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)
Bird endemism in Northern Melanesian islands (Mayr and Dimond 2001)
Interim General Model 2 (“IGM2”, Field et al. 2005)
2
Plant richness  R  mPET  mPET  log(ele)
Interim General Model 2 (“IGM2”, Field et al. 2005)
2
Plant richness  R  mPET  mPET  log(ele)
R  annual rainfall (mm)
mPET  minimum monthly
potential evapotrans piration (mm)
log(ele)  logarithm of range
in elevation (log[m])
Interim General Model 2 (“IGM2”, Field et al. 2005)
2
Plant richness  R  mPET  mPET  log(ele)
R  annual rainfall (mm)
mPET  minimum monthly
potential evapotrans piration (mm)
log(ele)  logarithm of range
in elevation (log[m])
energy and
water
availability
topographic
heterogeneity
Interim General Model 2 (“IGM2”, Field et al. 2005)
+
+
−
+
2
Plant richness  R  mPET  mPET  log(ele)
R  annual rainfall (mm)
mPET  minimum monthly
potential evapotrans piration (mm)
log(ele)  logarithm of range
in elevation (log[m])
energy and
water
availability
topographic
heterogeneity
Correlation coefficient
-1
0
1
Correlation coefficient
Correct confidence interval
-1
0
1
Correlation coefficient
Correct confidence interval
Confidence interval affected by
spatial correlation
-1
0
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
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