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Multi-scale spatial ecology analyses: a Kullback information approach

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Abstract

Context

The way organisms are patterned in space dictates the outcome of many ecological processes such as growth, survival, colonization, and migration. The field of landscape ecology has developed quantitative metrics to describe spatial patterning using the concept of entropy. However, a general theory of how these patterns relate to one another within and between different organizational levels and over different spatial scales has remained incomplete.

Objectives

Review how statistical versions of entropy have been applied to detect spatial organization and propose a theoretical framework to use Kullback–Leibler relative entropy for cross-scale analyses on a landscape of any size.

Methods

Examine previous efforts using entropy in landscape ecology and introduce a Kullback Information Index as a next step in the science of scaling.

Results

Entropic indices can provide compositional and configurational information about a system and can be used to detect landscape patterns. Yet, most entropy-based metrics are scale-dependent, highlighting the need to find a common currency for comparative analysis across scales. The non-symmetric unitless property of the Kullback–Leibler relative entropy may remedy that since it is theoretically capable of comparing variables and scales. The proposed framework can be extended to describe any system that contains scalable modules of interest, which will advance scaling in landscape ecology and other disciplines.

Conclusions

The Kullback Information Index describes landscapes’ compositional and configurational patterns across scales. Since relative entropy is connected to information theory and thermodynamics, the framework’s results can be interpreted within a broader ecological context.

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Data availability

The data is available in a supplementary folder. The figures were created with BioRender.com.

Code availability

Custom code is available as part of supplementary material.

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Acknowledgements

Thanks to Joel Huckeba and Caleigh Cornell for providing helpful advice throughout the writing process. We are grateful for the anonymous reviewers and the editor for taking time to assess our manuscript, providing the authors with constructive and insightful comments.

Funding

No funding was received for conducting this study.

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Authors and Affiliations

  1. Institute for Biodiversity and Ecosystem Dynamics (IBED), University of Amsterdam, Amsterdam, The Netherlands

    Gintarė Huckeba

  2. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    Bjarne Andresen

  3. Hawaiʻi Institute of Marine Biology, University of Hawaiʻi at Mānoa, Honolulu, USA

    Ty N. F. Roach

  4. The Viral Information Institute, San Diego State University, San Diego, CA, USA

    Ty N. F. Roach

Authors
  1. Gintarė Huckeba
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  2. Bjarne Andresen
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  3. Ty N. F. Roach
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All authors contributed to the theory design, read, edited, and approved this manuscript.

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Correspondence to Ty N. F. Roach.

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Huckeba, G., Andresen, B. & Roach, T.N.F. Multi-scale spatial ecology analyses: a Kullback information approach. Landsc Ecol 38, 645–657 (2023). https://doi.org/10.1007/s10980-022-01514-9

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