Instructor: Brian Klinkenberg

Office: Room 209
Office Hours: Tues 12:30-1:30
Wed 12:00-1:00

Lab Help: Jose Aparicio

Office: Room 240D

Computer Lab: Room 239


 

 

Scale and Pattern

Scale in Ecology

"The problem of pattern and scale is the central problem in ecology, unifying population biology and ecosystems science, and marrying basic and applied ecology. Applied challenges ... require the interfacing of phenomena that occur on very different scales of space, time, and ecological organization. Furthermore, there is no single natural scale at which ecological phenomena should be studied; systems generally show characteristic variability on a range of spatial, temporal, and organizational scales."

(Levin 1992)

Components of Scale: Definitions

Any discussion of scale must begin by defining terms. Scale, in particular, has been plagued by imprecise and inconsistent usage. Some basic definitions:

Grain
The minimum resolution of the data (defined by scale, the "length of the ruler"). In raster lattice data, the cell size; in field sample data, the quadrat size; in imagery, the pixel size; in vector GIS data, the minimum mapping unit.

Extent
The scope or domain of the data (defined as the size of the study area, typically)

Some rules:

  • Grain and extent are inversely correlated, a result of logistical constraints in measurement. Nature itself, of course, has fine grain and large extent. In sampling we sacrifice fine grain for large extent, or reciprocally, narrow the extent of our data when we require fine grain.

  • Information content is often correlated with grain (we tend to measure more variables in fine-grained studies).

Some clarification of terms:

  • "Scale" is not the same as "level of organization." Scale refers to the spatial domain of the study, while level of organization depends on the criteria used to define the system. For example, population-level studies are concerned with interactions among conspecific individuals, while ecosystem-level studies are concerned with interactions among biotic and abiotic components of some process such as nutrient cycling. One could conduct either a small- or large-scale study of either population- or ecosystem-level phenomena.

  • "Ecological scale" and "map scale" are exact opposites; in cartography, "scale" is a ratio of map to real distance, so a large-scale map is fine-grained and of small extent.
The term "scale" by itself typically connotes extent, carrying with it a corresponding change in grain. Thus, for example, we might in a lazy mood say "large scale" to connote large extent and coarse grain.

Characteristic Scaling

Many have argued that ecological phenomena tend to have characteristic spatial and temporal scales, or spatiotemporal domains (e.g., Delcourt et al. 1983, Urban et al. 1987). A central tenet of landscape ecology is that particular phenomena should be addressed at their characteristic scales. Likewise, if one changes scale of reference, the phenomena of interest change.

Consequences of Scaling

As one increases scale in a system:

  • Fine-scale processes or constraints average away and become constants. For example, at the scale of a forest sample quadrat (say, 0.01 ha), it is reasonable to ignore larger-scale variability in soil parent material: the trees on the quadrat all see the same soil type. Likewise, at the time-scale of years to decades, long-term climate trends are not apparent (although fluctuations in weather might be).

  • Reciprocally, as we increase the extent of our analysis parameters that were constant now become variable and must be accounted. If we were to extend the forest sampling (above) to cover a large watershed or basin, soil types would indeed vary and we would need to attend this variability. Likewise, microclimate as it varies with elevation and topographic position would become a real source of variability affecting forest pattern at this larger scale.

  • Finally, new interactions may arise as one increases the extent of inquiry. At the scale of a landscape mosaic, interactions among forest stands, such as via dispersal of plant or animal species, emerge as new phenomena for study.
As one changes scale (e.g., see Table 1 in Wiens 1989):

  • Systems may switch between "closed" and "open." "Openness" is defined by the strength of interactions among elements (habitat patches), and these vary with spatial extent due to physical and biogeographic patterns.

  • Statistical relationships may change:

    • The magnitude or sign of correlations may change with spatial extent. At the scale of a single habitat patch, abundances of different species might be negatively correlated due to interspecific interactions; but if one considers a set of these habitat patches in a heterogeneous landscape, any species inhabiting similar habitat types will be positively correlated.

    • Predictions change: important variables come and go with changes in scale. Potential evapotranspiration (PET) depends on physical parameters such as temperature, vapor pressure deficit, wind speed, and soil moisture status as well as biological parameters such as stomatal conductance and surface roughness. At very fine scales, one might include many of these factors to predict PET or actual evapotranspiration (AET) (e.g., Monteith 1965). At subcontinental scales, PET can be predicted adequately by temperature and latitude (e.g., Thornthwaite and Mather 1955). The nature of the process does not change with scale, but the relative contribution of explanatory variables does (and so does our ability to measure all the variables over a large extent!).
Thus: explanatory models are scale-dependent.