The Concept of Scale

1. The Concept of Scale

2. Outline • Introduction • Scale terminology • Scale problems • Scale concepts and hierarchy theory • Identifying the “right” scale(s) • Scaling up • Summary

3. Key Scaling Questions • Finding the characteristic scale of spatial heterogeneity or pattern (so-called "scaling techniques"); • Defining what a "patch" is, and devising aggregate descriptions of collections of patches (their sizes, diversity, and such), to more complex summaries - • Connectedness, fractal geometry, and percolating networks; • How these aspects of pattern are interrelated in landscapes, and how they vary according to physiography and landscape history.

4. What factors drive pattern? • The physical template of environmental constraints -- soils, topography, climate; • Biotic processes -- establishment and growth, dispersal, and mortality; • Disturbance regimes -- fires, floods, storms, and human land use.

5. Scale - Environmental Imperative • 1980s & 1990s – importance of scale in ecology widely published and discussed • Pressing environmental issues over large areas brought role of scale to forefront: • Acid rain • Global climate change • Habitat fragmentation • Conservation biology • Disturbance regimes • Fire and bugs!

6. Scale – Lessons Learned • “Lessons learned” from scale studies (esp. last 20 years): • No single scale is appropriate for study of all ecological problems • A challenge to understand how data collected at finer scales (e.g., small plots) relates to larger areas. • Can these results be extrapolated? CAUTION the scaling up/down problem

7. Scale – Lessons Learned • “Lessons learned”…con’t: • Changing the quadrat size (grain) or theextentof the area often yields a different numerical result or pattern • Disparate results from different studies of the same variable/organism might be due to differences in scale

8. Scale – Lessons Learned • “Lessons learned” …con’t: • Spatial and temporal scales important to humans are not necessarily the scales relevant to other organisms or processes • Biological interactions most likely occur at multiple scales (biocomplexity idea)

9. Scale Terminology (see Table 2.1) • Scale terminology – is not used consistently; leads to confusion • Scale – refers to spatial or temporal dimension of an object or area - vs - • Level of organization – place within a biotic (or other organizational) hierarchy (e.g., organism, population, community, etc.)

10. Scale Terminology con’t.: • Scale characterized by: • grain • extent • Grain – finest spatial resolution within a given data set (cell size or pixel size; or minimum mapping unit – MMU) • Extent – the size of the overall study area

11. Grain Size: • The minimum resolution of the data • defined by scale • grid data = the cell size • in field sample data, the quadrat (or plot) size • in imagery, the pixel size • in map-type (vector)data, the minimum mapping unit.

12. Spatial scale is characterized by... • Grain - size of the smallest feature that can be resolved from the observations • “resolution” is used synonymously • e.g., the length or area represented by 1 pixel in a digital image • Extent - size of the largest feature that can be captured in the observations • e.g., the length or area represented by the entire image

13. Temporal scale is characterized by... • Grain - duration or frequency the shortest (highest frequency) feature that can be resolved from the time series • e.g., the sampling rate • Extent - duration or frequency of the longest (lowest frequency) feature that can be captured in the time series • e.g., the length of the time series

14. Scale Terminology – con’t. • A scale-dependent pattern, process, or phenomenon = changes with grain or extent • Species-area (e.g., biodiversity) • Insect feeding • Disease patterns • Fire behavior • Plant or animal dispersal

15. Scale Terminology – con’t. • Absolute vs. relative scale: • Absolute scale = actual distance, time, or area, etc. • Relative scale = two points might be relatively closer in terms of energy expended vs. actual distance(e.g., barriers; mountains, canyons, water, etc.)

16. Scale Problems • Three basic scale problems (Haggett 1963): • Scale coverage problem (large areas difficult to map and understand) • Scale linkage problem (fine to broad-scale) • Scale standardization problem (compare locations, extrapolate from one place to another)

17. Scale concepts and hierarchy theory • Hierarchy • identified with levels organization(e.g., cell, organism, population, etc.) • higher levels constrain the lower levels to various degrees

18. Scale concepts and hierarchy theory • Three important points: • Any analysis should consider at least three hierarchical levels: • Focal level – level of interest; question or objective • Level above – constrains and controls the lower levels • Level below – provides the details needed to explain the behavior of the focal level

19. Scale concepts and hierarchy theory 2. “list” of variables may not change with scale, but see a shift in the relative importance or direction • Extending the spatial domain: Rate of organic matter dynamics example (Sollins et al. 1983. Soil OM accretion on mudflow series) (local = detail charac. litter, microclimate; global = P & T) • Extending the time frame of observation: magnitude and overall direction of change often more apparent over long-term

20. 3. Multiple scales of pattern will exist in landscapes Coarse-grained: geomorphology (substrate & soils); large disturbances (large fires, large insect epidemics) Fine-grained: local disturbances (individual tree blow down; canopy gaps, etc.) Collectively, spatial pattern of an ecosystem at any given time may reflect these processes operating over different scales in space & time Scale concepts and hierarchy theory

21. All of these ideas are provocative and interesting – this still leaves us with the burden of identifying the “relevant scale” There is no single correct scale or level to describe a system However, “(this)…does not mean that all scales serve equally well or that there are not scaling laws” (Levin 1992) Identifying the “right” scale

22. Scaling Up/Scaling Down • Simplest approach - multiply a measurement made at one scale (e.g., unit of area) to predict at a broad or coarser level; or its reverse • Example: standing biomass for a 10,000 ha forest – estimated by multiplying the amount of biomass measured in 1-ha stands by 10,000 • Approach assumes: • that the properties of the system do not change with scale • that the broader system behaves like the averaged finer one • that the relationships are linear

23. We must think and act at a scale and pace appropriate to the forest health crisis.

24. Forest Ecosystem Restoration Analysis (FORESTERA) • Uses remote sensing data, on site data (e.g., FIA data), GIS, and computer models to synthesize past, present, and future scenario data • Forest health restoration is the major impetus for greater ecosystem scale adaptive management activities

25. Delcourts’ – Scale Paradigm • Micro • Meso • Macro • Mega

26. Delcourts’ Paradigm

27. Scale Paradigms – Resource Planning

28. Summary • Scale is a prominent topic in restoration and adaptive management • Influences conclusions and extrapolations • Scale related to hierarchy; hierarchy theory provides a framework (consider focal level; level above constrains; level below explains [mechanisms]) • Extrapolation from fine to broad scale is straightforward if areas are homogeneous and relationship linear; spatial heterogeneity present, but need to know random vs. structured pattern; fractals and other methods possible if processes and constraints do not change across scales • Extrapolation a very difficult problem with spatial heterogeneity and nonlinear relationships (no general solution at present) • Just because you may not be able to scale up with great accuracy is no excuse for ignoring restoration and adaptive management problems at the landscape level !