15
Fuzzy Statistical
and Modeling Approach
to Ecological Assessments
Bai-Lian Li
15.1 Introduction
Increasing attention on the extreme sensitivity of
ecological systems to environmental insults has
been changing the traditional view that humans are
the most sensitive species. Ecological risk assessment, especially the relatively unexplored area of
applied ecotoxicology, has been developed to meet
this need. However, characterization, quantification, estimation, and prediction of ecological risks
at multiple scales are often very difficult. Valuation of ecosystem components and scaling from the
laboratory toxicity bioassay or intensive investigations of single sites (or relatively small geographic
areas) to population, community, ecosystem or
landscape level are also ill-defined. Some uncertainty is unavoidable in ecologists' assessment and
prediction about ecological systems, simply because uncertainty emerges whenever information
pertaining to the situation is deficient in some respect. It may be incomplete, imprecise, fragmentary, not fully reliable, vague, contradictory, or deficient in some other way. In these situations,
unexpected risks and/or environmental changes
may result from decisions that must be made. There
are various information deficiencies resulting in
different types of uncertainty. Traditionally, the
only well-developed mathematical apparatus for
This paper is based on my presentation at the VI International Congress of Ecology, August 21-26, 1994,
Manchester, UK. Several major changes and improvements have been included in this version. This work was
partially supported by the U.S. National Science Foundation (BSR-91-09240, DEB-93-06679, DEB-94-11976,
and INT-95-12739), DOE/Sandia National Laboratories
(BE-0229), the University of New Mexico start-up fund,
and USDA Forest Service-Northern Region. This is
Sevilleta LTER publication no. 137.
dealing with uncertainty in ecological risk assessment has been probability theory (Suter and Barnthouse, 1993). However, the probabilistic approach
alone cannot represent uncertainties attached to
systems for which some deterministic dynamical
characteristics are unknown or deliberately ignored, as well as uncertainties attached to their
mathematical model. We have recognized that uncertainty is a multidimensional concept. Which of
its dimensions are actually manifested in a description of an ecological situation is determined
by the mathematical theory employed. The challenge now is to introduce and/or develop new methods to address these concerns.
This chapter describes a fuzzy statistical and
modeling approach to ecological risk assessment
under uncertainty to improve risk-based decision
making for protection of our environment/ecosystem. This new method (maybe relatively new for
ecologists, but not for mathematicians and systems
engineers) integrates utilization of knowledge or
judgment of experts together with statistics of the
available vague data and imprecise information so
as to provide the modeling basis for a predictive
ecological risk assessment at multiple scales. Some
potential applications of the fuzzy statistical and
modeling approach to ecological assessment are
also introduced with the intent to begin the process
of bringing the concepts and principles of fuzzy
sets (logic) and systems into mainstream ecological assessments.
Although multivalued logic was developed early
in this century, the development of fuzzy set theory by Lotfi Zadeh of the University of California
at Berkeley in 1965 marks the turning point of its
development from an academic venue to modem
application (Zadeh, 1965). The central idea is that
members of a set may have only partial membership; that is, there is gray between the black and
211
Fuzzy Statistical
and Modeling Approach
to Ecological Assessments
Bai-Lian Li
15.1 Introduction
Increasing attention on the extreme sensitivity of
ecological systems to environmental insults has
been changing the traditional view that humans are
the most sensitive species. Ecological risk assessment, especially the relatively unexplored area of
applied ecotoxicology, has been developed to meet
this need. However, characterization, quantification, estimation, and prediction of ecological risks
at multiple scales are often very difficult. Valuation of ecosystem components and scaling from the
laboratory toxicity bioassay or intensive investigations of single sites (or relatively small geographic
areas) to population, community, ecosystem or
landscape level are also ill-defined. Some uncertainty is unavoidable in ecologists' assessment and
prediction about ecological systems, simply because uncertainty emerges whenever information
pertaining to the situation is deficient in some respect. It may be incomplete, imprecise, fragmentary, not fully reliable, vague, contradictory, or deficient in some other way. In these situations,
unexpected risks and/or environmental changes
may result from decisions that must be made. There
are various information deficiencies resulting in
different types of uncertainty. Traditionally, the
only well-developed mathematical apparatus for
This paper is based on my presentation at the VI International Congress of Ecology, August 21-26, 1994,
Manchester, UK. Several major changes and improvements have been included in this version. This work was
partially supported by the U.S. National Science Foundation (BSR-91-09240, DEB-93-06679, DEB-94-11976,
and INT-95-12739), DOE/Sandia National Laboratories
(BE-0229), the University of New Mexico start-up fund,
and USDA Forest Service-Northern Region. This is
Sevilleta LTER publication no. 137.
dealing with uncertainty in ecological risk assessment has been probability theory (Suter and Barnthouse, 1993). However, the probabilistic approach
alone cannot represent uncertainties attached to
systems for which some deterministic dynamical
characteristics are unknown or deliberately ignored, as well as uncertainties attached to their
mathematical model. We have recognized that uncertainty is a multidimensional concept. Which of
its dimensions are actually manifested in a description of an ecological situation is determined
by the mathematical theory employed. The challenge now is to introduce and/or develop new methods to address these concerns.
This chapter describes a fuzzy statistical and
modeling approach to ecological risk assessment
under uncertainty to improve risk-based decision
making for protection of our environment/ecosystem. This new method (maybe relatively new for
ecologists, but not for mathematicians and systems
engineers) integrates utilization of knowledge or
judgment of experts together with statistics of the
available vague data and imprecise information so
as to provide the modeling basis for a predictive
ecological risk assessment at multiple scales. Some
potential applications of the fuzzy statistical and
modeling approach to ecological assessment are
also introduced with the intent to begin the process
of bringing the concepts and principles of fuzzy
sets (logic) and systems into mainstream ecological assessments.
Although multivalued logic was developed early
in this century, the development of fuzzy set theory by Lotfi Zadeh of the University of California
at Berkeley in 1965 marks the turning point of its
development from an academic venue to modem
application (Zadeh, 1965). The central idea is that
members of a set may have only partial membership; that is, there is gray between the black and
211