AN ABSTRACT OF THE THESIS OF
Patrick J. Kennelly for the degree of Doctor of Philosophy in Geography presented on
October 25, 1997. Title: Effects of Scale Properties on Biodiversity Mgpping in Oregon.
Abstract approved:
The effect of scale is an important concern in mapping of biodiversity. Scale issues
include the grid cell size used for analysis and the effect of the extent and internal bound-
aries. Because biodiversity analysis involves combinatorial processes, determining the
proper scale is data dependent and cannot be predicted from the initial data values and
their distribution.
Biodiversity analysis often samples combinations of species within geopolitical
boundaries. The effects of ecoregion boundaries on prioritization analysis was analyzed
in two ways. This study determined that prioritization hexagons for Oregon do not fall
preferentially on ecoregion boundaries. This research also concluded that results of prioritization analysis are geographically stable with the elimination of hexagons on ecoregion
boundaries from analysis.
Species maps based on the Environmental Protection Agency's Environmental
Monitoring and Assessment Program (EMAP) grid were analyzed. Grid cells 7 times as
large result in species richness maps statistically similar to maps made with the EMAP
grid. Patterns of localized variation between grid cells indicate no one area is contributing
to the overall variation. Prioritization maps, however, show different patterns of selected
hexagons. Grid cells 49 times as large show a loss of species richness variation and a different pattern of prioritization hexagons.
Richness maps based on wildlife habitat relations were used to map species rich-
ness at seven different three-fold compositions and decompositions of the EMAP grid.
Analysis of statistics indicates that no scale shows a small relative decrease in coefficient
of variation(CV), indicating no scale is relatively superior for richness mapping.
Prioritization analysis was performed on the new combinations of species lists for
five grid cell sizes ranging from 1/9 to 9X's the size of the EMAP grid. Efficiency of prioritization and map patterns of prioritization areas indicate that grid cells 1/3 the size of
the EMAP hexagons are optimal.
Comparisons can be made between the two biodiversity analyses at the EMAP
scale for wildlife habitat vs. EMAP grid based species range maps. CV values have
increased and the efficiency of prioritization is enhanced. This can be attributed to finer
resolution sampling capturing additional information.
@Copyright by Patrick J. Kennelly
October 25, 1997
All Rights Reserved
Effects of Scale Properties on Biodiversity Mapping in Oregon
by
Patrick J. Kennelly
A Thesis Submitted
to
Oregon State University
In Partial Fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented October 25, 1997
Commencement June 1998
Doctor of Philosophy thesis of Patrick J. Kennelly presented on October 25. 1997
Approved:
Major Prof sor, representing eography
Chair of Department of Geosciences
Dean of Graduate School
I understand that my thesis will become part of the permanent collection of Oregon State
University libraries. My signature below authorizes release of my thesis to any reader
upon request.
ACKNOWLEDGEMENTS
I would like to thank my advisor Jon Kimerling for all of his help and guidance in
my research. I would also like to thank my committee, Blair Csuti, Ross Kiester, Denis
White and Dawn Wright for all of their help and support, as well as my Graduate Council
Representative Aaron Liston for facilitating the process.
I would especially like to thank Kevin Sahr for all of his assistance and patience in
helping with my programming for this study. I also express my gratitude to Dr. Dan
Johnson and the Portland State University Department of Geography for all of the
resources they have made available to me since my move to Portland at the beginning of
this year.
Special thanks always to my family and friends for their support, especially my
fiancee, Sharon Maier.
TABLE OF CONTENTS
Page
CHAPTER 1: INTRODUCTION
INTRODUCTION
1
1
OBJECTIVES
2
METHODOLOGIES
Objectives 1 and 2
Seven-Fold Composition
Three-Fold Composition
Objective 3
2
2
6
7
SIGNIFICANCE OF RESEARCH
CHAPTER 2. EFFECTS OF ECOREGION BOUNDARIES ON
PRIORITIZATION ANALYSIS
8
10
11
ABSTRACT
12
INTRODUCTION
12
ECOREGION BOUNDARIES
15
Bailey Ecoregions
Omernik Ecoregions
ONHP Ecoregions
Jaccard "Data Driven" Ecoregions
15
15
18
18
INITIAL PRIORITIZATION ANALYSIS
21
ECOREGION BOUNDARY STATISTICS
26
DISCUSSION OF ECOREGION BOUNDARY STATISTICS
28
PRIORITIZATION ANALYSIS WITH ECOREGION BUFFERS
31
DISCUSSION OF BUFFERED PRIORITIZATION ANALYSIS
31
CONCLUSIONS AND DISCUSSION
36
REFERENCES
38
TABLE OF CONTENTS (Continued)
Page
APPENDIX
CHAPTER 3. SCALE ANALYSIS USING SEVEN-FOLD
COMPOSITIONS OF THE EMAP GRID
39
46
ABSTRACT
47
INTRODUCTION
47
DATA
48
METHODOLOGY
Regional Variations in Biodiversity Mapping
Localized Variations in Biodiversity Mapping
49
53
58
RESULTS
61
DISCUSSION
73
CONCLUSIONS
74
REFERENCES
75
APPENDIX
CHAPTER 4. SCALE ANALYSIS USING THREE-FOLD COMPOSITIONS AND DECOMPOSTIONS OF THE EMAP GRID
77
80
ABSTRACT
81
INTRODUCTION
82
DATA
84
METHODOLOGY
86
TABLE OF CONTENTS (Continued)
Page
RESULTS
Richness Mapping
Prioritization Analysis
DISCUSSION
Optimal Scale for Richness Mapping
Optimal Scale for Prioritization Mapping
EMAP Scale Prioritization Analysis from Two Datasets
91
91
101
109
109
112
116
CONCLUSIONS
118
REFERENCES
119
APPENDIX
121
CHAPTER 5. SUMMARY
127
SUMMARY STATEMENT
127
ECOREGION BOUNDARY EFFECTS
128
SCALE EFFECTS USING SEVEN-FOLD EMAP HEXAGON
COMPOSITIONS
129
SCALE EFFECTS USING THREE-FOLD EMAP HEXAGON
COMPOSITIONS AND DECOMPOSITIONS
130
BIBLIOGRAPHY
132
LIST OF FIGURES
Figure
Page
1.1
Three compositions of a hexagonal grid
4
1.2
Two successive seven-fold compositions of the Oregon EMAP grid.
5
2.1
Complementarity at the second cardinality of prioritization of
Oregon summer birds.
14
2.2
Bailey ecoregion boundaries of Oregon.
16
2.3
Omernik ecoregion boundaries of Oregon.
17
2.4
Oregon Natural Heritage Program ecoregion boundaries of Oregon.
19
2.5
Magnitude of Jaccard index between all neighboring EMAP hexagons.
20
2.6
Hexagons defining two Jaccard "data driven" ecoregion boundaries.
22
2.7
Number of cardinalities for which prioritization hexagons were used.
24
2.8
Number of paths (all cardinalities) for which prioritization hexagons
were used.
25
2.9
Prioritization hexagons at cardinality 5.
33
2.10
Prioritization hexagons after removing hexagons on Bailey
ecoregion boundary.
34
Prioritization hexagons after removing hexagons on Omernik
ecoregion boundary.
35
Prioritization hexagons after removing hexagons on Jaccard
high cut data driven ecoregion boundary.
37
3.1
Variations with scale in combinatorial data.
50
3.2
Statistics for four scales of numerically averaged data.
55
3.3
Statistics for four scales of combinatorial averaged data.
56
3.4
Example of maximum - minimum number of species.
60
2.11
2.12
LIST OF FIGURES (CONTINUED)
Figure
Page
3.5
Richness map at EMAP scale.
63
3.6
Richness map using grid cells seven times EMAP scale (Example 1).
64
3.7
Richness map using grid cells seven times EMAP scale (Example 2).
65
3.8
Richness maps using grid cells 49 times the EMAP hexagon.
66
3.9
Maximum minus minimum richness values (See Figure 3.4).
68
3.10
Average richness values (See Figure 3.4).
69
3.11
Normalized max-min richness values [(Max-Min)/Ave.]
(See Figure 3.4).
70
3.12
Fifth cardinality of prioritization at seven times EMAP scale.
72
4.1
Richness map using 4 times a 3-fold decomposition of the EMAP grid.
93
4.2
Richness map using 3 times a 3-fold decomposition of the EMAP grid.
94
4.3
Richness map using 2 times a 3-fold decomposition of the EMAP grid.
96
4.4
Richness map using 1 times a 3-fold decomposition of the EMAP grid.
97
4.5
Richness map using the EMAP grid.
98
4.6
Richness map using 1 times a 3-fold composition of the EMAP grid.
99
4.7
Richness map using 2 times a 3-fold composition of the EMAP grid.
100
4.8
Cardinality 5 prioritization hexagons for 2 times 3-fold composition.
103
4.9
Cardinality 5 prioritization hexagons for 1 times 3-fold composition.
104
4.10
Cardinality 5 prioritization hexagons for EMAP grid.
106
4.11
Cardinality 5 prioritization hexagons for 1 times 3-fold decomposition.
107
4.12
Cardinality 5 prioritization hexagons for 2 times 3-fold decomposition.
108
LIST OF FIGURES (CONTINUED)
Figure
Page
4.13
Coefficient of variation vs. scale for 7-fold and 3-fold richness maps.
110
4.14
Species covered vs. scale for three cardinalities of prioritization.
113
LIST OF TABLES
Page
Table
Percentage of Hexagons vs. Prioritization Hexagons
on Ecoregion Boundaries
27
3.1
Richness Map Statistics for 7-Fold EMAP Compositions
62
4.1
Richness Map Statistics for 3-Fold EMAP Compositions
92
2.1
LIST OF APPENDIX TABLES
Table
Page
2.2
Oregon Prioritization Analysis
40
2.3
Bailey Ecoregion Buffer Prioritization
41
2.4
Revised Omernik Ecoregion Buffer Prioritization
42
2.5
ONHP Ecoregion Buffer Prioritization
43
2.6
Jaccard Low-Cut Ecoregion Buffer Prioritization
44
2.7
Jaccard High-Cut Ecoregion Buffer Prioritization
45
3.2
1X's 7-Fold Composition Prioritization Statistic
78
3.3
2X's 7-Fold Composition Prioritization Statistics
79
4.2
2X's 3-Fold Decomposition Prioritization Statistics
122
4.3
1X's 3-Fold Decomposition Prioritization Statistics
123
4.4
OX's 3-Fold Decomposition (EMAP) Prioritization Statistics
124
4.5
1X's 3-Fold CompositionPrioritization Statistics
125
4.6
2X's 3-Fold Composition Prioritization Statistics
126
EFFECTS OF SCALE PROPERTIES ON BIODIVERSITY MAPPING
IN OREGON
CHAPTER 1. INTRODUCTION
INTRODUCTION
Biodiversity analysis in the state of Oregon identifies areas in which species and
ecosystem biodiversity are represented completely or as completely as possible. Inherent
in this analysis is the need to sample distributions of species throughout an appropriate
area using a proper grid cell.
To measure the biodiversity of Oregon, it is necessary to "divide the state into sample areas and use an algorithm to select the subset of areas in which all types will be repre-
sented" (Csuti, 1994). Although much effort has been focused on the algorithm to select
these sample areas (Csuti et al., 1997), no work has been done to determine the proper
scale (grid cell size) into which sample areas should be divided, or whether the state
boundary is the proper extent on which to map these samples.
Other research has related grid cell size used for mapping to statistical measures
over the entire study area. Stoms (1992) related rank correlation coefficient to minimum
mapping unit (MMU) west of the Sierra Nevada crest in California for species richness
mapping. This method was refined by Stoms (1994) to relate coefficient of variation (CV)
to sampling unit area. Stoms recognized here that agglomerating sampling units and species contained within is not a classical spatial statistics problem that can be addressed by
such methods as calculating semivariance; "aggregation is not a simple numerical averaging over different sampling sizes, but is a logical union of sets (species lists)" (p. 347).
2
Biodiversity analysis has traditionally used political boundaries as the extent of
mapping, and effects of natural boundaries have not been extensively studied. Species dis-
tributions within an ecoregion and along its boundaries are important to understand in
selecting prioritization areas for potential reserves. The effect of ecoregions as natural
extents has never been addressed in the conservation literature.
OBJECTIVES
The purpose of this research is to determine scales of sampling and extent bound-
aries best suited for biodiversity mapping, which involves three objectives. The first two
objectives are to determine the proper grid cell size for minimizing species richness variance and to determine how this variance effects prioritization analysis for the state of Ore-
gon. The third objective is to determine if political boundaries (i.e. the state of Oregon)
should be used as the extent for prioritization analysis although natural, internal boundaries in the form of ecoregion boundaries exist.
METHODOLOGIES
Objectives 1 and 2
The first two objectives are to determine the proper grid cell size for minimizing
species richness variation and then to determine how this variance affects prioritization
analysis for the state of Oregon. Because species richness is a logical union of sets and not
a numerical average, variance at different scales can only be determined by performing
logical unions at all scales of interest and calculating variance directly (Stoms, 1994, p.
347).
3
The three most useful geometries for composition and decomposition of hexagonal
grids are resented in Figure 1.1. Hexagonal grids can be composed or decomposed to new
hexagonal grids by either a factor of three or four. Composing a hexagonal grid by a factor
of three involves taking a central hexagon and one third of all six neighboring hexagons.
The resulting hexagon will be rotated by 30 degrees with respect to the original. Composing a hexagonal grid by a factor of four involves taking a central hexagon and one half of
all neighboring hexagons. The resulting hexagons will show no rotation. Three and fourfold decompositions can be performed in a similar manner.
A seven-fold composition of a hexagonal grid is also possible by taking a central
hexagon and all six neighboring hexagons. Although the resulting polygon is not a hexagon, further iterations of composition can be performed on this polygon in a similar manner. Seven-fold decompositions are not possible on a hexagonal grid. All compositions
and decompositions described continue to produce a grid without gaps and with all polygons equidistant from all neighboring polygon.
The fold of the composition or decomposition determines the number of unique
grids capable of being iterated. For example, each of the seven hexagons in a seven-fold
composition can serve as the central hexagon. Each grid results in a unique union of species richness (Figure 1.2).
This study will look at the coefficient of variation of two sets of species richness
maps of terrestrial vertebrates at different scales. Terrestrial vertebrates include more than
420 species of amphibians, reptiles, summer birds, and mammals (ARSM) identified in
the state of Oregon. The first set of range maps is based on probable or confirmed occurrence of each species in grid cells of the Environmental Protection Agency's Environmen-
rl
tl
..r rrd
1
Figure 1.2: Two successive seven-fold compositions of the Oregon
6
tal Monitoring and Assessment Program (EMAP) 640 km2 grid (White et al., 1992). The
second set of range maps are more detailed maps determined from wildlife habitats.
Seven-fold compositions only are possible on range maps based on the EMAP hexagonal
grid without making further assumptions. These composite grids simply combine existing
hexagons and allow for logical unions of species data in their present form. Three-fold
analysis will use habitat range maps based on actual vegetation maps for the state of Oregon cut by the smallest hexagonal grid to be used in the analysis.
Seven-Fold Composition
Object oriented (C++) programming was used to perform two seven-fold composi-
tions, one iteration of which is presented as Figure 1.2. The program draws the boundary
of the new polygons and performs a logical union on lists of ARSM species present. The
first composition (1X's 7-fold composition) requires seven grid cells and associated
datasets and the second composition (2X's 7-fold composition) requires 49. The resulting
dataset allows the creation of a richness map using existing programs and the calculation
of the coefficient of variation(CV) for the map using Splus software.
The EMAP grid has a single iteration. The 1X's 7-fold composition has seven unique
combinations of EMAP hexagons for its grid cell size. The 2X's 7-fold composition has
49 unique combinations of hexagons for the same grid cell size.
The statistics for these ranges are determined after combining all grid cell richness
values at a given scale. Coefficient of variation (CV) values will be compared for pronounced breaks in slope representing rapid increases in variance. As this analysis represent only three grid cell sizes, analysis will be limited. Also, since both new compositions
7
will be larger, this analysis cannot address the question of whether richness should be
mapped with finer resolution.
Three-Fold Composition
The three-fold analysis begins with the smallest hexagonal grid to be used in this
study, a four times (4X's) 3-fold decomposition having grid cells of approximately 8 km2.
A three-fold composition has been chosen for this study over a four-fold composition to
obtain finer resolution between scales.
More detailed habitat-based range maps are used for this analysis. Habitat range
maps are input as Arc/Info coverages. This coverage is then united with a coverage containing all of the triangles that make up a 4X's 3-fold decomposition, resulting in a matrix
of triangular building blocks for all compositions.
Variance data from the three-fold analysis can then be compared to data from the
seven-fold analysis. Seven-fold data would be expected to correspond with three-fold data
where analysis overlaps. Lack of correspondence may be due to differences inherent in the
species range and habitat range mapping techniques.
Prioritization analysis at these scales demonstrates if variance of species richness has
any influence on the location of hexagons chosen. Results indicate not only the grid cell
size at which species richness should be mapped in the state of Oregon, but also whether
grid cell sizes associated with similar species richness variance result in any variations in
prioritization analysis.
8
Statistics associated with species accumulation can also be analyzed for prioritization maps created at multiple scales. As well as statistical analysis, a more qualitative anal-
ysis of the appearance of the maps at different scales is also attempted.
Objective 3
The third objective is to determine if political boundaries (i.e. the state of Oregon)
should be used as the extent for prioritization analysis although natural, internal boundaries in the form of ecoregion boundaries exist.Three ecoregion maps covering the state of
Oregon compiled by Bailey (1980), Omernik (1987) and Kagan(1996) of the Oregon Natural Heritage Program are used in this study. Also used are "data driven" ecoregion bound-
aries, based on a Jaccard analysis. Neighboring hexagons showing the maximum amount
of normalized difference in species lists are used as Jaccard ecoregion boundaries.
A potential species range boundary sampling problem can be evaluated by comparison of hexagons located along ecoregion boundaries with prioritization hexagons. Some
species ranges terminate abruptly, possibly due to ecoregion boundaries. Hexagons that
straddle ecoregion boundaries may include many edges of species ranges and not represent some species in the manner intended. The importance of the effect of hexagons straddling range boundaries can be evaluated in the following manner for each ecoregion map.
First, a list of hexagons selected by current prioritization analysis at all cardinalities
for ARSM is compiled. All hexagons that fall on a ecoregion boundary are then listed. The
ratio of hexagons that fall on ecoregion boundaries vs. within ecoregions are calculated.
The two lists of hexagons can then be compared to see which prioritization hexagons fall
upon ecoregion boundaries. The ratio of prioritization hexagons on ecoregion boundaries
9
vs. within ecoregions are calculated and compared. Any significant difference between
these ratios imply that hexagons on ecoregion boundaries may be sampling edges of many
species range values associated with those ecoregion boundaries.
Prioritization analysis using buffered ecoregions would require the elimination of all
hexagons on ecoregion boundaries. If boundary hexagons are statistically significant, prioritization analysis within ecoregions would be expected to yield significantly different
prioritization hexagon locations.
Prioritization analysis using buffered ecoregions can be used to evaluate the contribution to complementarity of differences inherent in ecoregions. Complementarity
explains how new hexagons can be chosen that do not correspond to hexagons at a lower
cardinality of prioritization(i.e. number of hexagons chosen to maximize species diversity); "a site may be relatively species poor, but if it adds the most species not already represented, then it has maximum complementarity" (Csuti and Kiester, 1996). Locations of
two prioritization hexagons with high complementarity can occupy significantly different
locations than any hexagon at the previous prioritization cardinality. Some or all complementarity currently observed may be caused in part by more homogenous species distribu-
tions at an ecoregion level and more heterogeneous species distributions between
ecoregions (e.g. at a state level).
The contribution of ecoregion heterogeneity to prioritization analysis can be evaluated by comparing the prioritization analyses after elimination of hexagons on ecoregion
boundaries. If different hexagons are eliminated but prioritization hexagons are still chosen in a proximal geographic location, the implication is that complementarity is more a
10
function of a species assemblage in an area, as opposed to a unique species list for an isolated hexagon.
SIGNIFICANCE OF RESEARCH
Some research has been done on the effects of scale properties on combinatorial
mapping methods. These include investigating the coefficient of variation of species richness with grid cell size (Stoms, 1994). No studies, however, had related variability inherent in the sampling scale of the analysis to effects on prioritization analysis. Results will
be applicable to all future prioritization mapping efforts in the state of Oregon, and similar
techniques can be applied to other geographic locations.
This study is the first to perform several spatial analyses. It is the first to analyze
variance in species richness on a hexagonal grid and compare results of multiple hexagonal fold compositions. It is the first to see if species richness variance can be related to
changes in hexagons selected for prioritization analysis. It is the first study to do prioritization mapping after removing grid cells associated with ecoregion boundaries.
Finally, future research in the state of Oregon will begin to evaluate biodiversity on a
landscape scale. The importance of understanding the effects of scale on all statewide
mapping could be quite significant, especially if the state scale mapping has been used in
part to determine the location or size of the landscape planning area.
11
CHAPTER 2
Effects of Ecoregion Boundaries on Prioritization Analysis
Patrick J. Kennelly
Submit to Conservation Biology
12
ABSTRACT
Biodiversity analysis is typically done by sampling combinations of species within
a geopolitical boundary. This study addresses issues associated with sampling along
ecoregion boundaries within the prioritization study area. Studying the effects of ecoregion boundaries on prioritization analysis resulted in two major conclusions. This study
determined that prioritization hexagons for the state of Oregon do not fall preferentially on
ecoregion boundaries. This research also concluded that results of prioritization analysis
are geographically stable with the elimination of hexagons on ecoregion boundaries from
analysis. Both of these results have implications concerning the scale of species distribution being evaluated in prioritization mapping.
INTRODUCTION
Prioritization analysis is used in studying biodiversity. Prioritization analysis of
species first requires sampling a region's species on a regular grid. Analysis begins by
selecting the one grid cell which contains the highest diversity of known species. Subsequent steps add one grid cell at a time to the analysis, which finds the combination of grid
cells with the highest diversity of species. Each step represents an increase of one in the
cardinality of the analysis. This process continues until all species are represented in the
selected grid cells. Inherent in this analysis is the idea of complementarity. The grid cell
richest in species may never again be chosen at subsequent cardinalities, as "a site may be
relatively species poor, but if it adds the most species not already represented, then it has
maximum complementarity" (Csuti and Kiester, 1996). An example of different hexagons
13
being chosen by prioritization analysis at cardinalities one and two is evident for summer
birds in the state of Oregon (Figure 2.1).
Several assumptions are inherent in the way in which most prioritization analysis
is performed. One is that geopolitical boundaries are appropriate extents for such analysis,
such as the use of the state boundary of Oregon in the example given above. This assumption is necessitated by the geopolitical organization of biodiversity analysis.A related
assumption is that internal boundaries such as ecoregions will not have a significant effect
on the analysis. An assumption about the utility of results from prioritization analysis is
also key to the way in which the analysis is done. Prioritization analysis selects grid cells
able to be used in reserve design. If grid cells selected straddle two or more very different
habitat assemblages (as may be found in different ecoregions) it is possible that no one
reserve within a selected grid cell could preserve all species selected in the analysis.
Although valid, the prioritization analysis would be giving a misleading picture to subse-
quent efforts in an area's reserve design.
The purpose of this study is to address the above issues in two ways. First, it will
be determined if prioritization grid cell hexagons in the state of Oregon preferentially fall
on ecoregion boundaries. This will be done by comparing percentages of total hexagons
with prioritization hexagons on ecoregion boundaries. Second, it will be determined if
ecoregion boundaries have a significant effect on the geographic location of prioritization
hexagons. This will be done by comparing results of prioritization analyses before and
after removing hexagons on ecoregion boundaries.
Figure 2.1: Complementarity at the second cardinality of prioritization of
Oregon summer birds.
Summer Birds
IP1
BRC
179 of 253 specks
IP2
prior.sbird.os101.v1.
BRC
207 of 253 specks
prior.sbirdos102.v 1.1
ECOREGION BOUNDARIES
Five ecoregion maps in the state of Oregon will be evaluated. These will include
the Omernik ecoregions, the Bailey ecoregions, a compilation ecoregion map put together
by the Oregon Natural Heritage Program, and two "data driven" ecoregion maps, developed by calculating differences in the species lists between adjacent hexagons.
Bailey Ecoregions
The Bailey ecoregion boundaries are based on the 1994 revised ecoregion map of
the United States (Bailey, 1994) and presented as Figure 2.2. The ecoregion classification
scheme is hierarchical; "the two broadest, domains and divisions, are based on the ... large
ecological climate zones" (Bailey, 1980, p. 1). Climate is emphasized at this level because
of "its overriding effect on the composition and productivity of ecosystems from region to
region" (Bailey, 1980, p. 1). Further divisions are provinces based on vegetational macrofeatures, believed to "express more refined climatic differences than the domain and divi-
sions" (p. 2). Finally, altitudinal climate changes are also taken into account. Ecoregion
boundaries on this map are the most generalized (i.e. least detailed) of the three non-data
driven boundaries.
Omernik Ecoregions
Omernik ecoregion boundaries are based on the 1987 ecoregions of the United
States map (Omernik, 1987) with recent revisions made in the northwestern United States
(Thiele et al., 1996). These revised boundaries are presented as Figure 2.3. Omernik
ecoregion boundaries are based on "perceived patterns of a combination of causal and
0
cU
W
Figure 2.2: Bailey ecoregion boundaries of Oregon.
Middle Rocky
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leave9 lbik1
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integrative factors including land use, land surface form, potential natural vegetation, and
soils" (Omemik, 1987, p. 118). Ecoregion boundaries on this map are the least generalized
(i.e. most detailed) of the three non-data driven boundaries.
ONHP Ecoregions
The Oregon Natural Heritage Program(ONHP) ecoregion map is a compilation of
the Bailey and revised Omernik ecoregion boundaries (Kagan, 1996, personal communi-
cation). ONHP ecoregion boundaries are presented as Figure 2.4. Ecoregion boundaries
on this map are of a level of generalization intermediate to the Bailey revised Omernik
ecoregion maps.
Jaccard "Data Driven" Ecoreglons
Jaccard analysis calculates numbers of species that are unique between all adjacent
hexagons in the state of Oregon. This is done by looking at the assemblage of species in a
list associated with each hexagon, and then accounting for all species unique when com-
pared to neighboring hexagons (See Magurran, 1988). A hexagon with six neighboring
hexagons, therefore, will have six unique Jaccard indices. Unpublished results of Jaccard
analysis by Kiester and Sahr(1996) are presented as Figure 2.5. Each triangle will have
the same Jaccard index as the adjacent triangle in the neighboring hexagon. Areas of large
differences in species between neighboring hexagons are assigned warmer colors.
Visual analysis allows areas of higher contrast to be readily identified. To make the
Jaccard index more quantitatively meaningful, however, it is necessary to normalize these
numbers to the background. To do this, the Jaccard index was recalculated normalizing
Figure 2.4: Oregon Natural Heritage Program ecoregion boundaries of Oregon.
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2
differences to the species richness of the hexagon. The normalized Jaccard index is thus a
percentage between 0% (i.e. no difference in species list between hexagons) and 100%
(i.e. no species the same between hexagons). The hexagons which contain at least one triangle with a" high" Jaccard index, therefore, can be thought of as part of "data driven"
ecoregion buffers.
In order to eliminate Jaccard ecoregion boundary hexagons, a threshold normalized Jaccard index must be selected. This study used two thresholds, a high cut which
eliminated 42.4% of the hexagons, defined by all neighboring hexagons with a normalized
Jaccard index over 19%, and a low cut which eliminated 25.4% of the hexagons defined
by all neighboring hexagons with a normalized Jaccard index over 25%. These cutoffs
were established after analysis of the three ecoregions discussed above, and are designed
to bracket the high and low number of hexagons eliminated. Hexagons remaining after
buffering are presented as Figure 2.6. Black hexagons were eliminated as part of low-cut
Jaccard ecoregion boundary. Gray hexagons were additionally eliminated as part of highcut Jaccard ecoregion boundary.
INITIAL PRIORITIZATION ANALYSIS
The initial prioritization analysis was conducted on 422 species of terrestrial vertebrates whose range maps were defined on the Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP) grid (White et al., 1992). This
includes 253 birds, 114 mammals, 27 amphibians, and 28 reptiles. The EMAP grid was
also used for sampling species lists. This hexagonal grid is a Lambert azimuthal equal area
projection composed of grid cells approximately 640 km2 in size.
xagons Eliminated by Jaccard High and Low Cut Buffers
2
Analysis was necessary at 23 cardinalities to achieve full coverage of the 422 terrestrial vertebrates for the state of Oregon. At any given cardinality, many different combi-
nation of hexagons can achieve an optimal prioritization solution, with each of these
solutions referred to as a path. An arbitrary limit of 1,000 paths was set in the prioritiza-
tion program. Thus, after finding 1,000 unique paths at any given cardinality, the program
discontinues its search. In all 23 cardinalities and all paths at these cardinalities, 110 of the
possible 441 hexagons were chosen at least once. Prioritization hexagons for terrestrial
vertebrates therefore account for one fourth of all Oregon hexagons. All of these hexagons
were selected at least once, and any of these hexagons could have been chosen at each of
the 23 cardinalities.
If the number of cardinalities for which each of the 110 prioritization hexagons is
selected is taken into account, 995 hexagons were selected in the 23 cardinalities. A map
showing the location of all 110 prioritization hexagons and the number of times each of
these hexagons was used at all cardinalities is included as Figure 2.7. It may be noted that
the locations of hexagons used most and least frequently are not located in one particular
geographic area.
Each of these cardinalities, moreover, can have up to 1,000 unique paths. When the
number of paths for each of the 995 prioritization hexagons at all cardinalities is taken into
account, 218,636 total hexagons were selected in the prioritization analysis. A map showing the number of times each hexagon was used on different paths at different cardinalities
is included as Figure 2.8. Once again, the locations of hexagons used most and least frequently do not appear clustered.
November 24, 1996
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richness.prior. arsm. v l .1
It should be noted that this is not an exhaustive solution to the prioritization analysis. If the arbitrary number of paths entered into the program were increased, hexagons at
new locations may be selected (i.e. 110 may not be the maximum number of hexagon
locations). This study assumes, therefore, that the 1,000 paths account for a statistically
representative sampling of solutions.
ECOREGION BOUNDARY STATISTICS
Results of comparing percentages of total hexagons and prioritization hexagons on
ecoregion boundaries is presented as Table 2.1. The Bailey ecoregion boundaries are
included in 113 of the 441, or 25.6%of the total hexagons. If prioritization hexagons were
selected preferentially on these boundaries, more than 25.6%, or more than 28 of the 110
prioritization hexagon sites would have been cut by the Bailey ecoregion boundaries.
Instead, only 21 of the 110 prioritization hexagons, or 19.1 %, are cut. If the total number
of prioritization hexagons at all cardinalities are included, 176 of the 995 prioritization
hexagons, or 17.7% are cut by the Bailey ecoregion boundaries. If the total number of prioritization hexagons at all cardinalities and on all paths are included, 42,258 of the
218,636, or 19.3% are cut by Bailey ecoregion boundaries. In each case, the statistical
implication is that prioritization hexagons are preferentially chosen within, not upon, the
Bailey ecoregion boundaries. The same trend is true with the ONHP ecoregion boundaries. 40.6% of total hexagons include the ONHP ecoregion boundaries. As for prioritiza-
tion hexagons, only 35.5% of the prioritization hexagon locations are cut. This number
changes to32.8% if prioritization hexagons selected at all cardinalities are included, and
27
'Fable 2.1: Percentage of Hexagons vs. Prioritization Hexagons on Ecoregion
Boundaries
Bailey
Omernik
Ecoreg
Ecoreg
ONHP
Ecoreg
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Total Hexagons
441
Hexagons on Ecoregion
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441
441
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All Locations
110
110
110
110
110
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21
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31
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32.7%
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Total Prioritization Hexes
AU Cardinalities (23)
995
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434
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32.8%
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Total Prioritization Hexes
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All Paths (<=1,000)
218,636
218,636
218,636
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218,636
Prioritization Hexagons on
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38.0% if all paths at all cardinalities are included. Once again, prioritization hexagons are
preferentially chosen within OHNP ecoregions.
This trend is not as evident for the Omernik ecoregion boundaries. 39.7% of total
hexagons are cut by the Omernik ecoregion boundaries. As for prioritization hexagons,
only 32.7% are cut. This number changes to 33.4% if prioritization hexagons selected at
all cardinalities are included. If, however, all prioritization hexagons on all paths are
included, the percentage cut increases to 44.3%, a ratio greater than that for total hexagons
of 39.7%. This increase may be due to the much greater range of values for prioritization
hexagons at all cardinalities and on all paths and will be discussed later in this paper.
The Jaccard low-cut filter eliminated 25.4% of total hexagons. Of the hexagons
eliminated, 17.3% were prioritization hexagon locations, 21.7% were prioritization hexagons at all cardinalities, and 24.3% were prioritization hexagons at all cardinalities on all
paths. This follows the general trend observed in the Bailey and ONHP ecoregion analysis. The Jaccard high-cut filter eliminated 42.4% of total hexagons. Of the hexagons elim-
inated, 28.2% were prioritization hexagon locations, which follows the general trend. The
percentage, however, increased to 43.6% for prioritization hexagons at all cardinalities,
and to 48.0% at all cardinalities on all paths. This difference from the norm will also be
discussed below.
DISCUSSION OF ECOREGION BOUNDARY STATISTICS
The general trend of the Bailey, ONHP and Omernik ecoregion analysis is that pri-
oritization hexagons were selected that preferentially fall within ecoregions. This is true in
all examples for both prioritization hexagon locations and prioritization hexagons at all
cardinalities. It is also true for all but the Omernik data with respect to prioritization hexagons at all cardinalities and on all paths.
This difference may be due in part to greater variation in number of occurrences.
For prioritization hexagons at all cardinalities, the range of values is between I and 21,
with the top 10% ranging between 17 and 21 (See key in Figure 2.7). Any of the 11 red
hexagons could thus change the percentages reported by 1.7% to 2.1%. For prioritization
hexagons at all cardinalities and on all paths, however, the range of values is from 1 to
12,913, with the top 10% ranging between 5,691 and 12,913 (See key in Figure 2.8). Any
of these 11 red hexagons, therefore, could change the percentages reported by 2.6% to
5.9%. In fact, the Bailey, Omernik, and ONHP ecoregion boundaries all cut the hexagon
chosen the most times (12,913) for all cardinalities on all paths. Excluding this one hexagon from this analysis could actually decrease all three percentages in the bottom row of
Table 2.1 by nearly 6%.
It is also unclear which of the three measures of hexagon use in prioritization analysis highlights the most important hexagons. Because a hexagon is part of a larger group
that can be recombined in a thousand ways to give an optimal prioritization solution at one
cardinality does not necessarily mean it is hundreds of times more important than a hexagon used on only one path at all 23 cardinalities.
Also, hexagons appearing in red (top 10%) in Figure 2.8 are generally not selected
until higher cardinalities. Of the 11 red hexagons in Figure 2.8, only one is selected below
a cardinality of 8. Prioritization analysis shows that the first seven cardinalities cover
94.3% of the terrestrial vertebrate species, and only include one hexagon that will go on to
be chosen most frequently. Most hexagons chosen on the numerous paths, therefore, seem
to be contributing combinations of two or three key species to the analysis.
The fact that the low cut Jaccard analysis showed the same trend of preferential
selection of hexagons within "data driven" ecoregions is significant. In essence, the Jaccard analysis eliminates hexagons that show a very localized difference in species lists,
which are on the scale of adjacent hexagons. Even if the two hexagons with the most different species list were separated by a single hexagon with an intermediate species list, it
is possible that none of these three hexagons would be eliminated as part of a Jaccard
ecoregion boundary. Alternatively, one hexagon with a very different species list than its
more homogenous neighbors can be responsible for eliminating all seven hexagons. Areas
remaining after Jaccard buffering, therefore, would have heterogeneities on a scale larger
than the grid cells used in analysis. The implication, therefore, is that prioritization analysis is driven by heterogeneity at a scale larger than the grid cell size used in this analysis.
In the case of the high-cut Jaccard analysis, much larger areas are being eliminated
from analysis.Unlike the Omernik ecoregion buffer, which also eliminated over 40% of
total hexagons, the Jaccard high-cut buffer eliminated large areas on the scale of entire
ecoregions. These areas are much more amalgamated, not nearly as linear as the other
ecoregions. This ecoregion-scale clustering of eliminated hexagons may explain why
more prioritization hexagons are eliminated percentage-wise on ecoregion boundaries for
all cardinalities and all paths of all cardinalities than total hexagons.
3
PRIORITIZATION ANALYSIS WITH ECOREGION BUFFERS
This study also performed prioritization analysis for five new datasets after eliminating hexagons on ecoregion boundaries. To eliminate these hexagons from analysis,
appropriate data were eliminated from the species and hexagon matrix. In removing the
rows associated with some hexagons, all occurrences of a few, narrowly endemic species
were also eliminated. This decreased the total number of species from the original 422 to
420 for the Bailey analysis, 418 for the ONHP analysis, 417 for the Omernik analysis, 419
for the Jaccard low-cut, and 411 for the Jaccard high-cut. Different levels of prioritization,
therefore, result in different percentages of species covered in all of these analyses.
Results of these analyses as well as the original analysis for Oregon are reported as Table
2.2 - Table 2.7 in this chapter's Appendix.
The Jaccard low-cut still required 23 cardinalities for total coverage, although it
covers three less species than the original analysis. The Jaccard high-cut and the Bailey
analysis required 22 cardinalities, and the Omernik and ONHP analyses required 21 cardi-
nalities. In all analyses, well over 90% of the species are covered by the fifth cardinality
(see this chapter's Appendix).
DISCUSSION OF BUFFERED PRIORITIZATION ANALYSIS
Prioritization analysis on buffered ecoregion maps demonstrates that prioritization
hexagons are geographically stable, even with the exclusion of hexagons on ecoregion
boundaries from analysis. To illustrate this stability, examples of prioritization analysis for
the fifth cardinality will be compared for the different analyses. This cardinality ensures
3
that well over 90% of all terrestrial vertebrates in the state of Oregon will be covered in
each analysis.
The original prioritization analysis for the state of Oregon is presented as Figure
2.9. Although two hexagons appear in the southwest comer of the state, the remaining
hexagons are well dispersed. This can be compared with the Bailey ecoregion analysis,
presented as Figure 2.10. In this analysis, two of the cardinality five hexagons are eliminated, 27490 and 26531. In both cases, the new prioritization analysis selects adjacent
hexagons, 27489 and 26421. It is also worth noting that all five of the prioritization hexagons fall in different Bailey ecoregions. Similar results apply to the ONHP analysis.
The original analysis is also quite similar to the cardinality five Omemik ecoregion
analysis, presented as Figure 2.11. In this example, two of the original prioritization hexagons are eliminated, 26531 and 24645. The same adjacent hexagon was once again chosen
in place of 26531, hexagon 26521. Instead of hexagon 24645, hexagon 24895 was
selected. This hexagon is not adjacent, but only two hexagon steps away. The presence of
two green and two yellow hexagons means that multiple paths exist for finding an optimal
solution. The green hexagons are adjacent and the yellow hexagons are two hexagon steps
separate. All five different colored hexagons occur exclusively within five different Omer-
nik ecoregions.
The low-cut Jaccard analysis has similar results. Once again, both original prioritization hexagons 27490 and 26531 were eliminated. The adjacent hexagon 26640 and the
hexagon two hexagon steps away, 27492, were used instead. It is more difficult to com-
ment on the distribution of prioritization hexagons throughout ecoregions, as Jaccard
"data driven" ecoregions are not divided into several disjoint areas.
All Terrestrial Vertebrates
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3
The elimination of large, continuous areas with the high cut Jaccard analysis pro-
vides the most dramatic change at cardinality five (Figure 2.12). Four of the five original
prioritization hexagons have been eliminated. The blue hexagon not eliminated in the
northeast part of the state has moved two hexagons steps. Two of the eliminated hexagons
have been replaced with adjacent hexagons. The other two original hexagons and all of
their adjacent hexagons save one have been eliminated in the Jaccard high cut buffer. This
has caused one location to move from the northwestern part of the state to the southeastern
part, near the other displaced hexagon. Once again, discussion of presence in different
ecoregions is made difficult by the lack of well defined disjoint areas.
CONCLUSIONS AND DISCUSSION
Results from this study lead to two major conclusions. The first is that prioritization hexagons do no fall preferentially on most ecoregion boundaries. The second is that
prioritization analysis results remain geographically stable after eliminating hexagons
along ecoregion boundaries.
These results have interesting implications concerning the scale of biodiversity
processes affecting prioritization analysis. First, hexagons straddling ecoregion bound-
aries and sampling different biotic assemblages are not a driving factor in prioritization
analysis. If this were true, percentages of prioritization hexagons on ecoregion boundaries
would be higher than the percentage of total hexagons that are prioritization hexagons.
The Jaccard buffer analysis also indicates that localized changes in species lists on the
order of adjacent hexagons are also not a scale which drives prioritization analysis.
All Terrestrial Vertebrates
5/Jaccard High Cut Ecoregion Buffer
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prior.arsm jaccard.hicut.v I. I
Inferences can also be drawn from the geographic stability of results. This implies
that geographic areas on the scale of ecoregions may be an important factor in prioritization analysis. Also, when multiple paths are selected, hexagons are often proximal and
within the same ecoregion. This may imply that the most important heterogeneity for prioritization analysis may be differences found at a scale similar to the sizes of ecoregions in
Oregon.
REFERENCES
Bailey, R. G. 1980. Description of the ecoregions of the United States. U.S.D.A.
Forest Service, Miscellaneous Publication Number 1391.
Bailey, R. G. 1994. Ecoregions of the United States. U.S.D.A. Forest Service,
(Revised map to accompany Miscellaneous Publication Number 1391).
Csuti, B. and A. R. Kiester. 1996. Hierarchical Gap analysis for identifying priority areas for biodiversity. ASPRS/Gap Symposium Proceedings, T. H. Tear, J. M.
Scott, and F. Davis, eds. In press
Kagan, J. July, 1996. Personal communication.
Kiester, A. R. and K. Sahr. November, 1996. Personal communication.
Magurran, A. E. 1988. Ecological Diversity and its Measurement. Princeton University Press, Princeton, NJ.
Omernik, J. M. 1986. Ecoregions of the United States. U.S. Environmental Protection Agency, Corvallis Environmental Research Laboratory.
Thiele, S., D. Pater, T. Thorson, J. Kagan, C. Chappell, and J. Omernik. 1996.
Level III and IV Ecoregions of Oregon and Washington (Draft copy).
White, D., A. J. Kimerling and W. S. Overton. 1992. Cartographic and geometric
components of a global sampling design for environmental modeling. Cartography and Geographic Information Systems. 19, 5-22.
Appendix
Results of Ecoregion Buffered Prioritization Analysis
Table 2.2: Oregon Prioritization Analysis
Oregon All Vertebrates Prioritization v1.1
441 hexes and 422 total species
# of
# of
# of
# species
hexes/path
paths
hexes
covered
% species
covered
I
1
1
259
61.38
2
2
3
319
75.60
3
3
5
357
84.60
4
4
6
376
89.10
5
1
5
387
91.71
6
2
7
393
93.13
7
10
12
398
94.32
8
109
26
401
95.03
9
64
23
404
95.74
10
877
47
406
96.21
11
>1000
51
408
96.69
12
>1000
53
410
97.16
13
112
32
412
97.64
14
>1000
73
413
97.87
15
>1000
84
414
98.11
16
>1000
86
415
98.35
17
>1000
82
416
98.58
18
>1000
57
417
98.82
19
>1000
57
418
99.06
20
>1000
55
419
99.29
21
945
70
420
99.53
22
>1000
80
421
99.77
23
>1000
80
422
100.00
Biodiversity Resource Consortium
February 9, 1996
Table 2.3: Bailey Ecoregion Buffer Prioritization
Oregon All Vertebrates Prioritization vl.!
328 hexagons and 420 total species
# of
paths
# of
# species
hexes/path
hexagons
covered
% species
covered
1
1
1
255
60.71
2
2
3
319
75.95
3
1
3
357
85.00
4
1
4
374
89.05
5
1
5
384
91.43
6
8
13
390
92.86
7
50
18
395
94.05
8
64
23
399
95.00
9
50
28
402
95.71
10
51
34
404
96.19
11
20
17
407
96.90
12
61
22
409
97.38
13
51
35
410
97.62
14
55
28
412
98.10
15
50
42
413
98.33
16
50
57
414
98.57
17
51
67
415
98.81
18
50
64
416
99.05
19
50
67
417
99.29
20
51
68
418
99.52
21
50
66
419
99.76
22
50
72
420
100.00
# of
Biodiversity Resource Consortium
January 20, 1997
4
Table 2.4: Revised Omernik Ecoregion Buffer Prioritization
Oregon All Vertebrates Prioritization v1.1
265 hexagons and 417 total species
# of
# species
hexes/path
# of
paths
hexagons
covered
% species
covered
1
1
1
255
61.15
2
2
3
319
76.50
3
1
3
357
85.61
4
1
4
376
90.17
5
3
7
385
92.33
6
25
16
390
93.53
7
8
14
395
94.72
8
50
23
399
95.68
9
52
29
402
96.40
10
50
24
404
96.88
11
51
25
406
97.36
12
50
30
408
97.84
13
50
37
409
98.08
14
50
42
410
98.32
15
50
48
411
98.56
16
50
44
412
98.80
17
50
54
413
99.04
18
50
51
414
99.28
19
50
46
415
99.52
20
50
51
416
99.76
21
50
51
417
100.00
# of
Biodiversity Resource Consortium
November 21, 1996
Table 2.5: ONHP Ecoregion Buffer Prioritization
Oregon All Vertebrates Prioritization v1.1
239 hexagons and 418 total species
# of
# of
# of
# species
hexes/path
paths
hexagons
covered
% species
covered
1
1
1
255
61.00
2
2
3
319
76.32
3
2
4
357
85.41
4
4
6
376
89.95
5
1
5
386
92.34
6
12
18
391
93.54
7
17
13
396
94.74
8
10
13
401
95.93
9
51
25
403
96.41
10
55
27
405
96.89
11
55
26
407
97.37
12
76
21
409
97.85
13
53
38
410
98.09
14
50
33
411
98.33
15
50
31
412
98.56
16
50
32
413
98.80
17
51
37
414
99.04
18
50
40
415
99.28
19
50
42
416
99.52
20
50
44
417
99.76
21
50
42
418
100.00
Biodiversity Resource Consortium
November 3, 1996
Table 2.6: Jaccard Low-Cut Ecoregion Buffer Prioritization
Oregon All Vertebrates Prioritization v1.1
329 hexagons and 419 total species
# of
# of
# of
hexes/path
paths
hexagons
# species
covered
% species
covered
1
2
2
245
58.47
2
1
2
319
76.13
3
1
3
357
85.20
4
17
13
373
89.02
5
1
5
383
91.41
6
16
21
388
92.60
7
2
10
394
94.03
8
2
11
398
94.99
9
2
11
401
95.70
10
16
19
403
96.18
11
49
25
405
96.66
12
64
22
407
97.14
13
50
34
408
97.37
14
32
20
410
97.85
15
54
43
411
98.09
16
51
38
412
98.33
17
50
36
413
98.57
18
50
36
414
98.81
19
50
36
415
99.05
20
50
37
416
99.28
21
52
40
417
99.52
22
50
40
418
99.76
23
50
41
419
100.00
Biodiversity Resource Consortium
February 28, 1997
Table 2.7: Jaccard High-Cut Ecoregion Buffer Prioritization
Oregon All Vertebrates Prioritization v1.1
254 hexagons and 411 total species
# of
# of
# of
hexes/path
paths
hexagons
# species
covered
% species
covered
1
2
2
245
59.61
2
1
2
316
76.89
3
1
3
347
84.43
4
1
4
364
88.57
5
2
6
376
91.48
6
1
6
384
93.43
7
4
9
389
94.65
8
2
9
393
95.62
9
2
10
396
96.35
10
11
16
398
96.84
11
9
15
400
97.32
12
53
33
401
97.57
13
60
40
402
97.81
14
50
40
403
98.05
15
50
40
404
98.30
16
50
36
405
98.54
17
50
43
406
98.78
18
50
44
407
99.03
19
50
47
408
99.27
20
50
44
409
99.51
21
50
49
410
99.76
22
50
49
411
100.00
Biodiversity Resource Consortium
February 28, 1997
46
I
CHAPTER 3
Scale Analysis Using Seven-Fold Compositions of the EMAP Grid
Patrick J. Kennelly
If
I
Submit to Cartography and Geographic Information Systems
ABSTRACT
The effect of scale on combinatorial mapping has received little attention to date.
This study looks at the effect of increasing grid cell size on biodiversity mapping in Oregon. The data being analyzed are species range maps, whose extents are based on the
Environmental Protection Agency's Environmental Monitoring and Assessment Program
(EMAP) grid. Species richness and prioritization maps are made with grid cells seven and
49 times as large as the original grid. Grid cells seven times as large result in species richness maps statistically similar to maps made with the EMAP grid. Patterns of localized
variation between grid cells at this scale can be mapped, indicating there is not just one
area contributing to the overall variation. Prioritization maps, however, show different patterns of selected hexagons. Grid cells 49 times as large show a loss of species richness
variation and a different pattern of prioritization hexagons.
INTRODUCTION
The purpose of this study is to determine the effect of increasing grid cell size by
two factors of seven on biodiversity mapping of terrestrial vertebrates in the state of Ore-
gon. This research will look at the effect of scale on both richness mapping and prioritiza-
tion mapping. Effects of scale on richness mapping will be examined at both a regional
and a localized level. All analysis will be based on species range maps delineated by the
Environmental Protection Agency's EMAP hexagonal grid discussed below.
Constructing richness maps at different scales is a combinatorial procedure. Each
hexagonal EMAP grid cell has a unique species list associated with it. As these hexagons
are combined into larger grid cells, a new data dependent species list will result. These
results cannot be predicted by traditional geostatistical techniques. Issues associated with
such procedures are addressed by Stoms (1994).
The effect of changes in grid cell size on prioritization mapping will also be examined. Prioritization mapping selects a given number of grid cells which maximize the
number of different species present. This analysis involves comparing species lists of multiple grid cells. As grid cells and their associated species list change with scale, new com-
binations may give geographically dissimilar results.
DATA
The grid currently used for mapping biodiversity in Oregon is the Environmental
Protection Agency EMAP hexagonal grid, which provides complete coverage for the contiguous United States. This Lambert azimuthal equal area map projection surface is composed of hexagonal grid cells approximately 640 km2. This size was selected as a "suitable
compromise between the desired spatial resolution of sampling and the projected available
financial resources" (White et al., 1992, p. 18).
Biodiversity analysis in Oregon has used this grid in mapping species ranges and
in sampling the data for richness and prioritization analysis. The first version of range
maps for 422 terrestrial vertebrates was compiled by The Nature Conservancy. These
range maps are based on several criteria. Documented species sitings from such resources
as museum specimens serve as the basis. Expert opinions are then used to augment these
maps, assigning hexagons a confirmed, probable, or possible status. All confirmed and
probable species are assigned to appropriate grid cells. The resulting list of hexagons and
associated species are used for all analysis in this study.
4
The EMAP grid acts both as the minimum mapping unit (MMU) for the input data
and the sampling unit for the output data. Analysis at a grid cell size smaller than 640km2,
therefore, is impossible with these data without making further assumptions.
METHODOLOGY
Species richness maps are created by summing the total number of species in each
grid cell. Although these maps provide spatial information on what areas are rich or poor
in number of species, they are not suited to answer other important questions in conserva-
tion biology (Williams et al., 1996, Prendergast et al., 1993). Prioritization maps look to
maximize the number of unique species in a given number of grid cells, an example of a
maximum covering location problem (MCLP) (Church et al., 1994). Analysis in Oregon
uses a linear programming algorithm, which ensures "optimal solutions to the reserve
selection algorithm" (Csuti et al., 1997, p. 83).
A change in the size of the grid cell will result in a new list of species associated
with each new grid cell sample. Stoms (1994) recognizes that agglomerating sampling
units and species contained within is not a classical spatial statistics problem that can be
addressed by such methods as calculating semivariance; "aggregation is not a simple
numerical averaging over different sampling sizes, but is a logical union of sets (species
lists)" (p. 347).
Figure 3.1 illustrates this principle of Stoms (1994) for a simple example. Grid
cell size 1 has eight cells with no variations in species richness between cells. All four grid
cells left of center contain the same 100 species. The logical union of these four would
still represent 100 species, as illustrated in the left cell of grid cell size 2. The right four
Grid cell size 1: No variation
100
100
100
100
100
100
100
100
Grid cell size 2: High variation
100
I
400
Figure 3.1: Variations with scale in combinatorial data (From an explanation
in Stoms, 1994).
grid cells for grid cell size 1, however, contain four sets of 100 mutually exclusive species.
Their logical union would contain 400 species, as illustrated in the right cell of grid cell
size 2. Stoms found that coefficient of variation(CV) decreased with increased sampling
area. No current research has attempted to relate changes in grid cell size to potential dif-
ferences in locations of samples selected by biodiversity prioritization analysis.
This study looks at biodiversity mapping on the EMAP hexagonal grid. Three
geometries for the composition and decomposition of these grid cells are presented as Fig-
ure 1.1. All three of these geometries will preserve the important attributes found in a hexagonal grid, such as grid cells filling 2-D space and all adjacent grid cells being
equidistant.
Two of these methods of composition require the hexagonal grid to be subdivided
into triangles for resampling. The three fold composition takes a central hexagon and one
third of all six neighboring hexagons. The four fold uses a central hexagon and one half of
all six neighboring hexagons. As the species range maps used in this study are based on
absence or presence in each hexagonal grid cell, three and four fold compositions are inap-
propriate without additional assumptions.
A seven fold composition of a hexagon takes a central hexagon and the six adjacent hexagons. The resulting polygon is not a hexagon. This polygonal grid, nevertheless,
can undergo further compositions to larger polygons and preserves all important properties of hexagonal grid cells. A seven fold decompositon is not possible from range maps
based on the original EMAP hexagon.
Two compositions of the EMAP grid cell are appropriate for analysis in Oregon. A
third iteration would create a grid cell nearly as large as the state. The two compositions
are illustrated in Figure 1.2. 441 EMAP grid cells of approximately 640 km2 cover the
state of Oregon. After one composition, the grid will contain approximately 50 polygonal
cells, each 7 times as large (approximately 4,480 km2). The 50 polygonal cells do not
include fractional grid cells produced, as biodiversity mapping requires all grid cells to be
equal in area. Fractional grid cells were thus eliminated from analysis. Two levels of com-
5
position results in a grid of approximately three polygonal cells, each 49 times as large
(approximately 31,360 km2). Once again, fractional grid cells were eliminated from analysis.
Seven unique grid cells can be constructed at the first composition. Figure 1.2
illustrates one example. Other seven fold compositions could be created by shifting the
first composition grid one EMAP hexagon to the north, northeast, southeast, south, southwest, or northwest with respect to the grid shown. Seven unique grids and unique combinations of species lists would result. This is not a sampling of the data in the statistical
sense. Each of the seven maps will be an exhaustive sample of the data captured at the
EMAP scale (except for edge effects). Unique, exhaustive combinations will help to better
define combinatorial changes in the data with scale. The above is also true for the second
composition, where 49 unique combinations of the EMAP grid are possible.
Species diversity maps in this study divide the range of species richness values into
classes for color map displays. Five classes are defined based on the statistical distribution
of species richness values. The class divisions are 0% to 15%, 15% to 40%, 40% to 65%,
65% to 90% and 90% to 100% of the species richness values, and represent suitable class
ranges for such distributions. This study combines richness values from all datasets at the
same composition level before dividing the distribution into classes. The first composition
will therefore have seven unique maps, but the classes on each map will be the same and
based on the entire distribution of values. Five of the maps have 50 grid cells and two of
the maps have 51, thus giving 352 unique richness values for defining quantiles of the dis-
tribution.
This method for determining a statistical distribution is necessary with the classes
for the composition 2 maps, as none of the 49 maps have more than five grid cells. Com-
bining richness values from all maps allows 167 richness values to define the distribution.
This number includes five maps with 2 grid cells, 23 maps with 3, 17 maps with 4, and
four maps with 5.
Prioritization analysis uses a matrix of grid cells and species to determine which
grid cells in combination will represent the most species for a given number of grid cells.
This study uses species lists combined from all maps at a given composition. The matrix
files for the first and second composition thus contain 352 and 167 lists of species present,
respectively.
This method of combining all data at a scale permits one comprehensive prioritization analysis to be done for each composition. Combining all species lists at one scale also
allows for the overlap of higher order grid cells in prioritization analysis. The implications
of overlapping grid cells to families of hexagons in prioritization areas will be discussed
later in this paper.
Regional Variations in Biodiversity Mapping
Statistical measures associated with the resulting biodiversity maps have rarely
been assessed. No obvious metric measures dissimilarity of locations of prioritization
hexagons on two different maps. This study will use observations of larger prioritization
hexagons overlapping, not overlapping or being adjacent to prioritization hexagons
selected at a smaller scale as a measure of spatial stability.
Several statistical measures, however, are possible for richness mapping at different scales. These include both measures made at a local level and ones made for the entire
range of values. Previous work in comparing statistics from maps based on the same
datasets includes Stoms (1992) relating of rank correlation coefficient to minimum mapping unit for richness mapping west of the Sierra Nevada crest in California. In more
recent work, Stoms (1994) relates coefficient of variation(CV) to sampling unit area.
CV is defined as the sample standard deviation expressed as a percentage of the
sample mean (Steel and Tome, p. 27). In combining species lists at larger scales, values
for average and standard deviation can be highly volatile. An example of the simplicity of
behavior for numerically averaged data as opposed to combinatorial data is presented as
Figures 3.2 and 3.3.
Figure 3.2 shows an example of a numerically averaged dataset sampled at four
different scales, each scale represented in a different graph. The length of the solid line
segments in each graph represents the grid cell size. The values on the y axis represent the
values associated with each grid cell. Average values as well as maximum minus minimum (max-min) are calculated at each scale. The dashed line displays the average value at
each scale. Although max-min is not a true measure of variance, it is similar in that it helps
define the range of values. As grid cell size increases, the max-min values decrease and the
average stays the same. In this example, calculating a value (max-min / average) as a
pseudo coefficient of variation ("CV") is not instructive, as average is a constant and thus
"CV" relates directly to max-min.
Figure 3.3 shows a similar example with combinatorial data. An addition is made
to this display from Figure 3.2 as a "Total" value of 360 is given. This number represents
55
tatistics for Four Scales of Numerically Averaged Data
'Max - Min 120
Average= 100
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Som
"CV" =.0 .4
.4
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160
12
Max-Min=0
Average = 100
"CV"=0
8
Figure 3.2: Statistics for four scales of numerically averaged data.
I
.56
Statistics for Four Scales of Combinatorial Data
Total=360..------------320
Max - Min = 120
Average = 100
24
"CV = 1.2:..
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8
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320;
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24h,
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Average = 340 - 140
"CV"= 1.00-0
Total;= 36
:-: -
320 -
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240-
Average = 360
"CV" = 0
11
16080-1
Figure 3.3: Statistics for four scales of combinatorial averaged data.
It
the total number of possible types of samples in an extent (e.g. total species in a state). As
grid cells are combined, the new grid cell could have a range of values based on the number of unique elements in each smaller grid cell. For example, the two smallest grid cells
to the left contain 80 and 120 elements. As they are combined into a larger grid cell in the
second graph, the new grid cell may have as few as 120 elements (i.e. all 80 elements in
the first grid cell also appear in second grid cell) or up to 200 elements(i.e. all 80 elements
in the first grid cell are different from all 120 elements present in the second grid cell).
Ranges of possible values are highlighted on appropriate graphs using shaded areas.
Because values span a range at the second and third scale, the average will also
have a range of values. The smallest and largest possible averages are displayed on appro-
priate graphs with two dashed lines. The fourth scale shows one grid cell equal to the
extent. In this example, all types are represented in the extent, thus the grid cell will have a
value and an average equal to the total of 360.
One important observation from this example is that for a smooth distribution of
high and low numbers, the top of high ranges can increase much faster than the base of the
low numbers. While the second grid cell at scale two takes an additive value (160 + 120 =
280) as the top of its range of values, the third grid cell at scale two takes a maximum of
two values value (the maximum of 40 and 80 is 80) as its minimum value. It is therefore
possible for max-min variation to increase with increasing grid cell size. Note that maxmin at scale two can be as much as 200, well over the max-min value of 120 at the first
scale.
In this example, the average value will increase in moving from the first to the sec)nd scale. If the max-min increases proportionately, the "CV" will remain the same
(where "CV" = max-min / ave). It is also possible, however, for the "CV" to decrease or
increase with increased grid cell size. Results are dependent on individual datasets.
Another important observation of this example is that the total number of types is
important to how ranges of values will change. At the third scale, the top of the range for
the left grid cell is not an additive value (200 + 280 = 480), but rather the maximum num-
ber of types in the extent (total = 360). This helps to limit the range of possible values, and
ultimately decrease the range of values as the average value continues to increase. The
resulting effect on "CV" will be a number destined to decrease and finally reach zero as
the grid cell size equals the extent. It should also be noted that CV could also decrease at
any step if average increases proportionately faster than max-min.
Although changes in variance and average will be data dependent with changes in
scale, CV seems to be an appropriate statistic for measuring these changes. Although CV
may increase, decrease, or stay the same at smaller scales, we should be able to detect
breaks due to reaching regional limits to the number of types present in an area. This may
also be true when using this procedure for detecting subregional limits at smaller scales,
where more species will not be added within a range of scales because areas with comple-
mentary species are too geographically distant to be included in grid cells.
Localized Variations in Biodiversity Mapping
Measuring changes in coefficient of variation provides a richness mapping statistic
for comparison of all data within the extent of the study area. Each set of maps at a different scale will have one coefficient of variation associated with all of the richness values.
Each map in the set, however, will show some localized variations. The geometry of the 7
fold composition allows a unique opportunity to measure and geographically display local
variations.
The method used for looking at localized variations is illustrated in Figure 3.4.
Most hexagons at the EMAP grid cell size (cyan hexagon) will contribute richness infor-
mation to seven larger polygons (red outlines) at the first seven fold composition. Each of
these larger red polygons will have a richness value, contributed in part by the cyan hexa-
gon. By looking at the maximum minus the minimum value (max-min), a measure of
localized variations in richness can be determined. By measuring this value at every
EMAP hexagon using the seven appropriate first composition polygonal grid cells, a map
of localized variation can be constructed.
EMAP hexagons in areas of greater richness would be expected to have a larger
difference in max-min simply because their values are larger. It is appropriate, therefore,
to calculate a localized "coefficient of variation" by dividing the max-min value for each
grid cell by its average richness value for all surrounding polygons. Maps of average richness, max-min richness, and normalized max-min richness can all be constructed for comparison.
The normalized max-min map will show the distribution of localized variation. A
random pattern of richness would indicate that no areas the size of all 19 EMAP hexagons
in Figure 3.4 contributes more to total variation than any other. A clustered richness map
pattern would highlight areas with greater and lesser amounts of variation. A pattern similar to the average richness pattern would indicate that areas of greater average richness are
also areas of greater normalized variation in richness. These map patterns will be discussed with the results of this study.
ko
Example of maximum - minimum number of species
Central polygon richness
250
North polygon richness
244
Northeast polygon richness
275 = Maximum
Southeast polygon richness
266
South polygon richness
240
Southwest polygon richness
233 = Minimum
Northwest polygon richness
252
Maximum - minimum
Average
42
(Max-Min)/Average
0.17
251.43
Figure 3.4: Example of maximum minus minimum number of species.
61
RESULTS
The results of richness mapping at three different scales is presented as Table 3.1.
OX's 7-fold composition is the EMAP grid, with the first and second compositions labeled
1X's 7-fold and 2X's 7-fold. The minimum, maximum and mean values increase at each
composition in accordance to the general pattern from Figure 3.3. The variance increases
for the first composition before decreasing from the first to the second. This increase and
decrease in variation is part of the data dependent volatility of these numbers, as illustrated
in the range of max-min in Figure 3.3.
The coefficient of variation (CV) stays virtually the same from the EMAP grid to
the first composition, changing from 10.45% to 10.66%. This implies that no statistical
variations in richness values are present between the two scales. The EMAP scale richness
map and two of the seven richness maps at the first composition are included as Figures
3.5,3.6, and 3.7.
The CV decreases at 2X's 7-fold composition. This implies that some of the varia-
tions seen at smaller scales have been lost at this scale. Seven of the 49 richness maps at
this scale are included as Figure 3.8 for comparison. Maps at 2X's 7-fold composition
contain only two to five grid cells. It is not surprising that variations seen at the two previous scales would be lost at this scale, as the grid cell size approaches the extent of the
study area. This same pattern of decreasing values of CV with increased grid cell size
were documented by Stoms (1994).
62
Table 3.1: Richness Map Statistics for 7-Fold. EMAP Compositions
OX's 7-Fold
1X's 7-Fold
(EMAP)
Comp
2X's 7-Fold
Comp
Number of
Polygons
441
352
167
Min
143
178
266
Max
259
307
357
Mean
197.11
232.08
308.89
Variance
424.28
612.52
528.29
St Dev
20.60
24.75
22.98
Coeff of
Variance
10.45%
10.66%
7.44%
269o1
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All Terrestrial Vertebrate Richness
Composition 2 using 7 central hexagons of first composition
9
Differences in map patterns can be detected by comparing the two maps from the
first composition(See Figures 3.6 &3.7). To quantify the differences between all seven
maps at this scale and display results in a geographical format, a normalized max-min map
was constructed at this scale. Figure 3.9 shows a map of max-min number of species. This
map is normalized by average values for each grid cell as presented in Figure 3.10.
Although the average map looks somewhat like a smoothed version of the EMAP richness
map (Figure 3.5), it was constructed by averaging richness values from all 7 overlapping
I X's 7-fold composition polygons for each EMAP grid cell (except EMAP edge hexagons
with insufficient hexagons to construct complete 1X's 7-fold composition grid cells).
The final normalized max-min map is presented as Figure 3.11. Although grid
cells of different richness are distributed throughout the state, some clustering of values
seems to occur. This implies that different areas of the state are contributing variations to
the summary CV for the scale of mapping referenced in Table 3.1. The change in scale
results in no overall change in variation, although localized changes in variation occur
throughout the entire state.
The richness map results allow us to gain insight into factors that may affect prioritization mapping. There is no significant change in CV from the EMAP scale to composition 1. It is possible, therefore, to perform prioritization analysis on two species lists
resulting from a change in scale with no statistical differences in CV of richness maps.
Results of prioritization of the 1X's 7-fold and 2X's 7-fold composition are presented in
this chapter's Appendix as Table 3.2 and 3.3. These results can be compared with the
original prioritization analysis for the EMAP grid presented as Table 2.2 in the Appendix
of Chapter 2.
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Prioritization based on the EMAP grid uses 441 non-overlapping hexagons and
422 total species of terrestrial vertebrates. Five hexagons are able to cover 387 species
(91.71%). Figure 2.9 shows the results of this prioritization. A total of 23 hexagons would
be necessary to cover all 422 species (100%).
Prioritization based on the first composition grids uses 352 overlapping polygons
for the same 422 species. This method allows two or more prioritization polygons at the
same scale to overlap. Five polygons are now able to cover 396 species (93.84%). 13 total
polygons are now needed for full coverage. Such changes are not surprising as now each
grid cell has seven times the area of an EMAP grid cell. Figure 3.12 shows the prioritization with five polygons. Two prioritization polygons selected on this map overlap the two
magenta polygonal grid cells in the west-central portion of the state. Although the idea of
a family of geographically aggregated grid cells has previously been recognized (see Csuti
and Kiester, 1996), this analysis allows for overlapping aggregations.
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eastern Oregon selected at a larger scale in Figure 3.12 overlaps a selected EMAP prioriti-
zation hexagon in Figure 2.9. In addition, the green polygon is one hexagon away from a
EMAP prioritization hexagon, and the red polygon two hexagons away.
Prioritization based on the second composition grids uses 167 overlapping polygons for the same 422 species. Five polygons cover 421 species, with one more polygon
necessary for 100% coverage. Prioritization using five hexagons now overlaps three of the
hexagons from the EMAP scale and portions of all five of the polygons from the fifth pri-
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prior.arsm.ipO5.v 1.1
oritization at 1X's 7-fold composition. This increase in overlapping prioritization hexagons is probably not significant, as a majority of the state's area is covered by
prioritization grid cells using the 2X's 7-fold composition. (i. e. of the original 441 EMAP
hexagons, approximately 245 hexagons [49 EMAP hexagons x five 2X's seven-fold com-
position prioritization polygons] will be used at this scale).
DISCUSSION
The relationship of prioritization to richness mapping is not straightforward. In the
above example, analysis at the EMAP and 1X's seven-fold composition scale is compared.
Both scales result in richness maps with statistically similar measures of CV. Localized
differences in the new composition 1 richness maps are not the result of localized varia-
tions in one particular geographic area. The statistical inference is that there is little difference between the amount of information on richness variation contained in richness maps
at these two scales.
Significant differences, however, exist in the location of prioritization grid cells at
the two scales. Two key factors could be influencing the difference in these maps. The
most important factor is undoubtedly the difference in the type of value being mapped.
Species richness maps sum species present in each grid cell, but do not account for differences in the actual species lists between grid cells. Mapping richness at different scales
and mapping prioritization at a single scale are both set theoretical processes. Prioritiza-
tion analysis is data dependent, and can only be mapped by looking at many combinations
of species lists at a single scale.
Another factor may be the extent used to study changes in grid cell size. Although
this study varies grid cell size, the mapping extent is always the state of Oregon. This
extent could contain areas in which the species list is more homogeneous than that for the
entire state. One example of this may be ecoregions. Identifying mapping scales which
minimize variation within sub-areas and maximize variation between sub-areas could help
to relate richness and prioritization mapping.
CONCLUSIONS
Multi-scale biodiversity analysis identifies proper scales for mapping species rich-
ness. An optimal scale would maximize variation and grid cell size while minimizing the
number of grid cells required for mapping. It cannot, however, be used to determine
proper scales for prioritization analysis.
The grid cell size for mapping richness of terrestrial vertebrates in Oregon could be
increased by a factor of seven over the EMAP grid cell without losing any statistically sig-
nificant information on species variation. Local changes in variation from the EMAP grid
to one seven times as large are not influenced by any single area within the mapping
extent. If the grid cell size is increased again by a factor of seven, variations previously
present in the map would be lost, as measured by the coefficient of variation.
The proper scale for prioritization analysis cannot be determined with this method.
It may be necessary to look at results of prioritization mapping at smaller scales, or mapping with less change in grid cell size between scales, to find geographically consistent
prioritization results. Richness maps based on more homogenous extents may also help to
relate proper scale and extent of species richness mapping to prioritization mapping.
REFERENCES
Church, R.L., D. M. Stoms, and F. W. Davis. 1994. Reserve selection as a maximum covering location problem. Biological Conservation. 78:353-355.
Csuti, B. 1994. Gap analysis: Identification of priority areas for biodiversity management and conservation. Gap Analysis Program Handbook Program.
Csuti, B. and A. R. Kiester. 1996. Hierarchical Gap analysis for identifying priority areas for biodiversity. ASPRS/Gap Symposium Proceedings, T. H. Tear, J.
M. Scott, and F.Davis, eds. In press.
Csuti, B., S. Polasky, P. H. Williams, R. L. Pressey, J. D. Camm, M. Kershaw,
A.R.Kiester, B. Downs, R. Hamilton, M. Huso, and K. Sahr. 1997. A comparison of reserve selection algorithms using data on terrestrial vertebrates in Oregon. Biological Conservation, 80, 83-97.
Prendergast, J. it, R. M. Quinn, J. H. Lawton, B. C. Eversham, and D. W. Gibbons. 1993. Rare species, the coincidence of diversity hotspots and conservation
strategies. Nature. 365:335-337.
Pressey, R. L. and M. Bedward. 1991. Mapping the environment at different
scales: benefits and costs for nature conservation. Pp. 7-13 in Nature Conservation: cost effective biological surveys and data analysis (C. R. Margules and M.
P. Austin, eds.). CSIRO Publications, East Melbourne, Australia
Steel, R. G. D. and J. H. Tome. 1980. Principles and Procedures of Statistics, a
Biometrical Approach. McGraw-Hill Book Co., New York.
Stoms, D. M. 1994. Scale dependence of species richness maps. Professional
Geographer. 46,456-58.
Stoms, D. M. 1992. Effects of habitat map generalization in biodiversity assessment. Photogrammetric Engineering and Remote Sensing. 11, 1587-91.
White, D., A. J. Kimerling and W. S. Overton. 1992. Cartographic and geometric
components of a global sampling design for environmental modeling. Cartography and Geographic Information Systems. 19, 5-22.
Williams, P., D. Gibbons, C. Margules, A. Rebelo, C. Humphries, and R. Pressey.
1996. A comparison of richness hotspots, rarity hotspots, and complementary
areas for conserving diversity of British birds. Conservation Biology. 10, 155174.
Appendix
Results of Multi-Scale Seven-Fold Prioritization Analysis
Table 3.2: 1X's 7-Fold Composition Prioritization Statistics
Oregon All Vertebrates Prioritization v1.1
352 overlapping polygons and 422 total species
# of
# of
# of
# species
hexes/path
paths
hexes
covered
% species
covered
1
1
1
307
72.75
2
4
5
356
84.36
3
2
4
381
90.28
4
1
4
396
93.84
5
2
6
405
95.97
6
8
13
410
97.16
7
42
27
413
97.87
8
22
24
416
98.58
9
51
32
418
99.05
10
50
32
419
99.29
11
50
55
420
99.53
12
50
72
421
99.76
13
50
66
422
100.00
Biodiversity Resource Consortium
July 19, 1996
Table 3.3: 2X's 7-Fold Composition Prioritization Statistics
Oregon All Vertebrates Prioritization v1.1
167 overlapping polygons and 422 total species
# of
# of
paths
# of
# species
hexes/path
polygons
covered
% species
covered
1
1
1
357
84.60
2
2
3
401
95.02
3
5
7
413
97.87
4
54
21
418
99.05
5
2
6
421
99.76
6
53
25
422
100.00
Biodiversity Resource Consortium
October 24, 1996
80
4
Scale Analysis Using Three-Fold Compositions and Decompositions of the EMAP Grid
Patrick J. Kennelly
Submit to Professional Geographer
ABSTRACT
The effect of scale is an important concern in mapping of biodiversity. Because
biodiversity analysis involves combinatorial processes, determining the proper scale is
data dependent and cannot be predicted from the initial data values and their distribution.
This study maps species richness at seven different compositions and decomposi-
tions of the Environmental Protection Agency's EMAP grid, from a scale 1/81 to nine
times (9X's) the size of the EMAP grid. Analysis of statistics indicates no relatively
small decrease in coefficient of variation (CV), indicating no optimal scale for richness
mapping.
Prioritization analysis was performed on the new combinations of species lists for
five grid cell sizes ranging from a scale of 1/9 to 9X's the size of the EMAP grid. Efficiency of prioritization and map patterns of prioritization areas indicates that of these five
scales, the grid cells 1/3 the size of the EMAP hexagons are relatively the best for this
analysis.
This study uses a second generation of species range maps as the basis for analy-
sis. New species range maps are based on habitat maps interpreted from Landsat MSS
imagery. This differs from previous studies which used species range maps, where species were assigned to EMAP grid cells based on sitings, samples and expert opinions.
Comparisons can be made between the two biodiversity analyses at the EMAP scale. CV
values have increased from 10.45% from earlier richness maps to 13.93% for the new richness maps.This change of nearly 3.5 percentage points represents an increase in variations
in richness values of nearly 33%. The efficiency of prioritization is also enhanced. Prioritization analysis based on the new data allows coverage of the same number of total spe-
cies with less than 60% of the grid cells required initially. Both of these improvements
indicate that new species range maps allow for the preservation of more information based
on an increase in overall variability of species richness values and presence of unique species in species grid cell lists. This can be attributed to finer resolution sampling capturing
additional information.
INTRODUCTION
The purpose of this study is to determine the proper grid cell size for biodiversity
mapping in the state of Oregon. Biodiversity mapping in this study includes both species
richness mapping and prioritization mapping. The study presented as Chapter 3 of this
dissertation maps species richness and prioritization hexagons at three scales for analysis.
This study will expand upon and contrast with the research reported in this previous chapter. It will expand upon this study by mapping biodiversity at seven as opposed to three
scales, including scales of finer resolution not possible in the previous study.
The most important contrast between the previous research and this research is the
source of data used in the analysis. Seven fold compositions used species range maps with
the EMAP hexagonal grid as the minimum mapping unit (MMU). These grid cells were
populated with confirmed and probable species determined from samples, sitings, and
expert opinions. This method of smoothing species ranges to a regular grid was used in
the initial stage of GAP analysis Oregon and other states (e.g. Kiester et. al., 1996)
This analysis uses species range maps based on interpretation of Landsat Multi-
Spectral Scanner (MSS) imagery. The resulting natural vegetation polygons are then clus-
tered into wildlife habitats, overlain with the original hexagon-based range maps, and
populated with species based on a Wildlife Habitat Relations (WHR) matrix. The resulting species range maps have a much smaller MMU which is equal to the smallest polygon
interpreted from satellite imagery.
Analysis can now be expanded to use smaller grid cells for biodiversity mapping.
Because the MMU in this study is much smaller than the EMAP hexagonal grid cell,
biodiversity can be mapped at scales smaller than the EMAP grid cell. Some hexagonal
compositions and decompositions also use fractions of EMAP grid cells (See Figure
1.1).The previous study was only able to compose the EMAP grid by a factor of 7,
because a 7-fold composition is the only composition that uses an entire hexagon.
With species assigned to habitat polygons in this study, any grid made from the tri-
angular building blocks derived from the smallest hexagonal grid can be used to construct
other hexagonal grids. The two other possibilities for composing and decomposing a hexagonal grid are three and four fold compositions (Figure 1.1). Three fold was selected in
order to minimize the scale change between biodiversity maps at successive steps.
Constructing richness maps at different scales is a combinatorial process. Grid
cells at each scale will have a unique species list. These results cannot be predicted by tra-
ditional geostatistical techniques and are data dependent. Issues associated with such pro-
cedures are addressed by Stoms (1994) and expanded upon in Chapter 3 of this
dissertation.
Constructing prioritization maps at any given scale is also a combinatorial proce-
dure. Prioritization mapping selects a given number of grid cells which maximize the
number of different species present, an example of a maximum covering location problem
(MCLP) (Church et. al., 1994). This analysis involves comparing species lists of multiple
grid cells. As grid cells and their associated species lists change with scale, new combinations may give geographically dissimilar results.
DATA
The species range maps used in this study are a second generation of maps devel-
oped for the state of Oregon. The maps used in this study are approximately equivalent to
those in the Atlas of Oregon Wildlife (Csuti et. al., 1997).
Construction of these range maps began with LANDSAT MSS imagery of Oregon.
Kagan and Caicco(1992) visually interpreted boundaries of vegetation cover types using
MSS false color infrared positive prints at a scale of 1:250,000. Vegetation polygons were
labeled with the assistance of a variety of ancillary maps. The MMU for this study was
polygons of 133 hectares(ha.). A total of 6,916 vegetation polygons were mapped in vec-
tor format, with the average polygon size being 3,296 ha. 130 different actual vegetation
types are represented in these polygons.
The actual vegetation map was then converted into a wildlife habitat map using a
wildlife habitat relation (WHR) developed by O'Neil et. al. (1995). This WHR combined
four existing WHR matrices and supplemented these data with "additional information
from past biological surveys, museum collections, and published literature"(O'Neil et. al.,
1995, p. 1484). This WHR matrix was used to assign 420 breeding species of terrestrial
vertebrates to appropriate vegetation types.
Wildlife habitats were then generalized into 30 classes. Multivariable statistical
analysis was used to find "consistent patterns of wildlife use within groups of vegetation
types suggest[ing] that wildlife species perceive these groups as similar habitats"(O'Neil
et. al., 1995, p. 1484). A matrix of vegetation types and species allowed calculation of
similarity for each element. This Jaccard coefficient "minimizes the within-cluster variance relative to the between-cluster variance" (O'Neil et. al., 1995, p. 1484).
A species may be present in a given habitat in one portion of the state, but not in
the same habitat in another part of the state. The EMAP hexagonal grid was thus intersected with the wildlife habitat coverage. The resulting coverage was composed of over
15,000 polygons. Object oriented programming written by Kevin Sahr created lists of
polygons for each species, based on the presence of the polygon within the species range
hexagonal outline and presence of the appropriate habitats (Csuti et. al., 1997).
Some polygons selected were portions of larger parent polygons that extended outside of the range based on hexagonal outlines. A species range was extended into adjacent
non-occurrence hexagons if the majority of the original parent polygon lay in an occurrence hexagon. This method of refining species boundaries may be an important factor in
contributing to the increased variations in species richness and more efficient prioritization
discussed later.
All sampling grids used in this study are based on a composition or decomposition
of a portion of the Environmental Protection Agency EMAP hexagonal grid. The entire
EMAP grid provides complete coverage for the contiguous United States. This Lambert
azimuthal equal area map projection is composed of grid cells approximately 640 km2.
This size was selected as a "suitable compromise between the desired spatial resolution of
sampling and the projected available financial resources" (White et. al., 1992, p. 18). Only
one set of grid cells used in this study matches the EMAP grid. All others consist of
smaller, larger or offset hexagons resulting from geometric constructions of elements
making up the EMAP grid and discussed in the methodology section of this paper.
METHODOLOGY
Species richness maps are created by summing the total number of species in each
grid cell. Although these maps provide spatial information on what areas are rich or poor
in number of species, they are not suited to answer important questions in conservation
biology (Williams et. al., 1996, Prendergast et. al., 1993). Prioritization maps look to
maximize the number of unique species in a given number of grid cells, an example of a
maximum covering location problem (MCLP) (Church et. al., 1994). Analysis in Oregon
uses a linear programming algorithm, which ensures "optimal solutions to the reserve
selection algorithm" (Church et. al., 1994, p.83).
A change in the size of the grid cell will result in a new list of species associated
with each new grid cell sample. Stoms (1994) recognizes that agglomerating sampling
units and species contained within is not a classical spatial statistics problem that can be
addressed by such methods as calculating seminarians; "aggregation is not a simple
numerical averaging over different sampling sizes, but is a logical union of sets (species
lists)" (p. 347). An example derived from Stom's (1994) explanation is presented as Fig-
ure 3.1 in the previous chapter.
This study looks at biodiversity mapping on the EMAP hexagonal grid. Three
geometries for the composition and decomposition of these grid cells are presented in Fig-
ure 1.1. All three of these geometries will preserve the important attributes found in a
hexagonal grid, such as grid cells filling 2-D space and all adjacent grid cells being equidistant.
In the previous study, the MMU for species range maps was based on the EMAP
grid cells. This limited the geometric constructions possible in two important ways. First,
no decomposition was possible without further assumptions, as the MMU was defined by
the EMAP grid cells. Also, 3-fold and 4-fold compositions would require further assumptions, as they involve taking fractions of surrounding hexagons. A 3-fold composition
takes a central hexagon and 1/3 of all adjacent hexagons, while a 4-fold composition takes
a central hexagon and 1/2 of all adjacent hexagons(See Figure 1.1).
In this study, the species range maps are not tied directly to the EMAP hexagonal
grid. The wildlife habitat map must be overlain with a hexagonal grid at some point to
assign wildlife habitat polygons to an equal area grid cell, but until this is done, any composition or decomposition of the EMAP hexagonal grid is possible. A three fold composition was selected to provide information on grid cells with the finest variations in size
between scales of mapping. Each composition will result in hexagonal grid cells three
times the area of the original hexagon.
This study was designed so that only one computationally intensive overlay of the
wildlife habitat coverage with a base grid for building hexagons was necessary. To do this,
the smallest elements that could be used as building blocks for all hexagonal grids were
constructed. First, a hexagonal grid with grid cells 1/81 the size of the EMAP grid was
obtained from Mike McDowell at the EPA. This would be equivalent to a 4 times 3 -fold
decomposition (4X's 3-fold decomposition), and each grid cell would be approximately 8
km2. Each of these hexagons has a unique address based on the EMAP code, plus a suffix
which uniquely identifies its location at this scale (Spence and White, 1992). Almost
33,000 of these hexagons were necessary to cover the state of Oregon.
This study used object oriented (C++) programming to divide each of these hexagons into 12 triangles. Each triangle was addressed using the number of the hexagon and
the location of the triangle within the hexagon. It was necessary to divide the hexagon
into 12 triangles, as 3-fold compositions rotate resulting hexagonal grid cells by 30
degrees, thus requiring different triangles at different compositions. The resulting triangular grid was composed of almost 400,000 triangles, each of approximately 0.67 km2(67
ha.). The size of an building block for a given hexagonal grid is four of these triangles (i.e.
1/3 of a hexagon) with an area approximately 267 ha. This size comes close to the 133
ha. MMU used in the construction of the Oregon Actual Vegetation map (Kagan and
Caicco, 1992). It should be noted, however, that the MMU for the habitat range maps is a
function of not only the habitat maps, but also the original EMAP species range maps
which have a MMU of 640 km2.
This triangular grid was then intersected with the Wildlife Habitat map (O'Neil et.
al., 1995) using ESRI Arc/Info software. The resulting coverage consisted of approxi-
mately 800,000 polygons. Each polygon identified a triangular grid cell and a polygon
code from the wildlife habitat map. Each species had a list of polygons from the wildlife
habitat map with which it was associated. An object oriented program was written to take
these data and create a matrix file. This matrix file has approximately 400,000 rows repre-
senting each unique triangular grid cell and 424 columns representing the 420 species
comprising the WHR matrix, and four additional species included in The Atlas of Oregon
Wildlife (Csuti et. al., 1997).
The first scale at which a species richness map can be constructed is the 4X's 3-
fold decomposition of the EMAP grid. The nature of the triangular grid will allow only
one hexagonal grid to be constructed at this scale, a reconstruction of the decomposed grid
from the EPA. The next scale at which species richness maps are constructed is 3X's 3fold decomposition, with grid cells approximately 24 km2. By using any three adjacent
hexagons at the 4X's 3-fold decomposition scale as a center, it is possible to construct
three unique and offset richness maps at this scale (See 7-fold example in Figure 1.2).
Any other geometric constructions from the triangular grid at this scale would be redundant. Three maps are constructed at this scale, and statistics associated with all grid cells
from the three maps are summarized into one set of numbers.
Each subsequent scale allows for the construction of three times as many unique
richness maps. At the EMAP scale, for example, 81 (i.e. 34) possible maps could be constructed from the triangular grid. This study does not construct all possible richness maps,
but rather three maps at all scales greater than 4X's 3-fold decomposition. This should be
sufficient, as each map is an exhaustive sample (save edge effects) of the richness data.
More grid cell values from the same data should not have a statistical impact on results.
The maximum grid cell size composed for species richness is approximately 5,760
km2, or 2X's 3-fold composition of the EMAP grid. This maximum size avoids grid cells
that approach the extent of the study area. If the next composition (i.e. 3X's 3-fold composition) were constructed, less than 10 grid cells of this size would fit on each map within
the boundary of Oregon.
Species richness maps in this study divide the range of species richness values into
classes for color map displays. Five classes are defined based on the statistical distribution
of species richness values. This study uses the combined statistics discussed above for
dividing the distribution into classes. At any scale above 4X's 3-fold decomposition,
therefore, three maps will exist, with each having classes based on grid cell values from
all three maps.
Statistical measures can be made from all richness grid cells at each scale. The
previous chapter argued for using coefficient of variance (CV) as a metric to compare
maps of different scales. CV is defined as the sample standard deviation expressed as a
percentage of the sample mean (Steel and Torrie, p. 27). It can provide a more stable measure of variation between scales of combinatorial maps, where variance and average are
both changing. This is the same measure initially proposed by Stoms (1994) in his comparison of multi-scale richness maps.
Prioritization analysis uses a matrix of grid cells and species to determine which
grid cells in combination will represent the most species for a given number of grid cells.
This study uses species lists combined from all maps at a given scale.
This method of combining all data at a scale permits one comprehensive prioritization analysis to be done for each composition or decomposition level. Combining all species lists at one scale also allows for the overlap of grid cells in prioritization analysis.
The implication of overlapping grid cells to families of hexagons in prioritization areas
will be discussed later in this paper.
9
RESULTS
Richness Mapping
Statistics associated with the richness maps at seven different scales are presented
in Table 4.1. Comp OX's 3-fold is the EMAP scale, with decomposition grid cells
decreasing in size to the left of the EMAP size and composition grid cells increasing in
size to the right. The decomp 4X's 3 scale is the finest scale possible from the triangular
grid. It was possible to construct only one geometry, resulting in a map with 32,899 hexa-
gons. The richness map for this construction is presented as Figure 4.1.
The decomp 3X's 3-fold statistics represent the 3-fold decompositions of the
EMAP grid cells. One of the three richness maps for this scale is presented as Figure 4.2.
The statistics are derived from three unique maps generated at this scale. The number of
hexagons reported (32,071) is a sum of all hexagons from the three maps (10,687 + 10,692
+ 10,692). Each of these numbers is smaller than one-third of the original number of
hexagons due to less edge hexagons lying completely within the area mapped for wildlife
habitats (Compare Figure 4.1 withFigure 4.2). Although the minimum number of species in a grid cell stays the same as in the finer grid cells, the maximum and average numbers increase. Variance, standard deviation and CV all decrease. The decrease in CV is the
largest between any two consecutive scales, as the value drops by more than 7%.
Statistics for maps associated with larger grid cells show predictable decreases in
number of hexagons and increases in minimum, maximum and average number of species
in grid cells. Variance and standard deviation continue to decrease at each step.The CV
values also decrease at each step, with larger decreases occurring between smaller grid
cell scales and smaller decreases occurring as grid cells increase in size. One map of the
92
Table 4.1: Richness Map Statistics for 3-Fold EMAP Compositions
Deomp
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Number
of
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Biodiversity Research Consortium
August 02. 1997
9
All Terrestrial Vertebrate Richness
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2X's 3-fold decomposition, 1X's 3-fold decomposition, OX's 3-fold composition, 1 X's 3fold composition and 2X's 3-fold composition are included as Figure 4.3, Figure 4.4,
Figure 4.5, Figure 4.6, and Figure 4.7 respectively.
Figure 4.5 is a recreation of the EMAP grid which covers the state of Oregon.
Labels on these grid cells are the EMAP hexagonal addresses, with a "01" suffix added to
indicate which of the 81 smaller hexagons making up that EMAP hexagon was used as the
center for the geometric construction. The other two maps at this scale are offset from the
EMAP grid. This map, however, differs from the EMAP scale richness map presented in
the previous chapter(Compare with Figure 3.5).
This EMAP scale richness map is different from the EMAP scale richness map
presented in the previous chapter in that presence of species is now derived from a second
generation of species range maps. Ranges are no longer based only on sitings and expert
opinion mapped to a hexagonal grid. Wildlife habitat maps are now constructed from vegetation maps and a WHR matrix in conjunction with EMAP grid based range maps, as dis-
cussed in the methods section of this chapter. Thus, although the MMU of the Oregon
Actual Vegetation map may be130 ha., the MMU of the wildlife range maps is more difficult to access.
This difference also results in the two maps having different extents. Figure 4.5
includes EMAP hexagons whose entire area covers the wildlife habitat map used in this
analysis. This is different than the previous richness map (Figure 3S), which included all
EMAP hexagons within or adjacent to the state of Oregon for which species presence or
absence was determined. This map included several grid cells which would have areas
outside of the wildlife habitat map (approximately equal to the boundary of Oregon). The
pecies Richn
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result is a decrease in total richness hexagons from 441 in the original map in Figure 3.5
to 352 in Figure 4.5.
Prioritization Analysis
Prioritization analysis was completed on five scales of maps from 2X's 3-fold
decomposition to 2X's 3-fold composition. Summaries of species coverages at each cardinality of these analyses is included as Table 4.2-Table 4.6 in this chapter's Appendix.
The number of hexagons per path is called the cardinality of the analysis. One important
observation from these tables is that all 424 species are not covered in analysis at any of
these scales. This is due to the presence of species with ranges near state boundaries not
being sampled by any hexagons at larger scales. The 2X's 3-fold decomposition, the 1X's
3-fold decomposition, and the OX's 3-fold composition all sample a maximum of 421 spe-
cies. The 1X's 3-fold composition and 2X's 3-fold compositions sample a maximum of
420 species as areas further inboard of state boundaries are no longer represented.
Because different numbers of species are covered in these prioritization analysis,
the cardinality necessary to cover 420 species will be referred to as "full coverage" to
compare prioritization at different scales. 420 species are covered at a cardinality of 14,
12, 12, 11, and 10 for scales 2X's 3-fold decomposition, TX's 3-fold decomposition, OX's
3-fold decomposition, 1X's 3-fold decomposition and 2X's 3-fold decomposition, respectively. The significance of two scales covering the same number of species at a cardinality
of 12, even with one analysis using one-third the area will be discussed in the next section.
A benchmark for prioritization analysis comparisons in Oregon is the coverage
achieved at cardinality 5. Five areas are consistently able to cover over 90% of total spe-
cies. This is consistent with prioritization analysis being used as a coarse filter to guide
conservation efforts(See Csuti, 1994 and Csuti and Kiester, 1996). The numbers of species covered at cardinality 5 are 395, 397, 399, 404, and 412 species for scales 2X's 3-fold
decomposition, 1X's 3-fold decomposition, OX's 3-fold decomposition, 1X's 3-fold composition and 2X's 3-fold composition respectively. These numbers reflect a cost associated
with the benefit of mapping smaller areas with a finer grid. The cost is the loss of species
covered, which is eight species in moving from the 2X's 3-fold decomposition scale to the
1X's 3-fold decomposition scale, five species in moving from the 1X's 3-fold decomposition scale to the OX's 3-fold decomposition scale, and two species in moving from both the
OX's 3-fold decomposition scale to the 1X's 3-fold decomposition scale and from the 1X's
3-fold decomposition scale to the 2X's 3-fold decomposition scale. The significance of
these steps will also be discussed in the next section.
The cardinality 5 prioritization map for the coarsest grid (2X's 3-fold composition)
is presented as Figure 4.8. 98.1% of all species with ranges within this grid are repre-
sented within the selected hexagons. The three areas to the west of the state are represented by a single hexagon. The two areas in the east of the state are defined by multiple
hexagons. These hexagons overlap, with each of these families of hexagons defining a
large, continuous area.
The cardinality 5 prioritization map for the 1X's 3-fold composition is presented
as Figure 4.9. This analysis uses only one-third the area of the previous analysis, and is
able to cover 96.2% of the species. All five of these new areas are contained partially or
completely within the areas selected using larger grid cells in Figure 4.8. Only one area
in the northeast of the state is now comprised of an overlapping family of hexagons.
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Figure 4.10 illustrates the cardinality 5 prioritization maps at the EMAP scale
(OX's 3-fold composition). Of all species with a range within this grid, 94.8% are covered, with the decrease due again to using an area one-third the size of the previous analy-
sis. This step is significant, as for the first time two of the areas, the blue areas to the
northeast, and the east-central magenta areas, have each splintered into two areas with sig-
nificant separation. Although these two new areas show no overlap with other prioritization hexagons, a portion of all five prioritization areas still lie partially or completely
within the areas selected using the next largest grid cell size. Overlapping families of
hexagons have also appeared for the first time to define the red and yellow prioritization
areas in the southwest corner of the state.
Figure 4.11 illustrates the cardinality 5 prioritization map at the 1X's 3-fold
decomposition. Using a total area one-third of the previous analysis allows 94.3% of the
species within the grid to be selected. Once again, portions of all five prioritization areas,
including the two disjoint areas, are at least partially within areas selected using the next
largest grid cell size. One area has again splintered, the blue area furthest to the northeast.
The separation between these two new areas, however, is much smaller than the distance
between disjoint areas created at the previous level. It is also worth noting that two new
areas are now comprised of overlapping families of hexagons. These are the magenta area
in the east-central portion of the state, and the more western blue area. Both of these areas
are narrow and elongate.
The finest resolution prioritization map for cardinality 5 is presented as Figure
4.12. 93.8% of all species with ranges within this grid are represented within the selected
hexagons. The two disjoint, elongate prioritization areas discussed at the previous scale
Figure 4.10: Cardinality 5 prioritization hexagons for EMAP grid.
Vertebrates
omposition)
3990(421 species
1!
Biodiversity Research Consortium
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August 02, 1991
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Figure 4.11: Cardinality 5 prioritization hexagons for 1 times 3-fold decomposition.
All "Terrestrial
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Biodiversity Research Consortium
Figure 4.12: Cardinality 5 prioritization hexagons for 2 times 3-fold decomposition.
Vertebr
are no longer present. Two of the areas have each splintered into four disjoint areas,
although distance between these areas is again on the scale of a few miles. In both cases,
only one of the new disjoint areas is contained within the prioritization area from the previous scale. Two other prioritization areas, the magenta area and the yellow area, are also
contained within the prioritization areas from the previous scale. The green area to the
southeast of the state has actually shifted some distance to the north. Not only is this new
green area not within the green prioritization area from the previously discussed scale, it is
not within any of the prioritization areas discussed above. All prioritization areas at this
scale are composed of overlapping or non-overlapping families of hexagons.
DISCUSSION
The most appropriate scales for mapping biodiversity in Oregon can be inferred
from the results of this study. This will be done by analyzing statistics associated with
both the species richness maps and the prioritization maps. Spatial patterns in all of these
maps will also be discussed quantitatively as indicators of preferred scales for biodiversity
mapping.
Optimal Scale for Richness Mapping
The best scale for richness mapping would preserve as much information as possi-
ble while using the maximum sized grid cell. Stoms (1994) recognizes this relative "little
loss of information (in terms of variability)" by graphing the log 1O(CV) vs. log1O(Grid
cell size). The results are graphs that show a small drop in CV at smaller grid cells and a
greater drop at larger grid cells. The edge of the flat area before the sharp dropoff would be
the most appropriate scale for richness mapping from a statistical perspective.
Results of this study follow a very different pattern, as illustrated by the blue line
in Figure 4.13. The steep slope at the smallest grid cells continues to slowly decrease
Coefficient of Variation vs. Scale
E
cale
-0.5
I
-0.6
-0.7
-0.8
V-,
-0.9
-1
1.1
IN
-1.2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
log (Scale in ha.)
Figure 4.13: Coefficient of Variation vs. scale for 7-fold and 3-fold richness maps.
with increase in grid cell size. The sharp decrease in CV between the two smallest grid
cells may be due to the smallest grid cells being able to sample within as well as on the
boundary of adjacent wildlife habitat polygons. Most triangles sampled only one or two
polygons from the wildlife habitat map. If the smallest hexagons also only sample one or
two polygons, then each hexagon would either contain the species list of one or two adjacent polygons. As grid cell samples become larger, more polygons would be covered in a
single grid cell. This argument seems to be supported by the observation that the richness
map using the smallest grid cells appears to have the most narrow linear patterns, possibly
associated with habitat boundaries (See Figure 4.1).
The absence of a sharp dropoff at higher scales may be the result of this study
using a maximum grid cell size nine times the size of the EMAP grid cells. In the previous
study, a map seven times the scale of the EMAP grid showed no change in CV. It was not
until the next scale, with grid cells 49 times as large, that CV dropped off considerably.
The results of CV calculations for the seven fold compositions are included for comparison in Figure 4.13.
Comparison of these two curves also reveals that overall, the new series of richness
maps has a significantly higher CV than the previous set. The shift of CV at the EMAP
scale from 10.45 to 13.93 represents an increase of 33%. This is due to the basis of species range maps changing from the EMAP hexagonal grid to the wildlife habitat maps.
These finer detailed maps with better defined edges and internal boundaries allow a
greater quantity of information to be captured as measured by statistical variability in species richness values at the EMAP scale.
Optimal Scale for Prioritization Mapping
The question of which scale is best suited for prioritization mapping can be
addressed in two ways. The first is to look at the relative efficiency of prioritization analy-
sis between each two adjacent scales. The second is to look at the locations of prioritization hexagons and the nature of their change with changes in scale.
Two measures of efficiency of prioritization analysis indicate that 1X's 3-fold
decomposition would be the most efficient scale. The first of these is that no additional
hexagons are required for "frill coverage" of all species at the 1X's 3-fold decomp scale
than at the next largest EMAP scale (See Appendix 3). Both analyses require 12 cardinalities to cover 420 species and 13 cardinalities to cover 421 species, despite the 1X's 3-fold
scale using grid cells and a total prioritization area one-third the size of the EMAP scale
analysis. Between all other scales, cardinalities must increase by one or two to cover the
420 species given the decrease in area associated with their scale.
A second measure of efficiency would be the decrease in the number of species
covered with decreasing grid cell size at a given cardinality. All five scales of prioritization are made up of at least 10 cardinalities. Comparisons between scales show which
two successive scales have the least change in species covered. For the 10 cardinalities, no
change is smaller than the change from the 1X's 3-fold decomposition to the EMAP scale
for seven of the ten cardinalities, a maximum between any two successive scales. Figure
4.14 graphs this trend for cardinalities 3 through 5 as an example.
The cardinality of 5, which covers 93.8% to 98.1% of species (depending on scale)
and is illustrated in Figures 4.8 - Figure 4.12 can be used as an example. The decrease in
number of species between the two largest scales is 8, the result of using only one third the
Species Covered vs. Scale
420 ,
410
...............
400
390
380
370
-e- Cardinality 3
360
2X's 3fold
decomp
1 X's 3-
OX's 3-
1 X's 3-
fold
decomp
fold
(EMAP)
fold
comp
2X's 3.
fold
comp
Scale
Figure 4.14: Species covered vs. scale for three cardinalities of prioritization.
area for prioritization. The decrease for the next step down in scale is 5. The next 2 steps
down in scale, however, show a net decrease of 2 species at each step. The change from
the EMAP scale to the 1X's 3-fold decomp scale is the first step that shows this relatively
small decrease of 2 species, indicating the efficiency of this scale of prioritization mapping.
A different approach for determining an appropriate scale for prioritization mapping is to look at the changes in location and pattern of prioritization hexagons with scale.
Based on qualitative observations, locational information may be equally important in
determining proper scale for prioritization analysis. This discussion will refer to the prioritization maps for cardinality 5 presented in the results portion of this study as Figures 4.8
- 4.12.
The analysis using the largest grid cells define large areas whose boundaries
directly reflect the shape of the hexagonal grid cells (See Figure 4.8). These sets of five
hexagons capture the most species, but possibly not in the most efficient manner. If no
other areas could contend to be included in prioritization analysis, prioritization analysis
using smaller grid cells would simply refine the area within these larger hexagons.
Figure 4.9 shows this process of refining, as five areas are selected within the pre-
vious areas. Shapes of prioritization areas continue to reflect the shape of the grid cells.
Figure 4.10, however, shows an important change in location and shape of prioritization
areas.
Prioritization areas within other previous prioritization areas continue to be
refined, but now two new and separate areas have been identified. By relaxing the number
of species that can be covered (because they will no longer all fit in a grid cell one-third
the size), new areas can be included in the analysis. Also, for the first time, the yellow
family of grid cells define an area that begins to look somewhat natural, as opposed to a
relic of the grid cells defining the area.
It can be argued that the loss of species at any of these levels is not significant.
With an increase of one cardinality, the 6 hexagons at this scale will now cover more spe-
cies than the five hexagons at the larger scale. This is accomplished by increasing the pri-
oritization area by 20% (by adding one hexagon) versus 200% (by mapping at the same
cardinality at a scale three times
as
large). The introduction of two new areas vying for
inclusion in prioritization results seems a much more important issue.
Figure 4.11 illustrates the smallest grid cells which represents all seven of the pri-
oritization areas at all scales examined. In addition to the yellow area, the coastal red area
is now taking on a more natural, less hexagonal shape. The furthest northeast blue area
has now split in two. This split, however, is very different from the two separations seen at
the previous scale. At this scale, both new blue hexagons are within the area selected at
the previous scale. Although separated, they do not define a new prioritization area, an
important difference from the splintering seen at the previous scale.
Figure 4.12 shows prioritization analysis at the finest scale. The most obvious difference here is that neither of two areas, the magenta area in the west-central state and the
eastern blue area, have been selected. At the previous scale, both of these areas consisted
of elongate patterns of hexagons. This could indicate that prioritization analysis would
only select these areas if a central area and peripheral areas almost out of reach at that
scale were included. Once the grid cell decreased in size again, an area large and diverse
enough to be included in prioritization could no longer be selected. It is also interesting to
note that the two areas that are no longer selected were areas originally selected with the
largest grid cells.
All prioritization areas in Figure 4.12 now look more natural, with less of a hexag-
onal pattern outlining most areas. Three of these areas are compact. Two areas, the red
coastal area and the blue area to the northeast, are broken into four localized but disjoint
areas. Both of these areas in part overlap areas selected with larger grid cells, but both are
expanding locally outside of areas selected at any other scale.
Although more detailed information is generally preferable in spatial analysis, this
scale may be of too fine a resolution for statewide biodiversity analysis. The creation of
these two disjoint areas at this scale may indicate that factors influencing selection are now
working on a habitat-type scale as opposed to a more regional ecoregion-type scale seen
in all other analyses. Also, with hexagons of approximately 72 km2, other issues such as
minimum area requirements(Csuti and Kiester, 1996) may come into play. Such a scale
may be more suited for reserve design as opposed to prioritization reserve selection (See
Csuti, 1994).
EMAP Scale Prioritization Analysis from Two Datasets
The prioritization at the EMAP scale can also be compared with the prioritization
done at the EMAP scale using the previous species range maps. A comparison of Figure
4.10 with Figure 2.9 gives an idea of the locational stability. All five prioritization areas
from Figure 2.9 overlap or are adjacent to prioritization areas from Figure 4.10. The two
splintered areas in Figure 4.10 are not represented in Figure 2.9. The addition of these
two areas in the new analysis could be the result of a more comprehensive and varied species list resulting from more detailed habitat based species range mapping.
The most salient difference between these analyses, however, is the efficiency of
species coverage. The previous analysis was able to obtain full coverage of all 422 terrestrial vertebrates in 23 cardinalities, and 421 species in 22 cardinalities. This study required
only 13 cardinalities to cover 421 species. This study, therefore, covered as many species
while using less than 60% of the hexagons of the other study.
The two differences between these analyses is that the species range maps were
based on different criteria, and that the new analysis used three sets of overlapping hexa-
gons. These sets of offset hexagons could have found more efficient representations of
species.
To test this hypothesis, a second prioritization analysis was done with the new data
at the EMAP scale. For this analysis, only one of the three sets of prioritization hexagons
was used, the set with no offset from the EMAP grid. This new prioritization was somewhat less efficient. The new total, 420 total species, were now covered at a cardinality of
13. Previously, 420 species were covered at a cardinality of 12. Also, at any cardinality
above 1, 1 to 8 less species were covered with the new analysis. This effect, however, is
minimal compared with the drop from 22 to 13 cardinalities to cover 421 species between
the old and new analysis
The most likely explanation for this drop would be the difference in the species
range maps. The new species range maps are based on habitat extents. The EMAP hexagon is no longer the MMU. With this finer scale mapping, species ranges can be extended
into portions of neighboring hexagons, allowing the hexagon to include a greater variation
of species. This interpretation is also consistent with the increase in CV between old and
new maps at the EMAP scale. In this case, the increased resolution of the species range
maps allows more species richness variations information to be captured in the new analysis.
CONCLUSIONS
The proper scale for biodiversity mapping can be determined by looking at maps
and statistics associated with these maps at several scales. This analysis indicates that the
EMAP scale is an appropriate scale for mapping species richness in Oregon. This study
also sees improvements in a grid cell 1/3 the EMAP cell being used for prioritization mapping in the state of Oregon.
Seven scales of richness maps were produced with grid cells varying by a factor of
three from 1/81 the size of the EMAP hexagon to 9 X's its size. A coefficient of variation
(CV) graph shows no strong patterns of the CV curve flattening, indicating that each scale
of richness map retains a relatively similar amount of information on the variation of
richness values present as at the previous level.
A subtle change in slope in moving to the
EMAP scale from the scale with grid cells 1/3 the size indicates that, relatively, the EMAP
scale is a marginally better scale for mapping species richness.
The grid cell one third the size of the EMAP hexagon is the best scale for prioriti-
zation mapping for two reasons. First, it is more efficient than the larger EMAP grid
cells. Both take the same number of cardinalities (12) to cover all 421 species. In examining species covered at several cardinalities, this scale is also most consistent at defining a
change in slope of number of species covered vs. size of grid cell.
The map pattern and location of prioritization hexagons could also be used to
argue for the use of this scale. This scale identifies a maximum number of prioritization
areas at cardinality 5 using a minimum grid cell size. Prioritization areas are specifically
located but not yet fragmented within an area, as occurs with prioritization areas selected
by smaller grid cells. All of this points to a grid cell 1/3 the size of the EMAP grid as
being most appropriate for prioritization mapping in Oregon.
It can also be concluded from this analysis that mapping species ranges based on
habitat maps is preferable to range maps based on EMAP grid cells. Comparing richness
maps at the EMAP scale indicates the new maps have a greater variation of value, indicat-
ing more diversity information was captured. Prioritization analysis was also much more
efficient with the new maps, the probable result of increased diversity information within
the data, which results from refining species range boundaries.
REFERENCES
Church, R. L., D. M. Stoms, and F. W. Davis. 1994. Reserve selection as a maximum covering location problem. Biological Conservation 78:353-355.
Csuti, B. 1994. Gap analysis: Identification of priority areas for biodiversity management and conservation. Gap Analysis Program Handbook Program.
Csuti, B., P. Kennelly, S. M. Meyers, and K. Sahr. 1997. Current status of biodiversity indicators using GIS. ESRI User's Conference Abstract.
Csuti, B., A.J. Kimerling, T. O'Neil, M. Shaughnessy, E. Gaines, and M. Huso.
1997. The Atlas of Oregon Wildlife. Oregon State University Press, Corvallis,
OR.
Csuti, B. and A. R. Kiester. 1996. Hierarchical Gap analysis for identifying priority areas for biodiversity. ASPRS/Gap Symposium Proceedings, T. H. Tear, J.
M. Scott, and F. Davis, eds. In press.
Kagan, J. and S. Caicco. 1992. Manual of Oregon actual vegetation. Report for the
Oregon Gap Analysis Program, directed by the Idaho Cooperative Fish and
Wildlife Research Unit, University of Idaho in cooperation with the Oregon
Department of Fish and Wildlife and the Oregon Natural Heritage Program.
Csuti, B., editor. 190 pp.
Kiester, A. R., J. M. Scott, B. Csuti, R. Noss, B. Butterfield, K. Sahr and D. White.
1996. Conservation prioritization using GAP data. Conservation Biology.
10:1332-1342.
O'Neil, T. A., R. J. Steidl, W. D. Edge, and B. Csuti. 1995. Using wildlife communities to improve vegetation classification for conserving biodiversity. Conservation Biology. 9:1482-1491.
Prendergast, J. R., R. M. Quinn, J. H. Lawton, B. C. Eversham, and D. W. Gibbons. 1993. Rare species, the coincidence of diversity hotspots and conservation strategies. Nature. 365:335-337.
Spence, M. H., and D. White. 1992. EMAP Sampling Grid Technical Report.
EMAP Statistics and Design Team.
Steel, R. G. D. and J. H. Tome. 1980. Principles and Procedures of Statistics, a
Biometric Approach. McGraw-Hill Book Co., New York.
Stoms,
D. M. 1994. Scale dependence of species richness maps. Professional
Geographer. 46:456-58.
White, D., A. J. Kimerling and W. S. Overton. 1992. Cartographic and geometric
components of a global sampling design for environmental modeling. Cartography and Geographic Information Systems. 19:5-22.
Williams, P., D. Gibbons, C. Margules, A. Rebelo, C. Humphries, and R. Pressey.
1996. A comparison of richness hotspots, rarity hotspots, and complementarity
areas for conserving diversity of British birds. Conservation Biology. 10: 155174.
121
Appendix
Results
of Multi-Scale Three-Fold Prioritization Analysis
Table 4.2: 2X's 3-Fold Decomposition Prioritization Statistics
Oregon All Vertebrates Prioritization
10504 hexagons and 421 total species
# of
# of
# of
hexes/path
paths
hexagons
# species
covered
% species
covered
1
2
2
281
66.75
2
1
2
338
80.29
3
4
6
365
86.70
4
50
25
384
91.21
5
50
46
395
93.82
6
50
27
403
95.72
7
50
37
408
96.91
8
>=1
>=9
411
97.62
9
>=1
>=9
414
98.34
10
>=1
>=10
415
98.57
11
>=1
>=11
417
99.05
12
>=1
>=12
418
99.29
13
>=1
>=13
419
99.52
14
>=1
>=14
420
99.76
15
>=1
>=15
421
100.00
Biodiversity Resource Consortium
August 18, 1997
Table 4.3: 1X's 3-Fold Decomposition Prioritization Statistics
Oregon All Vertebrates Prioritization
3377 hexagons and 421 total species
% species
hexagons
# species
covered
1
1
288
68.41
2
1
2
343
81.47
3
2
4
372
88.36
4
53
15
387
91.92
5
50
20
397
94.30
6
50
26
404
95.96
7
50
40
409
97.15
8
50
31
413
98.10
9
50
35
416
98.81
10
50
44
417
99.05
11
50
42
419
99.52
12
50
51
420
99.76
13
50
63
421
100.00
# of
hexes/path
# of
paths
1
# of
Biodiversity Resource Consortium
covered
August 18, 1997
Table 4.4: OX's 3-Fold Decomposition (EMAP) Prioritization Statistics
Oregon All Vertebrates Prioritization
1067 hexagons and 421 total species
# of
hexes/path
# of
paths
hexagons
# species
covered
% species
covered
1
2
2
298
70.72
2
2
3
348
82.66
3
3
5
373
88.60
4
10
9
388
92.16
5
36
14
399
94.77
6
36
14
407
96.67
7
50
26
411
97.62
8
50
34
414
98.34
9
50
36
416
98.81
10
50
38
418
99.29
11
50
66
419
99.52
12
50
54
420
99.76
13
50
55
421
100.00
# of
Biodiversity Resource Consortium
August 18, 1997
Table 4.5: 1X's 3-Fold Composition Prioritization Statistics
Oregon All Vertebrates Prioritization
321 hexagons and 420 total species
# of
# of
# of
hexes/path
paths
hexagons
# species
covered
% species
covered
1
2
2
312
74.29
2
4
5
356
84.76
3
2
4
380
90.48
4
1
4
393
93.57
5
2
6
404
96.19
6
40
16
409
97.38
7
50
25
413
98.33
8
53
18
417
99.29
9
50
27
418
99.52
10
50
32
419
99.76
11
50
38
420
100.00
Biodiversity Resource Consortium
August 18, 1997
Table 4.6: 2X's 3-Fold Composition Prioritization Statistics
Oregon All Vertebrates Prioritization
89 hexagons and 420 total species
# of
# of
# of
hexes/path
paths
hexagons
# species
covered
% species
covered
1
1
1
329
78.33
2
2
3
369
87.86
3
2
4
392
93.33
4
14
12
403
95.95
5
4
7
412
98.10
6
20
13
415
98.81
7
58
16
417
99.29
8
50
26
418
99.52
9
50
27
419
99.76
10
50
27
420
100.00
Biodiversity Resource Consortium
August 18, 1997
12
CHAPTER 5. SUMMARY
SUMMARY STATEMENT
The scale of study has a strong effect on biodiversity mapping, due to its combina-
torial nature. The proper scale for mapping can be determined by looking at both the
extent used for analysis and the grid cell size. Using geopolitical extents such as the state
of Oregon is not detrimental to prioritization analysis. Internal natural boundaries such as
the ecoregion boundaries of Oregon are not preferentially selected as prioritization areas.
These regions instead tend to break up the extent into areas where species data are more
homogenous within areas and heterogeneous between areas.
Proper grid cell size can be determined for richness mapping, and for prioritization
analysis if the change between scales is small. Proper grid cell size is also dependent on
the scale of species range maps used for analysis. Seven-fold analysis for range maps
based on the EMAP grid indicates grid cells seven times the EMAP size show no loss of
species richness information. No determination of proper prioritization scale can be
made, as the change in scale by a factor of seven is too large to see important changes.
Three-fold analysis indicates no strongly preferred grid cell size for richness maps
based on species range maps from wildlife habitat relationships. A proper scale, however,
was identified for these data from prioritization analysis. Grid cells one-third the size of
the EMAP grid are relatively the most efficient, as well as presenting the most choices for
prioritization areas.These areas are not simply alternative choices of wildlife habitat poly-
gons, but rather areas showing significant separation, possibly representing habitat assem-
blages from different ecoregions.
ECOREGION BOUNDARY EFFECTS
Two major conclusions have resulted from looking at the effect of ecoregion
boundaries on prioritization analysis. The first is that prioritization hexagons do not fall
preferentially on most ecoregion boundaries. The second is that prioritization analysis
results remain geographically stable after eliminating hexagons along ecoregion boundaries.
These results have interesting implications concerning the scale of biodiversity
processes affecting prioritization analysis. First, hexagons straddling ecoregion bound-
aries and sampling different biotic assemblages are not a driving factor in prioritization
analysis. If this were true, percentages of prioritization hexagons on ecoregion boundaries
would be higher than percentage of total hexagons that are prioritization hexagons. The
Jaccard buffer analysis also indicates that localized changes in species list on the order of
adjacent hexagons are also not of a scale which drives prioritization analysis.
Inferences can also be drawn from the geographic stability of results. This implies
that geographic areas on the scale of ecoregions may be an important factor in prioritization analysis. Also, when multiple paths are selected, hexagons are often proximal and
within the same ecoregion. This may imply that the most important heterogeneity for prioritization analysis may be differences found at a scale similar to the sizes of ecoregions in
Oregon.
SCALE EFFECTS USING SEVEN-FOLD EMAP HEXAGON COMPOSITIONS
Seven-fold compositions of the EMAP grid identifies proper scales for mapping
species richness for species range maps based on the EMAP grid. An optimal scale would
maximize variation and grid cell size while minimizing the number of grid cells required
for mapping. It cannot, however, be used to determine proper scales for prioritization analysis.
The grid cell size for mapping richness of terrestrial vertebrates in Oregon could be
increased by a factor of 7 over the EMAP grid cell without losing any statistically significant information on species richness variation. Local changes in variation from the EMAP
grid to one 7 times as large are not influenced by any single area within the mapping
extent. If the grid cell size is increased again by a factor of 7, variations previously present
in the map would be lost, as measured by the coefficient of variation.
The proper scale for prioritization analysis cannot be determined with this method.
It was necessary to create maps with less change in grid cell size between scales (i.e.
three-fold analysis) and to look at grid cells smaller and larger than the EMAP grid, to find
geographically consistent prioritization results. Richness maps based on more homogenous extents may also help to relate proper scale and extent of species richness mapping to
prioritization mapping.
SCALE EFFECTS USING THREE-FOLD EMAP HEXAGON
COMPOSITIONS AND DECOMPOSITIONS
The proper scale for biodiversity mapping can be determined by looking at maps
and statistics associated with these maps consisting of three-fold compositions and
decompositions of the EMAP grid. This analysis indicates that the EMAP scale is an
appropriate scale for mapping species richness in Oregon. This study also sees improve-
ments in a grid cell 1/3 the size of the EMAP cell being used for prioritization mapping in
the state of Oregon. Additionally, research indicates that more variation is captured in
species range maps based on wildlife habitat relationships, as the coefficient of variance of
species richness values at the EMAP scale and the efficiency of prioritization both
increase.
Seven scales of richness maps were produced with grid cells varying by a factor of
three from 1/81 the size of the EMAP hexagon to 9 X's its size. A graph of coefficient of
variation (CV) shows no strong patterns of the CV curve flattening, indicating that each
scale of richness maps retains a relatively similar amount of information on the variation
of richness values present as at the previous level.
The grid cell one third the size of the EMAP hexagon is the best scale for prioritization mapping for two reasons. First, it is more efficient than the larger EMAP grid
cells. Both take the same number of cardinalities (12) to cover all 421 species. In examining species covered at several cardinalities, this scale is also most consistent at defining a
change in slope of number of species covered vs. size of grid cell.
The map pattern and location of prioritization hexagons could also be used to
argue for the use of this scale. This scale identifies a maximum number of prioritization
areas at cardinality 5 using a minimum grid cell size. Prioritization areas are specifically
located but not yet fragmented within an area, as occurs with prioritization areas selected
by smaller grid cells. All of this points to a grid cell 1/3 the size of the EMAP grid as
being most appropriate for prioritization mapping in Oregon.
It can also be concluded from this analysis that mapping species ranges based on
habitat maps is preferable to range maps based on EMAP grid cells. Comparing richness
maps at the EMAP scale indicates the new maps have a greater variation of value, indicat-
ing more diversity information was captured. Prioritization analysis was also much more
efficient with the new maps, the probable result of increased diversity information within
the data, which results from refining species range boundaries.
BIBLIOGRAPHY
Bailey, R. G. 1980. Description of the ecoregions of the United States. U.S.D.A.
Forest Service, Miscellaneous Publication Number 1391.
Bailey, R. G. 1994. Ecoregions of the United States. U.S.D.A. Forest Service,
(Revised map to accompany Miscellaneous Publication Number 1391).
Church, R. L., D. M. Stoms, and F. W. Davis. 1994. Reserve selection as a maximum covering location problem. Biological Conservation 78:353-355.
Csuti, B. 1994. Gap analysis: Identification of priority areas for biodiversity management and conservation. Gap Analysis Program Handbook Program.
Csuti, B., S. Polasky, P. H. Williams, R. L. Pressey, J. D. Camm, M. Kershaw,
A.R.Kiester, B. Downs, R. Hamilton, M. Huso, and K. Sahr. 1997. A comparison of reserve selection algorithms using data on terrestrial vertebrates in Oregon. Biological Conservation, 80, 83-97.
Csuti, B., P. Kennelly, S. M. Meyers, and K. Sahr. 1997. Current status of biodiversity indicators using GIS. ESRI User's Conference Abstract.
Csuti, B., A.J. Kimerling, T. O'Neil, M. Shaughnessy, E. Gaines, and M. Huso.
1997. The Oregon Wildlife Atlas. Oregon State University Press, Corvallis, OR.
In press
Csuti, B. and A. R. Kiester. 1996. Hierarchical Gap analysis for identifying priority areas for biodiversity. ASPRS/Gap Symposium Proceedings, T. H. Tear, J.
M. Scott, and F. Davis, eds. In press.
Kagan, J. July 1996. Personal communication.
Kagan, J. and S. Caicco. 1992. Manual of Oregon actual vegetation. Report for the
Oregon Gap Analysis Program, directed by the Idaho Cooperative Fish and
Wildlife Research Unit, University of Idaho in cooperation with the Oregon
Department of Fish and Wildlife and the Oregon Natural Heritage Program.
Csuti, B., editor. 190 pp.
Kiester, A. R., J. M. Scott, B. Csuti, R. Noss, B. Butterfield, K. Sahr and D. White.
1996. Conservation prioritization using GAP data. Conservation Biology.
10:1332-1342.
Kiester, A. R. and K. Sahr. November, 1996. Personal communication.
Magurran, A. E. 1988. Ecological Diversity and its Measurement. Princeton University Press, Princeton, NJ.
Omernik, J. M. 1986. Ecoregions of the United States. U.S. Environmental Protection Agency, Corvallis Environmental Research Laboratory.
O'Neil, T. A., R. J. Steidl, W. D. Edge, and B. Csuti. 1995. Using wildlife communities to improve vegetation classification for conserving biodiversity. Conservation Biology. 9:1482-1491.
Prendergast, J. R., R. M. Quinn, J. H. Lawton, B. C. Eversham, and D. W. Gibbons. 1993. Rare species, the coincidence of diversity hotspots and conserva-
tion strategies. Nature. 365:335-337.
R. L. and M. Bedward. 1991. Mapping the environment at different
scales: benefits and costs for nature conservation. Pp. 7-13 in Nature Conservation: cost effective biological surveys and data analysis (C. R. Margules and M.
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