Note that the expressions “large scale” and “small scale” are somewhat ambiguous because their meanings in ecology and cartography are opposite. In ecology,
“small scale” refers to the fine structures and “large scale” to the broadest structures,
contrary to cartography where a large-scale map (e.g. 1:25,000) is more detailed than
a small-scale map (e.g. 1:1,000,000). Therefore we advocate the use of “broad scale”
(phenomena with large grains, large extents) and “fine scale” in ecology (Wiens
1989). Although these terms are not strict antonyms, we feel that they are less
ambiguous than “large” and “small scale”.
Finally, ecological processes occur at a variety of scales, resulting in complex,
multiscale patterns. Therefore, identifying the scale(s) of the patterns and relating
them to the appropriate processes are goals of paramount importance in modern
ecology. To reach them, the researcher must rely on appropriate sampling designs
and powerful analytical methods. The approaches presented in this chapter have
been devised for the latter purpose.
7.2.4 Spatial Heterogeneity
A process or a pattern that varies across an area is said to be spatially heterogeneous.
Many methods of spatial analysis are devoted to the measurement of the magnitude
and extent of this heterogeneity and testing for the presence of spatial correlation
(in other words, spatial structures of any kind). The latter may be done either to
support the hypothesis that no spatial correlation (in the broad sense) is present in the
data (if the researcher has statistical tests in mind) or, on the contrary, to show that
correlation is present and use that information in conceptual or statistical models
(Legendre and Legendre 2012).
Spatial heterogeneity in relation to inter-site distance is most often studied by
means of structure functions. Examples of these are correlograms, variograms and
periodograms. While it is not the purpose of this book to discuss these various
functions, it is useful to devote a section to correlograms, since the main underlying
measures of spatial correlation will be used later in Sect. 7.4 of this chapter.
7.2.5 Spatial Correlation or Autocorrelation Functions
and Spatial Correlograms
The two main statistics used to measure spatial correlation of univariate quantitative
variables are Moran’s I (Moran 1950) and Geary’s c (Geary 1954). The first is
constructed in much the same way as the Pearson correlation coefficient:
7.2 Spatial Structures and Spatial Analysis: A Short Overview
303
“small scale” refers to the fine structures and “large scale” to the broadest structures,
contrary to cartography where a large-scale map (e.g. 1:25,000) is more detailed than
a small-scale map (e.g. 1:1,000,000). Therefore we advocate the use of “broad scale”
(phenomena with large grains, large extents) and “fine scale” in ecology (Wiens
1989). Although these terms are not strict antonyms, we feel that they are less
ambiguous than “large” and “small scale”.
Finally, ecological processes occur at a variety of scales, resulting in complex,
multiscale patterns. Therefore, identifying the scale(s) of the patterns and relating
them to the appropriate processes are goals of paramount importance in modern
ecology. To reach them, the researcher must rely on appropriate sampling designs
and powerful analytical methods. The approaches presented in this chapter have
been devised for the latter purpose.
7.2.4 Spatial Heterogeneity
A process or a pattern that varies across an area is said to be spatially heterogeneous.
Many methods of spatial analysis are devoted to the measurement of the magnitude
and extent of this heterogeneity and testing for the presence of spatial correlation
(in other words, spatial structures of any kind). The latter may be done either to
support the hypothesis that no spatial correlation (in the broad sense) is present in the
data (if the researcher has statistical tests in mind) or, on the contrary, to show that
correlation is present and use that information in conceptual or statistical models
(Legendre and Legendre 2012).
Spatial heterogeneity in relation to inter-site distance is most often studied by
means of structure functions. Examples of these are correlograms, variograms and
periodograms. While it is not the purpose of this book to discuss these various
functions, it is useful to devote a section to correlograms, since the main underlying
measures of spatial correlation will be used later in Sect. 7.4 of this chapter.
7.2.5 Spatial Correlation or Autocorrelation Functions
and Spatial Correlograms
The two main statistics used to measure spatial correlation of univariate quantitative
variables are Moran’s I (Moran 1950) and Geary’s c (Geary 1954). The first is
constructed in much the same way as the Pearson correlation coefficient:
7.2 Spatial Structures and Spatial Analysis: A Short Overview
303