The Concept of Scale Outline Introduction

The Concept of Scale

Outline

• 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

• “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

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

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 !