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What Constitutes a Significant Difference in Landscape Pattern?

Abstract

Characterizing landscape spatial structure can provide insights about the underlying mechanisms that generate pattern. Quantifying spatial structure enables analysis of landscape change over time as well as comparisons among different locations. Although numerous landscape metrics (LMs) exist to quantify spatial structure and characterize a landscape, how do we know when two landscapes significantly differ? As a single landscape represents only one replicate, its metrics are not statistics; thus, testing for differences between two landscapes becomes difficult. To address this problem, randomization procedures can help assess statistical significance using simulation approaches that assess whether the observed spatial structure could have occurred by chance alone. In this chapter, exercises will allow students to accomplish the following objectives.

Keywords

  • Spatial Structure
  • Spatial Autocorrelation
  • Landscape Metrics
  • Randomization Procedure
  • Complete Spatial Randomness

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

We appreciate the contributions from Drs. Sándor Kabos and Ferko Csillag for their roles in providing some of the earlier programming work that we expanded upon. The chapter benefited from comments by R.H. Gardner, S.E. Gergel, M.G. Turner, and an anonymous reviewer.

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Correspondence to Tarmo K. Remmel .

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Appendix A. Explanation of Whittle’s algorithm (Whittle 1954)

Appendix A. Explanation of Whittle’s algorithm (Whittle 1954)

For continuous data, ρ can be estimated using Whittle’s algorithm (Whittle 1954) that extends the convention of time-series analysis to spatial processes reflected as collections of linear transects in geographic space. There is however the chance of bias in the estimated value of spatial autocorrelation when applying this algorithm to categorical data. This bias varies according to the composition, pi, such that around an even proportion of two classes, the bias is relatively small; however, it can be quite strong when the proportions differ greatly. Therefore, a correction factor needs to be applied to adjust the spatial autocorrelation estimate, resulting in the “true” ρ W for categorical data. This true ρ W needs to be multiplied by 4 to compensate for the isotropy of the algorithm and to scale the estimation to a range between 0 and 1. As this correction factor requires intensive computation, it has already been performed and stored as a lookup table in the provided Remmel–Fortin code as object DIFF50 and is used internally when estimating ρ W.

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Remmel, T.K., Fortin, MJ. (2017). What Constitutes a Significant Difference in Landscape Pattern?. In: Gergel, S., Turner, M. (eds) Learning Landscape Ecology. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6374-4_7

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