry season and disperses as precipitation increases. We show our results using heat maps describing this seasonal variation, showing peak density on the river in winter. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
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Header DbId: enr
DbLabel: Energy & Power Source
An: 194545649
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Label: Title
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  Data: Seasonal spatial distributions of amphibians and Gibbs measures: a new approach inspired by Hamiltonian mechanics.
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  Data: <searchLink fieldCode="AR" term="%22Ballesteros%2C+Miguel%22">Ballesteros, Miguel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> miguel.ballesteros@iimas.unam.mx</i><br /><searchLink fieldCode="AR" term="%22Iniesta%2C+Diego%22">Iniesta, Diego</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Morales%2C+Luis+B%2E%22">Morales, Luis B.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Garro%2C+Guillermo%22">Garro, Guillermo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hernández%2C+Omar%22">Hernández, Omar</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Aguilar%2C+Daniel%22">Aguilar, Daniel</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Guillén%2C+Fedro%22">Guillén, Fedro</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Environmental+%26+Ecological+Statistics%22">Environmental & Ecological Statistics</searchLink>. Jun2026, Vol. 33 Issue 2, p699-735. 37p.
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  Data: *<searchLink fieldCode="DE" term="%22Hamiltonian+mechanics%22">Hamiltonian mechanics</searchLink><br />*<searchLink fieldCode="DE" term="%22Markov+random+fields%22">Markov random fields</searchLink><br />*<searchLink fieldCode="DE" term="%22Habitat+selection%22">Habitat selection</searchLink><br />*<searchLink fieldCode="DE" term="%22Amphibians%22">Amphibians</searchLink><br />*<searchLink fieldCode="DE" term="%22Population+dynamics%22">Population dynamics</searchLink><br />*<searchLink fieldCode="DE" term="%22Spatial+analysis+%28Statistics%29%22">Spatial analysis (Statistics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Dispersal+%28Ecology%29%22">Dispersal (Ecology)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We introduce a model that describes the population dynamics of species in ecology. Our model employs a Hamiltonian framework from physics, where the balance between species dispersal and environmental attraction is governed by two competing energy terms: a kinetic-like term driving homogeneous spatial spread, and a potential-like term generating attraction to key landscape features such as rivers, with a coupling constant modulating their seasonal balance. An innovative aspect that we address in this paper is a dynamical picture in ecology in which we model the different distributions of individuals throughout the year (four seasons). Our main contribution is focused on applied mathematics and statistics. Our model presents a new perspective on how Markov random fields (Gibbs measures) can be used to describe spatial statistics in the context of ecology. We present a case study of our model using Plectrohyla sagorum, a vulnerable species of amphibians. Our model indicates that Plectrohyla sagorum concentrates near the river in the dry season and disperses as precipitation increases. We show our results using heat maps describing this seasonal variation, showing peak density on the river in winter. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1007/s10651-025-00690-6
    Languages:
      – Code: eng
        Text: English
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        PageCount: 37
        StartPage: 699
    Subjects:
      – SubjectFull: Hamiltonian mechanics
        Type: general
      – SubjectFull: Markov random fields
        Type: general
      – SubjectFull: Habitat selection
        Type: general
      – SubjectFull: Amphibians
        Type: general
      – SubjectFull: Population dynamics
        Type: general
      – SubjectFull: Spatial analysis (Statistics)
        Type: general
      – SubjectFull: Dispersal (Ecology)
        Type: general
    Titles:
      – TitleFull: Seasonal spatial distributions of amphibians and Gibbs measures: a new approach inspired by Hamiltonian mechanics.
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            NameFull: Ballesteros, Miguel
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            NameFull: Iniesta, Diego
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            NameFull: Morales, Luis B.
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            NameFull: Hernández, Omar
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            NameFull: Aguilar, Daniel
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 33
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          Titles:
            – TitleFull: Environmental & Ecological Statistics
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