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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note: An asterisk preceding the entry indicates that it is a suggested reading.
References and Recommended Readings
Note: An asterisk preceding the entry indicates that it is a suggested reading.
Chambers JM, Cleveland WS, Kleiner B et al (1983) Graphical methods for data analysis. Wadsworth & Brooks/Cole, Pacific Grove
Cressie NAC (1993) Statistics for spatial data, revised edn. Wiley, New York
*Fortin MJ, Boots B, Csillag F et al (2003) On the role of spatial stochastic models in understanding landscape indices in ecology. Oikos 102:203–212. This paper puts into perspective the use of stochastic models and simulations for studying complex ecological systems, specifically spatial patterns. The authors present a theoretical framework for the implementation of stochastic models to examine the confidence intervals around various landscape metrics.
Fortin MJ, Dale MRT (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, Cambridge
Fortin MJ, Jacquez GM, Shipley B (2012) Computer-intense methods. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, 2nd edn. Wiley, Chichester, pp 489–493
Gardner RH, Urban DL (2007) Neutral models for testing landscape hypotheses. Landsc Ecol 22:15–29
*Haines-Young R, Chopping M (1996) Quantifying landscape structure: a review of landscape indices and their application to forested landscapes. Progr Phys Geogr 20(4):418–445. One of few papers that provide a balanced summary of landscape pattern indices available for assessing spatial patterns. The authors elucidate uses and constraints on various metrics.
Hargrove WW, Hoffman FM, Schwartz PM (2002) A fractal landscape realize for generating synthetic maps. Conserv Ecol 6(1):2
Manly BFJ (2006) Randomization, bootstrap and Monte Carlo methods in biology. 3rd edn. CRC Press: Boca Raton, Florida
McGarigal K (2002) Landscape pattern metrics. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, vol 2. Wiley, Chichester, pp 1135–1142
McGarigal K, Marks BJ (1995) FRAGSTATS: spatial pattern analysis program for quantifying landscape structure. U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. Gen. Tech. Rep. PNW-GTR-351, p 122
Moran PAP (1950) Notes on continuous stochastic phenomena. Biometrika 37(1/2):17–23
Proulx R, Fahrig L (2010) Detecting human-driven deviations from trajectories in landscape composition and configuration. Landsc Ecol 25:1479–1487
R Development Core Team (2010) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.R-project.org/
*Remmel TK, Csillag F (2003) When are two landscape pattern indices significantly different? J Geogr Syst 5(4):331–351. The authors present an extensive simulation experiment that demonstrates how empirical distributions of landscape metrics can be used for statistically comparing spatial patterns expressed by binary gridded maps. The procedure improves on traditional hypothesis testes that assume normally distributed values for landscape metrics.
*Remmel TK, Fortin M-J (2013) Categorical class map patterns: characterization and comparison. Landsc Ecol 28(8):1587–1599. Provides much of the theoretical and statistical background and detail related to the exercises in this chapter. Here, the authors explore the use of landscape simulations to compare binary landscape patterns using class-level metrics.
*Riitters KH, O’Neill RV, Hunsaker CT et al (1995) A factor analysis of landscape pattern and structure metrics. Landsc Ecol 10(1):23–39. This keystone paper summarizes the redundancies present among many landscape pattern metrics and proposes new compound variables for characterizing landscape patterns. The new variables are produced by ordination of many commonly computed metrics.
Turner MG, Gardner RH, O’Neill RV (2001) Landscape ecology in theory and practice. Springer, New York
Van Der Wal J, Falconi L, Januchowski S et al (2011) SDMTools: species distribution modelling tools: tools for processing data associated with species distribution modelling exercises. 1.1–5. The Comprehensive R Archive Network (CRAN). GPL 2.0, http://cran.r-project.org/
Whittle P (1954) On stationary processes in the plane. Biometrika 41:434–449
*Wu JG, Shen WJ, Sun WZ et al (2002) Empirical patterns of the effects of changing scale on landscape metrics. Landsc Ecol 17(8):761–782. This pivotal paper examines the effect of spatial scale on landscape metrics. While scale is an important concept in ecology, the effects of grain size and extent are not always clearly understood in the analysis of spatial patterns.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
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.
Rights and permissions
Copyright information
© 2017 Springer-Verlag New York
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4939-6374-4_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-6372-0
Online ISBN: 978-1-4939-6374-4
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)