Center for Statistical Ecology
and Environmental Statistics
BIODIVERSITY IN THE AGE OF ECOLOGICAL INDICATORS
By W. Myers1 and G. P. Patil2
1
School of Forest Resources and Penn State Institutes of Environment
2
Center for Statistical Ecology and Environmental Statistics
Department of Statistics
The Pennsylvania State University
University Park, PA 16802
This material is based upon work supported by (i) the National Science Foundation under
Grant No. 0307010, and (ii) the United States Environmental Protection Agency under
Grants No. CR-83059301 and No. R-828684-01. Any opinions, findings, and
conclusions or recommendations expressed in this material are those of the author(s) and
do not necessarily reflect the views of the agencies.
[Invited Commentary Paper for Acta Biotheoretica]
Technical Report Number 2005-0702
TECHNICAL REPORTS AND REPRINTS SERIES
October 2005
Department of Statistic
The Pennsylvania State Universit
University Park, PA 1680
BIODIVERSITY IN THE AGE OF
INDICATORS
G. P. Pat
ECOLOGICAL
Distinguished Professor and Directo
Tel: (814)865-9442 Fax: (814)865-127
Email: gpp@stat.psu.ed
http: //www.stat.psu.edu/~gp
http://www.stat.psu.edu/hotspot
DGOnline New
Wayne Myers
School of Forest Resources and Penn State Institutes of Environment, The Pennsylvania
State University, University Park, PA USA (wlm@psu.edu)
G. P. Patil
Center for Statistical Ecology and Environmental Statistics, Department of Statistics, The
Pennsylvania State University, University Park, PA 16802 USA (gpp@stat.psu.edu).
1. INTRODUCTION
We offer here a perspective commentary on a perspective commentary by Carlo
Ricotta entitled “Through the Jungle of Biological Diversity”, in which he seems to argue
that biodiversity is so multi-faceted that it essentially lacks meaning as a subject for
measurement and expression with the suggestion that quantitative ecology would be
equally well served (or disserved) by confining attention to characterization of
‘community’. This is an interesting and somewhat anachronistic intellectual exercise in
the contemporary era of ecological work that might be termed an age of ecological
indicators, wherein there has arisen a journal called Ecological Indicators and multimillion dollar projects to develop targeted indicators of ecological characteristics are
finding sponsorship in public funding. Meanwhile, no complementary concern is raised
about the inherent indefiniteness and duality of interpretation surrounding ‘community’
in ecology, which is advocated as the conceptual backstop for biodiversity.
We first reexamine the issue of indefiniteness in terms of complexity, constructs,
components, spatial and temporal scope/scale, specification, comparison and
complements. We then proceed to consider ways of coping with complexity and
confounding that embrace multiple indicators rather than agonizing over choices and
conflicts. Finally, we contemplate enlarging the orders of indicators to encompass some
interactions in a formal manner that accommodates both parameterization and
visualization – with the intent of showing that biodiversity expression is still an
intellectually fertile field as well as an ecologically and economically important one. We
conclude by noting the convergence of biodiversity and ecological community concepts
at meter scales, but not for broader landscape, regional, and global scales of ecological
organization.
2. COMPLEXITY, SCOPE, SPECIFICITY, COMPARISON, COMPLEMENT
The indefiniteness regarding biodiversity that can give rise to frustration is well
expressed by L. R. Taylor (1978) in the following quote:
Diversity so pervades every aspect of biology that each author may safely
interpret the word as he wishes and there is consequently no central theme to
the subject. We cannot be sure if this flexibility is healthy or due to lack of
discipline, but it can be traced back to the beginnings of interest in biological
diversity …
The recent programs of the U.S. National Science Foundation probing biocomplexity in
many contexts serve to provide evidence that the flexibility addressed by Taylor is both
healthy and indicative of need for strengthening discipline with regard to scientific
constructs and means by which they are made operational. Much of the indefiniteness is
due to lack of specification.
Any inquiry into variety requires a construct of kind, which depends on the
taxonomic/genetic/functional level of interest that can span a broad taxonomic scale of
organization and association. Given a duly specified construct of kind, then inquiry into
variety also requires ability to determine presence that further depends on specification
of where and when. Where requires a scale of location and scope over which it
operates. Likewise, when requires a scale of time and scope over which it operates.
Variety of a kind in a place/volume during a span of time is of interest in a context that
provides error tolerance and economic/logistical feasibility and value. However, interest
also typically resides in variation of variety over a range of both spatial and temporal
scales (multiscale analysis). In all of this, indefiniteness lies only in lack of specification.
There may or may not be interest in amount of a kind (abundance) occurring in a
context. There may also be interest in the comparative abundances of different kinds in
either absolute terms or relative terms (proportions). Indicators/expressions of this nature
are appropriate, and therefore of value, if they convey the desired information within the
budget and delivery delays that are acceptable. One method is more efficient than
another if it conveys the required information either more rapidly or at less cost.
Conveying more information at the same cost and timing is not necessarily desirable if
unwanted information has to be processed or filtered.
Increasingly sophisticated management, intervention, remediation, and regulation
require a continuing flow of multiple indicators for various aspects of ecosystems – many
of which are directly or indirectly targeted at variety/diversity. Rarity is a special aspect
of variety that has become a focus of programs concerned with organisms that are at risk
of extirpation (Myers et al., 2001). Rarity has both aspects of infrequent occurrence
(encounter) and very low proportional abundance. Conservation has likewise become
duly concerned with stronghold species/subspecies that are characterized by continuing
high proportional abundance over a more or less extensive area. Assessment of the
several aspects of biodiversity becomes relatively more complicated for migratory fauna
as opposed to relatively sedentary or sessile animals or plants. However, the migratory
aspect only adds another suite of specifications to be made. It does not induce intrinsic
indefiniteness or reduce the value of indicators. Indicators are increasingly progressing
to a second order of inference whereby surrogates become substitutes for the actual target
of interest – as for example in the assessment of habitat diversity instead of actual
organism diversity.
Natural communities are also definite when defined simply as a (fully specified)
local assemblage of particular organisms. The community concept becomes intrinsically
more indefinite, however, when its existential nature is made dependent on pattern of
occurrence across landscapes and regions. This is because capturing the nature of pattern
is still very much a work in progress. Thus, community has a rather restricted scope of
spatial scale -- much more so than biodiversity.
What ecosystem managers and regulators seek is a complementary set of
indicators that captures all aspects of current interest. As we will show subsequently,
they need not be overly concerned if there is some redundancy in the set. An appropriate
jungle analogy is when the canopy elements are suitably aligned to capture all of the
(informational) light. Some tangles can be circumnavigated quite readily. Let us carry
forward, then, this idea of alignment on indicators.
3. ALIGNMENT ON MULTIPLE INDICATORS
It is conventional to think of multivariate analysis in terms of variables and
observational units upon which the variables (indicators) are observed. The true duality
of variables and observational units in characterizing each other comes to light in
correspondence analysis and related techniques. We propose to recognize that duality
more fully in considering alignment of multiple indicators. We consider each
observational unit as a sensorial entity that expresses its own nature in a suite of signals
(indicators or variables). In a typical collection of observational entities, some of the
entities will respond concordantly across the spectrum of indicators. In other words, all
of the signals across the spectrum will be either jointly strong or jointly weak. Among
other subsets of these entities there will be varying degrees of discord (or mixed signals)
that are generated. The degree of alignment on the indicators can be assessed in a
nonparametric (distribution free) manner in terms of the ranks of the indicators. That is,
the entities are ranked on each of the indicators and the rank numbers are then substituted
for the original indicators values. We use a place ranking whereby first place is ‘best’
and last place is ‘worst’. In this manner, increasing rank numbers give increasing contraindication regarding the aspect under study.
We first derive joint levels of contra-indication on the basis of dominance. There
is domination if some unit is equal to or better than another on all indicators. Level 1
consists of the entities that are not dominated. The level-one entities are then removed,
and level 2 consists of those among the remainder that are now not dominated. The
remaining levels are found recursively.
We next use the range of ranks for each entity to extract internally ordered series
as rank range runs (RRR) such that each successive member of a run is ‘worse’ than its
predecessor in the sense of being worse in its best rank and also worse in its worst rank.
Each successive run entails broader ranges of ranks for its members, and thus reflects
greater dissonance among the indicators.
We illustrate with 184 watersheds in the Piedmont Plateau region of the state of
Pennsylvania in northeastern USA, with the watersheds being rated relative to species
richness for taxonomic groupings of vertebrates having predominantly upland versus
lowland habitats. A map of the locations of these watersheds is given in Figure 1.
Figure 1. Watersheds in Piedmont physiographic region of Pennsylvania in NE USA.
Figure 2 shows a plot of contra-indication level on the vertical axis versus dissonance on
the horizontal axis as reflected in rank range runs. Watersheds in the leftmost series are
concordant among the rankings of the indicators, and indicator rankings become more
discordant as series progress to the right.
Corner Class (Y) vs. RRRsequence number (X)
35
30
25
20
15
10
5
0
0
20
40
60
80
100
120
140
160
Figure 2. Contra-indication level (Y) versus Dissonance for 184 watersheds.
This process has the flavor of a nonparametric inverted factor analysis on the watersheds.
For visualization on a color map, the lower third of the contra levels can be progressively
shaded in green, the middle third in yellow, and the upper third in red. Increasing
dissonance can be expressed by adding a progressive blue component to the foregoing
colors that increases toward the right. The more dissonant watersheds would then appear
in shades of magenta, cyan or gray according to degree of contra-indication. The
watersheds toward the far right of the plot are effectively outliers with regard to
consistency of ranks. One strategy is to remove such extremely discordant watersheds
from the rest and treat them as special cases for purposes of environmental management.
The process is thus an effective way of segregating the watersheds into subsets that are
expected to be consistent in terms of management needs and response to treatment.
Additional indicators are readily accommodated in the alignment process.
Increasing number of indicators usually tends to interject relatively more discordance
among the ranks, and consequently to reduce the number of contra-indication levels.
The successive series in the plot of Figure 2 constitute profiles that incorporate
multiple aspects of diversity, whether biodiversity or diversity of other subject matter.
Profiles are conducive to advanced work in expression/representation of diversity
relations because they have sufficient flexibility to integrate different aspects of diversity.
We could pursue this line of investigation relative to the more commonly considered
elements of diversity such as kind, richness, abundance, evenness and also rarity.
Carlo Ricotta has admirably touched on this theme with several pertinent references and
details. We leave this commentary at that with an update with two additional references.
We congratulate Carlo Ricotta and the editor for this discussion on this vital topic of the
day.
180
200
REFERENCES
1. Myers, W., Bishop, J., Brooks, R. and Patil, G. P. (2001). Composite Spatial
Indexing of Regional Habitat Importance. Community Ecology 2(2): 213-220.
2. Myers, W. L., Patil, G. P., and Cai, Yun (2005). Exploring patterns of habitat
diversity across landscapes using partial ordering. Technical Report 2005-0701, Center
for Statistical Ecology and Environmental Statistics, Penn State University, University
Park, PA.
http://www.stat.psu.edu/%7Egpp/pdfs/TR2005_0701.pdf
3. Patil, G. P. (2002). Diversity profiles. Technical Report 2001-0206, Center for
Statistical Ecology and Environmental Statistics, Penn State University, University Park,
PA. Also in Encyclopedia of Environmentrics, A. El-Shaarawi and W. W. Piegorsch,
eds. John Wiley & Sons, UK. pp. 555-561.
http://www.stat.psu.edu/%7Egpp/pdfs/TR2001-0206.pdf
4. Patil, G. P. (2001). Statistical ecology and environmental statistics. Technical Report
2001-0401, Center for Statistical Ecology and Environmental Statistics, Penn State
University, University Park, PA. Also in Encyclopedia of Life Support Systems, EOLSS
Publishers Co., Ltd. Jeff Wood, ed.
http://www.stat.psu.edu/%7Egpp/pdfs/TR2001-0401pap.pdf
5. Taylor, L. R. (1978). Bates, Williams, Hutchinson – a variety of diversities. In
Diversity of Insect Faunas. I. A. Mound and N. Waloff, eds. Blackwell Scientific
Publications, Oxford. 1-18.