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 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 move forward at the scale of the greater ecosystem (200,000 to 1,000,000 acres) if we are to prevent the collapse of Arizona’s forest ecosystems. 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 !