The Concept of Scale Outline Introduction

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The Concept of Scale


  • Introduction

  • Scale terminology

  • Scale problems

  • Scale concepts and hierarchy theory

  • Identifying the “right” scale(s)

  • Scaling up

  • Summary

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.

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.

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!

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

Scale – Lessons Learned

  • “Lessons learned”…con’t:

    • Changing the quadrat size (grain) or the extent of 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

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)

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.)

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

  • 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.

Spatial scale is characterized by...

  • Grain - size of the smallest feature that can be resolved from the observations

  • Extent - size of the largest feature that can be captured in the observations

    • e.g., the length or area represented by the entire image

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

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

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.)

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)

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

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

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

Scale concepts and hierarchy theory

  • 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

Identifying the “right” scale

  • 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)

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

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

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

Delcourts’ – Scale Paradigm

  • Micro

  • Meso

  • Macro

  • Mega

Delcourts’ Paradigm

Scale Paradigms – Resource Planning


  • 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 !

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