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Workshop 2: Spatial scale and dependence in biogeographical patterns

Workshop 2: Spatial scale and dependence in biogeographical patterns. Objective: introduce the following fundamental concepts on spatial data analysis: - What is spatial data analysis and why it is important - Pattern vs process

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Workshop 2: Spatial scale and dependence in biogeographical patterns

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  1. Workshop 2: Spatial scale and dependence in biogeographical patterns Objective: introduce the following fundamental concepts on spatial data analysis: - What is spatial data analysis and why it is important - Pattern vs process - Spatial correlation, induced spatial dependence and autocorrelation - Stationary process - Scale and its components Main sources: Legendre and Legendre (2012) Numerical Ecology. Elsevier. Fortin and Dale (2005) Spatial analysis: a guide for ecologists. Cambridege University Press Bailey and Gatrell (1995) Interactive spatial data analysis. Prentice Hall.

  2. Bird endemism in Northern Melanesian islands (Mayr and Dimond 2001)

  3. Bird endemism in Northern Melanesian islands (Mayr and Dimond 2001)

  4. Interim General Model 2 (“IGM2”, Field et al. 2005)

  5. Interim General Model 2 (“IGM2”, Field et al. 2005)

  6. Interim General Model 2 (“IGM2”, Field et al. 2005) energy and water availability topographic heterogeneity

  7. Interim General Model 2 (“IGM2”, Field et al. 2005) + + − + energy and water availability topographic heterogeneity

  8. Correlation coefficient -1 1 0

  9. Correlation coefficient Correct confidence interval -1 1 0

  10. Correlation coefficient Correct confidence interval Confidence interval affected byspatial correlation -1 1 0

  11. Workshop 2: Spatial scale and dependence in biogeographical patterns Objective: introduce the following fundamental concepts on spatial data analysis: - What is spatial data analysis and why it is important - Pattern vs process - Spatial correlation, induced spatial dependence and autocorrelation - Stationary process - Scale and its components

  12. Pattern: a single realization of or a “snapshot” of a process or combination of processes at one given time (Fortin and Dale 2005) Process: a phenomenon (response variable), or a set of pehnomena, which are organized along some independent axis (Legendre and Legendre 2012) Spatial process: a set of possibly non-independent random variables (Bailey and Gatrell 1995): {Y(s) = s belongs to region R}

  13. Workshop 2: Spatial scale and dependence in biogeographical patterns Objective: introduce the following fundamental concepts on spatial data analysis: - What is spatial data analysis and why it is important - Pattern vs process - Spatial correlation, induced spatial dependence and autocorrelation - Stationary process - Scale and its components

  14. Spatial correlation: relationships between values observed at neighboring points in space, hence lack of independence of values of the observed variables. • Induced spatial dependence: functional dependence of the response variables (Y) on explanatory variables (X) that are themselves spatially correlated. • Autocorrelation: spatial correlation in the error component of a response variable

  15. Workshop 2: Spatial scale and dependence in biogeographical patterns Objective: introduce the following fundamental concepts on spatial data analysis: - What is spatial data analysis and why it is important - Pattern vs process - Spatial correlation, induced spatial dependence and autocorrelation - Stationary process - Scale and its components

  16. Stationary process: informally, a spatial process is stationary (or homogeneous) if its statistical properties are independent of the absolute location in region R. • Mean, variance, covariance

  17. Workshop 2: Spatial scale and dependence in biogeographical patterns Objective: introduce the following fundamental concepts on spatial data analysis: - What is spatial data analysis and why it is important - Pattern vs process - Spatial correlation, induced spatial dependence and autocorrelation - Stationary process - Scale and its components

  18. Scale and its components in sampling theory: • Grain: size of elementary sampling units • Sampling interval: average distance between neighboring sampling units • Extent: total length, area or volume included in the study • Scale of pattern or process: • Size of “unit object” or “unit process” • Distance between unit objects of unit process • Space over which unit objects or unit process exist

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