Ecological Economics 69 (2010) 478–485

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Ecological Economics

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Methods

The ecological importance of species and the Noah's Ark problem

Neil Perry ⁎Department of Business and Economics, Lebanon Valley College, Annville, PA 17003, United States

⁎ Fax: +1 717 867 6019.E-mail address: nperry@lvc.edu.

1 For example, see Czech and Krausman (2001, p. 5(2007, Table 2) for discussions of the consequences of lEndangered Species Act 1973.

0921-8009/$ – see front matter © 2009 Elsevier B.V. Adoi:10.1016/j.ecolecon.2009.09.016

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 January 2009Received in revised form 27 September 2009Accepted 28 September 2009Available online 28 October 2009

Keywords:Ecological importanceEcosystem processFunctional diversityBiodiversityEndangered species conservation

Using the Noah's Ark problem – the problem of efficiently allocating limited funds to conserve biodiversity –

the standard economic approach to endangered species conservation constructs a human-centeredbiodiversity by favoring species directly valuable to humans. I analyze this approach and draw on thefunctional ecology literature to offer an alternative emphasizing the role species play in their ecosystems.The aim is to create a working ecosystem on the Ark rather than a collection of charismatic and distinctspecies. To do so, I construct a new measure of a species' ecological importance and an ecological objectiveappropriate for cost-effective resource allocation. The ecological approach fundamentally changes the notionof species-value from a direct value based on a species' appearance or taxonomic difference to an indirectvalue based on a species' ecological role in its ecosystem. In the process, ‘populations’ of species become thefundamental unit of biodiversity rather than ‘species’, and abiotic processes also possess value. Whencompared to the economic approach, the ecological approach prioritizes different species for the Ark andachieves superior economic outcomes in all but the mythical Noah's Ark scenario where interactions arenon-existent. The analysis challenges the approach of US endangered species legislation and I call for areformulation based on endangered ecological interactions.

3) and Kerkvliet and Langpapimited resources under the US 2 Maresova and

macroevolutionary p

ll rights reserved.

© 2009 Elsevier B.V. All rights reserved.

1. Ecosystems need different species on the Ark

The standard economic approach to endangered species conser-vation constructs a biodiversity by emphasizing direct economicvalues. I propose a construction based on ecological values and justifyit from an economic perspective. The economic approach begins withthe Noah's Ark metaphor and problem which represents the dilemmafacing a conservation decision maker with finite resources. Withlimited space, Noahmust choose the order of species for the Ark. Withlimited economic resources, the conservation decision maker mustchoose which species to preserve and which to leave behind. Ethicallyone may favor the ‘Noah principle’, which refers to the objective ofsaving all species (Mann and Plummer, 1995, p. 25), but economicresources are limited and choices must be made.1

In the economic literature, Noah maximizes the non-use value(NUV) and direct-use value (DUV) of a collection of species. Forexample, Solow et al. (1993), Weitzman (1992, 1998), and Nehringand Puppe (2002) all develop measures of ‘taxonomic diversity’ — thetotal (expected) genetic or morphological diversity of a group ofspecies. As a consequence, a species' taxonomic difference measuresits marginal value. People value taxonomic diversity due to the varietyit offers for aesthetic or existence reasons (Weitzman, 1998, p. 1283),

and the information and security it provides for medicines and food(Brown and Goldstein, 1984, p. 303; Solow et al., 1993, p. 64;Weitzman, 1998, p. 1283). It thus constitutes both NUV and DUV.

People also value species for their charismatic characteristics andWeitzman (1998) adds an expected utility objective to taxonomicdiversity. A species' marginal value is its direct utility or “how muchwe like or value the existence of species i” (Weitzman, 1998, p. 1280).This “amorphous” value (Metrick and Weitzman, 1999) includescommercial, aesthetic, and moral values (Metrick and Weitzman(1998, p. 23), and again constitutes both NUV and DUV. In particular,direct utility depends on a species' charisma; as Weitzman (1998,p. 1280) explains, “most of us like Pandas more than mosquitoes”. Insupport, Nehring and Puppe (2002) associate their measure ofdiversity with existence value.

The standard economic approach models Noah as a consumerchoosing commodities from a shelf. Noah chooses taxonomicallydifferent and charismatic species, and those easily saved (inexpensivegoods), because these provide the greatest direct satisfaction(marginal value) per dollar of conservation expenditure. Thisconstructs a biodiversity of cute, fuzzy, enormous, unique, and bizarrespecies favored by humans.2 Metrick and Weitzman (1999) providethe supporting argument that consumers are sovereign and have theright to impose their values. However, species are not commodities.They interact with other species and have ecological roles thatproduce ecosystems and valuable ecosystem services. Moreover,

Frynta (2008, p. 557) refer to this as “an anthropogenousrocess forming the fauna of the future.”

479N. Perry / Ecological Economics 69 (2010) 478–485

treating species like commodities undermines ecological values andproves counterproductive for the very values the economic approachaspires to maximize. To maximize the total economic value (TEV) ofbiodiversity, which includes DUV, NUV, and the indirect use value(IUV) of ecosystem services, we must ensure the integrity ofecosystems, which ultimately house species. In short, we mustincorporate ecological values and the production function of ecosys-tems when constructing biodiversity.

The approach pursued here draws on the functional ecologyliterature to establish the required ecological objective. In thisliterature, ecosystems are viewed as collections of interactions orfunctions carried out by species and other abiotic processes (such asfire and wind). ‘Functional diversity’, or the variety of interactions,determines the integrity (productivity and resilience) of ecosystems.It is natures' production function. To think about the Noah's Arkmetaphor in a different way, Noah must create a thriving ecosystemon the Ark rather than a zoo. In the process, Noah will maximize theTEV of biodiversity. The ‘ecological importance’ or functionaldifference of species will determine their marginal value and alsorepresents their indirect economic value. In the following, I provide aunique method for prioritizing species based on their ecologicalimportance, explain the economic outcomes, and discuss theimplications for endangered species legislation.

2. Creating an ecosystem on the Ark

2.1. In search of an ecological objective: functional diversity

Creating a working ecosystem on the Ark requires representing allfunctions performed in an ecosystem. To do this, Noah will use theecological objective of functional diversity. This aspect of biodiversityderives from ecological research on the functioning of ecosystems.Functional diversity divides ecosystems into functional components.Species and abiotic disturbance events perform the functions, whichare defined as “interactions with ecosystem processes” (Martinez,1996, p. 118). Interactions include predation and resource competi-tion, but more generally are ecological functions, such as denitrifica-tion, nitrogen fixation, carbon usage, lignin metabolization,decomposition, and resource provision (ibid.). Martinez (ibid.)defines functional diversity as “the variety of interactions withecological processes”. An alternative definition is “the number offunctional groups in an ecological system” (Martinez, 1996, p. 123).Chapin et al. (1992, p. 107) define a functional group as a group ofspecies with “‘similar’ effects on ecosystem processes”. At a highlyaggregated level, functional groups include primary producers ofbiomass (plants), macroconsumers (animals), and decomposers(microorganisms) (Meyer, 1994, p. 90). However, each group can bedisaggregated based on the unique functions performed by memberspecies.

Together, the functional components produce the output of theecosystem (ecosystem processes), and ensure its resilience. Theecosystem processes include biogeochemical cycling, energy flow,primary productivity, population growth, pollination, soil productionand others. Some processes are economically valuable ecosystemservices themselves, such as pollination and soil production. Others,such as primary productivity (the growth in biomass), summarizeor represent the valuable ecosystem services. Others produce valuableecosystem services such as biogeochemical cycling and energy flowwhich “set an upper limit on the quantities and numbers oforganisms” and trophic levels existing in an ecosystem (Hollinget al., 1995, p. 54).

These ecosystem processes depend on functional diversity. Amissing functional group, perhaps due to extinction, reduces the staticoutput of the ecosystem because it compromises the use of criticallimiting resources (Tilman, 1997, pp. 96–98). It also reduces resiliencebecause each group potentially performs a critical function in the

dynamic cycling of the ecosystem. Holling et al. (1995, pp. 62–64)explain that ecosystems cycle in four distinct stages: exploitation ofrecently disturbed areas; conservation of energy and nutrients; releaseof biomass and nutrients by a disturbance event such as pest, wind, orfire; and reorganization, where soil processes minimize nutrient lossand prepare for the next exploitation phase. A missing functionalgroup can affect the ability of the ecosystem to reorganize afterrelease, making it less resilient.

In terms of species protection, certain species are critical — thosewith unique functions that few other species perform. As Holling et al.(1995, p. 48) explain, the “least resilient or the most sensitivecomponents of food webs, energy flows and biogeochemical cyclesappear to be those where the number of species carrying out thatfunction is very small.” In support, Walker (1995, p. 747) argues thatfunctional groups with “only one or very few species deserve priorityconservation attention because their functions could be quickly lostwith species extinctions”.

The critical species are often referred to as keystone species. Fromthe perspective of functional diversity, a “keystone species is afunctional group without redundancy” (Chapin et al., 1992, p. 107).That is, no other species can take over their role. In contrast, Collinsand Benning (1996, p. 254) define a redundant species as one withhigh or exact functional similarity to other species. However, evenredundant species have insurance value because conditions change.As Holling et al. (1995, p. 61) indicate, “species that invade afterdisturbance and during succession can be highly variable and aredetermined by the type, timing and intensity of chance events”. Thus,a redundant species may end up being unique and is thereforevaluable as insurance (Walker, 1995; Perrings et al., 1995, pp. 3–4).

This discussion implies that for the Noah's Ark problem we need aconcrete definition or measure of a species' importance as it relates tofunctional diversity. The measure must be capable of determiningimportance before boarding the species, and useful for comparingspecies in different ecosystems. In the next subsection, a quick reviewof ‘importance’ measures in ecology reveals that a new definition isrequired. The discussion also implies that abiotic disturbance eventssuch as fire, wind, and herbivore activity have important functionalroles, along with species, and form an “inherent part of the internaldynamics and in many cases set the timing of successional cycles”(Holling et al., 1995, p. 61).

2.2. A quick review of ‘importance’ in ecology

Hurlbert (1997) discusses three interpretations of importance inecology. Firstly, species may be important for particular other species,which is analyzed using models of population, competition, andpredator–prey relationships (ibid., p. 370). Secondly, the keystonespecies concept interprets importance as a species' influence on thewhole community or ecosystem (ibid.). Thirdly, a species role as a“conduit for energy and materials” determines its importance (ibid.,p. 369). The second and third interpretations have formal definitionsand measures.

Originally, a keystone species was defined as a predator controllingthe density of a primary consumer or prey that would otherwisedominate the ecosystem and reduce diversity, and the predators'influence was disproportionate to its abundance (Mills et al., 1993;Power et al., 1996). For example, sea otters (Enhydra lutris) control thedensity of sea urchins (Strongylocentrotus spp.) which would, if leftunchecked, destroy kelp populations and reduce diversity (Mills et al.,1993, p. 220). However, researchers use the term loosely withHurlbert (1997, p. 374) citing thirteen different categories of keystonespecies including prey, modifiers, mutualists, plants, and keystoneprocesses. In response to critiques by Mills et al. (1993) and others,Power et al. (1996), a group of experts in the field, clarified thekeystone concept and defined it formally.

3 This is justified in more detail in Section 3. See Perry (2006) for justifications of theother restrictions.

480 N. Perry / Ecological Economics 69 (2010) 478–485

Power et al. (1996, p. 609) define a keystone species “as one whoseimpact on its community or ecosystem is large, and disproportion-ately large relative to its abundance”. Thus, the species need not be apredator or otherwise have a top-down influence on the ecosystem.To measure ‘impact’, the authors use the change in a community trait,such as productivity, nutrient cycling, or species richness when aspecies is (hypothetically or experimentally) removed (ibid.).Mathematically, the community importance (CI) of species i is(ibid., p. 610)

CIi =ðT0−T1Þ

T0

� �1ri

� �ð1Þ

where T0 represents the value of the trait before removing the species,T1 represents the value after removal, and ri represents theproportional abundance of the species with ri<1. In contrast tomost species, keystone species have a large impact (T0−T1) relativeto their abundance and CI is large.

Hurlbert (1997, p. 369) prefers the third interpretation ofimportance. Important species are a “conduit for energy andmaterials” (ibid.) regardless of their relative abundance. Generalfunctional importance (GFI) measures the impact of removing aspecies on the abundance or productivity of the remaining species:(ibid., p. 371)

GFIi = ∑n

j=1jPj;t=1−Pj;t=0 j ð2Þ

where Pj,t=1 represents productivity of the jth species after removal,and Pj,t=0 represents productivity before, although productivity couldbe replaced by the abundance (Aj) of species or other traits.

CI and GFI cannot measure importance before removing thespecies because they require the trait value after removal. We need ameasure that predicts the impact of extinction. Davic (2003) developssuch a measure using notions of functional dominance and redun-dancy. To Davic (2003, p. 3), any “species that is dominant in terms ofits biomass within an occupied functional group would represent apotential [keystone species] that could regulate species diversity infunctional groups from lower trophic levels”. Thus, a keystone speciesdominates its functional group. The definition of functional groupdominance (FGD) derives from the general literature on dominance:

FGD =Amax

Að3Þ

where Amax represents the abundance of the most abundant specieswithin its functional group, and A represents the total abundance ofspecies in the functional group (=∑Ai). If, as defined in the previoussection, a keystone species is a functional group without redundancy,FGD would equal 1.

While useful for determining importance prior to removal, FGDcannot compare two dominant species in different ecosystems. Thiswould require a weighting procedure based on the impact of eachspecies' group on its ecosystem. CI also suffers from this critiquebecause it weights a species' overall importance by relative abun-dance. A species may be important relative to its small abundance butnot necessarily important to save. A dominant species (with highabundance) might be more important for the ecosystem. As Hurlbert(1997, p. 375) explains: “No rationale has ever been explicitly putforward for that [relative to abundance] criterion. It apparentlyreflects a desire to create an artificial dichotomy between functionallyimportant species that are abundant,… and functionally importantspecies that are less abundant”.

Hurlbert's measure could be used to compare dominant speciesassuming the trait (productivity, abundance or an alternative) has aconsistent meaning in different ecosystems. However, as mentionedpreviously and recognized by Hurlbert (1997, p. 371), this measure

cannot be “reasonably estimated” prior to removal. In the nextsubsection, I develop ameasure of ecological importancewhich can bedetermined prior to removal and compared across ecosystems.

2.3. Ecological importance defined

An ecologically important species performs an important functionand few other species can take over its role. Fi represents functionalgroup richness — the number of species in the ith species' functionalgroup in its ecosystem. As Fi falls, the species' ecological importanceincreases, ceteris paribus. For example, a keystone species performs aunique function and Fi=1. An ecologically important species alsoperforms a significant function for the ecosystem, perhaps one thatdrives ecosystem dynamics. Ri, the number of species affected byspecies i's function, represents the significance of the function. As Rigrows, the importance of species i grows. Depending on the speciesand function, Ri may be the number of species in the entire ecosystemor community. The measure of ecological importance (EI) for the ithspecies (labeled Mi), in general form, is

Mi = mðFi;RiÞ ð4Þ

where MF (partial derivative of M with respect to F) is negative, MR ispositive, and further restrictions on second order derivatives mightapply. For example, one possible functional form is

Mi =

ffiffiffiffiffiRi

pFi

ð5Þ

which is appropriate when MFF>0, MRR<0, and MFR=MRF<0. Inparticular, the restrictions that MR>0 and MRR<0 imply thatimportance increases with the number of species affected but at adecreasing rate.3 In addition, note that each species receives a positivevalue which reflects the insurance it provides.

Unlike FGD, the EI measure can compare functionally dominantspecies in different ecosystems because it weights functionaldominance by the significance of the function. For example, acomparison of two keystone species will depend on the number ofspecies each affects (the size of Ri). Unlike CI and GFI, the measuredetermines importance prior to removal because it does not rely on atrait value before and after extinction. EI predicts which specieswould, if they went extinct, lead to large losses in species richness,productivity, or abundance. In addition, EI does not support the falsedichotomy inherent in the CI concept criticized by Hurlbert (1997)and Kotliar (2000). It does not necessarily favor species with lowabundance over dominant species. Similarly, it removes the keystone/redundant species dichotomy because importance is a relativeconcept and each species has a positive EI value.

Depending on the situation and data, we could adjust EI in anumber of ways. Fi could be replaced by FGD so that the abundance ofspecies in the functional group determines importance rather than thenumber of species. Similarly, to provide more information, we couldreplace Fi with a variable representing the endangerment of otherspecies in the group. We could also replace Fi with a measure offunctional difference based on the unique functional attributespossessed by a species (Perry, 2006), which removes the need forspecies to be classed within distinct functional groups. Finally, the Rivariable could be adjusted to measure different traits, such asproductivity, biomass, or abundance.

Although EI can compare species in different ecosystems beforetheir removal, Noah still needs more information before prioritizingspecies for the Ark. In the context of allocating limited resources, thecost of saving species and the impact of each dollar spent also

481N. Perry / Ecological Economics 69 (2010) 478–485

determine importance. These variables appear when we incorporateEI into the Noah's Ark choice problem.

2.4. Ecological importance and Noah's choice problem

Noah's objective function utilizes EI but also depends on theprobability of survival of species. A species will not fulfill its normalecological role if extinct. Thus, a low probability of survival indicates alow expected ecological importance (piMi), where pi is the probabilityof survival of species i, a number between zero and one. Indeed, Noahmust increase the probability of survival of species to increasethe functioning and integrity of ecosystems. The objective function(E(M)) for the group of endangered species i=1,…, n is the sum oftheir expected ecological importance:

EðMÞ = ∑n

i=1piMi: ð6Þ

The remainder of the choice problem follows Weitzman (1998). Aset X represents a finite universe of species with n members labeledi=1,…, n. Each species in X could become extinct as given by itsprobability of survival, pi. Noah's effort or resources can change theprobability of survival of species, modeled as an adjustment from aminimum or no effort level (−pi) to a level occurring with effort andresources (−pi). Choosing to change the probability of survival ofspecies i (Δpi = −pi−−pi) comes at a cost ci, and with limited budget B,choices must be made.4 Thus, Noah must choose the probabilitiesof survival to maximize the sum of expected ecological importance(E(M)) subject to the budget constraint and probability constraints5:

maxpi ;:::;pn

∑n

i=1piMi

� �ð7Þ

subject to

∑n

i=1ci

pi−−pi−pi−−pi

!= B ð8Þ

−pi≤pi≤−pi ∀i∈S: ð9Þ

The first-order conditions imply the following ranking equation(see Appendix A):

Ranki =ΔpiðMiÞ

ci: ð10Þ

Noah compares the rank of species i to the rank of other speciesand allocates funds to the species with greatest rank until p⁎i = −pi ,assuming enough funds are available. Subsequently, Noah finds thespecies with the next highest rank and allocates to this species. Thiscontinues until no funds are available when at most one species willhave a pi⁎ in between −pi and

−pi (see Appendix A).The ranking equation can still be used to compare species in

different ecosystems prior to extinction. However, the rank nowdepends on its ecological impact (Mi) and the impact of the

4 The cost of conservation effort (ci) could be interpreted narrowly as the moneyspent conserving a species. However, a broader interpretation of the Noah's Arkproblem refers to the choices made in development versus preservation decisions. Inthis case, the cost includes foregone economic benefits, such as foregone forestryincome.

5 Note that I assume independent survival probabilities. Species in the set X aregeographically segregated. Perry (1999) and Mainwaring (2001, pp. 88–89) criticizethis assumption when the objective is taxonomic diversity or direct economic value.Extinction will have indirect effects on valuable species in each species' ecosystem, andneglecting this makes the economic approach suboptimal, as explained in thefollowing section. However, the assumption can be maintained when using theecological objective because EI inherently considers the indirect effect of species.

conservation funds (Δpi/ci). That is, the change in expected ecologicalimportance per conservation dollar determines a species' rank andecologically important and inexpensive species will be boarded first.The idea is to be cost-effective with the available funds. This maymean rejecting programs for highly endangered or less abundantspecies if they are too expensive to save. The cost-effectiveness aspectthe Noah's Ark framework can be enhanced by including aconservation program's ‘likelihood of success’ in the analysis, whichdepends on operational, legal, political, and social constraints (Josephet al., 2009, p.333). In this case, programs with a low likelihood ofsuccess will also not be supported.

As a heuristic device or a theoretical construct, the rankingequation can be used to analyze endangered species programs and theeconomics of endangered species. For example, while the rankingequation typifies an economic approach to allocation – choose the‘good’with the greatest marginal benefit per dollar – ecological valuesdetermine the marginal benefit rather than direct-use values. Thespecies valuable for nature receive funds rather than those directlyvaluable for humans. Thus, the ranking equation constructs an‘optimal’ ecosystem on the Ark rather than an optimal zoo. In thefollowing sections, I explain the economic outcomes of the ecologicalapproach, consider an example, and discuss the implications forendangered species legislation.

3. Comparing the economic outcomes of the ecological andeconomic approaches

The ecological and economic approaches obviously prioritizedifferent species. For example, charismatic species favored underthe economic approach, such as spotted owls (Strix occidentalis),grizzly bears (Ursus arctos) and Californian condors (Gymnogypscaliforniacus), have little role in the functioning of ecosystems (Millset al., 1993, p. 222) and will not be prioritized under the ecologicalapproach. However, charismatic species may indirectly be protectedunder the ecological approach because it preserves the integrity andresilience of the largest and most valuable ecosystems. Charismaticspecies increase the value of ecosystems making it more likely theecologically important species, population, or process in thatecosystem will be targeted. If not, it must be the case that targetinga functionally unique species elsewhere supportsmore total economicvalue and this is correct for economic efficiency. In this section, Idevelop this argument by explaining the fundamental differences andeconomic outcomes of the economic and ecological approaches.

The ecological approach fundamentally changes the notion ofspecies-value. In the economic approach, value derives from theobject itself; species possess value due to their inherent difference,appearance, or charisma. This value depends on a comparison of thespecies to other species anywhere in the world.6 The characteristicsare not ecosystem centered. In the ecological approach, value derivesfrom a species' actions (its interactions) and this value is ecosystemcentered. A species' functional uniqueness depends on the character-istics of other species in its ecosystem. This means a ‘population’ of aspecies – an ecosystem-specific or geographically isolated collectionof individuals of a species – is valuable, and the population level,rather than the species level, is the operational taxonomic unit ofchoice.7 Value also derives from abiotic processes, such as wind andfire, which perform essential ecosystem functions. Thus, althoughreferred to as ‘species’, the ecological approach ranks populations,abiotic processes, and species endemic to one ecosystem.

6 For example, the characteristics of crane species (Gruidae spp.) in Africa reduce thevalue of similar characteristics in North American species (Weitzman, 1993; Solow etal., 1993).

7 For example, Walker (1995, p. 751) suggests the acorn banksia (Banksia prionotes)provides unique services in some ecosystems as the only source of nectar during acritical period but not in others.

482 N. Perry / Ecological Economics 69 (2010) 478–485

The economic approach also focusses on the direct value of speciesand the ecological approach on the indirect value. Under the economicapproach, the extinction of a species leads to the direct loss of its ownvalue. Under the ecological approach, the extinction of a species leadsto the indirect loss of the IUV, NUV, and DUV its community provides.Not every species in the community will become extinct. However,some will, others will reduce in abundance or range, and interactionswill be lost. Thus, EI represents the marginal indirect value of thespecies.8 However, the size of the community or the number ofspecies supported (Ri) only represents the TEV lost upon extinction.To make the EI measure more theoretically correct, we could replacethe square root of Ri with (Vi,t=0−Vi,t=1), the total economic valueprovided by the species' community (including its own value) beforeits removal minus the total economic value after. However, this is notpractical especially when we require rapid assessment of prioritiesand knowledge of a species' value before removal. Thus, Ri representsthe TEV provided by a species' ecosystem and this is justified in thefollowing way.

First, when Ri is large, the IUV (ecosystem services) provided bythe community is also large. Research into the functioning ofecosystems reveals that primary productivity (a proxy for ecosystemservices) increases with the number of species due to both rate andresilience. Any collection of species provides some ecosystem services,even a monoculture. But such ecosystems will not use limitingresources to the fullest extent (Tilman, 1997, pp. 96–104). They willalso be less resilient, which increases the variance of ecosystemservices (ibid., pp. 104–108). Second, a species supporting manyspecies also indirectly provides a great amount of NUV and DUV. Thisargument relies on the notion that a charismatic or distinct species ismore likely to be present in a highly diverse collection (see Tilman(1997, p. 96) for a similar argument related to ecosystem functioningand highly productive species). Finally, it is expected that productivityand resilience increasewith the number of species at a decreasing rate(Tilman, 1997, pp. 95–96). Similarly, diminishing returns are likely forthe NUV and DUV. Hence, I use the square root of species richness inthe numerator of the EI measure.

In general, the ecological approach recognizes that large commu-nities provide more TEV and prioritizes the ecologically importantspecies supporting these ecosystems. That is, it prioritizes specieswith the greatest indirect marginal value. The economic approachprioritizes directly valuable species which provide DUV and NUV butmay aid relatively few other species. In essence, the ecologicalapproach treats the cause of biodiversity loss by preserving theintegrity and stability of ecosystems, while the economic approachtreats the symptom of such integrity losses — the endangerment ofparticular species. The economic outcomes diverge due to thesedifferences.

As a result of neglecting the indirect value of species, the economicapproach does not maximize DUV and NUV. A species with little or nodirect value may indirectly support more DUV and NUV than acharismatic or distinct species and not be targeted (Perry, 1999).Although the economic approach can be theoretically adjusted toaccount for interactions and the indirect value of species usinginteraction constraints or dependence in the survival probabilities(Solow et al., 1993, p. 61; Metrick andWeitzman, 1999; Baumgartner,2004), a suboptimal result still occurs. Because it neglects ecologicalroles, the economic approach does not include populations of speciesand abiotic processes in the analysis. An ecologically importantspecies can be targeted under the adjusted approach if it providesenough indirect value but an indirectly valuable population or process

8 This type of indirect value has been discussed previously in economics. Forexample, Brown (1990, p. 213) and McNeeley (1988, p. 19) discuss the value thatspecies indirectly possess due to the support of other valuable species. Fromm (2000)discusses other related concepts such as contributory value and primary value.

cannot. Nor is it practical to include interaction constraints for everyspecies in each species' ecosystem in the analysis (Mainwaring, 2001,p. 89). For similar reasons, the economic approach does not maximizethe TEV of biodiversity. Targeting a charismatic or distinct speciesmayindirectly provide other economic values but this is unlikely to beoptimal because the effects are not considered.

In contrast, the ecological approach may lead to a greater amountof DUV and NUV than the economic approach. Indeed, somecharismatic and distinct species will be protected if they arefunctionally unique themselves or if targeting ecologically importantspecies improves the integrity and resilience of their ecosystem. Thepresence of a charismatic or distinct species makes it more likely thatecologically important species in their ecosystem will be targeted. Ofcourse, the charismatic species targeted under the economic approachwill not necessarily be indirectly protected under the ecologicalapproach. In particular, the ecological approach will probably notprotect a small ecosystem with an isolated charismatic species.However, economic efficiency requires this; it must be the case that anecologically important species elsewhere supports more TEV. Inaddition, since the economic approach is suboptimal, it may still bebetter overall for DUV and NUV. In the next section, I use an exampleto illustrate these issues concretely.

4. Illustrating the concepts

Consider two species listed under the US Endangered Species Act1973, the Northern spotted owl (Strix occidentalis caurina) and theDelhi Sands ‘flower loving’ fly (Rhaphiomidas terminatus abdominalis).The charismatic Northern spotted owl exists within old-growthDouglas-fir habitat in the Pacific North–West which suffers fromlogging pressure. It provides minimal taxonomic distinctivenessbecause two close relatives are relatively safe, the Mexican spottedowl (Strix occidentalis lucida) and the California spotted owl (Strixoccidentalis occidentalis) (Chapman, 2000, p. 277). It also has little rolein the functioning of its ecosystem (Mills et al., 1993, p. 222) and is notecologically important.

The ecologically important ‘flower loving’ fly exists in a semi-aridsand dune ecosystem in southern California which suffers fromdevelopment pressure (Grandberry and Nagano, 1998, p. 24). Itpollinates native flowering plants using its “long tubular proboscis”(ibid.) and is the only pollinator in its ecosystem. It therefore supportsthese plant species and in turn the unique Delhi Sands ecosystem andthe species using it for habitat, such as burrowing owls (Athenecunicularia) (Longcore, 1997). The fly provides minimal charismaticvalue with segments of the media suggesting the “Feds have gonecrazy” when it was originally listed (Grandberry and Nagano, 1998,p. 24). However, it provides distinctiveness value with its closestrelative almost certainly extinct, the El Segundo ‘flower-loving’ fly(R. terminatus terminatus) (ibid.).

The economic approach focuses on the DUV and NUV provided bythese species only, and in all likelihood will board the charismatic owlon the Ark first.9 The ecological approach changes the conception ofthis choice because it focuses on the indirect TEV provided by species,populations, and processes. It directs Noah to prioritize amongst theendangered ecologically important ‘species’ in each ecosystem.Therefore, Noah will compare the ecological importance of the fly tothe ecologically important species in the owl's ecosystem, theendangered old-growth tree population. The tree population providesa critical and unique function in its ecosystem. For example, incontrast to younger forest, old-growth Douglas-fir trees have fibrous,grainy structures and cavities, which make them perfect for nesting(American Museum of Natural History, 1996). Noah will choose the

9 I assume each species has the same recovery potential per dollar of conservationexpenditure (Δpi/ci) so that the marginal value determines the rank order.

483N. Perry / Ecological Economics 69 (2010) 478–485

tree population before the fly because it supports themost species andTEV due to its functional role.10

The economic outcomes mirror the theoretical discussion above.Firstly, the choice of the owl under the economic approach will notmaximize DUV and NUV because it neglects the large indirect value ofthe fly. Although the owl does have unconsidered indirect benefitsitself because its recovery program establishes Managed OwlConservation Areas within forests (Fish and Wildlife Service, 2007),I assume the indirect value of the fly outweighs the direct and indirectvalue of the owl. Thus, choosing the owl is suboptimal. Theinteraction-adjusted economic approach will correct this anomalyand target the fly first. However, this choice neglects the marginalvalue of endangered populations and abiotic processes and is againsuboptimal. In particular, the old-growth tree population providesmore DUV and NUV in this example. Of course, choosing the tree usesmore of the budget, but the algorithm of the Noah's Ark solutionensures this remains a valid example. Noah must choose the specieswith the greatest marginal benefit per dollar first. Even if enoughfunds remain to save only part of the forest, the tree's marginal benefitper dollar is still greater.11

In contrast, the ecological approach chooses the tree first whichmaximizes TEV and in this example DUV and NUV. In particular, it stillprotects the charismatic owl and other species discussed because theyincrease the value of the ecosystem and the ecological importance ofthe tree. The ecological approach achieves better economic resultsbecause it changes the discourse surrounding the economics ofendangered species conservation from a species-centered to anecosystem-centered approach.12 It will always outperform theeconomic approach unless interactions are weak or non-existent, inwhich case populations and processes have zero indirect value. Thisonly occurs when species exist outside of ecosystems, such as in themythical Noah's Ark story.

5. Implications for endangered species legislation

Any solution to the Noah's Ark problem has implications forendangered species legislation such as the U.S. Endangered SpeciesAct 1973 (ESA) and the administration of the Act through governmentagencies such as the US Fish andWildlife Service (FWS). Together, theESA and FWS have the role of Noah. They set the agenda for allocatingthe limited economic resources available for saving species. Thisoccurs explicitly in the way the budget is allocated for the recovery ofspecies and implicitly because certain species are prioritized at thelisting stage and when critical habitat is designated. The FWS hastraditionally followed the standard economic approach in theirdecision-making. Although the ESA requires the FWS to consideronly scientific factors when listing species, such as species vulner-abilities (Borck, 2005, p. 70), evidence suggests that they prioritizespecies based on their direct economic value (and charisma inparticular). For example, Metrick and Weitzman (1996 p. 14–15)investigate listing and spending patterns under the ESA and findbiases towards charismatic species with “visceral characteristics”playing a particularly strong role in spending decisions (see also

10 Although the fly supports many species, the old-growth tree population supportsthe charismatic owl as well as the threatened marbled murrelet (Brachyramphusmarmoratus), the chinook salmon (Oncorhynchus tshawytscha), the bald eagle(Haliaeetus leucocephalus), the grizzly bear (Ursus arctos), the wolf (Canis lupus) andthe important Pacific yew tree (Taxus brevifolia) (Chapman, 2000, p. 278).11 Note however that I do assume the tree's Δpi/ci equals that of the owl and the fly.Conserving the tree guarantees its probability of survival increases from a very lowlevel to a very high level (more so than any recovery program for the owl or the fly).Thus, a higher numerator and denominator cancel out.12 In our example, this is represented by the difference between the North–Westforest plan (or something even more general) which aims to protect many species byprotecting old-growth forests, and the recovery program for the owl which, in itsobjectives, does not mention the benefit to other species (Fish andWildlife Service, US,2007, p. viii).

Borck, 2005; Czech and Krausman, 2001). In addition, the ESA hasbeen criticized for treating the symptom rather than the cause ofbiodiversity loss. For example, Mann and Plummer (1995, p. 223)suggest the FWS is running “frantically from bedside to bedside,doling out painkillers. Meanwhile, the injured bodies pile up in theemergency room just outside”. Thus, since the ESA and FWS favor theeconomic approach, it is worth investigating the ecological approachas an alternative.

The ecological approach suggests two specific, and fundamental,reformulations of the ESA. These are supported, to some degree, bythe Australian Environmental Protection and Biodiversity Conserva-tion Act 1999 (EPBC), a more preventative Act which neverthelessrequires adjustment. The first issue concerns what can be listed andprotected under the ESA. The ecological approach suggests thatecological processes, species' ecological functions, and ‘populations’ ofall species should be protected under the Act. The ESA only seeks toprotect endangered species, which includes “populations” of “verte-brate fish or wildlife” but excludes populations of invertebrates orplants (section 3(15)). This implies an unwarranted bias towardvertebrate species (Czech and Krausman, 2001, p. 166) and excludesecological processes altogether.

The EPBC is more closely aligned with the ecological approach. Forexample, it seeks to promote “the conservation of biodiversity”(section 3(1)(c)), which includes “species, habitats, ecologicalcommunities, genes, ecosystems and ecological processes” (sec-tion 171(3)). As a result, it allows “key threatening processes” to belisted and eradicated (section 183).13 It also protects “ecologicalcommunities” (section 181), and these explicitly include the interac-tions between its “biological and non-biological components” (regu-lation 7.06). A population of any species can also be protected underthe EPBC (section 528). However, in practice, only four populationshave been listed, two mammals and two fish (Department of theEnvironment, Water, Heritage and the Arts, 2009). This suggests thebias for vertebrate wildlife and fish exists in the administration of theAct which needs to be corrected. The EPBC should also bestrengthened to include positive keystone processes.

The second major issue concerns which ‘species’ are prioritizedunder the ESA. The Act itself makes no formal statement aboutpriorities. However, the FWS officially uses a lexicographic prioritysystem for listing and spending decisions with the highest prioritybeing the degree of threat followed by the recovery potential, thetaxonomic uniqueness of species and, if necessary, the immediacy ofthreat from economic development acts as a tiebreaker (Metrick andWeitzman, 1996, pp. 12–13). The Act should be reformulated toexplicitly consider ecological importance as a variable for makingpriorities. In contrast, the EPBC does mention ecological importancewhen discussing the criteria for accepting recovery plans and listingcommunities (section 274(2); regulation 7.02), although it shouldalso explicitlymention ecological importance as an important variablefor listing decisions (regulation 7.01).

A different paradigm of biodiversity protection based on ecologicalinteractions would solve these problems. The ESA (and the EPBC)should be reformulated as an Endangered Ecological Interaction Act,which would protect abiotic processes and populations of species (toprotect their ecological functions). Related points have been made inthe conservation biology and ecology literature. For example,Simberloff (1998, p. 250) discusses an Endangered Communities orEcosystemAct and Davic (2003, p. 6) discusses the proposed KeystoneSpecies Conservation Act. In ecology, it has long been mentioned thatconservation measures should be aimed at ecologically important orfunctionally unique species (Cousins, 1991, p. 192; Mills et al., 1993,

13 A key threatening process is one that “threatens, or may threaten, the survival,abundance or evolutionary development of a native species or ecological community”(section 188(3)), such as an invasive species.

484 N. Perry / Ecological Economics 69 (2010) 478–485

p. 222). The analysis in this paper supports and extends thesearguments to ecological processes and the explicit conservation ofspecies' functions, and justifies the arguments from an economicperspective.

6. Conclusion

The standard economic approach to endangered species conser-vation views species as ecologically separate units and ranks thembased on their marginal contribution to direct economic value perdollar. A more ecologically enlightened approach views species asvaluable due to the actions they perform in functioning ecosystems. Inaddition, the ecological approach values the functions of abioticprocesses. Using the notion of functional diversity and the Noah's Arkproblem, the measure of ecological importance developed in thispaper extends measures from the biology literature to situationswhere species in different ecosystems can be compared before theirextinction and cost-effective resource allocation matters. To ensurethe integrity of ecosystems and therefore maximize the TEV ofbiodiversity, we must target ecologically important species and createa working ecosystem on the Ark by reformulating endangered specieslegislation to protect ecological interactions.

Acknowledgements

I thank two anonymous referees andmy PhD advisors, Dr John O.S.Kennedy and Dr Iain Fraser, for extremely helpful comments onearlier versions of this paper. I would also like to thank Dr GillianHewitson for her insightful comments on earlier versions, and DrHewitson and Anthony Crawford for engaging and challengingconversations throughout the construction of the ideology andmethodology present in the paper.

Appendix A

To determine the optimal ranking procedure the Lagrangian isformed from Eqs. (7), (8), and (9):

L = EðMÞ + λ B−∑n

i=1ci

pi−−pi−pi−−pi

! !ðA1Þ

where λ is the Lagrange multiplier.For the first-order conditions, the partial derivative of the objective

function (7) with respect to pi is simply Mi becauseMi is independentof the level of pi chosen

∂EðMÞ∂pi = Mi

� �. Thus, the relevant first-order

conditions for the reformulated Noah's Ark problem are the following:

ΔpiðMiÞci

> λ if p⁎i = −pi ∀i∈S

ΔpiðMiÞci

= λ if −pi < p⁎i < −pi ∀i∈S

ΔpiðMiÞci

< λ if p⁎i = −pi ∀i∈S:

ðA2Þ

The first-order conditions compare the marginal benefit per dollarof conservation expenditure to the Lagrange multiplier and can beexplained as follows. If the left hand side of the conditions in (A2) isless than the Lagrange multiplier, it is never optimal to spend on thespecies and optimal pi equals the lower bound pi. If it is greater thanthe Lagrange multiplier, spend on the species until the upper boundhas been reached as long as funds remain. This rule arises because ifΔpiðMiÞ

ci>

ΔpjðMjÞcj

> λ for one level of pi, it will be for all levels of pi sincethe partial derivatives remain unchanged when pi is increased for allspecies. If funds run out before the upper bound has been reached, aninterior solution arises. Because of this, the upper bound will bereached for all but one species, which Weitzman (1998, p. 1287)

refers to as an “extreme policy solution” because the option favored atthe beginning is always favored. Thus, the first-order conditions implythat the size of the following determines the expenditure on species i:

Ranki =ΔpiðMiÞ

ci: ðA3Þ

References

American Museum of Natural History, 1996. Northern Spotted Owl: Strix occidentaliscaurina. Retrieved: June 5, 2003, from http://www.amnh.org/nationalcenter/Endangered/owl/owl.html.

Baumgartner, S., 2004. Optimal investment in multi-species protection: interactingspecies and ecosystem health. EcoHealth 1, 101–110.

Borck, J.C., 2005. Decision-making in endangered species management. Journal ofPublic and International Affairs 16, 70–93.

Brown Jr., G.M., 1990. Valuation of genetic resources. In: Orians, G.H., Brown, G.M.,Kunin, W.E., Swierzbinski, J.E. (Eds.), The Preservation and Valuation of BiologicalResources. University of Washington Press, Seattle, pp. 203–228.

Brown Jr., G.M., Goldstein, J.H., 1984. Amodel for valuing endangered species. Journal ofEnvironmental Economics and Management 11, 303–309.

Chapin III, F.S., Schulze, E.-D., Mooney, H.A., 1992. Biodiversity and ecosystemprocesses. Tree 7, 107–108.

Chapman, D., 2000. Environmental Economics: Theory, Application, and Policy. AddisonWesley Longman, Boston. 415 pp.

Collins, S.L., Benning, T.L., 1996. Spatial and Temporal Patterns in Functional Diversity.In: Gaston, K.J. (Ed.), Biodiversity: A biology of numbers and difference. BlackwellScience, Oxford, pp. 253–280.

Cousins, S.H., 1991. Species diversity measurement: choosing the right index. Tree 6,190–192.

Czech, B., Krausman, P.R., 2001. The Endangered Species Act: History, ConservationBiology, and Public Policy. Johns Hopkins Press, Baltimore. 212 pp.

Davic, R.D., 2003. Linking keystone species and functional groups: a new operationaldefinition of the keystone species concept. Conservation Ecology [Online] 7 (1), r11(Retrieved: December 24, 2005, from http://www.consecol.org/vol7/iss1/resp11).

Department of the Environment, Water, Heritage and the Arts, (Australian Govern-ment), 2009. EPBC Act list of threatened fauna. . Retrieved: January, 17, 2009, fromhttp://www.environment.gov.au/cgi-bin/sprat/public/publicthreatenedlist.pl?wanted=fauna.

Endangered Species Act 1973. U.S. Congress. Retrieved: March 31, 2004, from http://endangered.fws.gov/esa.html.

Environment Protection and Biodiversity Conservation Act 1999. Commonwealth ofAustralia. Retrieved: December 29, 2004, from http://scaleplus.law.gov.au/html/pasteact/3/3295/top.htm.

Fish andWildlife Service (US), 2007. Draft Recovery Plan for the Northern Spotted Owl,Strix occidentalis caurina: Merged Options 1 and 2. . Portland, Oregon, 170 pp.,Retrieved: June 8, 2009, from http://www.fws.gov/pacific/ecoservices/endan-gered/recovery/rec_plan.html.

Fromm, O., 2000. Ecological structure and functions of biodiversity as elements of itstotal economic value. Environmental and Resource Economics 16, 303–328.

Grandberry, S., Nagano, C., 1998. Protecting a flower-loving fly. Endangered SpeciesBulletin 23 (5), 24–25 (Retrieved: June 6, 2009, from http://www.fws.gov/endangered/bulletin/98/09-10/24-25.pdf).

Holling, C.S., Schindler, D.W., Walker, B.W., Roughgarden, J., 1995. Biodiversity in thefunctioning of ecosystems: an ecological synthesis. In: Perrings, C., Maler, K.-G.,Folke, C., Holling, C.S., Jansson, B.-O. (Eds.), Biodiversity Loss: Economic andEcological Issues. Cambridge University Press, Cambridge, pp. 44–83.

Hurlbert, S.H., 1997. Functional importance vs keystoneness: reformulating somequestions in theoretical biocenology. Australian Journal of Ecology 22, 369–382.

Joseph, L.N., Maloney, R.M., Possingham, H.P., 2009. Optimal allocation of resourcesamong threatened species: a project prioritization protocol. Conservation Biology23, 328–338.

Kerkvliet, J., Langpap, C., 2007. Learning from endangered and threatened speciesrecovery programs: a case study using U.S. Endangered Species Act recovery scores.Ecological Economics 63, 499–510.

Kotliar, N.B., 2000. Application of the new keystone-species concept to prairie dogs:how well does it work? Conservation Biology 14, 1715–1721.

Longcore, T., 1997. The endangered Delhi sand dunes. Western Tanager 63 (8), 1–2(Retrieved: June 5, 2009, from http://www.urbanwildlands.org/delhi.html).

Mainwaring, L., 2001. Biodiversity, biocomplexity, and the economics of geneticdissimilarity. Land Economics 77, 79–83.

Mann, C.C., Plummer, M.L., 1995. Noah's Choice: The Future of Endangered Species.Alfred A. Knopf, New York. 302 pp.

Maresova, J., Frynta, D., 2008. Noah's Ark is full of common species attractive tohumans: the case of Boid snakes in zoos. Ecological Economics 64, 554–558.

Martinez, N.D., 1996. Defining and measuring functional aspects of biodiversity. In:Gaston, K.J. (Ed.), Biodiversity: A Biology of Numbers and Difference. BlackwellScience, Oxford, pp. 114–148.

McNeeley, J.A., 1988. Economics and Biological Diversity: Developing and UsingEconomic Incentives to Conserve Biological Resources. IUCN, Gland, Switzerland.236 pp.

Metrick, A., Weitzman, M.L., 1996. Patterns of behavior in endangered speciespreservation. Land Economics 72, 1–16.

485N. Perry / Ecological Economics 69 (2010) 478–485

Metrick, A., Weitzman, M.L., 1998. Conflicts and choices in biodiversity preservation.Journal of Economic Perspectives 12, 21–34.

Metrick, A., Weitzman, M.L., 1999. Reply from AndrewMetrick andMartin L.Weitzman.Journal of Economic Perspectives 13, 239.

Meyer, O., 1994. Functional groups of microorganisms. In: Schulze, E.D., Mooney, H.A.(Eds.), Biodiversity and Ecosystem Function. Springer-Verlag, Berlin, pp. 67–96.

Mills, L.S., Soule, M.E., Doak, D.F., 1993. The keystone-species concept in ecology andconservation: management and policy must explicitly consider the complexity ofinteractions in natural systems. BioScience 43, 219–224.

Nehring, K., Puppe, C., 2002. A theory of diversity. Econometrica 70, 1155–1198.Perrings, C., Maler, K.-G., Folke, C., Holling, C.S., Jansson, B.-O., 1995. Introduction:

framing the problem of biodiversity loss. In: Perrings, C., Maler, K.-G., Folke, C.,Holling, C.S., Jansson, B.-O. (Eds.), Biodiversity Loss: Economic and EcologicalIssues. Cambridge University Press, Cambridge, pp. 1–17.

Perry, N., 1999. Biodiversity preservation. Journal of Economic Perspectives 13,238–239.

Perry, N., 2006. The economics of endangered species conservation: An ecosystemfunction approach. PhD Dissertation, La Trobe University.

Power, M.E., Tilman, D., Estes, J.A., Menge, B.A., Bond, W.J., Mills, L.S., Daily, G., Castilla, J.C.,Lubchenco, J., Paine, R.T., 1996. Challenges in the quest for keystones. BioScience 46,609–620.

Simberloff, D., 1998. Flagships, umbrellas, and keystones: is single-species manage-ment passé in the landscape era? Biological Conservation 83, 247–257.

Solow, A., Polasky, S., Broadus, J., 1993. On the measurement of biological diversity.Journal of Environmental Economics and Management 24, 60–68.

Tilman, D., 1997. Biodiversity and ecosystem functioning. In: Daily, G.C. (Ed.), Nature'sServices: Societal Dependence on Natural Ecosystems. Island Press, Washington,DC, pp. 93–112.

Walker, B.H., 1995. Conserving biological diversity through ecosystem resilience.Conservation Biology 9, 747–752.

Weitzman, M.L., 1992. On diversity. Quarterly Journal of Economics 107, 363–406.Weitzman, M.L., 1993. What to preserve? An application of diversity theory to crane

conservation. Quarterly Journal of Economics 108, 157–183.Weitzman, M.L., 1998. The Noah's Ark problem. Econometrica 66, 1279–1298.