Agricultural Water Management 96 (2009) 1652–1658

Modeling the potential for closing quinoa yield gaps under varying wateravailability in the Bolivian Altiplano

S. Geerts a,*, D. Raes a, M. Garcia b, C. Taboada b, R. Miranda b, J. Cusicanqui b, T. Mhizha c, J. Vacher d

a K.U. Leuven University, Division of Soil and Water Management, Celestijnenlaan 200 E, B-3001 Leuven, Belgiumb Universidad Mayor de San Andres, UMSA, Facultad de Agronomıa, La Paz, Boliviac Department of Physics, University of Zimbabwe, Mount Pleasant Drive, Harare, Zimbabwed Ambassade de France au Perou, Lima, Peru

A R T I C L E I N F O

Article history:

Received 15 December 2008

Accepted 30 June 2009

Available online 28 July 2009

Keywords:

Water stress

Scenario analysis

Yield probability curve

Crop water productivity

Water shortage

Deficit irrigation

A B S T R A C T

In the Bolivian Altiplano, the yields of rainfed quinoa are relatively low and highly unstable. We use a

validated crop water productivity model to examine the potential of closing quinoa yield gaps in this

region. We simulate the expectable yields under rainfed cultivation and under different deficit irrigation

(DI) strategies using the AquaCrop model for the Northern, Central and Southern Bolivian Altiplano.

Simulated DI scenarios include a reference strategy avoiding stomatal closure during all sensitive growth

stages and allowing drought stress during the tolerant growth stages (DI0) and various restrictive deficit

irrigation strategies (DIi) representing cases when water resources are limited. We obtain a logistic crop

water production function for quinoa by plotting the seasonal actual evapotranspiration versus total

grain yield. Due to the large scatter, this function only indicatively provides expectable yields. From the

scenario analysis, we derive yield probability curves for the 3 agro-climatic regions. DI, without

restriction in irrigation water during the drought sensitive growth stages, is able to close the yield gaps in

the Northern, Central and Southern Bolivian Altiplano, and would guarantee a high and stable level of

water productivity (WP). The yields of quinoa under rainfed cultivation during dry years are only 1.1, 0.5

and 0.2 Mg ha�1 in the Northern, Central and Southern Bolivian Altiplano, whereas under DI0 they are

2.2, 1.6 and 1.5 Mg ha�1, respectively. Under limited water availability for irrigation, these stable yield

levels decrease, most drastically in the Southern Bolivian Altiplano. Below a minimum water availability

of 600 m3 per ha and 700 m3 per ha in the Central and Southern Bolivian Altiplano, respectively, the

application of DI for quinoa is not significantly effective and should be avoided to save valuable

resources. The yield probability curves we derive can serve as input for stochastic economic analysis of DI

of quinoa in the Bolivian Altiplano.

� 2009 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

Agricultural Water Management

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1. Introduction

Quinoa (Chenopodium quinoa Willd.) is a traditional Andeanpseudo-cereal that is rapidly gaining interest throughout the world(Jacobsen, 2003; Bhargava et al., 2006), due largely to its highnutritional value (Comai et al., 2007) and its adaptability tounfavorable soil and climatic conditions (Garcia et al., 2003; Geertset al., 2006).

A quarter of the rural population of Bolivia lives in the Altiplano(Vacher, 1998), which is an arid plane at 4000 m.a.s.l. Crop yields inthe region are notably unstable, due to harsh cropping conditions(Garcia et al., 2004). Quinoa, one of the few staple crops in the

* Corresponding author. Tel.: +32 16 32 97 54; fax: +32 16 32 97 60.

E-mail addresses: sam.geerts@biw.kuleuven.be, samgeerts@yahoo.com

(S. Geerts).

0378-3774/$ – see front matter � 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.agwat.2009.06.020

region, is typically cultivated under rainfed conditions. In recentdecades, the average quinoa yield was 0.6 Mg ha�1 in the BolivianAltiplano, with extremely low yields in dry years (INE, 2003). Dueto limited water resources in the region (Garcia et al., 2003) fullirrigation of the crop is not an option for stabilizing yields. Fieldexperiments at various locations in the region have demonstratedthat deficit irrigation (DI) can result in reliable quinoa yields andhigh crop water productivity (WP) (Geerts et al., 2008a,b).Although DI (English, 1990; Zhang and Oweis, 1999; Pereiraet al., 2002; Geerts and Raes, 2009) does not provide the totalseasonal crop water requirement, it stabilizes yields if a certainminimum amount of water is supplied (Fereres and Soriano, 2007;Geerts et al., 2008b).

To further study the long-term beneficial effect of DI, the yieldresponse of quinoa to various levels of water supply by rainfall andirrigation is required. This type of response function is typicallyused in econometric studies (English and Raja, 1996). Because DI of

Table 1Textural class, soil water content at various matrix potentials (C) and saturated hydraulic conductivity (Ksat) for typical soils in the Northern (Huarina), Central (Patacamaya)

and Southern (Rio Mulatos) Bolivian Altiplano.

Textural class Soil water content (vol.%) at Ksat (mm day�1)

Wilting point (C = �1.5 MPa) Field capacity (C = �15.5 kPa) Saturation (C = 0 kPa)

Huarina

Sandy loam 6 23 46 700

Patacamaya

Sandy loam 6 23 46 700

Rio Mulatos

Sand 4 15 40 2000

Table 2Strategies of deficit irrigation (DI) under different levels of water availability, with

their tolerated level of soil water depletion in the root zone, expressed as a

percentage of the total available soil water (TAW).

Strategy Tolerated level of soil

water depletion from

the root zone (% TAW)

Scenario of water

availability

DI0 61 High

DI1 85 Intermediate

DI2 90 Intermediate

DI3 95 Low

S. Geerts et al. / Agricultural Water Management 96 (2009) 1652–1658 1653

quinoa is not yet a common practice in the Bolivian Altiplano, andthere is little information regarding cases when water resources forDI are very limited, simulations by crop models are useful instudying the yield response to water (Hoogenboom, 2000; vanIttersum et al., 2003; Timsina et al., 2008; Bhatia et al., 2008).

The crop water productivity model AquaCrop (Steduto et al.,2009; Raes et al., 2009), which provides a good balance betweenmodel robustness, data requirements and accuracy, has beencalibrated and validated for simulating quinoa production in theBolivian Altiplano (Geerts et al., 2009). We use the AquaCrop modelto derive probability curves for quinoa grain yields. We considerdaily weather data for the last 25–30 years in three representativelocations of the Bolivian Altiplano and examine different scenariosof water availability for DI. Our results describe the expected yieldsfor rainfed quinoa and quinoa under DI in the various agro-climaticzones, as well as the related WP and the minimum amount ofirrigation water that is required to have a significant effect of DIcompared with rainfed cultivation.

2. Methodology

2.1. Simulations of quinoa production

We simulated quinoa yields with AquaCrop for three locationsin the Bolivian Altiplano: Huarina (168120S, 688360W,3825 m.a.s.l.), Patacamaya (178160S, 678570W, 3799 m.a.s.l.) andRio Mulatos (198410, 668460, 3815 m.a.s.l.). The locations arerepresentative of the Northern, Central and Southern part of theBolivian Altiplano from an agro-climatic point of view (Geertset al., 2006). We obtained daily climatic data for rainfall andreference evapotranspiration (ET0) for 25–30 recent years between1970 and 2003 from the agro-climatic GIS library of Geerts et al.(2006). For each year, we determined the best sowing date in theNorthern and Central Bolivian Altiplano using the onset criterion ofGeerts et al. (2006), with a latest possible sowing date on 10November. We obtained the initial soil water content byconsidering the preceding rainfall or by pre-sowing irrigation inthe case of DI. For the Southern Bolivian Altiplano, we assumedsowing on 20 September with an initial soil water content of 50% ofthe total available water content (TAW). This relatively high initialsoil water content is the result of considerable soil wateraccumulation during the preceding fallow year in case of rainfedcultivation, or as a result of pre-sowing irrigation. Soil character-istics typical for the region were considered in the simulations(Table 1). We considered a soil depth of 2 m, with a root restrictivelayer at 0.5 m in the Northern and Central Bolivian Altiplano due tocompaction by repeated mechanical cultivation. We used thequinoa crop inputs as specified by Geerts et al. (2009).

Considering the soil types, we assumed fixed net irrigationapplication depths of 20 mm (North and Central) and 10 mm(South). On the loamy soils of the Northern and Central BolivianAltiplano the depth of 20 mm can be applied by short furrow

irrigation, whereas on the sandy soils of the Southern BolivianAltiplano, the irrigation depth of 10 mm should be applied by dripirrigation or irrigation with a mobile cistern for wide spacedsowing pits. Since only DI is assessed, irrigation is only applied inthe model during the drought sensitive growth stages of quinoa.For the initial establishment phase, irrigation in the model wasapplied before sowing. During the sensitive flowering and earlygrain filling phase, the crop was irrigated whenever a givenpercentage of TAW was depleted. We set the reference depletionlevel during the sensitive growth stages (DI0) at 100% of the readilyavailable soil water (RAW), which equals 61% TAW. At this level allthe readily available soil water is depleted and delaying irrigationwill result in stomatal closure (Garcia, 2003). Further on, if thisdepletion level is not exceeded during flowering or early grainfilling, a maximal harvest index (HI) is guaranteed (Geerts et al.,2008a). To consider levels of restricted water resources forirrigation, we increased the allowable depletion level from 61%TAW to 95% TAW (low water availability; DI3) with intermediatedepletion levels of 85% (DI1) and 90% TAW (DI2) (Table 2). Theselevels simulate a delay in irrigation and will invoke yield decline.

To consider the spatial (3 locations) and temporal (25–30 yearsof historical data) variations in weather conditions in the BolivianAltiplano, and the different scenarios of water availability, wegenerated about 400 simulations for quinoa with the calibratedAquaCrop model. By summing the actual transpiration over thereference evapotranspiration (Ta/ET0) for each simulation run weassessed the possible shift in anthesis and time to maturity (Geertset al., 2008c). In case of a low (Ta/ET0) sum for the first 60 days aftersowing, we repeated the simulation with a crop cycle adjusted forthe late anthesis and maturity according to Geerts et al. (2008c).The sum of (Ta/ET0) also served to assess possible nutrientdepletion during wet years. In these cases, we used a lowerbiomass water productivity coefficient (Steduto et al., 2007) in thesimulations (Steduto and Albrizio, 2005; Geerts, 2008).

2.2. Crop water production functions and yield probability curves

We obtained a crop water production (CWP) function byplotting the seasonal actual evapotranspiration (ETa) versus total

Fig. 1. Crop water production function (a) for quinoa in all experimental fields (full

black circle) and for quinoa under varying deficit irrigation strategies, simulated in

the Northern (hollow circle), Central (plus sign) and Southern Bolivian Altiplano

(asterisk) with indication (bold line) of the logistic curve (***a = 0.001), and (b) the

corresponding seasonal water productivity with indication (full line) of the upper

envelope function. The target zone with high WP and the dependable rainfall for dry

(start solid line) and wet (end solid line) years for the three regions of the Bolivian

Altiplano are indicated.

Table 3Dependable levels of rainfall and net irrigation requirement for quinoa under the

reference deficit irrigation strategy (DI0) in the Northern, Central and Southern

Bolivian Altiplano with indication of the corresponding probability of exceedance

(PE).

Region Dry year (80% PE) Wet year (20% PE)

Rainfall (mm)

Northern 375 513

Central 261 412

Southern 207 377

Region Dry year (20% PE) Wet year (80% PE)

Net irrigation requirement for DI0 deficit irrigation (mm)

Northern 120 60

Central 160 100

Southern 190 90

S. Geerts et al. / Agricultural Water Management 96 (2009) 1652–16581654

grain yield for each of the 400 simulation runs and for the observedquinoa yields reported by Geerts (2008). We calculated thecorresponding WP as the total grain yield divided by the seasonalETa (kg m�3). In a second step, we derived curves of expected yieldsunder various DI strategies from the simulations for the three agro-climatic zones and calculated the corresponding average andmaximum required amounts of irrigation water. To assess whethera certain DI strategy with limited water application results insignificantly higher quinoa yields than rainfed cultivation, wecompared the average WP for each DI strategy per location byusing paired sample t-tests at a significance level of 0.05. Finally wederived the required minimum irrigation water amount belowwhich DI does not result in significantly higher WP as compared torainfed cultivation by increasing the soil water depletion beforeirrigating in the simulations.

3. Results and discussion

3.1. Crop water production functions

Observed yields (Geerts, 2008) and simulated yields for each ofthe 25–30 historical years, for each of the three locations in theBolivian Altiplano, and for the varying conditions of wateravailability in the region are presented in Fig. 1. The resultingcrop water production (CWP) function for quinoa (Fig. 1a) islogistic (Hexem and Heady, 1978; Taylor et al., 1983; DeTar, 2008).The corresponding seasonal WP is plotted versus seasonal ETa inFig. 1b. The maximum WP (between 320 and 360 mm seasonalETa), obtained from the envelope function above the individualpoints, is considered as target (Bos, 1997) for quinoa cultivation inthe region. If calculated on the basis of the actual equation, theseasonal target is higher (between 400 and 440 mm seasonal ETa).We summarize additional information on dependable rainfall(Geerts et al., 2006) and net DI requirement (Dinet) for theNorthern, Central and Southern Bolivian Altiplano in Fig. 1 andTable 3.

Since AquaCrop was calibrated for fields with good sowingmaterial and intensive pest management (Geerts, 2008), yieldsunder farmers’ conditions (sometimes without pest management,or with low quality seeds) might be somewhat lower than thosedepicted in Fig. 1. However, yield levels for the Northern andCentral Altiplano could increase if raised bed sowing is adopted.This would allow for additional irrigation during the establishmentstage and rainwater harvesting in the closed furrows. In thepresence of capillary rise in the Southern Bolivian Altiplano (Geertset al., 2008b), reported yields could also be higher.

The functional relationship (Fig. 1a) summarizes all of thesimulation results. This function is a lumped relation for rapidappraisal of quinoa yield response to water stress in the BolivianAltiplano. Following English (1990) and English and Raja(1996), the derived CWP function can generate revenue functionsunder different seasonal ETa. If combined with a validated costfunction, the optimum irrigation amount to be applied underdifferent economical conditions can be derived. The functionshould nevertheless be used with great care since depending onthe water distribution within the season, quinoa yield can varythree fold for a similar seasonal ETa (e.g. a seasonal ETa sum of300 mm can result in 0.5–1.5 Mg ha�1 of grain yield). We canonly slightly improve the regression by plotting the resultsindividually for a particular water application strategy for eachlocation (Fig. 2).

3.2. Yield probability curves under varying irrigation water supply

Because of the large scatter in Figs. 1 and 2, we recommendusing more accurate representation of the yield response to water

Fig. 2. Crop water production function for quinoa in Patacamaya (Central Bolivian Altiplano) under (a) rainfed cultivation and (b) under the reference deficit irrigation strategy

(DI0) with indication of the logistic curve (bold line) and the 95% confidence interval.

S. Geerts et al. / Agricultural Water Management 96 (2009) 1652–1658 1655

within econometric models. One possibility is incorporating thevalidated crop water productivity model into the econometricmodel. Another option is deriving probability distributions fromthe obtained simulation results (Fig. 3).

In Fig. 3 we present the probability of exceedance for obtaininga particular quinoa yield level under a certain DI strategy. Weestimate expected yields in a dry year and a wet year with yields at80% and 20% probability of exceedance (PE), respectively. Sincesome extreme rain events can still occur on a longer time scale, theupper and lower ends of the probability functions should beconsidered with some care. Because mildew, and other diseasesand pests, are important causes of yield loss in quinoa when fieldconditions become very humid (Danielsen and Munk, 2004; Kumaret al., 2006), the graphs are less reliable for deriving the probabilityof high yields in wet years (20% PE). In addition, soil fertility

Fig. 3. Probability of exceedance of total grain yields in the Northern (a), Central (b) and

Rainfed, DI0 is the reference DI strategy, and DI1, DI2 and DI3 are strategies for differen

limitations are also more stringent for well-watered conditions(Heng et al., 2007). Due to small differences between DI strategiesin the Northern Bolivian Altiplano, we present the results of a fewstrategies for reasons of clarity. Table 4 shows the correspondingmaximum and average required irrigation water for the various DIstrategies in the 3 agro-climatic regions.

The difference in expected quinoa yield between rainfedcultivation and DI0 cultivation is substantial in each location(Fig. 3). Under rainfed conditions the minimum yield in dry years(80% PE) is only 1.1, 0.5 and 0.2 Mg ha�1 in Huarina, Patacamayaand Rio Mulatos, respectively. The DI0 strategy stabilizes theminimal yields that can be expected in dry years at 2.2, 1.6 and1.5 Mg ha�1, respectively. If less irrigation water is available(intermediate DI strategies with limited supply), the dependableminimum yield levels decrease gradually but remain substantial

Southern Bolivian Altiplano (c) under different deficit irrigation (DI) strategies (R:

t levels of water availability (n = 25–30).

Table 4Maximum and average required seasonal irrigation water for the 3 regions in the Bolivian Altiplano, and for different irrigation

strategies (DIi; Table 2 considering varying water availability in the region. Values are presented �1 standard deviation (n = 25–30).

Applied irrigation Rainfed DI0 DI1 DI2 DI3

Huarina (Northern Bolivian Altiplano)

Maximum (mm) 0 140 80

Average (mm) 0 87 � 29 46 � 23

Patacamaya (Central Bolivian Altiplano)

Maximum (mm) 0 200 180 120 100

Average (mm) 0 130 � 38 101 � 37 71 � 29 55 � 23

Rio Mulatos (Southern Bolivian Altiplano)

Maximum (mm) 0 220 160 120 90

Average (mm) 0 153 � 50 102 � 35 75 � 24 54 � 16

Fig. 4. Probability of exceedance of required irrigation water for the deficit irrigation

(DI) strategies under varying seasonal water availability in Patacamaya (n = 30).

S. Geerts et al. / Agricultural Water Management 96 (2009) 1652–16581656

and above the yields under rainfed conditions. Commercialproducers and associations with a good water supply can usethe DI0 strategy to maximize water productivity by completelyavoiding drought stress during sensitive growth stages. The otherDI strategies are more appropriate for farmers with limited inputs,especially if soil fertility is a constraint.

The yields of quinoa under DI are more stable than those underrainfed conditions. Differences between yields in normal (50% PE)and dry (80% PE) years are indeed much smaller under DIthan under rainfed cultivation. Hence, DI aims to stabilize yieldsand is a management practice for risk reduction (English and Raja,1996).

Although in 1 year out of 2, yield levels under rainfed and DIcultivation in the more humid Northern Altiplano (Huarina) aresimilar, serious yield reductions are expected under rainfedconditions in the dry years. This confirms previous findings byGeerts et al. (2006). They mention that in 1 year out of 5, DI canincrease quinoa yield and WP by mitigating intra-seasonal dryspells (Fox and Rockstrom, 2003), notwithstanding the humidcharacter of the Northern Bolivian Altiplano. For instance, in thedry El Nino year 1990–1991 (Delaet, 2006) all rainfall occurredoutside the sensitive growth stages of quinoa. In these conditionswe can only obtain reliable yields with irrigation.

In the arid Southern Bolivian Altiplano (Rio Mulatos), applyingthe DI0 strategy has a pronounced effect. This positive impactreduces drastically under dry and normal weather conditions ifirrigation water is limited. Geerts et al. (2008b) confirm thatlimited DI supply in dry years does not significantly increasequinoa yield compared to rainfed cultivation, due to a low harvestindex of the crop under those conditions. To apply the DI2 strategy,a farmer needs on average 71 and 75 mm of water in Patacamayaand Rio Mulatos, respectively. With this strategy the expectedyield in dry years is around 1.1 Mg ha�1 in Patacamaya and only0.7 Mg ha�1 in Rio Mulatos.

The presented yield probability functions under varyingavailable irrigation water (Fig. 3) can be used as stochastic revenuefunctions in economic studies on DI of quinoa. The water use per

Table 5Water productivity (kg m�3) for different deficit irrigation (DI) strateg

indicate significant statistical groups (a = 0.05) from paired sample t

location-strategy combination).

Rainfed DI0 DI1

Huarina (Northern Bolivian Altiplano)

0.43a � 0.10 0.48a � 0.05

Patacamaya (Central Bolivian Altiplano)

0.29a � 0.12 0.42e � 0.05 0.41d �

Rio Mulatos (Southern Bolivian Altiplano)

0.22a � 0.13 0.48e � 0.04 0.42d �

irrigation strategy and per year can be plotted to obtain stochasticcost functions. We present an example for the DI strategies inPatacamaya in Fig. 4.

Table 5 presents the average simulated WP of quinoa undervarying DI strategies. The significant differences in WP can beexplained by a number of reasons. First, the harvest index variesdue to drought stress (e.g. Ferris et al., 1999; Tourneaux et al.,2003; Xue et al., 2006; Fereres and Soriano, 2007). The overallaverage harvest indices of quinoa under rainfed conditions are7% lower than those of quinoa under the DI0 treatment, withespecially low harvest indices under rainfed cultivation in dryyears. Second, the flexible phenology of quinoa in response todrought stress has an effect on WP. Sensitive phenological stages ofquinoa under varying DI strategies can occur at a different time due

ies in the 3 regions in the Bolivian Altiplano. Letters in superscript

-tests. Values are presented �1 standard deviation (n = 25–30 per

DI2 DI3

0.46a � 0.07

0.05 0.39c � 0.06 0.37b � 0.07

0.03 0.38c � 0.06 0.34b � 0.08

S. Geerts et al. / Agricultural Water Management 96 (2009) 1652–1658 1657

to the dynamic nature of the growth cycle (e.g. Abrecht andCarberry, 1993; Farre and Faci, 2006; Geerts et al., 2008c).Therefore, the effect of dry spells in a particular period of theyear can vary. Third, evaporation losses from fields with poorcanopy cover can decrease WP. Next, if the seasonal sum of rainfalland irrigation is considerable, soil nutrients can become a limitingfactor. In this case, the resulting vigorous biomass development inthe initial stages cannot be maintained by the low soil fertility (e.g.Azam-Ali and Squire, 2002; Heng et al., 2007; Geerts, 2008).Finally, water logging due to over-irrigation during wet years canreduce transpiration (Raes et al., 2006).

WP increases from South to North for quinoa under rainfedconditions or with limited water application (DI3). The differencesin WP between the locations and treatments decrease if waterapplication is considerable (DI0 and DI1). In the Northern BolivianAltiplano, the average WP of rainfed quinoa is not significantlydifferent from quinoa under DI. This is due to water logging andnutrient depletion when DI is applied in wet years. In the Centraland Southern Bolivian Altiplano, DI0 results in the significantlyhighest WP. Applying DI0 in these regions maximizes the output ofevery drop of water. The lower standard deviations of the yieldsunder DI show the small inter-annual variation compared torainfed quinoa.

Limited iterations for more severe soil water depletion levelsthan those presented in Table 2 depict the minimum requiredseasonal irrigation water volume. Irrigation should not beconsidered if less than 60 mm (600 m3 ha�1) and 70 mm(700 m3 ha�1) of irrigation water is available per season in theCentral and Southern Altiplano, respectively.

4. Conclusion

Crop water productivity models are valuable tools for examin-ing the cumulative effect of the water stress tolerance mechanismsof quinoa. We derived a logistic seasonal crop water productionfunction for quinoa in the Bolivian Altiplano using simulations oflong series of historical cropping seasons (daily data). The targetvalue of seasonal water application is about 340 mm. Since thisfunction contains a large scatter, it only gives a first indication onthe yield response to seasonal water use. From the simulations wealso derived yield probability curves, presenting dependable yieldlevels for varying availability of irrigation water. These probabilitycurves are considered to be more precise and preferable instochastic economic studies.

Deficit irrigation can stabilize yields at a level that issignificantly higher than under rainfed cultivation. While notmaximizing yields, deficit irrigation minimizes the occurrence ofyears in which yields fail. Yield gaps are closed in both space andtime by deficit irrigation under the condition that irrigation wateris not restrictive during the drought sensitive growth stages. Thenatural agro-climatic differences between the Northern andSouthern Bolivian Altiplano are leveled out and extreme yieldgaps in time (e.g. El Nino year 1990–1991) are prevented. In theCentral and Southern Bolivian Altiplano deficit irrigation results insignificantly higher water productivity compared with rainfedcultivation, whereas in the Northern Bolivian Altiplano, deficitirrigation is beneficial only in 1 year out of 5 in terms of waterproductivity. Throughout the Bolivian Altiplano, a relatively highand stable average water productivity of 0.46 kg m�3 is reached.

By reducing irrigation water supply during the droughtsensitive growth stages of quinoa, the positive effect of deficitirrigation declines, mostly in the Central and Southern BolivianAltiplano. Below 60 and 70 mm of seasonally available water,respectively, deficit irrigation does not significantly improve waterproductivity compared with rainfed cultivation. These thresholds

should be considered in efforts to avoid wasting limited resources(time, energy and water) in dry regions.

Acknowledgements

Research funded by a PhD grant of the Flemish InteruniversityCouncil (VLIR) and by the Research Fund K.U.Leuven for post-doctoral fellowships. The research was carried out in Bolivia in theframe of the VLIR Own Initiative Project QuinAgua, scientificcollaboration between K.U.Leuven and the Universidad Mayor deSan Andres. We are grateful for additional comments by PasqualeSteduto, Jan Feyen and Guido Wyseure.

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