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.
Bird endemism in Northern Melanesian islands (Mayr and Dimond 2001)
Interim General Model 2 (“IGM2”, Field et al. 2005)
energy and water availability topographic heterogeneity
Interim General Model 2 (“IGM2”, Field et al. 2005) energy and water availability topographic heterogeneity ++−+
0 1 Correlation coefficient
0 1 Correlation coefficient Correct confidence interval
0 1 Correlation coefficient Confidence interval affected by spatial correlation Correct confidence interval
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
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}
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
-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
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
- 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
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
- 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