The Concept of ScaleThe Concept of Scale

OutlineOutline

► IntroductionIntroduction► Scale terminologyScale terminology► Scale problemsScale problems► Scale concepts and hierarchy theoryScale concepts and hierarchy theory► Identifying the “right” scale(s)Identifying the “right” scale(s)► Scaling upScaling up► SummarySummary

Key Scaling QuestionsKey Scaling Questions

► Finding the characteristic scale of spatial Finding the characteristic scale of spatial heterogeneity or pattern (so-called "scaling heterogeneity or pattern (so-called "scaling techniques"); techniques");

► Defining what a "patch" is, and devising Defining what a "patch" is, and devising aggregate descriptions of collections of aggregate descriptions of collections of patches (their sizes, diversity, and such), to patches (their sizes, diversity, and such), to more complex summaries -more complex summaries -

► Connectedness, fractal geometry, and Connectedness, fractal geometry, and percolating networks; percolating networks;

► How these aspects of pattern are interrelated How these aspects of pattern are interrelated in landscapes, and how they vary according in landscapes, and how they vary according to physiography and landscape history. to physiography and landscape history.

What factors drive pattern?What factors drive pattern?

►The physical template of The physical template of environmental constraints -- soils, environmental constraints -- soils, topography, climate; topography, climate;

►Biotic processes -- establishment and Biotic processes -- establishment and growth, dispersal, and mortality; growth, dispersal, and mortality;

►Disturbance regimes -- fires, floods, Disturbance regimes -- fires, floods, storms, and human land use.storms, and human land use.

Scale - Environmental Imperative Scale - Environmental Imperative

► 1980s & 1990s – importance 1980s & 1990s – importance of scale in ecology widely of scale in ecology widely published and discussedpublished and discussed

► Pressing environmental Pressing environmental issues over large areas issues over large areas brought role of scale to brought role of scale to forefront:forefront: Acid rainAcid rain Global climate changeGlobal climate change Habitat fragmentationHabitat fragmentation Conservation biologyConservation biology Disturbance regimesDisturbance regimes Fire and bugs!Fire and bugs!

Scale – Lessons LearnedScale – Lessons Learned

► ““Lessons learned” from Lessons learned” from scale studies (esp. last 20 scale studies (esp. last 20 years):years):

No single scale is No single scale is appropriate for study of all appropriate for study of all ecological problemsecological problems

A challenge to understand A challenge to understand how data collected at finer how data collected at finer scales (e.g., small plots) scales (e.g., small plots) relates to larger areas.relates to larger areas.

Can these results be Can these results be extrapolated? CAUTION the extrapolated? CAUTION the scaling up/down problem scaling up/down problem

Scale – Lessons LearnedScale – Lessons Learned

► ““Lessons learned”…con’t:Lessons learned”…con’t:

Changing the quadrat size Changing the quadrat size (grain) or the(grain) or the extentextent of the of the area often yields a different area often yields a different numerical result or patternnumerical result or pattern

Disparate results from Disparate results from different studies of the different studies of the same variable/organism same variable/organism might be due to differences might be due to differences in scalein scale

Scale – Lessons LearnedScale – Lessons Learned

► ““Lessons learned” …con’t:Lessons learned” …con’t:

Spatial and temporal scales Spatial and temporal scales important to humans are not important to humans are not necessarily the scales relevant necessarily the scales relevant to other organisms or processesto other organisms or processes

Biological interactions most Biological interactions most likely occur at multiple scales likely occur at multiple scales (biocomplexity idea)(biocomplexity idea)

Scale Terminology (Scale Terminology (see Table 2.1see Table 2.1))

► Scale terminology – is not Scale terminology – is not used consistently; leads to used consistently; leads to confusionconfusion

► Scale Scale – refers to spatial or – refers to spatial or temporal dimension of an temporal dimension of an object or area object or area

- vs -- vs -

► Level of organizationLevel of organization – place – place within a biotic (or other within a biotic (or other organizational) hierarchy organizational) hierarchy (e.g., (e.g., organism, population, community, etc.)organism, population, community, etc.)

Scale Terminology Scale Terminology con’t.:con’t.:

► Scale characterized Scale characterized by:by: graingrain extentextent

► GrainGrain – finest – finest spatial spatial resolutionresolution within a given data within a given data set (cell size or pixel size; or set (cell size or pixel size; or minimum mapping unit – MMU)minimum mapping unit – MMU)

► Extent Extent – the – the sizesize of the of the overall study areaoverall study area

► Grain Size:Grain Size: The minimum The minimum

resolution of the resolution of the data data

defined by scaledefined by scale► grid data = the cell sizegrid data = the cell size► in field sample data, the in field sample data, the

quadrat (or plot) sizequadrat (or plot) size► in imagery, the pixel in imagery, the pixel

sizesize► in map-type in map-type

(vector)data, the (vector)data, the minimum mapping unit. minimum mapping unit.

SpatialSpatial scale is characterized scale is characterized by...by...

► GrainGrain - size of the smallest feature that can - size of the smallest feature that can be resolved from the observationsbe resolved from the observations ““resolution” is used synonymouslyresolution” is used synonymously e.g.e.g., the length or area represented by 1 pixel in , the length or area represented by 1 pixel in

a digital imagea digital image

► ExtentExtent - size of the largest feature that can - size of the largest feature that can be captured in the observationsbe captured in the observations e.g.e.g., the length or area represented by the entire , the length or area represented by the entire

imageimage

TemporalTemporal scale is characterized scale is characterized by...by...

►GrainGrain - duration or frequency the - duration or frequency the shortest (highest frequency) feature shortest (highest frequency) feature that can be resolved from the time that can be resolved from the time seriesseries e.g.e.g., the sampling rate, the sampling rate

►ExtentExtent - duration or frequency of the - duration or frequency of the longest (lowest frequency) feature that longest (lowest frequency) feature that can be captured in the time seriescan be captured in the time series e.g.e.g., the length of the time series, the length of the time series

Scale Terminology – con’t. Scale Terminology – con’t.

► A A scale-dependentscale-dependent pattern, process, or pattern, process, or phenomenon = changes phenomenon = changes with grain or extentwith grain or extent

Species-area (e.g., biodiversity)Species-area (e.g., biodiversity) Insect feedingInsect feeding Disease patternsDisease patterns Fire behaviorFire behavior Plant or animal dispersalPlant or animal dispersal

Scale Terminology – con’t.Scale Terminology – con’t.

► Absolute vs. relative Absolute vs. relative scale:scale:

► Absolute scaleAbsolute scale = actual = actual distance, time, or area, etc.distance, time, or area, etc.

► Relative scaleRelative scale = two points = two points might be relatively closer in might be relatively closer in terms of energy expended vs. terms of energy expended vs.

actual distanceactual distance (e.g., barriers; (e.g., barriers;

mountains, canyons, water, etc.)mountains, canyons, water, etc.)

Scale ProblemsScale Problems

► Three basic scale Three basic scale problemsproblems (Haggett (Haggett 1963):1963): Scale coverage problem Scale coverage problem

(large areas difficult to map and (large areas difficult to map and understand)understand)

Scale linkage problem Scale linkage problem (fine to broad-scale)(fine to broad-scale)

Scale standardization Scale standardization problem problem (compare locations, (compare locations, extrapolate from one place to extrapolate from one place to another)another)

Scale concepts and hierarchy theoryScale concepts and hierarchy theory

► Hierarchy Hierarchy identified with levels identified with levels

organizationorganization (e.g., cell, (e.g., cell, organism, population, etc.)organism, population, etc.)

higher levels constrain the higher levels constrain the lower levels to various lower levels to various degreesdegrees

Scale concepts and hierarchy theoryScale concepts and hierarchy theory

► Three important points:Three important points:

1.1. Any analysis should consider Any analysis should consider at least at least three three hierarchical hierarchical levels:levels:

Focal level – level of interest; Focal level – level of interest; question or objectivequestion or objective

Level above – constrains and Level above – constrains and controls the lower levelscontrols the lower levels

Level below – provides the Level below – provides the details needed to explain the details needed to explain the behavior of the focal levelbehavior of the focal level

Scale concepts Scale concepts and hierarchy theoryand hierarchy theory

2. “list” of variables may not change 2. “list” of variables may not change with scale, with scale, but but see a shift in the see a shift in the relative importance or direction relative importance or direction

Extending the spatial domain:Extending the spatial domain:

Rate of organic matter dynamics Rate of organic matter dynamics example (Sollins et al. 1983. Soil example (Sollins et al. 1983. Soil OM accretion on mudflow series)OM accretion on mudflow series)

(local = detail charac. litter, (local = detail charac. litter, microclimate; global = P & T)microclimate; global = P & T)

Extending the time frame of Extending the time frame of observation: magnitude and overall observation: magnitude and overall direction of change often more direction of change often more apparent over long-termapparent over long-term

Scale concepts and hierarchy theoryScale concepts and hierarchy theory

3. Multiple scales of pattern will 3. Multiple scales of pattern will exist in landscapes exist in landscapes

► Coarse-grained: geomorphology Coarse-grained: geomorphology (substrate & soils); large (substrate & soils); large disturbances (large fires, large disturbances (large fires, large insect epidemics)insect epidemics)

► Fine-grained: local disturbances Fine-grained: local disturbances (individual tree blow down; canopy (individual tree blow down; canopy gaps, etc.)gaps, etc.)

► Collectively, spatial pattern of an Collectively, spatial pattern of an ecosystem at any given time may ecosystem at any given time may reflect these processes operating reflect these processes operating over different scales in space & over different scales in space & timetime

Identifying the “right” scaleIdentifying the “right” scale

► All of these ideas are All of these ideas are provocative and interesting provocative and interesting – this still leaves us with the – this still leaves us with the burden of identifying the burden of identifying the “relevant scale” “relevant scale”

► There is no single correct There is no single correct scale or level to describe a scale or level to describe a systemsystem

► However, “(this)…does not However, “(this)…does not mean that all scales serve mean that all scales serve equally well or that there equally well or that there are not scaling laws” (Levin are not scaling laws” (Levin 1992)1992)

Scaling Up/Scaling DownScaling Up/Scaling Down

► Simplest approach - multiply a Simplest approach - multiply a measurement made at one measurement made at one scale (e.g., unit of area) to scale (e.g., unit of area) to predict at a broad or coarser predict at a broad or coarser level; or its reverselevel; or its reverse

► Example: standing biomass for Example: standing biomass for a 10,000 ha forest – estimated a 10,000 ha forest – estimated by multiplying the amount of by multiplying the amount of biomass measured in 1-ha biomass measured in 1-ha stands by 10,000stands by 10,000

► Approach assumes:Approach assumes: that the properties of the system do that the properties of the system do

not change with scalenot change with scale that the broader system behaves that the broader system behaves

like the averaged finer onelike the averaged finer one that the relationships are linearthat the relationships are linear

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

Forest Ecosystem Restoration Forest Ecosystem Restoration Analysis (FORESTERA)Analysis (FORESTERA)

►Uses remote sensing data, on site data Uses remote sensing data, on site data (e.g., FIA data), GIS, and computer (e.g., FIA data), GIS, and computer models to synthesize past, present, models to synthesize past, present, and future scenario dataand future scenario data

►Forest health restoration is the major Forest health restoration is the major impetus for greater ecosystem scale impetus for greater ecosystem scale adaptive management activitiesadaptive management activities

Delcourts’ – Scale ParadigmDelcourts’ – Scale Paradigm

► MicroMicro► MesoMeso► MacroMacro► MegaMega

Delcourts’ ParadigmDelcourts’ Paradigm

Scale Paradigms – Resource Scale Paradigms – Resource PlanningPlanning

SummarySummary

► Scale is a prominent topic in restoration and adaptive Scale is a prominent topic in restoration and adaptive managementmanagement

► Influences conclusions and extrapolationsInfluences conclusions and extrapolations► Scale related to hierarchy; hierarchy theory provides a Scale related to hierarchy; hierarchy theory provides a

framework (consider focal level; level above constrains; level framework (consider focal level; level above constrains; level below explains [mechanisms])below explains [mechanisms])

► Extrapolation from fine to broad scale is straightforward if areas Extrapolation from fine to broad scale is straightforward if areas are homogeneous and relationship linear; spatial heterogeneity are homogeneous and relationship linear; spatial heterogeneity present, but need to know random vs. structured pattern; present, but need to know random vs. structured pattern; fractals and other methods possible if processes and constraints fractals and other methods possible if processes and constraints do not change across scalesdo not change across scales

► Extrapolation a very difficult problem with spatial heterogeneity Extrapolation a very difficult problem with spatial heterogeneity and nonlinear relationships (no general solution at present)and nonlinear relationships (no general solution at present)

► Just because you may not be able to scale up with great Just because you may not be able to scale up with great accuracy is no excuse for ignoring restoration and accuracy is no excuse for ignoring restoration and adaptive management problems at the landscape level !adaptive management problems at the landscape level !