Workshop 2: Spatial scale and dependence in biogeographical patterns
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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

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.






Interim General Model 2 (“IGM2”, Field et al. 2005) Dimond 2001)

energy and water availability

topographic heterogeneity


Interim General Model 2 (“IGM2”, Field et al. 2005) Dimond 2001)

+

+

+

energy and water availability

topographic heterogeneity


Correlation coefficient Dimond 2001)

-1

1

0


Correlation coefficient Dimond 2001)

Correct confidence interval

-1

1

0


Correlation coefficient Dimond 2001)

Correct confidence interval

Confidence interval affected byspatial correlation

-1

1

0


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



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: patterns

  • 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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