International Review of Economics and Finance 9 2000 69–77
Aspects of ecosystem persistence and the optimal conservation of species
Amitrajeet A. Batabyal
Department of Economics, Utah State University, 3530 Old Main Hill, Logan, UT 84322-3530, USA
Received 15 September 1998; accepted 11 April 1999
Abstract
Although ecologists have long recognized the salience of persistence in determining the static and the dynamic behavior of ecological systems, it is only very recently that economists
have begun to study this concept in relation to the use of services that are provided by jointly determined ecological-economic systems ecosystems. As such, there are very few studies of
ecosystems that explicitly analyze the ecological and the economic aspects of this use issue. Given this state of affairs, this article has two objectives. First, a new method is used to formally
describe and bound the notion of ecosystem persistence. This method explicitly incorporates the stochastic aspects of ecosystems. Second, the bound on persistence is used to study the
problem of optimal species conservation.
2000 Elsevier Science Inc. All rights reserved.
JEL classification: Q30; D80
Keywords: Conservation; Ecosystem; Persistence
1. Introduction
The problems posed by desertification, habitat loss, and species extinction are clearly global in scope. However, the solutions to these problems that have been
proposed by researchers working within the confines of ecology and economics have generally been narrow in scope. Moreover, as Ludwig et al. 1993 and Holling 1995
have noted, the recent history of ecosystem management tells us that these uni- disciplinary solutions have not worked very well. Consequently, it is now necessary
for scholarly research in ecological economics to explicitly recognize the facts that 1 ecological and economic systems are jointly determined, and 2 that if we are to
Corresponding author. Tel.: 435-797-2314; fax: 435-797-2701. E-mail address
: batabyalb202.usu.edu A.A. Batabyal 1059-056000 – see front matter
2000 Elsevier Science Inc. All rights reserved.
PII: S1059-05609900049-0
70 A.A. Batabyal International Review of Economics and Finance 9 2000 69–77
comprehend the functioning of such systems, then we must also understand the many and varied interdependencies between such systems.
1
Once it is recognized that ecological-economic systems are jointly determined, it follows that these systems should be studied as one system.
2
However, because this recognition has been recent, a number of issues pertaining to the functioning of jointly
determined ecosystems remain inadequately understood. As such, this article has two objectives. First, we use reliability theory to characterize and to bound the ecosystem
stability property known as persistence. Next, we use this bound on persistence to study a species conservation problem in which society derives benefits from the persistence of
the underlying ecosystem and from the pursuit of economic activities on this ecosystem.
The health or the well being of an ecosystem can be described by a number of different concepts. In this article, we shall focus on the notion of persistence. Be-
cause persistence refers to “how long a variable lasts before it is changed to another value . . .” Pimm, 1991, p. 14, it is the appropriate concept to focus on whenever
the longevity of the species in an ecosystem is salient. For instance, the work of Costanza et al. 1995 has informed us that in coastal and estuarine ecosystems, the
health of the ecosystem depends on how long the composition of a small number of generalist species—that collectively determine the health of the ecosystem—lasts. As
such, it should be clear to the reader that for such ecosystems, the notion of persistence provides us with an apposite measure of ecosystem health.
Despite the significance of the concept of persistence, there are very few studies of persistence in the economics literature. In particular, we are aware of only one article
that has studied persistence, and linked persistence to the number of species in an ecosystem. Batabyal 1999c has provided an explicit characterization of ecosystem
persistence. However, in his modeling framework, Batabyal makes two key assumptions. First, he supposes that persistence depends only on the keystone
3
species of an ecosys- tem. Second, he assumes that there are no interaction effects between the keystone
species of an ecosystem. These assumptions detract from the generality of his analysis. Although Batabyal’s definition does provide a link between persistence and the
number of species in an ecosystem, this definition does not account for the fact that there will generally exist interaction effects between the different species in an
ecosystem.
4
Given this state of affairs, in this article we use reliability theory
5
to provide a bound on the persistence of a stylized ecosystem. This bound explicitly accounts
for interaction effects between the species of our stylized ecosystem. The rest of this article is organized as follows. Section 2 describes the theoretical framework and then
computes an upper bound on ecosystem persistence. Section 3 uses this bound to study a species conservation problem in which society derives benefits from the persistence of
the underlying ecosystem and from the pursuit of economic activities on this ecosystem. Finally, section 4 concludes and offers suggestions for future research.
2. Theoretical framework
