Procrustes analysis as a tool for land management
Silvia D. Matteucci
a,
*
, Laura Pla
b
a
Consejo Nacional de Investigaciones Cientı
´
ficas y Te
´
cnicas, Grupo de Ecologı
´
a del Paisaje (GEPAMA), Universidad de Buenos Aires,
Washington 1821, C1430ETA Buenos Aires, Argentina
b
Universidad Nacional Experimental Francisco de Miranda (UNEFM), Department of Agricultural Technology, Coro, Venezuela
1. Introduction
Environmental problems tend to accelerate at a faster rate
than the capture and updating of biophysical and socioeconomic
information, particularly in Argentina, where databases have
always been scarce and outdated. This constitutes a serious
drawback at a time when decision making is urgent. The use of
statistical methods to minimize uncertainty in environmental
management has become a common practice. Most of the
multivariate methods are based on mean values taking into
account variable association through covariance or correlation
matrices (Jenerette et al., 2002; Caeiro et al., 2003; Jansen,
2006). The Generalized Procrustes analysis (GPA) is a multi-
variate technique that involves transformations (translation,
rotation, reflection, isotropic rescaling) of individual data
matrices to provide optimal comparability (Gower, 1975). This
method has been routinely used in food science to analyze
sensory data specially with free choice profiles for scoring the
samples (Dijksterhuis, 1994), to investigate association between
sets of site properties and biological communities through
concordance between site classifications based on environ-
mental factors and species assemblages (for example, Jackson
and Harvey, 1993),andrecentlyappliedtocharacterizeentries
in a germplasm bank (Bramardi et al., 2005). However, GPA has
not been applied in the classification of administrative entities
on the basis of concordance among sets of variables that
characterize each of their subsystems (natural, human and
production).
In a stable system, these sets of variables should represent the
entity’s state in a similar fashion; that is, they should associate
through stabilized mutual interactions. On the other hand, in a
situation of instability each set of variables operates in diverse
directions causing the reduction of resilience and sustainability.
Each data set summarizes key attributes in the system’s
functioning. Whenever the land use data set concurs with the
physical resources data set, a coincidence between the land use
and the social well-being data sets is expected. Public policy for
sustainable management should aim at maintaining and improv-
ing this consistency.
We hypothesize that, if the land use fits in with the physical
support of agricultural production, people’s well-being should be
evident in a high concordance between the land use and social data
sets. Since the smallest administrative unit is the county, in order
to help decision makers at this level, we propose a statistical
procedure to classify the counties according to the degree of
concordance between pairs of data sets resulting from GPA. The
interplay between the pair of concordance values constitutes a bi-
dimensional index which serves as an ecological indicator to
contribute in the guidance of sustainable management.
Ecological Indicators 10 (2010) 516–526
ARTICLE INFO
Article history:
Received 28 February 2009
Received in revised form 21 September 2009
Accepted 24 September 2009
Keywords:
Ecological indicator
Matrix concordance space
Environmental policy
Land use
Concordance Class
Pampa Ecoregion
Argentina
ABSTRACT
Generalized Procrustes analysis (GPA) is a multivariate technique that involves transformations of data
matrices to provide optimal comparability. We propose GPA to quantify the concordance among sets of
variables that characterize natural, human and productive subsystems. When the land use fits in with
the physical support of agricultural production, people’s well-being should be evident in a high
concordance between the land use and the social conditions. In a situation of instability each set of
variables operates in diverse directions resulting in lower resilience and sustainability. Two GPA were
performed, between physical support and land use data sets (concordance = 67.4%), and between land
use and social conditions data sets (concordance = 65.3%). The interplay between the pair of concordance
values constitutes a bi-dimensional index which serves as an ecological indicator. Based on bootstrap
confidence interval, the 49 counties of the Pampa Ecoregion, Argentina, were classified in medium, high
or low concordance. The lack of concordance is an indicator of imbalances which may contribute to guide
environmental management.
ß 2009 Elsevier Ltd. All rights reserved.
* Corresponding author.
E-mail addresses: smatt@arnet.com.ar (S.D. Matteucci), laura@reacciun.ve
(L. Pla).
Contents lists available at ScienceDirect
Ecological Indicators
journal homepage: www.elsevier.com/locate/ecolind
1470-160X/$ – see front matter ß 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ecolind.2009.09.005