Searching an EX SITU Collection of Wheat Genetic Resources Douglas Gollin, Melinda Smale, and Bent Skovmand A theoretical model is developed and applied to the search for disease and pest resistance in ex situ collections of wheat genetic resources, employing actual data on frequency distributions, disease losses, and search costs. Experiments developed from case studies clarify several misperceptions about the value of gene banks and their utilization by breeders. The observation that wheat breeders “use” gene banks rarely does not imply that marginal accessions have low value. High costs of transferring genes with conventional breeding techniques mean that it may be efficient to store certain categories of genetic resources (such as landraces) “unused” for many years. Key words: gene bank management, valuation of genetic resources, optimal search, economics of agricultural research.
Fears about the loss of potentially valuable genes and the widespread cultivation of genetically uniform varieties have heightened public concern for the conservation of crop genetic resources (Shiva, Raeburn). International organizations have spent large sums in the construction of gene banks—cold storage units designed to conserve seeds and other plant materials for future use. But some critics have challenged the usefulness of such collections of crop germplasm ex situ (out of their place of origin). One criticism, drawn from principles of evolutionary biology, is that materials stored ex situ are removed from the selection pressures, both human and Douglas Gollin is assistant professor of economics at Williams College and affiliate scientist, CIMMYT Economics Program. Melinda Smale is an economist at CIMMYT and the International Plant Genetic Resources Institute (IPGRI) and a Visiting Research Fellow with the International Food Policy Research Institute (IFPRI). Bent Skovmand is the head of the Wheat Genetic Resources Program, CIMMYT. CIMMYT is the International Maize and Wheat Improvement Center. Portions of this paper were written while Gollin was a Gaylord Donnelley Fellow at Yale University, and he gratefully acknowledges the support and funding of the Yale Institute for Biospheric Studies and the Economic Growth Center at Yale. Among those who have contributed helpful comments and suggestions are: Norman Borlaug, Cheryl Doss, Jesse Dubin, Bob Evenson, Lucy Gilchrist, James Gollin, Paul Heisey, Stephane Lemarie, ´ Sanjaya Rajaram, Matthew Reynolds, Daniel Rondeau, Maarten van Ginkel, and Brian Wright. Harold Bockelman, director of the U.S. Department of Agriculture’s National Small Grains Collection, was instrumental in making available part of the GRIN data base. Will Chang provided research assistance. The authors are indebted to two anonymous reviewers for raising important points. The views represented here are those of the authors, and do not represent the official policy of CIMMYT, IPGRI, or IFPRI.
natural, that ensure their continued adaptation and utility in crop breeding (Frankel and Soule). ´ A second criticism stems primarily from the casual observation that crop breeders rarely resort to gene banks. Most genetic resource specialists would agree that “accessions should be used, and breeders need to know what the packets or bottles of seeds on the shelves contain” (Plucknett et al.: 174). Wright has argued that the utilization of gene banks has not kept pace with their expansion. Does infrequent “use” of gene banks by crop breeders imply that marginal accessions have low value? Are seed banks merely “seed morgues” (Raeburn)? This article develops a theoretical model and applies it to the search for disease and pest resistance in ex situ collections of wheat genetic resources. Three questions are posed about the economics of searching wheat gene banks. First, how many gene bank accessions of one type of genetic resource should be searched for disease or pest resistance, in either a single search or a multiple-stage “batch search.” Second, the value of specialized knowledge about the distribution of desirable traits within subcollections of germplasm is estimated. Third, we ask how a search should proceed when scientists can hunt for a trait in more than one type of genetic resource. To answer these questions, numerical experiments were conducted using three types of data. We draw on actual distributions of pest and disease resistance from
Amer. J. Agr. Econ. 82(4) (November 2000): 812–827 Copyright 2000 American Agricultural Economics Association
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agricultural experiments. Search costs were computed from primary data generated by the gene bank at the International Maize and Wheat Improvement Center (CIMMYT). Finally, benefits parameters from historical adoption data were calculated. These experiments lead to some intuitive findings. For example, the optimal size of a search is sensitive to the distribution of the desired trait and the time lags involved in making use of a new source of resistance, as well as the magnitudes of search costs and benefits. Other findings are less obvious. For example, the presence of many “unused” materials in a gene bank does not imply that marginal accessions have no use value; sporadic use may be associated with large payoffs. Theoretical Model A theoretical model was employed that builds on previous work by Evenson and Kislev and Simpson, Sedjo, and Reid. In the model proposed by Evenson and Kislev, new varieties of sugarcane were “discovered” through a costly search (research) process. The model was used to answer questions about optimal search strategies, investigate the effects of changes in research technology, and explore stopping rules and other issues of research policy. Their primary interest is the total value of applied research, and they conclude that additional investments in research often pay off either through the “discovery” of improved varieties or through a reduction in search costs. More recently, Simpson, Sedjo, and Reid applied a search model to the problem of valuing a marginal species in a tropical rainforest, in which pharmaceutical researchers test a large number of species for a trait of economic value. The trait is assumed to be distributed randomly and uniformly across the entire population: with a given probability, each species either possesses the trait or fails to possess the trait. The search process thus consists of repeated and independent Bernoulli trials. Using data from the pharmaceutical industry, the authors arrived at the striking conclusion that under most plausible specifications, the expected value of a marginal species is minuscule. By extension, marginal accessions in a “large” gene bank may have little value. Like Evenson and Kislev, we investigate optimal strategies for agricultural research.
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But where they focused on searches among the outputs of crop breeding programs (improved varieties), we focus on the search among inputs—specifically, genetic resources stored in a gene bank. In this respect, our paper is similar to that of Simpson, Sedjo, and Reid, who model the exploitation of a large collection of genetic resources as an input into pharmaceutical research. Unlike Simpson, Sedjo, and Reid, however, we analyze alternative strategies for utilizing the collection, with emphasis on current policy concerns in gene bank management. Searching for Resistance Economically important traits are distributed in varying degrees across any set of accessions conserved in a gene bank. For many traits, such as plant height or leaf size, the distribution in the set is approximately normal. For other traits, the distribution follows some other pattern. With diseases and pathogens, for example, resistance may be found only in small numbers of accessions. Typically, scientists screen accessions for resistance or other useful traits and assign scores accordingly. Let s denote the score achieved by an accession, where s ∈ S. For simplicity, let S = [0 1]. In keeping with common practice, let low scores be considered “better” than high scores; in other words, an accession with s = 0 is superior to one with s = 1. Let the distribution of traits within a subcollection of accessions j be denoted by j (S), where j indexes the relevant subcollections. For example, we might be interested in comparing the distributions found among categories of genetic resources such as landraces, obsolete lines, synthetics, and elite lines.1 Let J denote the number of subcollections to be considered. Suppose that n draws are taken from the distribution j (S), where these draws are taken simultaneously. (For example, consider these to be seed samples of n different gene bank accessions, which are to be grown and j tested in a single growing season.) Let si be the score achieved on the ith draw from this distribution (the score of the ith accession). Note that a particular draw of size n represents an element of the sample space, ω ∈ . 1 A landrace is a cultivated form of a crop species, which has evolved over generations of selection by farmers. In genetic resource conservation, the term “landrace” refers to a specific category of biological materials.
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For each draw ω ∈ , si (ω) is a real number. j Define the order statistic Zn as follows: (1)
j
j
Znj = min[s1 s2 snj ]
continuous and integrability conditions apply, we get the expected value: (6) E Znj = zhjn (z) dz z∈S
j
Then Zn is a random variable defined over the domain . For any given ω ∈ , there j is a corresponding value of Zn , the minimum value attained on that draw. Recall that the minimum value is the most resistant (and hence most desirable) material. The expected minimum value depends on the number of materials drawn from the distribution. In fact, given a distribution of scores, j (S), it is straightforward to derive an expression for the distribution of the minimum value. Let z be a particular score, such that z ∈ S. Then the probability that the minimum value attained in n draws from the distribution j exceeds z is given by j j (2) Pr s1 > z; s2 > z; snj > z Let fj (·) denote the probability density function for the distribution j (S), and let Fj (·) denote the cumulative density function. j Then the probability that si ≥ z can be written, for all i, as [1 − Fj (z)]. Assuming that the n draws are independent and identically distributed, the probability that all the draws will exceed z can be written simply as j j Pr z ≤ min[s1 s2 snj ] (3) n
= [1 − Fj (z)] j
Let Hn (z) designate the corresponding cumulative density function; thus, j j (4) Hnj (z) = Pr z ≥ min[s1 s2 snj ] Then it follows directly from equation (4) j that Hn (z) = 1−[1−Fj (z)]n . From this cumulative density function, we can also derive a j probability density function, hn (z). Assuming that Fj (z) is differentiable, we can write: (5)
hjn (z) = n[1 − Fj (z)]n−1 fj (z) j
Note that hn (z) is defined for all possible values z ∈ S. Also note that we can derive an j expression for hn (z) simply from information about the underlying distribution fj (z) and the number of draws, n, made from subcollection j. Assuming that all the functions are
=
zn[1 − Fj (z)]
n−1
fj (z) dz
z∈S
The expected value of this minimum varies with n. The more draws that are taken from the distribution, the smaller the expected j j value of Zn becomes. The variance of Zn is also well defined. For some traits, the actual minimum score attained. May be interesting. For other traits, it may matter only whether some threshold value is obtained. In the Bernoulli case considered by Simpson, Sedjo, and Reid and used in our experiments, we simply define some threshold of usefulness, saying that any variety with a resistance score below s ∗ is useful, and anything with a score above s ∗ is not useful. The Bernoulli probability, p, is thus the probability that a variety has a resistance score below s ∗ , (7)
p = Fj (s ∗ )
The probability that a “useful” variety will be j found in a search of size n is given by Hn (s ∗ ), n which reduces to 1 − (1 − p) . The Value of Successful Search Now consider the benefits of finding resistance to a pest or disease and incorporating it into an advanced line of wheat that is developed by CIMMYT and adapted or finished by collaborating wheat breeders in national programs. CIMMYT classifies the world’s bread wheat production zones into “megaenvironments” that span different continents and regions within the developing world, viewing them as distinct from the point of view of variety development. Suppose that in a particular mega-environment, m, the wheat varieties grown by farmers have an average score of z¯ for a particular trait. The value of production given this level of the trait ¯ If a new variety were introduced is vm (z). into this mega-environment with a better trait score of z, ˆ the single-period benefits would ˆ − vm (z). ¯ Typically, the benbe given by vm (z) efits associated with the new variety would decrease over time, in part because of a kind of varietal depreciation. For example, resistance to pests and diseases is typically overcome as new pathogens emerge. We do not
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attempt to model this breakdown directly, as a decline from zˆ to z. ¯ Instead, however, we can simplify the story to imagine that the stream of benefits simply decays over time. Let δ(t) represent the decay parameter for the benefit stream, and let it be considered as a known parameter of the model. The discount factor β corresponds to the rate of time preference. Then the returns at date t obtained from achieving the score zˆ today can be written as:
t (8) β δ(t)[vm (z) ˆ − vm (z)] ¯ 2 m∈M
Now consider the cost structure of the search process. Several types of costs are incurred when the search is initiated. The fixed costs of searching include the costs of developing search techniques or setting up a new experiment. These may depend on the type of material when different techniques are required to screen for resistance, so we denote them by Cj . The variable cost cj is the cost of screening and evaluating one more accession of type j. Upon completion of the search, which takes place in the initial period, scientists observe the best material of each type and choose which one to use in breeding. A time lag, Tj , is associated with “pre-breeding” materials of type j. A fixed cost of prebreeding, Kj , is also incurred when transferring resistance genes from source materials into a breeding program. Kj includes crossing and genetic studies and depends on the trait and the type of material. Costs of prebreeding typically decrease with the improvement status of the source material. Simple traits and those that are highly heritable are relatively easy to transfer. At one extreme, no pre-breeding is required to transfer a trait that is found within a released variety or an elite line. At the other, a wild relative of wheat has high transfer costs because (at present) special techniques are required to make it useful to the breeding program. Assume that Kj only applies to the single category of material that is chosen for use in breeding. The time lag associated with developing a usable variety once the material has reached 2
In some sense, it would be more accurate to model varietal advantage as breaking down over time, so that date t, the at new variety would have a production value of vm δ (t) zˆ . But it is unclear whether varietal depreciation actually follows this pattern. As a result, we stay with a simple formulation in which monetary benefits fall over time.
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the breeding program also affects the benefits of successful search. This time lag differs with the target mega-environment. Varieties may be developed more quickly for environments that are favorable for wheat production. Further, factors related to farmer adoption slow the diffusion of materials that carry the resis m tance in some areas relative to others. Let T denote this time lag, and let τ denote the time horizon of relevance to wheat breeders. Now consider the costs and benefits of search. Let Rj (nj ) denote the benefit stream from using the best material found in a search of nj accessions of type j. These benefits are given by (9)
Rj (nj ) =
m +τ Tj +T
βt δ(t)
m m∈M t=Tj +T
× vm zj − vm (z) ¯
Rj (nj ) is a random variable. Depending on the realization of the draw of nj materin als, the returns will vary. Let FRjj (y) denote the cumulative density function for Rj (nj ). In n other words, FRjj (y) represents the probability that Rj (nj ) ≤ y. The researcher will initially choose a vector of draws, n, where n = (n1 n2 nJ ). After making all of the J draws, researchers will look at the realization of draws and will choose to work with the type of material that gives the highest returns. Ultimately, the researchers will face a discrete maximization problem—to choose the maximum value from J independent draws from J different distributions; i.e., the researcher obtains: (10) R∗ (n) = max[R1 (n1 ) − K1 R2 (n2 ) −K2 RJ (nJ ) − KJ ] Because Rj (nj ) is a random variable, the researcher’s total returns R∗ (n) are also a random variable. As above, we are interested in an order statistic—the maximum return attained through drawing once from each of the distributions Rj (nj ). Thus, we can define a cumulative density function for overall returns. This is given as FRn∗ (y), where: (11) FRn∗ (y) = Pr[R∗ (n) ≤ y] = Pr[Rj (nj ) − Kj ≤ y ∀j ∈ J ] =
J
j=1
n
FRjj (y)
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We can also define a probability density function fRn∗ (y) that is derived from FRn∗ (y). nj Since the functions FRj (y) are different from one another, we cannot easily derive a closed form expression for fRn∗ (y), but it can be approximated computationally by differencing FRn∗ (y). Assuming that fRn∗ (y) is integrable, the expected value of the researcher’s returns can be written as E[R∗ (n)], where: ∞ (12) E[R∗ (n)] = yfRn∗ (y) dy 0
The problem for a risk-neutral gene bank manager who seeks to sample J types of materials in order to maximize expected returns subject to a budget constraint is maxn E[R∗ (n)] (13)
st
J
j=1
C j + c j n j Ij ≤ W
where Ij =
1 0
if nj > 0 if nj = 0
W represents the total budget available for search, cj denotes the variable costs associated with screening materials, as described above, and Cj denotes the fixed costs of search. This is a complicated optimization problem. Its form serves to remind us that corner solutions are likely. The following section deals with the relatively tractable case of a single type of material, for which an analytic solution can be found. In general, however, we need to check for corner solutions. In a subsequent section, we consider a case in which a corner solution is optimal. Data and Methods We applied the model in four numerical experiments, using three types of data: (1) the probability distributions for useful levels of resistance generated with Monte Carlo simulations from smoothed, actual distributions for the trait, (2) estimates of benefit streams, and (3) representative cost data. Methods used to develop each of these are summarized below and described in greater detail in Gollin, Smale, and Skovmand.
any subcollection of wheat varieties, the j probability density function hn (z) can be calculated for the minimum value that will be obtained from n draws from subcollection j. The Genetic Resources Information Network (GRIN)3 provides data on discrete distributions for certain traits within the collection of wheats, taken from performance scores in various agronomic trials. Agricultural scientists assign integer-valued scores for convenience, but the underlying distribution is presumably smooth. A least squares technique was used to fit a smooth beta distribution to each discrete distribution of disease and pest resistance. The parameters of a beta distribution can be written as a and b. Values of (a, b) were chosen to minimize the sum of squared residuals when the discrete distribution was compared with the smoothed distribution. The beta distribution is flexible and can be used effectively to approximate a wide range of shapes. Beta distributions can also allow for tails of varying thickness, which is important for this type of analysis. Benefits and Costs Crop losses averted were used to estimate the benefits associated with transferring a new source of genetic resistance into released varieties, based on scenarios defined by different parameter values. Losses averted were calculated as the product of: (1) the area planted to varieties carrying resistance in environment m in year t; (2) the percentage of yield lost due to disease in year t averaged over the area usually affected by disease; and (3) the average wheat yield in farmers’ fields. Average yields by environment were obtained from the Wheat Impacts databases held by the CIMMYT Economics Program, and adjusted for yield potential (Sayre et al., Byerlee and Moya). Areas affected by diseases, average annual yield losses, and expected lifetimes of resistance were drawn from published literature and personal communication. Yield losses averted decrease in magnitude over the time period t as the new source of resistance depreciates or decays with the evolution of pathotypes. The areas planted to varieties carrying resistance follow a diffusion path that differs by environment.
Probability Distributions for Traits Given an actual discrete distribution of scores for disease or pest resistance over
3 The GRIN database for wheat reports data on the wheat collections managed by the National Small Grains Collection, U.S. Department of Agriculture, Agricultural Research Service.
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Cumulative adoption ceilings reflect the proportion of materials grown in 1990 that were CIMMYT crosses or had at least one CIMMYT parent. The starting point from which the benefits are calculated depends on the type of material in which the resistance is identified and the environment in which the resistant varieties are grown. The growing and economic environment affects the time until the adoption of resistant varieties begins. The average research lag in each mega-environment covers the time from entry of the resistant lines into the breeding program, through the development of finished varieties, until the time at which m ). The time farmers begin to grow them(T horizon is thirty five years. Cost estimates in this study are based on historical experience with the CIMMYT wheat gene bank. The costs of constructing, operating, and managing a gene bank do not vary with the size of a search or the type of material searched, and are viewed as fixed. Relevant costs for optimal search decisions in a single-period model are those associated with evaluating wheat varieties for specific traits and transferring them to advanced lines (Cj cj ). In the examples used, fixed transfer costs (Kj ) had little quantitative significance. By contrast, the time to transfer (Tj ) and the time until farmers begin to grow the m ) were critical in determining the varieties (T discounted net benefits stream. Simplifying Assumptions Estimates in all scenarios reflect a number of implicit assumptions, most of which understate the magnitude of benefits and lead to more conservative results. First, we computed the benefits of finding useful materials on the assumption that CIMMYT performs the search, incorporates the materials into breeding lines, and disseminates the resulting breeding lines into national programs. The benefit streams are generally based only on the major environments in which spring bread wheats are grown in the developing world. Our calculation ignores (1) other avenues through which useful materials might pass into national programs and farmers’ fields; (2) the potential for incorporating resistance into other wheat types; (3) benefits from avoiding the negative externalities associated with chemical control as compared to genetic resistance; and (4) benefits obtained by producers and consumers in
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countries and zones that do not fall under CIMMYT’s mandate. Second, we assume that the diffusion of varieties carrying a new source of resistance would follow a trajectory similar to the diffusion pattern of semi-dwarf wheats that was observed between 1967 and 1990. Chances are, however, that today’s diffusion would occur more rapidly due to improved seed systems and increased commercialization of wheat production in many environments. In our simulations, we assume the same differences in diffusion between marginal and favorable environments that occurred historically. Third, in order not to overestimate the benefits, we consider only the benefits obtained through the diffusion of CIMMYT lines and varieties with direct CIMMYT parents, excluding the subsequent diffusion of varieties that incorporate the resistance trait through more distant CIMMYT ancestors. To the extent that useful traits are disseminated through succeeding generations of wheat varieties, we understate benefits. Finally, it is assumed that the evolution of new disease and pest biotypes can be adequately captured through the simple structure used to model the breakdown of resistance over time as a constant rate of depreciation. The diffusion of resistant varieties can actually contribute to the emergence of new disease and pest pathotypes, but the emergence of new pathotypes are treated as an exogenous event. Whether this assumption leads us to systematic errors in estimating benefits is unclear.
Experiments We conduct numerical experiments that represent special cases of the search problem to address three questions. First, we analyze the problem of the size of search in one type of material when the distribution of the desirable trait is known or “guessed” based on prior information, in both a single search activity and a multi-stage search. Second, we consider the value of specialized knowledge about the distribution of the trait across subcollections of one type of material. Third, we consider the case of searching among two types of materials.
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Figure 1. Actual and fitted distribution of resistance to Russian Wheat Aphid in 10,190 landraces of Triticum aestivum Case 1. Optimal Search in a Single Type of Material Consider that the researcher is only interested in searching for resistance within a single subcollection of material. Assume that the researcher initially knows the (approximate) distribution of resistance but does not know the scores of individual accessions.4 The researcher will choose to make the search just large enough that the expected marginal benefit of search equaled the marginal j search cost. The function Hnj (s ∗ ) gives the probability that a search of size nj among materials of type j will result in a “useful” discovery, where the usefulness of resistance is defined by having a score below s ∗ . We also j know that Hnj (s ∗ ) depends on the parameters of the underlying distribution of resistance, j (S). Denote these parameters by θ. To emphasize its dependence on nj , we can express this cumulative density function as H j (nj ; s ∗ θ). 4 This assumption may seem extreme, but it reasonably approximates the actual information available to researchers. Typically, at the outset of a search, scientists have a general idea of the distribution that they face, based on casual observation of different accessions, along with previous studies of relatively small samples. We interpret this knowledge literally, in the sense that we assume that scientists know the actual parameters of the distribution. Clearly this abstracts from reality, but it is better than the alternative assumption that scientists begin the search with little or no knowledge of the distribution.
Then the optimal search is given by (14)
m +τ Tj +T
m m∈M t=Tj +T
βt δ(t) Evm (zj ) − vm (z) ¯
∂H j nj ; s ∗ θ = cj × ∂nj
The left-hand side of this equation represents the marginal benefit of expanding the search. The first term is the total benefit stream and the second is the marginal change in the probability of successful search when nj is increased. The right-hand side of the equation is the marginal cost of search. We use the example of Russian wheat aphid (Diuraphis noxia) to illustrate the solution to the problem of optimal size of search for resistance in one category of genetic resources. From its center of origin in the Caucasus and Central Asia, Russian wheat aphid (RWA) has emerged as a pest of some importance in the United States, the Republic of South Africa, parts of the Southern Cone of Latin America, and North and East Africa. The pest is potentially important in Australia and in parts of the People’s Republic of China (Robinson). Some (but not all) wheat lines from the countries of origin of the pest display resistance (Marasas et al.). Searches among bread wheat varieties in the USDA collection uncovered almost no
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Table 1. Benefit streams associated with finding a source of resistance to Russian Wheat Aphid in a bread wheat landrace, under alternative assumptions (million dollars U.S.) Assumptions and parameters Global 23 mill ha affected 8.3 mill ha ceiling adoption 5% initial average yeild loss 15 years duration of resistance variable adoption lag Major CIMMYT Spring Wheat Megaenvironments 9 mill ha affected 3.4 mill ha ceiling adoption 5% initial average yeild loss 15 years duration of resistance no adoption lag Major CIMMYT Spring Wheat Megaenvironments 4 mill ha affected 1.6 mill ha ceiling adoption 5% initial average yeild loss 15 years duration of resistance no adoption lag
Transfer lag: 2 yrs Breeding lag: 5 yrs
Transfer lag: 5 yrs Breeding lag: 10 yrs
Transfer lag: 10 yrs Breeding lag: 10 yrs
16582
4897
1861
292
997
377
1567
3315
12
resistant material. Of 41,109 wheat accessions evaluated by the USDA—most of them elite lines and released varieties—just over 100 displayed resistance. None of these was a spring-habit bread wheat. Literature summarizing searches for resistance also reports the near absence of resistance in improved materials or in any materials originating outside of Central Asia (Robinson and Skovmand, Souza et al., Harvey and Martin, du Toit). Figure 1 shows both the raw histogram and the fitted beta distribution that approximates the underlying distribution of resistance among 10,190 landraces for which data were available in the GRIN. The distribution has a very thin left-hand tail; almost no resistant landraces were found. Using the data and methods summarized above, we estimated the total discounted net benefits of incorporating a single source of resistance to RWA into CIMMYT bread wheat with scenarios defined by assumptions about areas affected, average yield losses, longevity of resistance, and research time lags (table 1). In all scenarios, the cost of search was estimated at $82.97 per landrace screened (Skovmand, unpublished data). In this case, fixed costs were unimportant and variable search costs did not change substantially with the size of the search, resulting in
a constant average search cost equivalent to a constant marginal cost. Figure 2 shows the marginal benefits, marginal costs, and optimal size of search for the least favorable scenario. In this scenario, we assumed initial average yield losses of 5% on a total of 4 million affected hectares, with an adoption ceiling of only 1.6 million hectares, and a fifteen-year longevity of resistance. The time lag for transferring resistance was ten years, with an additional ten-year research lag for breeding. Optimal search size in this scenario is given by the intersection of the marginal benefit curve with the marginal cost curve, at 4,700 landrace accessions. The expected total benefits of finding a landrace with resistance to RWA are $865,000 with a total cost of $406,000 for expected net benefits of $459,000. The benefits in the least favorable scenario reflect lengthy research lags and limited diffusion of varieties carrying RWA resistance, since a relatively small proportion of the global area potentially affected by the pest is found in the spring-habit, wheatgrowing areas of developing countries within CIMMYT’s mandate. These zones are generally marginal for wheat production, and average yields are low. When losses to producers outside these areas are also consid-
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Figure 2. Marginal costs and marginal benefits of searching for Russian Wheat Aphid resistance in a sample of Triticum aestivum landraces, Least Favorable Scenario (Total Benefits = 1.2 million) ered, the benefits are large enough to justify a search of 18,800 landraces. Total search costs are $1.560 million and expected benefits are $18.343 million for an expected net benefit of $16.784 million. When benefits begin seven years later rather than twenty, the economic problem becomes trivial: the optimal size of search is larger than the number of landraces in the CIMMYT gene bank. The benefits are so great relative to costs that a search of all accessions would be justified. In general, our sensitivity analysis confirms that the time lag for transfer, breeding, and adoption is of crucial economic importance. Transferring a source of resistance from a landrace using conventional breeding techniques would undoubtedly require considerably longer than one or two years. Changes in the technology of search and transfer, such as those promised through the application of biotechnology, would fundamentally alter both the magnitude of benefits and the relative costs of tapping specific categories of genetic resources.5 5 Relevant changes in technology are not confined to widecross and molecular methods. Hede et al. have found that seed regeneration and multiplication can be combined with evaluation for desirable traits, enabling the screening of large numbers of accessions at low cost.
Case 2. Multi-Stage Search in a Single Type of Material In some cases, it may be optimal for a researcher to implement a search in more than one stage. Researchers might, for example, choose to screen n1 accessions in an initial stage followed by an additional n2 accessions in a second-stage search, should the first search prove unsuccessful. Alternatively, a search might consist of any number L of stages. In practice, gene bank managers often search for desirable traits in batches, reflecting the budget constraints that they face for searches in any given time period. The advantages of a multi-stage search are several. First, it may allow researchers to reduce the overall size of the search (and hence the cost of searching). In a T -period search, if the date t search proves successful, then subsequent searches (t +1 t +2 · · · T ) become redundant and are omitted. Second, early stages of the search may provide information that allows researchers to focus the subsequent stages of the search more effectively (Rausser and Small). The principle disadvantage of a multi-stage search is that it may lengthen the amount of time required to achieve success. Discounting creates incen-
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tives to conduct more of the search in the earliest stages. Consider the general case of a finitehorizon dynamic batch search, in which search takes place over T periods. The potential population to be searched consists of N accessions (a gene bank, for example). The distribution of resistance is known. The researcher chooses the sizes of a sequence of batch searches, {nt }Tt=0 , to maximize the expected discounted value of the search. Note that once a search has yielded a successful outcome, no future batches are searched. We can write the researcher’s optimization problem as: max{nt }Tt=0 [π(n0 )B − cn0 ] (15)
+
T
t=1
×
t−1
s=0
[1 − π(ns )] st
T
t=0
nt ≤ N
This is a straightforward dynamic program, albeit one with many possible corner solutions to be checked. For the purposes of this paper, we make only a few observations about the general finite-horizon solution, and then we present an illustration for the case of two periods. Looking at the general finite-horizon problem, consider first the case of an interior solution, such that nt > 0 t = 0 1 T . The first-order necessary condition for the final period requires that nT be chosen such that: (16)
These problems can be handled with standard dynamic programming techniques. Note that the discount factor β is an important parameter in determining the sequence of search sizes. With a high value of β, it makes sense to delay a substantial portion of a search, in hopes of finding something in a small search early. In the extreme case, with β = 1, there is no added benefit in achieving early success in a search.6 By contrast, with a low value of β, it is optimal to emphasize early stages of the search. To provide a concrete example, consider the case of a two-stage search. There are three possible cases of interest: (i)
βt [π(nt )B − cnt ]
βT [1 − π(n0 )][1 − π(n1 )] [1 − π(nT −1 )][π (nT )B − c] = 0
But by construction, all of the bracketed expressions save the last are non-zero. Thus, it must be the case that nT satisfies the condition that [π (nT )B − c] = 0. From this condition, we can solve for n∗T and hence by backward induction we can recover the entire optimal sequence of searches. The interior solution is the simplest case, and we will need to check a number of alternative solutions. In particular, it may be optimal to search the entire collection, so that the constraint binds. In this case, it will generally be true that [π (nT )B − c] > 0, so finding a solution by backward induction is more difficult. Moreover, it may prove optimal to exhaust the entire collection at some date s prior to date T , so that nt = 0 t > s.
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n1 n2 > 0 and λ = 0
This is the case in which the search continues for both periods and does not exhaust the collection, so that the constraint does not bind. (ii)
n1 n2 > 0 and λ > 0
In this case, the search exhausts the collection in the second period and the constraint binds. (iii)
n1 > 0 n2 = 0 and λ > 0
In this case, the search exhausts the collection in the first period. Note that several other theoretically feasible cases can be ruled out. For example, it would be possible to have a solution with n1 > 0 and λ = 0, implying that the search ends after one stage without exhausting the collection. But this cannot be dynamically consistent, because conditional on reaching the second stage without having achieved success and without having exhausted the collection, it must be optimal to have n2 > 0. Similarly, eliminate the case with n1 = 0 and n2 > 0, which cannot be optimal for any discount rate β < 1. Consider the two-stage search problem using estimates of search costs and benefits 6 We are grateful to an anonymous reviewer for pointing out that in the case with an infinite time horizon and an infinite collection, as β → 1, the optimal search goes to zero. This is intuitively sensible; because there is no benefit to finding a solution sooner, rather than later, it makes sense to minimize cost by never searching unnecessarily. Even with an integer constraint on search size, the large size of the wheat gene bank suggests that this strategy could lead to searches lasting many millennia!
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from the earlier analysis of Russian wheat aphid. To begin with, we use the case in which benefits are $18.61 million and β = 09. For convenience, we take the total size of the gene bank, N , to be 50,000 accessions. To ascertain the optimal search strategy, consider the interior solution implied by (i) above; the interior solution with the size of the collection a binding constraint (ii); and the corner solution of (iii). Evaluating these alternatives shows that the optimum is the interior solution described in (i). This requires as a necessary condition that [π (n2 )B − c] = 0. From this, we can calculate that an optimal second-stage search sets n∗2 = 18800 (as in the singleperiod search). Furthermore, we know that [π (n1 )B − c] = βπ (n1 )[π(n2 )B − cn2 ]. Thus, by backward induction, we derive a value of n∗1 = 9100 and a discounted net expected benefit of $17.492 million. For this case, this turns out to be a superior search strategy when compared with the two alternatives.7 Suppose instead that we discount the future less heavily, so that β = 099. Using the same benefit and cost calculations, the optimal search continues to remain within the bounds of the collection, but the optimal first-stage search size falls to n∗1 = 6900, while the second-stage search remains the same size with n∗2 = 18800. The discounted net expected value rises to $17.961 million. The higher value of β makes it sensible to perform less of the search in the early stage, since it increases the value of finding useful material in the later stage. In general, a multi-stage search process implies that researchers will make “large” searches less frequently. Comparing the multi-stage search to the single-period search, the two-period search will most frequently search a smaller number of accessions. In the illustration above, with about 90% probability, the search will stop at 9,100 accessions, rather than the 18,800 evaluated in the single-period search. In some cases, however, the multi-stage search leads to “larger” searches than the single-period searches. In the example above, with about 10% probability, the search will evaluate a total of 27,900 accessions. The ability to search in multiple stages thus has implications for the marginal value 7 Note that as logic would suggest, this also represents a substantial increase (about $700,000) in the expected value of search, relative to the single-period search strategy.
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of accessions. Suppose that accessions in the gene bank are numbered and are searched in order. The ability to conduct multi-stage searches will tend to increase the marginal value of both “low” accession numbers and “high” accession numbers, relative to the marginal values based on single-period searches. At the same time, the ability to search in multiple stages will tend to reduce the marginal value of “intermediate” accessions. The reason for this is that searches will often stop after (small) initial-stage searches, but with some positive probability, searches will extend further into the collection than would be the case with a single-period search. Case 3. Specialized Knowledge The next experiment asks the value of specialized knowledge about the distributions of desirable traits in subcollections of wheat landraces. Figure 3 displays the actual and fitted distributions of resistance in a subset of 1,089 Iranian landraces evaluated by the CIMMYT gene bank. Searches of size fifteen among this subset were almost certain to result in resistant materials.8 For the most favorable scenario, expected net benefits rise by $1.69 million by searching Iranian landraces rather than the entire landrace collection. For the least favorable scenario, expected net benefits rise by $0.73 million. When a gene bank manager knows how to focus a search, both cost savings and the higher probability of finding useful material contribute positively to expected net benefits. It is clear that specialized knowledge can be extraordinarily valuable. We do not make any claim, however, as to the uniqueness of this specialized knowledge. It may be that many people share the specialized knowledge, so that we are measuring the value of public information. In many cases, though, it seems reasonable to imagine that the specialized knowledge is held by a relatively small number of scientists. Conceivably, technology may substitute gradually for this knowledge. Case 4. Searching Multiple Categories of Genetic Resources Researchers usually have the option of searching for desirable traits in more than one category of germplasm such as landraces, 8 The CIMMYT gene bank appears to contain a higher proportion of Iranian landraces than does the USDA collection for which screening results are reported in the GRIN.
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Figure 3. Actual and fitted distribution of resistance to Russian Wheat Aphid in 1,089 Iranian landraces of Triticum aestivum elite lines, and wild relatives. If more than one category is searched then the efficiency conditions of economic theory require that the expected marginal benefits of search be equalized across categories. Commonly such problems have corner solutions: when the distribution in each material is known, optimal search will omit all but the category with the highest expected marginal benefits. To explore this question, the case of Septoria tritici, is used a pathogen causing a leaf blotch that affects over 10 million hectares of wheat worldwide. Most of the area affected by the disease is found in the CIMMYT mandate areas (9 million hectares), including large portions of the Southern Cone of South America (Brazil, Chile, Argentina and Uruguay). In an effort to diversify the genetic basis of resistance to this pathogen, CIMMYT scientists searched for new sources of resistance in breeding lines, landraces and other materials, including emmer wheat (Fuentes and Gilchrist, Gilchrist and Mujeeb-Kazi, Gilchrist and Skovmand).9 We compared the distributions of resistance between breeding materials that had been drawn from working collections and accessions of emmer wheat from the gene bank. The actual and fitted distributions of 9
Emmer (T. dicoccon) is an ancestor of cultivated bread wheat.
resistance are shown in figure 4 and figure 5. Almost all of the emmer wheats, but relatively few of the breeding materials, displayed resistance. Time lags associated with transferring resistance into advanced lines created big differences in benefit streams’ however, transfer occurred within a year or two for breeding materials, while at least five years were required for emmer wheats. The variable costs of searching for resistant breeding materials are also much lower. Lines can be subjected to disease stress and resistant materials selected. Accessions of emmer wheat must first be head-selected to remove heterogeneity, and it is more timeconsuming to grow the plants and subject them to the necessary stresses because they are taller and less uniform. Average variable search costs for resistance to septoria tritici leaf blotch were estimated at about $6 per accession for breeding material and about $80 per accession for emmer wheats. Despite the superior distribution of resistance among emmer wheats, it is optimal to search only within the collection of breeding materials. To see why, suppose that we could be certain of finding a resistant emmer wheat in a draw of size one. Benefits would be $6.376 million (less $80 in search costs) in the most favorable scenario. Among breeding materials a search of at most 220 varieties will
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Figure 4. Actual and fitted distributions of resistance for Septoria leaf blotch in 1,834 breeding lines of Triticum aestivum
Figure 5. Actual and fitted distribution of resistance to septoria leaf blotech in 1,729 accessions of emmer
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have a 99% probability of finding resistant materials. The costs of this search are negligible (at most $912), and the benefit stream is higher, because the yield gains are attained sooner due to the ease of transferring resistance into advanced lines. The net benefit is $6.992 million, exceeding the expected benefits from the emmers. Other benefit scenarios lead to the same conclusion: it makes no sense to search for resistance in emmer wheat because the same trait can be found at lower cost in materials from the breeders’ collection. This experiment demonstrates why plant breeders, pathologists, and other scientists are sometimes reluctant to use unimproved materials from the gene bank. In explaining their choice, they appeal explicitly or implicitly to ideas of cost and time lags associated with using unimproved materials. Given the search cost differentials and time lags, it is often rational for researchers not to use the gene bank. When objectives are more complex than the identification of a single new trait, there may be good reasons to search in multiple populations, even if the payoffs are similar to those generated by this experiment. Researchers may turn to unimproved materials in an effort to ensure a “broader base of resistance” to a disease or pest problem by locating alternative resistance genes. Searching more than one population simultaneously may generate information of future value. Joint search may result from cost complementarity, meaning that the marginal costs of searching one type of material decline when another is searched. Where the search can help achieve an additional objective, such as a scientific advance or the testing of a new technique, or where two materials can be more cheaply searched if screened simultaneously, it may make economic sense to search more than one category of genetic resource.
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points about the valuation and utilization of ex situ collections. One conclusion is that the optimal size of a search for traits is highly sensitive to the economic magnitude of the problem, the research time lag, and the probability distribution of the trait. For some traits, the payoffs are not large enough to justify exhaustive searches. For others, the distributions are such that small searches will suffice. As illustrated by the case of Russian wheat aphid, there are occasional situations where the distribution of resistance and the payoffs to discovery are such that large searches are justified. These will be the situations from which large collections derive their value. A second conclusion is that differences in search costs and time lags across types of genetic materials can lead to optimal search strategies in which some categories are systematically ignored. With current search and transfer techniques, subcollections of landraces or wild relatives will indeed be used only on rare occasions—but high values may be associated with those occasions. In many situations it will be economically efficient to keep landraces sitting unused in banks. Until new wide-cross and molecular techniques can substantially reduce the costs and time lags of search for and transfer of traits into advanced lines, we should expect that collections of landraces and wild relatives will be seldom used. Most important, the observation that gene banks and some categories of accessions are infrequently demanded by crop breeders does not in itself imply that marginal accessions have low value. The short-term payoffs in the examples presented have been modest—which is not inconsistent with the conjecture that the long-term value of gene banks is high. The question that remains is how often large searches are warranted, and with what expected payoffs.
Conclusions We have developed a theoretical model and applied it to the search for disease and pest resistance in ex situ collections of wheat, employing actual frequency distributions from searches, parameters estimated from historical adoption data, and cost information from a gene bank. Numerical experiments enable us to clarify some essential
Implications for Further Research Experiments conducted on the basis of our single period model are sufficient to demonstrate some fundamental, qualitative points about the utilization of gene banks and their value. A single-period model of this type cannot be used to estimate the full marginal
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value of accessions because the costs of collection and conservation are fixed in the short-run, and option value has not been invoked. The search for a single trait, whether it is determined by a single gene or several, typically occurs when specific problems must be solved in crop breeding, such as the sudden mutation of a pathotype that challenges genetic resistance to disease. A multi-period model in which traits are first identified in populations and then recombined may better represent the routine operation of a plant breeding program, which involves the continual assembly and bundling of traits (Evenson and Lemarie). ´ Dynamic models, such as that proposed by Rausser and Small can be used to describe the effects of learning in sequential search decisions. Further research should analyze the effects of new technology on the costs of search and the exploitation of different categories of genetic resources, including novel sources of genetic diversity. [Received December 1997; Accepted February 2000.]
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Derived from Bread Wheat/D Genome Synthetic Hexaploids.” Poster presented at the Annual Meetings of the American Society of Agronomy, Indianapolis IN, August, 1996. Gilchrist, L.I., and B. Skovmand. “Evaluation of Emmer Wheat (Triticum dicoccon) for Resistance to Septoria tritici.” Proceedings of a Septoria tritici Workshop. L. Gilchrist, M. van Ginkel, A. McNab, and G.H.J. Kema, eds., Mexico DF: International Maize and Wheat Improvement Center (CIMMYT), 1995. Gollin, D., M. Smale, and B. Skovmand. Optimal Search in Ex Situ Collections of Wheat Genetic Resources. CIMMYT Economics Working Paper 98–03. Mexico DF: International Maize and Wheat Improvement Center (CIMMYT), 1998. Harvey, T.L., and T.J. Martin. “Resistance to Russian Wheat Aphid, Diuraphis Noxia, in Wheat (Triticum aestivum).” Cereal Res. Comm. 18(1990):127–9. Hede, A.R., B. Skovmand, M.P. Reynolds, J. Crossa, A.L. Vilhelmsen, and O. Stolen. “Evaluating Genetic Diversity for Heat Tolerance Traits in Mexican Landraces.” Genetic Resources and Crop Evolution 46(February 1999). Marasas, C., P. Anandajayasekeram, V. Tolnay, D. Martella, J. Purchase, G. Prinsloo. SocioEconomic Impact of the Russian Wheat Aphid Control Research Program. Southern African Center for Cooperation in Agricultural and Natural Resources Research and Training (SACCAR), Gaborone, Botswana, 1997. Plucknett, D.L., N.J.H. Smith, J.T. Williams, and N.M. Anishetty. Gene Banks and the World’s Food. Princeton NJ: Princeton University Press, 1987. Raeburn, P. The Last Harvest: the Genetic Gamble that Threatens to Destroy American Agriculture. New York: Simon & Schuster, 1995. Rausser, G.C., and A.A. Small. “Valuing Research Leads: Bioprospecting and the Conservation of Genetic Resources.” J. of Pol. Econ. 108(February 2000). Robinson, J. Identification and Characterization of Resistance to the Russian Wheat Aphid in Small-Grain Cereals: Investigations at CIMMYT, 1990–92. CIMMYT Research Report No. 3. Mexico DF: International Maize and Wheat Improvement Center (CIMMYT), 1994. Robinson, J. and B. Skovmand. “Evaluation of Emmer Wheat and Other Triticeae for Resistance to Russian Wheat Aphid.” Genetic Resources and Crop Evolution 39(June 1992):159–63.
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Sayre, K.D., R.P. Singh, J. Huerta-Espino, and S. Rajaram. “Genetic Progress in Reducing Losses to Leaf Rust in CIMMYT-Derived Mexican Spring Wheat Cultivars.” Crop Science 38(May–June 1998):654–69. Shiva, V. Monocultures of the Mind: Perspectives on Biodiversity and Biotechnology. Atlantic Highlands NJ.: Zed Books, 1993.
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