valuing research leads: bioprospecting and the conservation of … · 2002-09-06 · valuing...

Valuing Research Leads: Bioprospecting andthe Conservation of Genetic Resources

Gordon C. RausserUniversity of California, Berkeley

Arthur A. SmallColumbia University

Bioprospecting has been touted as a source of finance for biodiver-sity conservation. Recent work has suggested that the bioprospect-ing value of the ‘‘marginal unit’’ of genetic resources is likely tobe vanishingly small, creating essentially no conservation incentive.This result is shown to flow specifically from a stylized descriptionof the research process as one of brute-force testing, unaided byan organizing scientific framework. Scientific models channel re-search effort toward leads for which the expected productivity ofdiscoveries is highest. Leads of unusual promise then commandinformation rents, associated with their role in reducing the costsof search. When genetic materials are abundant, information rentsare virtually unaffected by increases in the profitability of productdiscovery and decline as technology improvements lower searchcosts. Numerical simulation results suggest that, under plausibleconditions, the bioprospecting value of certain genetic resourcescould be large enough to support market-based conservation ofbiodiversity.

We acknowledge generous financial support from the National Science Founda-tion–Environmental Protection Agency Partnership for Environmental Research,from the Giannini Foundation of Agricultural Economics, and from the Universityof California Systemwide Biotechnology Research and Education Program. We aregrateful for comments from Peter Berck, Ignacio Chapela, Andrew Dabalen, An-thony Fisher, Peter Lupu, Astrid Scholz, Michael Ward, Brian Wright, Joshua Zivin,and an anonymous referee. The work also benefited from feedback by seminar par-ticipants at Berkeley, Columbia, Georgia Institute of Technology, Georgia State,Iowa State, Rutgers, the University of Washington, and the 1997 NSF-EPA Valuationand Environmental Policy Workshop.

[ Journal of Political Economy, 2000, vol. 108, no. 1] 2000 by The University of Chicago. All rights reserved. 0022-3808/2000/10801-0007$02.50

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174 journal of political economy

Biodiversity prospecting, the search for valuable compounds fromwild organisms, has been touted as a potential source of finance forbiodiversity conservation. An open question is whether, or underwhat conditions, revenues from bioprospecting could be largeenough to offset the opportunity costs that host institutions mayhave to incur in order to preserve genetic resources. A recent paperby Simpson, Sedjo, and Reid (1996) argues that the returns to hold-ing genetic resource assets are unlikely to be large enough to createsignificant conservation incentives. The claim is based on a modelof the research process in which firms sample without replacementfrom a large set of research leads, incurring a fixed cost per draw.Two features of the process are key. The first is uncertainty: it is un-known, prior to testing, whether a given lead is good or bad, whetherit will or will not generate a discovery. The second essential featureconcerns the potential for redundancy among the leads. A lead thatenables an innovation may not do so uniquely, just as caffeine canbe found both in coffee and in tea. Under the assumption that agiven discovery can be made only once, multiple copies of a ‘‘poten-tial discovery’’ are, in this sense, superfluous. The authors pose thefollowing question: If it is supposed that each lead carries a fixedprobability of yielding a breakthrough, how much would a privatefirm be willing to pay to prevent the collection of leads from becom-ing slightly smaller? In other words, what is the value of the marginalresearch opportunity, in this research and development process?Formal analysis confirms what intuition suggests: if the original col-lection is sufficiently large, then one additional lead is likely to beeither infertile (if the probability of success per test is very low) orredundant (if the probability of success is sufficiently high). Giventhat the number of species in the world is very large indeed, theexpected return to the ‘‘marginal species’’ is likely to be vanishinglysmall. It will, then, exert no genuine incentive toward conservation,in the context of a market for genetic resources. Extensions to casesin which discoveries vary in quality or in which success rates covaryaccording to an average degree of genetic distance (Polasky and So-low 1995) generate somewhat higher values but do not alter the sub-stance of this conclusion.

The result is intriguing. We argue in this paper, however, that itflows specifically from a stylized description of the research processas one of brute-force testing, unaided by an organizing scientificframework. Given the progress of biological and ecological science,the realism of this assumption is suspect. While exceptions can benoted, it is a powerfully general rule that no one ever searches foranything by examining large collections of objects in random order.The essence of efficient search is the identification of clues that allow

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the universe of potential leads to be narrowed down. Expensive testsare then conducted, ideally, only on that handful of prospects thatshow special promise. In research targeting the development of in-novations, the clues that identify these prospects are provided byscientific models—maps of the world that highlight areas in whichthe productivity of research effort is likely to be highest. The abilityof models to point out rich veins of ore explains exactly why appliedresearchers acquaint themselves with basic theory. It is substantiallyfrom this ability that the human capital of an applied research scien-tist derives its value. Brute-force search—the sequential testing oflarge numbers of leads in no particular order—is by contrast a nearlycost-maximizing approach to discovery. It is deployed, if at all, onlyas a backstop technology, when all possibilities for directed searchhave been exhausted.

Theory, in other words, partitions collections of potential researchprojects into categories of greater and lesser expected quality. A use-ful model thereby converts leads from commodities into differenti-ated products. The market for research opportunities shifts from apurely competitive to a monopolistically competitive structure. Thischange has profound implications for the valuation of leads and,therefore, for the incentives surrounding their production or con-servation. In particular, leads of unusual promise can be shown tocommand information rents associated with their role in reducingsearch costs. A private firm will be willing to pay a premium for accessto a bin of promising leads in order to avoid the cost of pickingthrough the mass of low-quality prospects, even if the low-qualityones are available at bargain prices.

The point is clarified by pursuing the metaphor of applied re-search as an extractive industry. Imagine that technologies aremined from a landscape marbled, unevenly, with patentable discov-eries. Innovations could, in principle, be uncovered by digging with-out pattern or purpose, just as oil could be sought by sinking wellsat randomly chosen sites. Provided that the domain of explorationis large enough, undistinguished areas will not, for this purpose, bea scarce resource: one site is about as good as any other.

In practice, of course, the right to drill for oil can command largerents. These rents depend partly on the price of oil and are partlya function of the prior information available about the stake. If oilhas been found nearby or if the geological structures are promising,then this intelligence raises prospectors’ willingness to pay. Indeed,if the market for extraction services is competitive, then the rentaccruing to the high-quality site should reflect, approximately, theamount of search and processing costs a firm avoids by focusingthere rather than on an inferior ‘‘average’’ site.


When genetic materials are viewed as candidate sources for newproducts, this image can be applied to bioprospecting. In this en-deavor, leads of unusual promise are distinguished with the aid ofscientific information gleaned from fields such as ecology and taxon-omy. Researchers can, and do, draw on rich bases of publicly avail-able data describing the location and properties of plants, animals,and microbes, their evolutionary history, and their survival and re-productive strategies. These data, when filtered through a modelthat makes sense of them, can serve to tag those creatures most likelyto display economically valuable characteristics. Just as a cataloghelps a library patron to focus quickly on those few volumes that aremost likely to contain information she desires, so can an ecologicalmodel parse the living world into categories suggesting potentialuse.

Through product differentiation, scientific understanding gener-ates information rents: if a particular lead is believed to show prom-ise as an aid to a lucrative research discovery, a rational investigatorwill be willing to pay an access fee. This principle is fundamental tounderstanding how genetic resources will be, or should be, valuedin the marketplace. In particular, it is central to an analysis that iden-tifies conditions under which bioprospecting creates effective mar-ket-based financial incentives for biodiversity conservation. Rents ac-crue to the owners of leads as they absorb part of the knowledgespillovers generated by publicly available science.

To structure this theme formally, we present a model of appliedresearch in which leads are differentiated by their expected qualityand then tested sequentially. A complete characterization is devel-oped of the relationship between the costs and benefits of research,the degree of product differentiation, and the value of options onresearch leads. The value of a lead is shown to be driven almostentirely by its probability, relative to alternative options, of generat-ing success and by the costs of search. Surprisingly, the value islargely insensitive to the size of the payoff from a successful discov-ery. This payoff does, of course, affect the overall value of the searchproject to the researcher. However, as long as the jackpot is largeenough to make the project a viable undertaking, additional in-creases have almost no effect on the rents accruing to research leads.Furthermore, a technology shock that lowers search costs actuallydecreases these values: since the amount of a lead’s rent reflects whatit contributes, in expectation, to reducing the costs of research, adrop in the price of brute-force testing shrinks the benefits of guid-ance.

The balance of the paper is divided into four sections. Section Iexamines evidence on the pivotal question of whether bioprospect-


ing benefits from scientific prior information. The biological litera-ture and the behavior of industry actors are shown to support theclaim that bioprospecting takes generous advantage of a significantbase of useful scientific guidance. Section II presents the model, ana-lyzing the effect of product differentiation on the value of researchleads. Section III addresses the empirical question of whether infor-mation rents associated with genetic resources might be largeenough to play a significant role as a source of finance for biodiver-sity conservation. Numerical results indicate that, under plausibleassumptions concerning the demand for discoveries and costs oftesting in the pharmaceutical industry, high-quality leads could com-mand rents large enough to tilt land use decisions toward conserva-tion. Section IV addresses the implications of the argument for thedesign of intellectual property rights and other institutions govern-ing the market in genetic materials. Mathematical proofs and ananalysis of the model’s robustness are presented as appendices.

I. Availability of Prior Information forBioprospecting: Evidence from Biology andEconomic Behavior

A market in genetic resources will appear only if the expected bene-fits of conservation exceed the opportunity costs of holding theseassets. While costs can be measured more or less directly (as a func-tion of forgone logging profits and the like), benefits must be esti-mated using indirect methods. Theoretical approaches to valuingnatural intellectual capital have been investigated by Brown andGoldstein (1984) and Heal (1995). The R & D option value of biodi-versity has also been addressed at the microeconomic level of singlespecies by Weisbrod (1964) and Arrow and Fisher (1974). Nonethe-less, few empirical estimates have appeared in the formal economicsliterature.

Studies that find low values for genetic resources in situ share incommon an assumption that the materials are, in their role as inputsto the innovation process, essentially fungible. Every ‘‘unit’’ of bio-diversity is viewed as making an equal marginal contribution to thesuccess of the bioprospecting enterprise; one species is about asgood as any other. We claim that this assumption matters. Do bio-prospectors actually treat different types of genetic materials as per-fect substitutes for one another? This factual issue is most appropri-ately resolved by specialists in biology and in related technologyindustries.

In the published writings of these specialists, the economic utilityof organisms appears as a topic of lively discussion, attracting contri-


butions from ecologists, systematicists, evolutionary biologists, andethnobotanists. Their findings occupy several journals, includingsuch titles as Economic Botany, Journal of Ethnopharmacology, and Jour-nal of Natural Products. One active line of inquiry concerns how theevolutionary histories and survival strategies of species relate to thekinds of useful compounds they may produce. Plants, for example,appear in general to be more chemically creative than animals. Un-able to respond to predatory attacks by fleeing, plants have insteaddeveloped a wide array of complex chemical means of defense.These strategies are especially well developed in deserts, rain forests,and coral reefs—zones of ‘‘biological warfare’’ in which biotic andenvironmental stresses are particularly acute (Myers 1997). Such ob-servations can be valuable: a fern that prospers in a region richlypopulated with insects may have evolved pest-control solutions thatwould impress the research staff at an agrochemicals firm. Otheruseful environmental indicators can be quite taxonomically specific.Frogs, lacking a hard defensive shell, make themselves unappetizingby secreting toxins prolifically. Abbot Laboratories reportedly has aproject underway to synthesize a painkiller based on a toxin fromthe threatened Ecuadorian poison dart frog (Sawhill 1998). In an-other case, an anticoagulant approved for human trials was devel-oped after screening venom from only 70 species of snakes (Pollak1992). Natural-products researchers are moving to organize knownecological and taxonomic indicators of utility into comprehensivemodels in order to provide systematic guidance to the drug discoveryprocess (Dreyfuss and Chapela 1994). Pursuing this approach, No-vartis Pharmaceuticals is reportedly spending several million dollarsin the attempt to identify observable factors that correlate with thebiochemical ‘‘creativity’’ of microorganisms, that is, their fertility assources of molecules that could form the basis for new drugs(Moeller 1996).

Clues based on general biological observations and formal modelscan be supplemented by indications gleaned from the historic rec-ord of product discovery. Many natural-products scientists hold thatclasses of organisms that have proved useful in the past are relativelylikely to provide similar compounds for related uses (Phillips andMeilleur 1998). The rosy periwinkle, a flowering plant native to EastAfrica, has already produced two anticancer drugs, vincristine andvinblastine (Reid et al. 1993). The Himalayan yew tree is now theprimary source of another anticancer drug, taxol, that was originallysourced from its North American cousin, the Pacific yew. Indeed,some firms base their entire product discovery programs on lev-eraging the experience of traditional healers concerning the thera-


peutic properties of plants used in herbal medicine. Such historicalclues need not be based only on taxonomic similarity. Certain geo-graphic regions have particular prominence as sources of valuableresearch leads, functioning as ecological Silicon Valleys. Tradition-ally cultivated varieties of domesticated crop plants and their wildrelatives, which are especially important sources of agronomicallyuseful genes, for example, are not distributed uniformly on theglobe. Instead, they are concentrated in relatively compact ‘‘centersof diversity,’’ usually mountainous areas in which species adapt lo-cally to a fragmented set of agroclimatic conditions (Chrispeels andSadava 1994).

The suggestion that bioprospecting is a targeted, rather than hap-hazard, activity is confirmed by the behavior of industry actors. Ifevery organism was in fact an equally promising source of any givencompound, then we might expect to see search projects spread moreor less evenly across the globe. The industry’s interest in the hotsprings at Yellowstone National Park provides a singular counterex-ample. The U.S. National Park Service now grants about 25 permitsannually for the right to collect biological samples from this ecosys-tem (Pennisi 1998), which is distinctive both for its link to the valu-able polymerase chain reaction technology and as home to the mostgenetically diverse community of bacteria known to science (Pace1997). This degree of localized interest is apparently inconsistentwith a hypothesis that natural-product potential follows a geographi-cally uniform distribution (Polasky and Solow 1995).

If the hypothesis were nonetheless to be entertained, any observedclustering would have to be explained by differentials in the cost ofcollecting and evaluating samples from different regions. The loca-tion of a collection site would be explained largely by variables suchas distance to the firms’ R & D labs, ease of access, and so on. Inaddition, we would expect the market for samples to be almostpurely competitive, with all rents accruing to the innovating firms.These outcomes do not appear to obtain in practice. Bioprospectingfirms have shown a durable willingness to mount expensive collec-tion efforts in remote but ecologically distinctive locations, includingunderseas. To gain admittance to these areas, they are now com-monly compelled to spend a great many staff hours negotiating ac-cess contracts with host country governments and their agents. Un-der these agreements, firms routinely forfeit shares in the profitsarising from their product discovery efforts. The firms, one pre-sumes, believe that they are getting something in return for theseresources. Their behavior cannot readily be explained by a modelthat assigns equal promise to every species and region.


II. A Model for Valuing Research Leads

In sum, the claim that bioprospecting is always conducted in brute-force fashion in an impoverished informational context does notappear to withstand close scrutiny. It remains to be shown whetherthis simplification is benign or leads to a fundamental misspecifica-tion of the value of genetic resources in their role as research op-tions.

The theory of valuing search options seems to have received littleattention in the economics literature, particularly in the context oftechnology development. Search theories developed within eco-nomics (Lippman and McCall 1979) and elsewhere (DeGroot 1970;Stone 1975) have focused on the identification of optimal selectionand stopping rules (Weitzman 1979) and on how these rules areaffected by changes in various parameters (the probability distribu-tions of rewards, agents’ appetites for risk, time preferences, Bayes-ian updating, etc.). Further, much of this work is based on an as-sumption that rewards per trial are identically distributed or thatthe number of search opportunities is unlimited (Kohn and Shavell1974). Interactions between the size of the search space and thedegree of quality differentiation among search opportunities haveapparently not been investigated.

To address the question, we analyze a simple model of the appliedresearch process. Research opportunities appear as lottery tickets,each characterized by a price (the cost of testing), a probability ofwinning, and a jackpot that is paid in the case of a lucky draw. Theinvestigator ranks tickets by quality and then draws them one at atime until she either wins the prize or exhausts her supply. The focusis on the investigator’s willingness to pay for an additional ticket ofa given quality. Formally, the model generalizes that of Simpson etal. (1996) by allowing success probabilities to differ across leads. Themodel also echoes the representation by Evenson and Kislev (1976)of applied research as an act of repeated sampling from a knowndistribution, the parameters of which can be changed through basicresearch.

A. The Model

An investigator conducts a search for a compound that will makepossible the development of a new product. Research is conductedby testing ‘‘leads.’’ There are a large number N of leads available,each of which embodies some potential to yield a discovery. Dataare available that describe leads in several dimensions: to each leadn 5 1, . . . , N, there is associated a vector xn ∈ X , where X is a


space of characteristics. The investigator filters these data througha model, represented by a function P : X → (0, 1), to estimate theprobability that a test of a lead with a given set of characteristics willgenerate an enabling discovery. Both the theory and the data areavailable freely, as public goods. (The investigator’s costs of usingthese resources to formulate her beliefs are considered to be small,relative to the costs of testing leads and the potential benefits of adiscovery.) The collection of leads is then treated as a set of N Ber-noulli trials, in which the nth lead carries probability pn 5 P(xn) ofyielding a success, or ‘‘hit.’’ Without loss of generality, leads are la-beled in order of decreasing hit probability, so that p 1 $ ⋅ ⋅ ⋅ $ p N.The hit probabilities of different leads are assumed to be statisticallyindependent. It is not assumed that the collection of leads containsexactly one discovery; it is also possible that the discovery is presentin multiple copies or not at all.

The investigator tests leads sequentially, at a cost c per test, wherec is a positive constant. When a test is successful, a payoff R is realized.It is assumed that a discovery need be made only once; multiple hitsare redundant. The sole behavioral assumption is that the investiga-tor selects the order in which she tests leads so as to maximize theexpected payoff to the project.

Given our assumptions about the incentives facing the biopros-pecting firm, its behavior is characterized by the following result, asimple application in the theory of search.

Proposition 1. An optimal search program involves testing, ateach stage, a lead with maximal hit probability among those not yetexamined. Search terminates either when a hit is reached or whenno leads remain for which testing promises a nonnegative return inexpectation.

In other words, optimal search involves checking the most promis-ing leads first—an intuitive and well-known result (Weitzman 1979).

All proofs are included in Appendix A.In light of the result, the probability ordering (p 1, p 2, . . . , pN)

determines the sequence in which leads are examined.1 The stop-ping rule implies that leads for which p n , c/R are never testedunder any conditions and have no effect on search behavior or pay-offs. Without violence to our results, therefore, we assume in whatfollows that pn $ c/R for all n .2

1 More exactly, the probability ordering determines the search queue up to a per-mutation of leads with equal hit probabilities. Such permutations have no effect onlead values or on aggregate returns to research (corollary 1).

2 Alternatively, the stopping rule can be interpreted as defining endogenously theeffective number of available leads. If N denotes the total number of potential leads,then N # N can be defined as the largest integer such that p N $ c/R .


Given optimizing behavior, a value function can be derived thatgives the expected payoff of the search at each stage, conditional onresults at previous stages. Let Vn denote the ex post expected valueof continuing the search after n 2 1 leads have been tested unsuc-cessfully. When Bellman’s principle of optimality is applied, this con-tinuation value is characterized by the recursive relationship

Vn 5 pn R 1 (1 2 p n)Vn11 2 c, n 5 1, . . . , N, (1)

where VN11 ; 0. The equation can be interpreted as follows. Withprobability pn, the n th test is successful, a payoff R is realized, andsearch terminates; with probability 1 2 p n, the test is a failure, andsearch proceeds to the n 1 1st lead. The ‘‘consolation prize’’ in caseof failure is the opportunity to continue the search with the n 1 1stlead, the value of which is, by definition, Vn11. In either event, a costc is incurred for the test. The expected payoff to the search at itsoutset is then given by

V1 5 ^N

n51

a n(pn R 2 c), (2)

where a n ; ∏n21i51 (1 2 p i) is the probability that the search is carried

to the n th stage, that is, the probability of failure in each of the firstn 2 1 tests; and pn R 2 c is the expected return to a test of the n thlead. Here, a n p n is the probability that search terminates with a suc-cess at the n th lead. If we treat the event ‘‘the project fails’’ as anN 1 1st lead, then the vector ⟨a 1 p 1, . . . , a N p N, a N11⟩ forms a probabil-ity distribution over the set {1, . . . , N, N 1 1}, with associated payoffs⟨R 2 c, R 2 2c, . . . , R 2 Nc, 2Nc⟩. Specifically, this is a truncatednonhomogeneous geometric distribution, where ∑n

i51 a i p i 5 1 2 a n11

gives the cumulative probability distribution. This relation can beused to express V1 as a difference between expected benefits andcosts:

V1 5 ^N

n51

a n p n R 2 ^N

n51

a n c 5 (1 2 a N11)R 2 Tc . (3)

The first term denotes the ex ante expected benefit of the project:the probability 1 2 a N11 of a successful conclusion times the payoffR if a hit is scored. The second term denotes the ex ante expectedcost, expressed as the expected number T 5 ∑ a n of trials carriedout times the cost c per trial.

Using equation (2), we can derive an expression for the expectedincremental contribution of the n th lead to the overall value of the


search. Define V2n as the expected value of the search process, forthe case in which the n th lead is skipped:

V2n 5 ^n21

i51

a i(p i R 2 c) 1 a n Vn11. (4)

The incremental value of the n th lead, denoted vn, is defined as thedifference between these two terms:

v n ; V1 2 V2n 5 a n[p n(R 2 Vn11) 2 c]. (5)

The value vn can be viewed as the maximum a firm will be willingto pay at the start of a search project for a call option on the n thlead. The option ensures that the lead will be available if it shouldbe needed, that is, if all tests of more promising leads end in failure.The formula is interpreted as follows: With probability a n, the firstn 2 1 tests are unsuccessful and search proceeds to lead n, whichis tested at cost c. With probability pn, this test is successful, a rewardR is realized, and search terminates. The effective payoff in this caseis, however, net of the continuation value Vn11 that would have ap-plied if the search had instead been forced to skip the n th lead.That is, since multiple discoveries are redundant, a success at the n thstage destroys the value associated with the opportunity to continuesearching.

Because a portfolio of leads may contain multiple copies of a givenpotential discovery, the expected value of the project does not equalthe sum of the values of the leads. Indeed, ∑ v n 5 V1 2 ∑ a n pn Vn11;the sum of lead values equals the expected value of the project lessthe expected ‘‘redundancy cost’’ that a discovery at one lead imposeson the others. The latter term is analogous to the social welfare costassociated with redundant R & D programs in patent races.

B. The Value of Research Leads: Scarcity Rents andInformation Rents

If a lead might merely duplicate another one in the portfolio, howdoes it add value to a research project? For leads that are unusuallypromising, early, high-probability options contribute more than theothers to the chance of an eventually successful outcome forthe project. As repeated failures push investigators to pick throughlower-grade ‘‘ore,’’ it becomes increasingly unlikely that a hit willever be scored. More important, the opportunity to focus initial re-search effort on the high-quality leads increases the chance that adiscovery will be made early in the process. If there is an early discov-ery, the costs of continued search are avoided. If high-quality leads


are removed from the menu of search options, the shift to low-qual-ity sources implies an increase in the expected number of trials todiscovery.

Intuition behind the argument can be strengthened by examiningequation (3). Deleting a lead from the search queue raises a N11, theprobability that the project ends in an expensive failure. In addition,removal of a high-quality lead can increase the expected length(hence cost) of the search, an effect represented by an increase inT. Both effects are more pronounced for leads early in the searchqueue. This holds because these leads, if available, are more likelyto be tested. Removal of leads toward the back of the queue has aneffect on search payoffs only in cases in which all early tests end infailure.

In sum, when search procedures are optimized to incorporate use-ful prior information, high-probability leads command informationrents associated with their unusual contribution to the chance ofsuccess and to the avoidance of search costs. These informationrents apply in addition to any scarcity rents resulting from a limiton the total number of leads. This distinction between scarcityand information rents is formalized in the following proposition,which characterizes completely the relationship between the costsand potential benefits of search, the quality of available informa-tion, and the value of differentiated search opportunities. Here,a lead n is referred to as marginal if its hit probability is equal tothat of the lowest-quality viable alternative, that is, if p n 5 p N 5min{p i |p iR 2 c $ 0, i 5 1, . . . , N }.

Proposition 2. Let {pn}Nn51 be the sequence of hit probabilities on

a collection of leads, indexed in order of decreasing probability. Letthe incremental value v n of the n th lead be defined as in (5) above.Then vn can be decomposed into components vn 5 v n 1 v N, where

v n ;a N

1 2 pn

(pn 2 p N)R 1 3 ^N21

i5n11

a i

1 2 p n

(pn 2 p i)4c (6)

and where vN 5 a N(pN R 2 c) is the value of a marginal lead. Werefer to these components, respectively, as the information rent andthe scarcity rent of lead n .

A lead’s scarcity rent can be interpreted as the expected amountit would contribute to the value of the project if it were undistin-guished from the mass of other leads and was, therefore, a perfectsubstitute for any other marginal lead, ex ante. Scarcity rents can bepositive if the project is constrained by a technical bound on thenumber of feasible research opportunities, that is, if N is finite, and


if marginal leads carry a positive expected return (pN R 2 c . 0), sothat random screening is, in expectation, profitable.

The information rent captures the degree to which a distinguish-ing prior increases a lead’s expected incremental value. The expres-sion for v n can be interpreted with the aid of a thought experiment.Suppose that a researcher who is seeking a treatment for musclespasms learns that people of a particular location, when thus af-flicted, boil the roots of a certain plant to make a tea that is locallyrenowned for its soothing powers. Although she had planned to visitthe area eventually to conduct random screening of samples, shehad previously thought it unpromising for her purpose, assigningit the lowest probability, pN. On hearing the news, she raises herexpectation that the region will provide what she seeks, increasingher prior to p n . pN. She also rearranges her search queue so thatthe area now occupies the prominent n th position on her itinerary,where n , N. What effect does the change in her prior entail forher expected return to the research project?

There are two effects. First, there is an increase in the expectedprobability that she will find what she seeks before exhausting allher leads. The amount of the consequent rise in expected benefitsis represented by the first term in the expression for v n, the probabil-ity a N/(1 2 p n) that no other lead contains the discovery times theincrease in the expected benefit of testing this remaining lead. Sec-ond, if this n th test is successful, then she will have avoided the costof visiting at least some of the leads that now occupy positionsn 1 1, . . . , N 2 1. The second term in the expression for v n repre-sents the drop in her expected costs of search.

As the discussion makes clear, the magnitude of the informationrent associated with a given lead depends not only (or even primar-ily) on the lead’s own hit probability but also on how this value com-pares with those of other leads. The reason is that a lead’s hit proba-bility determines not only the chance of a successful test but also itsposition in the search queue and, therefore, the probability that itwill ever be tested at all.

C. Resource Abundance, Research Costs and Payoffs,and Resource Value

Under what conditions are information rents large enough to carrysignificant weight in land use and conservation decisions? In particu-lar, can genetic resources have significant value, in their role as bio-prospecting search opportunities, even when genetic materials areabundant? The characterization of information and scarcity rentsallows several general results to be proved that bear on these ques-


tions. It is shown that when research payoffs are large and resourcesare abundant, conservation incentives are driven almost entirely bythe magnitude of search costs and the quality of available informa-tion. They depend only weakly on the potential returns to the re-search project. In these cases, the size of the payoff will be importantfor a firm undertaking the research but will have little effect on thatfirm’s willingness to pay for access to resources. It has, therefore,little bearing on conservation decisions.

Inspection of the formulas in proposition 2 shows that scarcity andinformation rents have nonnegative values (v N $ 0 and v n $ 0 for alln) and that marginal leads command zero information rents. Moreimportant, it confirms the claim advanced earlier that leads of un-usual promise have strictly greater value than their less promisingneighbors.

Corollary 1. For all m, n 5 1, . . . , N, if p n 5 pm, then vn 5 vm;and if p n . pm, then vn . vm. Hence the sequence {v n} is monotonedecreasing. In particular, information rents are everywhere zero ifand only if all priors are equal.

The intuition is straightforward: since a lead’s incremental valueis defined as the difference in expected returns with the lead andwithout it, the removal of any two leads with equal probability willyield the same effect on project returns.

The comparative static effects on lead values of changes in theparameters describing search benefits and costs can also be exam-ined. To facilitate the discussion, let B n ; [a N/(1 2 pn)](p n 2 p N)R ,the first, ‘‘benefit-increasing,’’ term in equation (6). Note that thepayoff R from a success enters into the expression for vn onlythrough v N and B n and that both these terms are linear in a N, theprobability of reaching the last lead in the search queue. Since pn $c/R for all n, a N is bounded above by [1 2 (c/R )]N21, which becomessmall as N grows large. Hence, the size of project rewards has onlya limited effect on lead values, a claim formalized in the followingresult.

Corollary 2. The effect on lead values of a change in researchpayoffs R is given by

∂v n

∂R5 a N111 pn

1 2 pn2.

Hence, ∂vn/∂R is strictly positive and is independent of R and c . Forpn # 1/2, it is bounded above by a N11, the probability of project failure.

The expression for ∂vn/∂R can be interpreted as follows. An in-crease in project rewards raises a lead’s value only in proportion tothe probability that the lead contains the discovery uniquely (i.e.,


in proportion to pn, the probability of success at lead n, timesa N11/[1 2 pn], the probability that tests at all other leads would re-sult in failure). In particular, when the expected probability of aneventual discovery is high (a N11 < 0), lead values are largely insensi-tive to changes in the project payoffs. This result may seem counter-intuitive; one might expect that large increases in potential projectrewards would generate substantial increases in the value of a chanceto realize those rewards. To understand the result, it is importantto distinguish sharply between the project’s overall value V1 and theincremental contribution to that value of any one lead. By equation(3), the overall value of the project increases linearly with R . Theshare of this surplus accruing to the leads is affected, however, bythe potential presence of duplicate discoveries in the portfolio. Inan extreme case, the space of viable options may be sufficiently largethat eventual discovery becomes virtually certain. In this case, thefirm assurance of realizing the discovery is unaffected by the loss ofany single lead. If the project’s payoff increases (e.g., if demand fora target drug rises), the associated increase in surplus accrues tothe firm’s research capacity, not to the leads. The precise value ofa lucrative discovery has, then, little bearing on incentives to con-serve the resource.

Note, however, that the ‘‘cost-reducing’’ term

^N21

i5n11

a i

1 2 pn

(p n 2 p i)c

in (6) remains positive even if there are many viable leads. Indeed,this term is increasing in N : as the haystack grows, information onthe whereabouts of the needle becomes increasingly valuable. Thisobservation is fundamental to the relationship between search costsand lead values.

Corollary 3. The effect on lead values of a change in searchcosts c is given by

∂v n

∂c5 ^

N21

i5n11

a i

1 2 p n

(pn 2 p i) 2 a N.

This rate of change is independent of research costs c and payoffsR . Furthermore, an increase in search costs makes the n th lead morevaluable if and only if p n . 1/Tn, where Tn 5 ∑N

i5n (ai/a n) is theexpected number of trials conducted after n 2 1 failures.

Roughly speaking, the condition in the last sentence applies when-ever a lead is ‘‘much better’’ than those in a large pool of alterna-tives. It suggests a second surprising result. Intuitively, we might ex-


pect the value of a search opportunity to decrease with any rise inthe unit cost of search effort. Such a change, after all, decreases theexpected return to any trial. However, for the relatively promisingleads, there is a second, countervailing effect. As shown in proposi-tion 2, a large fraction of the value of these leads is associated withtheir potential help in avoiding the costs of resorting to low-qualityalternative sources. Conversely, as unit search costs decline, thevalue of this ‘‘competitive advantage’’ is eroded: brute-force searchbecomes an increasingly viable alternative to directed search. Hence,an improvement in search technology increases (weakly) the valueof the lowest-quality leads but can reduce the value of high-qualityleads.3

As viable search opportunities become increasingly abundant,these counterintuitive features of the value function become domi-nant. To show this, consider the case in which there are a relativelysmall number of leads known to be especially promising and a largernumber that share an ‘‘average background’’ probability of makinga discovery at a lead sampled at random from a large pool of poten-tial sources. Concretely, let M ,, N be given, and suppose that p M 5p M11 5 ⋅ ⋅ ⋅ 5 pN 5 p, where p is a constant such that pR 2 c $ 0;and suppose that pn . p for all n 5 1, . . . , M 2 1. We refer to leads1, . . . , M 2 1 as ‘‘promising,’’ whereas leads M, . . . , N are called‘‘marginal,’’ as above. The following proposition characterizes thevalue of genetic materials as marginal leads become abundant, thatis, as N grows without bound.

Proposition 3. Let leads 1, . . . , M 2 1 be promising and leadsM, . . . , N be marginal, as defined above. Then for n 5 1, . . . , M 21, the incremental value vn has a strictly positive lower bound givenby the relation

vn $ 3 ^M21

i5n11

a i

1 2 pn

(p n 2 p i) 1a M

1 2 p n

⋅pn 2 p

p 4c.

Further, this relation becomes an equality in the limit as N → ∞.

3 Some readers have questioned whether combinatorial chemistry, the massivelyparallel engineering of drug candidates, constitutes a brute-force approach to dis-covery that renders bioprospecting obsolete. In practice, combinatorial chemistryrarely involves a truly random search through the set of all possible molecules; theset of configurations is simply too vast. Instead, the approach usually starts from acompound that has shown some activity against a target disease and looks for varia-tions that generate superior responses. Rather than supplanting bioprospecting, thetechnique’s ability to refine the activity of naturally produced compounds arguablycomplements bioprospecting’s potential role in the production of pharmaceuticaldiscoveries.


Accordingly, a lead that is worth testing at all and is more promis-ing than at least some of its ‘‘competitors’’ commands a rent thatis strictly positive and bounded away from zero. Note that the bounddoes not depend on the degree of resource abundance N. Nor doesit depend on the potential reward R beyond a threshold level ofproject viability. The bound can be interpreted as the ex ante reduc-tion in search costs associated with the opportunity to test the n thlead before moving on to the pool of less promising sources, a poolthat includes an infinite number of leads with hit probability p. Thusit depends only on search costs and prior information. (Again, weassume away the trivial case in which one or more leads contain thediscovery with certainty.) The final claim of the proposition, con-cerning the limiting behavior as N → ∞, implies striking results aboutthe value of genetic resources under conditions of abundance.

Corollary 4. Let leads 1, . . . , M 2 1 be promising and leadsM, . . . , N be marginal, as defined above. Suppose that the payofffrom a successful discovery is large enough to make random sam-pling of marginal leads profitable in expectation (R $ c/p). Thenas leads become abundant (in the limit as N → ∞), the followingclaims hold: (1) Marginal leads have zero value. (2) An increase inthe potential profitability of product discovery has no effect on theincremental value of any lead. (3) A technology improvement thatlowers search costs induces a drop in the incremental value of everypromising lead.

If search opportunities are in effectively unlimited supply, scarcityrents are negligible. In this case, the value of a lead is, to a very goodapproximation, entirely a function of the quality of information asso-ciated with it. The composite good (material plus information) en-hances the profitability of the project not so much by creating suc-cess as by aiding the avoidance of failure.

D. The Effects of Basic Scientific Research

Improvements in ecological, taxonomic, and ethnobotanical knowl-edge can change researchers’ beliefs about lead values. The nexttwo propositions clarify the magnitude of this effect. In particular,it is shown that lead values respond to changes in scientific informa-tion in a continuous manner. The avoidance of search costs pro-vides, therefore, a robust criterion for the valuation of researchleads.

Proposition 4. The value of a lead is a piecewise-linear, continu-ous, increasing, and weakly convex function of its own hit probabil-


ity. Furthermore, on the interval p n21 . p n . p n11, the elasticity ofv n with respect to p n is given by

∂vn

∂p n

⋅pn

vn

5 1 1a n c

vn

.

Interpreting the elasticity formula, we see that the twin effects ofvalue enhancement and cost reduction are identified. A pair of anal-ogous results characterizes the effect of changes in hit probabilitiesfor other leads.

Proposition 5. The value of a lead is a piecewise-linear, decreas-ing function of the hit probability of every other lead. For m ≠ n, vn

is continuous in pm except where pm 5 pn. Furthermore, the follow-ing claims hold: (i) For m 5 1, . . . , n 2 1, on the intervals pm21 .p m . pm11, the elasticity of v n with respect to pm is given by

∂vn

∂p m

⋅p m

vn

5 2pm

1 2 pm

.

(ii) For m 5 n 1 1, . . . , N, on the interval p m21 . pm . pm11, theelasticity of v n with respect to pm is given by

∂vn

∂pm

⋅pm

vn

5 2pm

1 2 pm31 1 1a n 2 p n ^

m

i5n11

a i

1 2 p n2 c

vn4 .

The form of the equation in point i reflects the fact that, condi-tioned on the superiority of lead m over lead n, a further increasein p m reduces the chance that lead n will ever be tested. (It is interest-ing to note that this effect depends only on the magnitude of pm,and not on the position of m in the list 1, . . . , n 2 1.) For m . n,an increase in p m reduces the perceived probability that, if the n thlead provides a success, then it would have done so uniquely. It alsoreduces the expected cost savings associated with the opportunity totest the n th lead before the m th.

The claims in propositions 4 and 5 are conditioned on constraintsin the ordering of the search queue. It turns out that the qualitativeresults do not depend on this restriction. The effect of improvedscientific information on the value of research leads can be summa-rized in a simple form.

Corollary 5. An increase in the hit probability of a lead inducesa more than proportionate increase in the value of that lead and adecrease in the value of every other lead.

This corollary implies in turn that the bound described in proposi-


tion 3 applies to all probability orderings (and not just in the specialcase for which hit probabilities are constant for all but a few superiorsites).

Corollary 6. Let {pn}Nn51 define a probability ordering for the bio-

prospecting problem, and let p be a constant with 1 . p $ p N. LetM 5 M(p) 5 min{m |p m # p}. Then for n 5 1, . . . , M 2 1, theincremental value vn of lead n has a strictly positive lower boundgiven by

vn $ 3 ^M21

i5n11

a i

1 2 pn

(pn 2 p i) 1a M

1 2 p n

⋅pn 2 p

p 4c.

Further, in the limit as N → ∞, the conclusions of corollary 4 hold.The inequality provides a bound on value that depends only on

the first few elements p 1, p 2, . . . , p M21 of the probability orderingand on the search cost parameter c . In particular, it does not dependon knowledge of the entire probability ordering, nor on the exactsize of the payoff R from a successful discovery. Apparently, this for-mula shows promise as the basis for empirical valuation studies.

III. A Numerical Illustration

Could bioprospecting information rents be large enough, in prac-tice, to affect land use decisions? Uncertainties about relevant pa-rameter values preclude definitive empirical estimation of these val-ues. Insight into this qualitative question can be gained, however,by revisiting Simpson et al.’s (1996) numerical calculations on thevalue of genetic resources as inputs to drug discovery. The exercisehas two purposes. First, it demonstrates how the framework of Sec-tion II could be used, in the context of suitable scientific informa-tion, as the basis for assigning economic value to genetic resources.Second, it offers support for the claim that, under a range of plausi-ble parameter choices, such information could generate rents largeenough to create significant conservation incentives.

A set of N leads is partitioned into K classes of varying quality. Forn 5 1, . . . , N, let k(n) denote the index of the class containing leadn . Let e k be a measure of the quality of leads in the k th class, fork 5 1, . . . , K . Hit rates are proportional to lead quality: pn 5 p ⋅e k(n), where p is constant. Given financial parameters c and R andunder the assumption of an optimal program of search, the contri-bution vn of the n th lead to a single search project is given by equa-tion (5). A number λ projects are carried out per year, and futurecosts and benefits are discounted using a constant interest rate r.


The net present bioprospecting value of the n th lead is then givenby

^∞

t50

λ(1 1 r)2t v n 5λvn

r. (7)

To compute these values numerically, decisions must be made abouthow the domain of search should be characterized, how it shouldbe parsed into individual ‘‘leads,’’ and how the quality of leadsshould be measured. These questions are the subject of extensivedebate in the natural-products literature. A thorough airing of theissues involved would go well beyond the scope of this paper. Weproceed by considering a particular case, addressing briefly the pos-sible sensitivity of our conclusions to these choices.

As in Simpson et al. (1996), the search domain corresponds toa group of 18 ecologically distinctive ecosystems listed in table 1,described in Myers (1988, 1990) as ‘‘biodiversity hot spots.’’ Singleleads correspond to land parcels of a uniform area (1,000 hectares,or 10 square kilometers), where an investigator can collect biologicalsamples. The quality of a parcel (or ‘‘site’’) as a potential source ofnew drugs is proxied by the degree of endemism among higher plantspecies. Specifically, for ecosystems k 5 1, . . . , 18, the quality indexe k is defined as the density of endemic higher plant species in thatecosystem, measured as the average number of species per hectare.4

Other parameters on the drug discovery process are based onthose developed by Simpson et al. (1996), who draw on data fromDiMasi et al. (1991) and Office of Technology Assessment (1993).The probability that a test of a site in ecosystem k will yield a discoveryis p ⋅ e k, where p 5 1.2 3 1025. The probability that a project willterminate unsuccessfully, exhausting the available leads withoutyielding a discovery, is ∏18

k51 (1 2 p ⋅ e k)Nk 5 63 percent. Here, Nk

denotes the number of sites in ecosystem k (table 1). To achieve arealistic yield of 10 new natural-source drugs per year therefore re-quires that projects be launched at a rate of λ 5 26 per year. Eachsuccessful discovery generates a return of R 5 $450,000,000. Firmsdiscount future costs and benefits at r 5 10 percent per year. In thebaseline case, costs are set at c 5 $485 per test, at which level theformula (7) assigns negligible value to marginal sites in the leastpromising ecosystem. (Alternative values of the cost parameter werealso examined.) Calculations of marginal bioprospecting values perhectare in each of the 18 ecosystems are presented in table 1 and

4 A species is ‘‘endemic’’ to a region if it is found nowhere else. It must be empha-sized that endemism is not necessarily a realistic way to measure the quality of anarea for drug discovery purposes. Endemism is used here, rather, as a stand-in formore sophisticated indicators.

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Fig. 1.—Bioprospecting values in several ecosystems, as a function of success prob-abilities. Assumes 10 successes per year, revenues of $450,000,000 per success, a costof $483 per test, hit rates based on 1.2E-05 per species, and a discount rate of 10percent. Source: Myers (1988, 1990), Simpson et al. (1996), and authors’ calcula-tions.

in figure 1. The corresponding values generated in the Simpson etal. study are presented to facilitate comparison.5

Figure 1 shows the relationship between ecosystem size, hit rates,and value. Information rents can be several orders of magnitudelarger than scarcity rents and can be substantial even when scarcityrents are negligible. The values associated with the highest-qualitysites—on the order of $9,000 per hectare in our simulation—can belarge enough to motivate conservation activities. Sensitivity analysisshows that these qualitative results are robust with respect to theselected parameter values. In particular, a 10-fold increase in thecost per test raises the net present value of the highest-quality sitesto approximately $11,000 per hectare.

The computations reported in table 1 are not designed to giverigorous empirical estimates of bioprospecting values for the geo-graphic areas described. The derivation of such estimates will de-pend on the development of scientific and ethnobotanical bases forassigning priors to search opportunities (better P functions and datasources) over a range of potential natural products. In particular,we do not make the empirical claim that the density of endemic

5 In the Simpson et al. study, tests are carried out on individual species. Valuesper unit area are derived from a (constant) value per species using a widely acceptedlog-linear species-area relationship. This step is not necessary in our approach be-cause the site itself is taken as the unit of testing. Hence, values per unit area arecalculated directly.


species is a good indicator of chemical creativity or site quality. Theintended take-home message is that whatever basis is used to differen-tiate leads by quality, those leads that are marked as having distinc-tive promise will carry distinctive value under plausible conditionsof market demand. There is no reason to believe a priori that thebioprospecting values of all areas are so small as to play no role inland management decisions.

IV. Summary and Conclusions

A sequential-search model of biodiversity prospecting has been ana-lyzed. When search procedures are optimized to take advantage ofuseful prior information, high-probability leads command informa-tion rents associated with their contribution to the chance of successand, more important, to the avoidance of search costs. These rentsapply in addition to any scarcity rents arising from a bound on thetotal number of leads available for testing. The magnitude of infor-mation rents depends on the degree to which ecological and taxo-nomic knowledge turns leads into ‘‘differentiated products,’’ creat-ing a monopolistically competitive market in research opportunities.Rents for high-quality leads can be significant even when the aggre-gate supply of genetic materials is large. When biological resourcesare abundant, an increase in the potential profitability of productdiscovery has virtually no effect on the value of any lead, whereastechnology improvements that lower search costs induce (weakly) adecline in the value of every lead. Numerical results suggest thatbioprospecting information rents could, in some cases, be largeenough to finance meaningful biodiversity conservation. These con-clusions stand in opposition to those advanced in an earlier analysisby Simpson et al. (1996), who argued that biodiversity prospectingholds out no hope as a meaningful source of finance for biodiversityconservation. That result, it was shown, holds only in the degeneratecase in which no prior information is available to sort leads intocategories of differentiated quality.

Given the amount of attention that has been attached to this pol-icy question, it is important to be clear about why the two studiesdraw such divergent implications. Nothing in the present analysisalters the conclusion on truly ‘‘marginal’’ species. Species that ex-hibit insignificant commercial promise in every known applicationwill generate de minimus financial incentives for conservation. How-ever, the observation that there exist species that will not be conservedthrough a market-based scheme does not imply that all species willbe similarly condemned. The pivotal issue concerns whether everyspecies—more generally, every unit of biodiversity—can be consid-


ered equally ‘‘marginal.’’ This is an empirical question that cannotbe resolved through a priori theorizing. Yet neither the biologicalliterature nor the behavior of industry actors lends clear support tothe contention that natural-products prospecting proceeds on thebasis of randomized search.

Viewed as inputs to the innovation process, genetic materials havethe potential to become genuine resources in the context of a suffi-ciently rich set of complementary knowledge assets. The effectivefunctioning of a market in genetic resources depends on theseknowledge assets just as much as, if not more than, it relies on asound system of intellectual property rights and a robust capital mar-ket. This suggests that attempts to estimate the value of genetic re-sources should focus attention on how researchers form and updatetheir beliefs. It also suggests that the institutions regulating biopros-pecting, including systems of intellectual property rights, should re-ward the provision of helpful prior information, as well as the conser-vation of the base biological material.

The analysis has examined the marginal social value of researchoptions. A significant question for further work concerns how firms’willingness to pay for research leads would be affected by competi-tion in the race to patent biologically based innovations. As we haveseen, willingness to pay may be depressed by the potential for dupli-cative discovery: a given lead may not be unique as the source of aninnovation. As a firm considers how much to bid, it must attend tothe associated ‘‘redundancy cost’’ that the new lead imposes on thefirm’s existing portfolio of research options. The firm does not, how-ever, internalize costs imposed on competitors. As the number offirms competing in a given patent race grows large, redundancy costsbecome less important; the market price of genetic resources shouldrise. Moreover, if firms bid against one another in the market toacquire research options, a countervailing effect emerges: each firmhas an incentive to acquire options defensively, to keep them fromthe hands of competitors. When R & D firms compete both in themarket for leads and in the race to patent commercial discoveries,they will be willing to pay a premium for exclusive access to researchoptions.

Appendix A

Proof of Proposition 1

The proof of the first sentence, which relies on the independence of theBernoulli trials, involves a straightforward confirmation that no alternativesearch sequence can improve payoffs in expectation (see Weitzman 1979).Given that multiple discoveries are strictly redundant, the stopping rule isobvious. Q.E.D.



Repeated application of the recursive relationship (1) yields the closed-form expression

Vn11 5 ^N

i5n111 a i

a n112(p i R 2 c) 5 1 ^

N

i5n11

a ip i

a n112R 2 1 ^

N

i5n11

a i

a n112c .

Substituting this into (5) gives

v n 5 a n pn11 2 ^N

i5n11

a ip i

a n112R 1 a n3p n1 ^

N

i5n11

a i

a n112 2 14c . (A1)

Since a i11 5 a i(1 2 p i), the identity a i p i 5 a i 2 a i11 can be applied tosimplify the first expression in parentheses:

a n11 2 ^N

i5n11

a i 2 a i11

a n112 5 a n11 2

a n11 2 a N11

a n112 5

a N11

1 2 p n

,

where a N11 ; ∏Ni51 (1 2 p i), the probability of project failure. Rewriting

(A1) yields

v n 5a N11

1 2 pn

p nR 1 an3pn1 ^N

i5n11

a i

a n112 2 14c

5a N11

1 2 pn

(pn R 2 c) 11

1 2 pn31 ^

N

i5n11

p na i2 1 a N11 2 a n114c (A2)

5a N11

1 2 pn

(pn R 2 c) 1 3 ^N

i5n11

a i

1 2 pn

(p n 2 p i)4c .

Now

a N11

1 2 pn

(p nR 2 c) 5a N

1 2 p n

(pn 2 pn pN)R 2a N

1 2 p n

(1 2 p N)c

and

vN 5 a N(pN R 2 c) 5a N

1 2 pn

(p N 2 pnp N)R 2a N

1 2 p n

(1 2 p n)c .

Hence

vn 2 vN 5a N

1 2 pn

(p n 2 pN)R 1 3 ^N21

i5n11

a i

1 2 p n

(pn 2 p i)4c

1a N

1 2 p n

[(1 2 p n) 2 (1 2 p N) 1 (pn 2 p N)]c .

Since the last term disappears, the proposition is shown. Q.E.D.


Proof of Corollary 1

Let m and n be given. Without loss of generality, assume n # m . Considerfirst the case pn 5 p m ; p. By proposition 2,

v n 2 v m 5 ^m

i5n11

a i

1 2 p(p 2 p i)c .

But by proposition 1, p n 5 p and p m 5 p implies p i 5 p for all intermediatei 5 m 1 1, m 1 2, . . . , n 2 1. Hence the first claim is shown. For the casepn . pm, proposition 1 implies n , m . Hence

v n 2 v m 5 1p n 2 p N

1 2 p n

2pm 2 p N

1 2 pm2a N R 1 ^

m

i5n11

a i

1 2 p n

(pn 2 p i)c

1 ^N21

i5m11

a i1p n 2 p i

1 2 p n

2pm 2 p i

1 2 p m2c .

Since p n . pm implies 1/(1 2 p n) . 1/(1 2 p m), all three terms in theexpression on the right-hand side are positive, and the second claim isproved. The last two sentences are then immediate from proposition 1 andthe definition of information rents. Q.E.D.

Proof of Corollaries 2 and 3

Immediate from (A2). Q.E.D.


It suffices to show that vn is decreasing, as a function of N, and convergesto the specified lower bound in the limit as N → ∞. To prove the first claim,use (A2) to express vn as a function of N :

v n(N ) 5a N11

1 2 p n

pnR 1 1 ^N

i5n11

a i

1 2 pn

pn 2 a n2c . (A3)

Since a N11 5 (1 2 p)a N, we have

v n(N ) 2 vn(N 1 1) 5a N11

1 2 p n

p n(pR 2 c) . 0

by the assumption pR 2 c . 0. Hence vn(N ) is decreasing in N. To provethe convergence claim, use the relation a i11 5 (1 2 p)a i for i . M to rewrite


the formula in proposition 2:

vn(N ) 5 v N(N ) 1 v n(N )

5 a M(1 2 p)N2M (pR 2 c) 1 a M(1 2 p)N2M 1pn 2 p

1 2 pn2R

1 3 ^M21

i5n11

a i

1 2 pn

(p n 2 p i) 1 ^N21

i5M

a M(1 2 p)i2M 1pn 2 p

1 2 pn24c .

As N → ∞, (1 2 p)N2M → 0, and ∑N21i5M (1 2 p)i2M → 1/p, so

limN → ∞

v n(N ) 5 3 ^M21

i5n11

a i

1 2 pn

(p n 2 p i) 1a M

1 2 pn

⋅p n 2 p

p 4c . (A4)

Since convergence is monotonic, the expression on the right forms a lowerbound for all terms in the sequence. The bound is strictly positive for n ,M and zero for n $ M . Q.E.D.


Claim i restates equation (A4) for the case n 5 M, . . . , N. Claims ii andiii follow since limN → ∞ vn(N ) does not depend on R and is increasing in c .Q.E.D.


To carry out the proof, we expand notation to allow for variability in theordering of the search queue. Let I 5 [c/R , 1) be the interval of hit proba-bilities on which leads are viable. Then each point p ∈ I N corresponds toan assignment of hit probabilities to an unordered collection of N viableleads. Let p 1 be variable, and let p21 5 ⟨p 2, p 3, . . . , p N⟩ be a fixed vectorof the other hit probabilities. Without loss of generality, label leads so thatp 2 $ ⋅ ⋅ ⋅ $ pN. Now let Z be the set of all N ! permutations of the set {1, 2,. . . , N }. Let a rule s: I 3 I N21 → Z for ranking the N leads into a searchqueue be defined as follows: for leads with index n 5 2, . . . , N, let theposition s n(p 1 |p21) be given by

s n(p 1 |p21) 5 5n 2 1 if p 1 # p n

n if p 1 . pn.

By exhaustion, this expression determines the position s 1(p 1 |p21) of thelead with index 1. Thus leads are examined in the order 2, 3, 4, . . . , s 1,1, s 1 1 1, . . . , N. In particular, if s 1 . 1, the lead with index s 1 occupiesthe s 1 2 1st position in the queue, immediately preceding the lead withindex 1. Since, for n . 1, s 1 . s n if and only if p 1 # p n, this queuing rulesatisfies the optimality condition of proposition 1.


Now let u n(p 1) ; vsn(p1 |p21) denote the incremental value of the lead withindex n, viewed as a function of p 1. By corollary 1, this value depends onlyon the magnitudes of the components of p : any other queuing rule s ′(p)that satisfies the optimality condition of proposition 1 (i.e., any involving apermutation of equiprobable leads) will yield the same incremental values.Hence u n is well defined for all n .

We can now prove the proposition. Rewriting (A3) in terms of the newnotation, we can express the value of the lead with index 1 as a functionof its own hit probability:

u 1(p 1) 5 pN

i 52

(1 2 p i)p 1 R 1 ^N

i5 s1

pi

j 52

(1 2 p j)p 1c 2 ps 1

i 52

(1 2 p i)c . (A5)

By inspection, u 1 is linear in p 1 on all intervals for which s 1 is constant.Hence, u 1 is continuous on intervals of the form pn . p 1 . p n11 for n 5 2,. . . , N 2 1 and on the interval pN . p 1 $ c/R . In addition, since s 1 . s n

whenever p 1 5 p n, s 1 is constant on intervals p 1 ∈[pn 2 e, pn] for e sufficientlysmall. Hence u 1 is continuous from the left at the finitely many ‘‘switchingpoints’’ at which p 1 5 pn, for some n . 1. To prove continuity from theright, suppose that p n2k . p n2k11 5 ⋅ ⋅ ⋅ 5 p n . p n11. Then s 1(p 1 5 p n |p21) 5n, and for positive e , pn2k 2 pn, s 1(p 1 5 pn 1 e |p21) 5 n 2 k . Applyingequation (A5) yields

u 1(p n 1 e) 2 u 1(p n) 5 pN

i 52

(1 2 p i)Re 1 ^N

i5n2kp

i

j 52

(1 2 p j)ce

1 ^n21

i5n2kp

i

j 52

(1 2 p j)pn c

1 3pn

i 52

(1 2 p i) 2 pn2k

i 52

(1 2 p i)4c .

Since p n2k11 5 p n2k12 5 ⋅ ⋅ ⋅ 5 pn, the third and fourth terms cancel:

^n21

i5n2kp

i

j 52

(1 2 p j)p nc 5 pn2k

i 52

(1 2 p i) 3^k21

j50

(1 2 p n) j4p nc

5 pn2k

i 52

(1 2 p i)[1 2 (1 2 pn)k]c

5 3pn2k

i 52

(1 2 p i) 2 pn

i 52

(1 2 p i)4c .

Hence u 1(p n 1 e) → u 1(p n) as e → 0, and so u 1 is continuous for allp 1 ∈I. Equation (A5) also implies that, on any open interval of argumentsp 1 for which s 1 is constant, u 1 is differentiable, with


du 1(p 1 |s 1)

dp 1

5 pN

i 52

(1 2 p i)R 1 ^N

i5 s1

pi

j 52

(1 2 p j)c . (A6)

Since the expression on the right is positive, u 1 is increasing on each suchopen subinterval. Continuity then implies that u 1 is increasing on the entireinterval I. Further, since du 1/dp 1 is monotone decreasing in s 1 and s 1 ismonotone decreasing in p 1, u 1 is weakly convex on I. Finally, (A6) impliesthat

du 1(p 1 |s 1)

dp 1

⋅ p 1 5 pN

i 52

(1 2 p i)p 1R 1 ^N

i5s1

pi21

j 52

(1 2 p j)p 1 c 5 u 1 1 a s1c ,

where, from our established conventions, a s15 ∏s1

i 52 (1 2 p i) denotes theprobability that the lead with index 1 is tested. Q.E.D.


Let n ∈ {2, 3, . . . , N } be the index for a given lead. We use the notationdeveloped for the proof of proposition 4 to derive a formula for un(p 1),the value of the lead with index n, expressed as a function of p 1. For argu-ments p 1 . pn (so that s n 5 n . s 1), this value is given by

u n(p 1 |p 1 . pn) 5 pN

i 51i ≠ n

(1 2 p i)pn R

1 ^N

i5np

i

j 51j ≠ n

(1 2 p j)p nc 2 pn21

i 51

(1 2 p i)c ;

(A7)

so u n is linear, and hence continuous, in p 1 on the interval 1 . p 1 . p n.Further, since

du n(p 1 |p 1 . pn)

dp 1

5 2u n

1 2 p 1

,

the elasticity relation claimed in point i is shown. For p 1 # pn (so that s n 5n 2 1 , s 1), the value is given by

u n(p 1 |p 1 # pn) 5 pN

i 51i ≠ n

(1 2 p i)pn R 1 3^s 1

i5np

i

j 52j ≠ n

(1 2 p j) 1 ^N

i5 s 1

pi

j 51j ≠ n

(1 2 p j)4pnc

2 pn21

i 52

(1 2 p i)c .

This function is linear, hence continuous, in p 1 on subintervals for whichs 1 is constant. On each such subinterval, we have that


du n(p 1 |s 1 . s n)

dp 1

5 21

1 2 p 13p

N

i 51i ≠ n

(1 2 p i)pn R 1 ^N

i5s 1

pi

j 51j ≠ n

(1 2 p j)p nc4

5 21

1 2 p 13u n 1 p

n21

i 52

(1 2 p i)c 2 ^s 1

i5np

i

j 52j ≠ n

(1 2 p j)pnc4,

(A8)

which expresses the elasticity relation of claim ii in the new notation. Thatu n is continuous at points p 1 5 pm, for pm , pn, follows from an argumentanalogous to the one used in the proof of proposition 4.

A similar argument shows that lime→ 0 u n(pn 1 e) , u n(pn), so u n is discon-tinuous at p 1 5 p n. To complete the proof, it must be shown that u n isdecreasing in p 1. Equation (A7) implies that u n is decreasing in p 1 on theinterval 1 . p 1 . p n. For p 1 , pn, equation (A8) implies that u n is decreasingon subintervals of [c/R , pn] on which s 1 is constant. But since u n is continu-ous on [c/R , pn], this implies that un is decreasing on any interval not con-taining p n. Finally, at the point of discontinuity p 1 5 pn, we have lime→ 0

u n(p n 1 e) , u n(p n). Thus u n is decreasing for all p 1 ∈ I. Q.E.D.


We showed in proposition 4 that the elasticity of a lead’s value u 1 with re-spect to its own hit probability p 1 is greater than unity on subintervals of Ifor which the search ordering is constant. The first claim of the corollarythen follows from the fact that u 1 is continuous, increasing, and convex inp 1. The second claim, that u n is decreasing in p 1 for n . 1, was proved inproposition 5. Q.E.D.


Consider a second probability ordering {p ′n}Nn51 such that p ′n 5 p n for n ,

M and p ′n 5 p for n $ M . Let v ′n be the value of lead n with respect to thisordering. Then for n , M,

v ′n $ 3 ^M21

i5n11

a i

1 2 p n

(p n 2 p i) 1a M

1 2 pn

⋅pn 2 p

p 4c

by proposition 3 and v n 5 v ′n by proposition 5. To prove the limit results,note that p n $ c/R for all n implies a N # [1 2 (c/R )]N21. Hence a N → 0as N → ∞. Then by proposition 2 and the inequality above, limN→ ∞ vn(N )does not depend on R , is increasing in c for n , M(p), and is zero for n 5N. Q.E.D.

Appendix B

Model Robustness

The model incorporates several salient features of bioprospecting as wellas applied generic research: total costs increase with project duration, inno-


vations are nonrival goods, and scientific knowledge gives direction to theeffort overall. Nonetheless, parsimony requires that some considerationsbe treated in reduced form or swept aside. It is important to considerwhether the implications of the analysis are likely to be robust with respectto potential generalizations.

The model treated success probabilities for different leads as statisticallyindependent. If hit rates are instead correlated, then the investigator canupdate her search itinerary on the basis of information revealed in the lightof sequential test outcomes. The value of a given lead then depends bothon its own fertility as a potential source of a discovery and on what a testof it reveals about the likelihood of discoveries elsewhere. Since search haltsafter the first success, a test affects the course of the itinerary only when itresults in failure. Knowing this, the investigator can map her entire itineraryin advance, using an appropriate backward-induction procedure to deter-mine the optimal sequencing of leads. She can then calculate ex ante theprobability a n that her search will ever visit the n th lead and the value v n

of a call option on the lead, using formulas identical to those derived here.The only change involves replacing the unconditioned probability parame-ters {p i}N

i51 with corresponding conditional probabilities. The central mes-sage—that leads have value insofar as they improve the productivity ofsearch effort—would be unchanged, if not strengthened.

Research costs c and payoffs R were treated as constant across projectsand known in advance. In practice, bioprospecting projects often involvemultistage testing, in which samples that show promise in an initial screen-ing are subjected to more rigorous and expensive follow-on investigation.Samples can thus differ with respect to their ultimate cost of testing. In thiscase, however, the researcher will not know ex ante which samples will re-quire additional expense. For the purpose of modeling the researcher’sincentives, we can therefore treat c as a constant expected cost per test andhit rate pn as the ex ante probability that the n th sample will clear all thestage hurdles associated with R & D, leading ultimately to the marketingof a new product.

Likewise, the payoff R may be uncertain at the outset of a product devel-opment process. The payoff ultimately realized will depend on the resolu-tion of multiple contingencies concerning consumer demand, competition,and so forth. It is assumed, however, that the firm can formulate beliefsabout its payoffs over a rich set of contingencies and calculate R as an ex-pected value. If the firm is risk-neutral, its approach to the project will bethe same in either case, and the use of the reduced-form expression is justi-fied. More generally, R can be viewed as the certainty equivalent of thepayoff distribution under the objective function of a risk-averse firm. If Rvaries across different projects (e.g., if a cure for cancer is worth more thana cure for the common cold), conservation incentives can be calculated asthe simple sum of the incremental values for each of the several proj-ects.

The model incorporates no role for discounting during the life of anindividual research project. Suppose instead that each test required someamount of time to carry out and that future costs and benefits were dis-


counted at some (possibly variable) rate. In this setting, a lead that enablesrapid discovery is doubly beneficial: an early discovery not only reducesthe direct expense of testing but also increases the present value of thepayoff. Incorporating a role for in-project discounting would apparentlystrengthen the qualitative conclusions about the importance of informationrents.

In the numerical illustration, an individual ‘‘lead’’ corresponds to a par-cel of land of a certain size. Previous studies in the economics of biopros-pecting have typically identified leads with individual species. However, inpharmaceutical natural products especially, the objects tested are oftencomplexes of microorganisms, large and lumpy aggregates of living mate-rial found in soil, leaf litter, and so on. The firm may not know, or careabout, the identity of the species in a sample. The operative question iswhether something in a biological sample generates a chemical compoundwith desirable properties. From this perspective, the individual species ismerely an intermediate carrier of chemical creativity. Indeed, an atomisticfocus on species, in abstraction from ecological and environmental rela-tionships, can interfere with the discovery process. A plant may producedefensive chemicals, for example, only in its stems or leaves or only whenunder attack from insects. The identification of leads with species presup-poses an impoverished informational context. Several considerations arguefor a geographic definition of ‘‘leads.’’ Data on species distributions andother features of ecology and habitat are typically organized along geo-graphic lines. More important from the policy perspective, propertyrights, access agreements, and investment decisions are generally location-specific.

Numerical results were based on the additional simplifying assumptionthat the hit rate for a given lead is constant across different classes of re-search projects. In practice, this pattern is unlikely to hold exactly: a mush-room that produces psychotropic chemicals may be of no use against highblood pressure. If hit rates displayed no correlation across projects, then alead with high value in one application might have low value in others andonly modest aggregate rent. To the extent that hit rates exhibit positivecorrelation across applications, significant lead valuations become morelikely. The degree to which organisms of potential economic use are con-centrated in certain biological taxa is an empirical issue that is far fromresolved. One of the few studies that attempt to address the question com-prehensively within a subset of U.S. plant species (Phillips and Meilleur1998) finds a substantial variance across genera in the incidence of reportedeconomic use, with certain taxa displaying uncommon fertility as productsources. As noted in the text, certain environments (Yellowstone hotsprings, centers of crop diversity, areas rich in chemically creative microbes)appear to be durably promising as sources of innovations in lucrative prod-uct areas. A pattern of positive correlation could also be strengthenedthrough path-dependent learning: as investigators examine an organismfor use in one application, they may learn things about its suitability inothers. While the correlation question merits further study, a reasonablenull hypothesis at this point is that some biological leads are systematically


superior as sources of innovations and embody potentially significant com-mercial value.

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