African Crop Science Journal, Vol. 29, No. 1, pp. 141 - 156 ISSN 1021-9730/2021 $4.00 Printed in Uganda. All rights reserved © 2021, African Crop Science Society

African Crop Science Journal by African Crop Science Society is licensed under a Creative Commons Attribution 3.0 Uganda License. Based on a work at www.ajol.info/ and www.bioline.org.br/cs DOI: https://dx.doi.org/10.4314/acsj.v29i1.10

MAPPING OF SOIL NUTRIENT DEFICIENCY IN OIL PALM PLANTATIONS OF SOUTHERN

N.S. KINDOHOUNDÉ1, 2, L. NODICHAO1, N.S.H. AHOLOUKPÈ1 and A. SAÏDOU2

1Institut National des Recherches Agricoles du Bénin (INRAB)/Centre de Recherches Agricoles sur les Plantes Pérennes (CRA-PP) BP. 01 Pobè, Bénin 2 Unité de Recherche sur la Gestion Intégrée des Sols et des Cultures (ISCM), Laboratoire des Sciences du Sol, Ecole des Sciences et Techniques de Production Végétale, Faculté des Sciences Agronomiques (FSA), Université d’-Calavi (UAC) Bénin, 04 BP 1510 Cadjèhoun, , Bénin Corresponding author: [email protected]

(Received 9 June 2020; accepted 17 February 2021)

ABSTRACT

Soil degradation poses a threat to sub-Saharan sustainability of agriculture namely because of chemical and physical degradation. The objective of this study was to characterise soil properties in oil palm plantation in the districts of Ouémé and Plateau and develop spatial maps for soil nutrients useful in agricultural land use as a basis for designing soil fertility management strategies. A survey carried out in oil palm (Elaeis guineensis Jacq.) plantations in the southern Benin, revealed mineral deficiency symptoms consequent to poor mineral nutrition of the plant. A total of 428 soil composite samples were collected under farmers’ adult oil palm trees, randomly selected. These oil palm plantations were located on four soil types: Acrisol, Plintics and luvisols, Hydromorphic soil and Vertisols. In total, 370 samples were collected on plantations under Acrisols, 22 samples under Plintics and luvisols, 26 samples under Hydromorphic soil and 10 samples under Vertisols. Geostatistic methods were used to determine the spatial variability; and semi-variogram methods were established using ordinary kriging. A strong spatial dependency for nitrogen, phosphorus, potassium and magnesium was observed; while spatial dependency of calcium was moderated. The map of nutrient deficiency revealed two large areas. The first, included the districts of , , Sakété, Adja-Ouèrè, and Pobè, where oil palm plants showed an acute nitrogen, phosphorus and potassium deficiency; and the second area of , Missérété, , , which presented nitrogen, potassium and slight phosphorus deficiency in the oil palm plantations. Most of the soils under the oil palm plantations showed nitrogen, phosphorus and potassium deficiency.

Key Words: Deficiency mapping, nutrient deficiency, semivariogram 142 N.S. KINDOHOUNDÉ et al. RÉSUMÉ

Afin d’apporter une solution à la manifestation des symptômes de déficience minérale dans les plantations paysannes de palmier à huile, la présente étude vise à déterminer la variabilité spatiale des déficiences en nutriments au niveau de trois types de sol au sud Bénin pour une cartographie des manifestations. A cet effet, 428 échantillons composites de sol ont été collectés au niveau des plantations paysannes de palmier à huile sur sols Ferrallitiques, sols Ferrugineux tropicaux, sols Hydromophes et Vertisols. Au total 370 échantillons ont été prélevés au niveau des sols Ferrallitiques, 22 au niveau des sols Ferrugineux tropicaux, 26 au niveau des sols Hydromorphes et 10 au niveau des Vertisols. La géostatistique a permis de déterminer la variabilité spatiale des carences minérales des sols et les semi- variogrammes ont été établis à l’aide du krigeage ordinaire. Un grand nombre d’arbres ont présenté des carences en azote, phosphore, potassium et magnésium, en revanche, la dispersion spatiale des arbres présentant une carence en calcium était modérée. La cartographie des déficiences minérales des sols a révélé deux grandes zones similaires : la première présentant des signes de carence en azote, phosphore et potassium regroupe les communes de Bonou, Adjohoun, Sakété, Adja-Ouèrè, et Pobè, la seconde constituée des communes de Dangbo, Missérété, Ifangni, Avrankou, Adjarra avec des palmeraies présentant des signes de carence sévère en azote et potassium et des signes de carence moins prononcés en phosphore.

Mots Clés : Cartographie des carences, carences nutritionnelles, semivariogramme

INTRODUCTION were discolored and deformed, displaying chlorosis, orange spots, wavy and embossed Soil degradation poses a threat to sub-Saharan leaves, stunted/malformed leaves and white sustainability of agriculture mainly because of strips, mostly typical of nitrogen and chemical and physical degradation. The loss potassium deficiencies as well as probable of soil organic matter (SOM), nutrient boron and magnesium deficiencies. On depletion, soil erosion and changes in soil average, 45.92% nutrient deficiency symptoms structure are by far the most outstanding manifested with a weak appearance symptom phenomena (Seutloali and Beckedahl, 2015). in the fertilised oil palm plantation. This calls In Benin, especially in the Ouémé and Plateau for appropriate soil management actions to districts, selective establishment of oil palm improve the yield of farmers’ oil palm plantations in the past led to the conversion of plantation. forests into oil palm plantations. This Furthermore, micro variability of soil under contributed to increase of oil palm plantation oil palm plantation in the districts of Ouémé area from 867 ha in 1997 to 16,000 ha in 2012 and Plateau in Benin is weakly studied, and (Adjadi et al., 2012). This forest conversion fertilisers are applied without into palm oil plantations, drained soil fertility recommendation. In general, the spatio- depending on plantation age (Dewi, 2007). temporal variation of physical, chemical and This change in soil properties will be more biological processes, as well as the crucial if farmers do not apply fertilisers to anthropogenic land use patterns and the supply nutrients to the plants, as it is the case combination of their action, may result in in the Ouémé and Plateau districts where about spatial variability of soil properties 50.09 and 58.5%, respectively, of the oil palm (Goovaerets, 1998). plantations are not fertilised (Kindohoundé et The objective of this study was to al., 2018). In fact, in the farmers’ oil palm characterise soil properties in oil palm plantations in the south Benin, several leaves plantation in the districts of Ouémé and Plateau Mapping of soil nutrient deficiency in oil palm plantations 143 with a view to developing spatial maps for soil and 1 300 mm per year (Nouy, 1999), which nutrients useful in agricultural land use and provides good growth conditions of the oil designing of soil fertility management palm trees, compared to other districts of strategies. Benin.

MATERIALS AND METHODS Soil sampling. Farmers’ mature oil palm plantations (more than 6 years, Von Uexkull Study area. The study was carried in the and Fairhurst, 1991) were used for the districts of Ouémé (especially in the districts identification of nutrient deficiency symptoms of Bonou, Adjohoun, Dangbo, Missérété, manifestation (Kindohoundé et al., 2018). A Avrankou and Adjarra) and Plateau (Ifangni, binomial approximation formula of Dagnelie Sakété, Adja-Ouèrè and Pobè) located in the (1998) was used to define the size of the south-East of Benin (Fig. 1). These two plantation, from which soil samples were districts are under a sub-equatorial climate, collected. with an alternation of two rainy seasons from Sampling was done in 214 farmers’ mature March to July and from September to oil palm plantations (with an average of 2.5 ha November. Acrisols (dominant), Vertisols (at per farmer); 108 in the district of Ouémé and Pobè and Adja-Ouèrè), hydromorphic soils (in 106 in the district of Plateau. For each sampled the lowland) and Ferric and Plintic luvisols site, the distribution of nutrient deficiency (northern of the ) (FAO, symptoms, and the history of land use and the 2006) are dominant soils of the study area. soil nature were recorded across both Rainfall in those districts ranges between 900 diagonals, especially at the extremities of

Figure 1. Study area and sampling points in oil palm plantations in Benin. 144 N.S. KINDOHOUNDÉ et al. diagonals and the centre of the field. But when Data analysis. The descriptive statistics land size was less than 1 ha, soil samples were (mean and standard deviation) were calculated only collected from both extremities and the for each soil property using XLSTAT software. centre of the field. In addition, a two-way analysis of variance The oil palm trees were randomly selected was done for each nutrient, considering the before soil sampling. The procedure developed soil depth and soil type. The means were by Behera et al. (2015, 2016) was adopted compared using Student Newman Keuls test and soil samples were collected under three at 5% level. The critical nutrient concentration oil palm trees (for plantation < 1 ha) or five value in the soil for mature oil palm elaborated (for plantation > 1 ha). by Goh and Chew (1997) for nitrogen and Composite soil samples were taken at 0 - phosphorus, Young and Brown (1962) (K and 30 and 30-60 cm depth, around the oil palm Ca), Rossiter and van Wambeke (1993) (Mg) trees, as the majority of oil palm’s roots were and Jacquemard (2011) (pH and CEC) was concentrated at 0-60 cm depth. Due to fair used to assess deficiency level (Table 1) in soil homogeneity observed in the oil palm the oil palm plantation. plantation, subsamples collected in each of area defined were mixed to constitute composite Geostatistical analysis. The spatial sample considering each soil depth and per oil distribution of soil nutrient concentrations was palm plantation. Finally, 428 composite established on a map to appreciate the samples of approximately 500 g each were correlation between them; and make collected (214 composite samples for each relationships with oil palm tree’s leaf depth), air dried and sieved at through 2 mm, symptoms. Variograms or semi-variograms before sealing in polythene bags for analysis (Christakos et al., 2002) were achieved to at laboratory. The latitude, longitude, and highlight the spatial correlation previously elevation at each sampling point were observed by kindohoundé et al. (2018). recorded using global positioning system Different variogram model (exponential, (GPS). spherical, Gaussian and Matern) were evaluated to determine the best fit for Soil analysis. The samples were analysed for explaining the spatial structure of each soil physical and chemical characteristics. Soil variable. The models were compared and particle sizes were determined using Robinson variograms constructed using autofit pipette method, pH (water) was determined Variogram function of the package of automap based on soil/water 1: 2.5 v/v ratio, using the (Hiemstra et al., 2008). From the best fitted potentiometric method (Jackson, 1973). Total model of variogram, nutrient concentrations N was determined using micro-Kjeldahl in the oil palm plantations were predicted using digestion in H2SO4 and Selenium, followed by ordinary kriging (Christakos et al., 2002; distillation and titration. Exchangeable Ca2+ and Kumar and Remadevi, 2006), following the Mg2+ were determined by atomic absorption auto Krige function of the automap package spectrophotometry; and K+ by flame of R software version 3.5.3 (R Core Team, photometry. Before the test, samples were 2019). extracted following standard procedures. Mineral deficiency maps of each nutrient Phosphorus was measured colorimetrically by were developed using ArcGIS 10.4.1 software ammonium molybdate with ascorbic acid at a (Esri, Los Angeles, USA), based on the wavelength of 660 nm. The analyses were previous predictions homogeneous sites and carried out at the Laboratory of Soil Science classes of nutrient deficiency status. Water and Environment of the Benin National The experimental semivariograms of soil Agricultural Research Institute (INRAB). properties were derived from Equation 1: Mapping of soil nutrient deficiency in oil palm plantations 145

...... Equation 1 ambeke (1993) W Where:

ã(h) is the experimental semivariogram, h is the lag, N(h) is number of sample value pairs oung and Brown (1962) oung and Brown (1962) separated by h; Z(Xi) and Z(Xi +h) are sample Jacquemard (2011) Jacquemard (2011) Goh and Chew (1997) Goh and Chew (1997) Y Rossiter and van Y values at two points at Xi and (Xi + h) locations, respectively.

Source The distance between the sample pairs is rarely equal to h in irregular sampling, and h is often represented by a distance interval. The >60 >2.5 >0.3 >1.9

>0.80 semivariogram parameters like nugget/sill ratio and range, were obtained for soil properties. The nugget/sill ratio was used to classify the High spatial dependency of the variables (Oliver and Webster, 2014). Ratios less than or equal to 0.25, between 0.25, and 0.75, more than 0.75 1.35-1.9 were considered strongly, moderately and weakly spatially dependent, respectively

Optimum (Cambardella et al. 1994).

RESULTS 0.2-0.25 0.25-0.3 0.20-0.40 0.40-0.80 0.75-1.35 Soil properties in oil palm plantations. Soil characteristics in the different oil palm plantations are presented in Table 2. It appears that the soils are mostly sandy loam texture,

<0.2 except vertisols. Soil pH were neutral to 10-25 25-40 40-60 <0.20 <0.75 0.8-1.2 1.2-1.5 1.5-2.5 slightly acid. The highest N value was recorded in the Plintic and luvisol, and the lowest in the ) -1 Hydromorphic soil. The highest concentration ) ) -1 of available P was recorded in the -1

) Hydromorphic soil and the lowest in the -1 Vertisols. As for the CEC, the highest value of was registered on the Plintic and luvisol; while the lowest was in the Hydromorphic soil. ) -1 Exchangeable cations followed a similar trend. Deficiency Moderate Generally, total nitrogen values were under the threshold value of soil nitrogen, 0.8 g kg-1 (Table 1), and exchangeable potassium was 1. Sufficiency rating for nutrient concentrations soils of mature oil palm also less than the threshold value of 0.20 cmol kg-1 (Table 1). Consequently, nitrogen and vailable phosphorus (Bray 1 in mg.kg ABLE otal nitrogen (g.kg Favorable level of pH: 4 0.05) according to test of Student Newman Keuls Mapping of soil nutrient deficiency in oil palm plantations 147 the soil in the study area. Available phosphorus prediction of nutrients concentration by kriging values were also below the threshold of 10 - interpolation, associated with the different 25 mg kg-1) (Table 1) in the Acrisol, Plintic classes of nutrients status. In general, the oil and Luvisols and in the Vertisols. palm plantations’ soils are deficient in nitrogen. Overall, levels of exchangeable magnesium The soils of the oil palm plantations were and calcium compared closely with the deficient in exchangeable K+ and available P, threshold values for all soil types. Magnesium except in the districts of Bonou, Adjohoun, presented moderate levels in the Hydromorphic Dangbo, Akpro-Missérété, Avrankou and soil type (Table 2). Adjarra, Ifangni and Sakété where available P Figure 2 presents the number of oil palm were at some optimum, moderate and high plantation showing nutrients deficiency by soil level. In these areas, small homogeny areas types. It is clear that most of the oil palm were classified as moderate, optimum and high plantations showed nitrogen (100%), phosphorus deficiency. The oil palm potassium (88%) and phosphorus (76%) plantations of these areas presented optimum deficiency. Calcium and Mg2+ showed to high exchangeable Mg2+ and Ca2+ soil levels. moderate deficiency in the oil palm fields. Soil nutrient deficiency maps of the oil palm plantation show two large areas presenting Spatial distribution of nutrient deficiency similar deficiency (Fig. 5). The first zone status. The best fit model and semivariogram includes districts of Bonou, Adjohoun, Sakété, parameters obtained from the geostatistical Adja-Ouèrè, and Pobè (soils are deficient in analysis are presented in the Figure 3. The total nitrogen, available P and exchangeable spatial dependency of soil nutrients varied from K+); while the second zone includes Dangbo, moderate to strong in the oil palm plantations Missérété, Ifangni, Avrankou, Adjarra present by soil types. According to the spatial deficiency in total nitrogen, exchangeable K+ dependency ratio, it appears that total nitrogen and available P (slightly deficient at some point). (0%), available phosphorus (0.05%), In general, the kriging interpolation maps exchangeable potassium (0%) and magnesium of the soils under oil palm plantation are almost (0%) had a strong (nugget/sill ratio < 25%) deficient in total N, available P and spatial dependency; whereas exchangeable exchangeable K+ (Fig. 5a, b and c). calcium (38%) showed moderate spatial dependency (nugget/sill ratio between 25 and DISCUSSION 75%). Soil nutrient concentrations varied spatially Soil properties in oil palm plantations. in the oil palm plantations by soil types, Results of the present study showed that soils between 1.12 and 16.13 Km. The lowest range under oil palm plantation are threatened with of values was observed with total N (22.4 nutrient depletion. Total nitrogen, exchangeable Km), exchangeable K+, Mg2+, and Ca2+ (1.12, K+ and available P are deficient in the different 1.12 Km and 26.88 Km respectively); whereas soil types under oil palm plantation in the study the range value of available P (16.13 Km) was area. However, for exchangeable Mg2+, only the largest. the oil palm plantations on Vertisols did not Prediction of nutrient concentration in the show deficiency. The Acrisols did not present oil palm plantation regarding the soil types, exchangeable Ca2+ deficiency. These results considering the best model of variogram is are partly consequent to inadequate fertiliser presented in Figure 4. The prediction shows management in the farmers’ fields, which does variation of each soil nutrient concentration not guarantee sustainable oil palm productivity. and light homogeneity zones in the oil palm Moreover, oil palm is a tree with high nutrient plantations. Figure 5 presents soil nutrient requirement and, therefore, nutrient supply deficiency maps obtained using the previous must adequately compensate for potential 148 N.S. KINDOHOUNDÉ et al.

Figure 2. Nutrient sufficiency rating for different soil types under oil palm plantation at different soil depths in Benin. Mapping of soil nutrient deficiency in oil palm plantations 149

Distances are expressed in (°): 1 degree=112 Km

Figure 3. Variogram of soil nutrients in the study of area: nitrogen (a), phosphorus (b), potassium (c), calcium (d) and magnesium (e). 150 N.S. KINDOHOUNDÉ et al.

Figure 4. Assessment of nutrient concentrations in soil (depth of 0-30 cm) of oil palm plantations in southern Benin. Nitrogen (a), Phosphorus (b), Potassium (c), Calcium (d), and Magnesium (e). Mapping of soil nutrient deficiency in oil palm plantations 151 152 N.S. KINDOHOUNDÉ et al.

Figure 5. Soil nutrients (depth of 0-30 cm) status spatial mappings in oil palm plantations in southern Benin. (a) nitrogen, (b) phosphorus, (c) potassium, (d) magnesium, and (e) calcium. nutrient depletion. In addition, our results soil nutrient mining, further causing nitrogen showed that soil nutrient concentrations deficiency. decrease from top layer to deep layer. These In the farmers’ oil palm plantations, soil results might be due to the organic matter available P concentrations across soil types, content derived from the decomposition of the were virtually deficient (Table 2). According biomass under the oil palm plantation. The to Rendana et al. (2016), low amounts of fronds of the oil palm are always let by the phosphorus is normally associated with high farmers around the trees and are sometimes Al concentration in the soil, erosion and non- put in swath. sufficient phosphate fertiliser application to the In general, total nitrogen in the oil palm trees. In fact, the type of fertiliser applied plantation was classified as deficient (Table 2). (most growers apply urea + KCl) by farmers Low nitrogen concentrations in the soil could did not contain sufficient P nutrient to satisfy be due to many factors, especially the non- the oil palm tree demand. Phosphorus is an application of fertilisers; nutrient leaching from important nutrient for the plant growth and the soil; and loss through runoff and erosion quality fruit production, yet it is on the verge processes (Gasim et al., 2013; Mohidin et al., of depletion even though Kindohoundé et al. 2015). According to Aholoukpè et al. (2013) (2018) hardly found leaves with P deficiency and Kindohoundé et al. (2018), oil palm symptoms. plantation owners in the study area hardly used Soil exchangeable K+ in the oil palm fertilisers regularly; such practice could cause plantation for the different soil types was almost Mapping of soil nutrient deficiency in oil palm plantations 153 deficient, confirming the leaf discolouration adopted by the oil palm growers, consisting observed by Kindohoundé et al. (2018). The of application of uniform nutrient doses exchangeable K+ level in the soil is influenced regardless of soil micro variability, could be a by soil pH (Hargreaves et al., 2015), which at constraint for oil palm yield improvement. In low level interferes with the adsorption of fact, fertiliser application in the oil palm exchangeable K+. Besides, the presence of plantation should be site specific, regarding soil calcium and magnesium in the process of heterogeneity. cation exchange, might also lead to low Regular soil sampling should be done before potassium concentrations in soil (Rendana et fertiliser application to avoid over or under al., 2016). nutrient application. In the case of the present As for exchangeable Mg2+ (at 0- 30 cm study, we can assert based on the work carried depth), a high level was found in all the study out by Kindohoundé et al. (2018) in the same area (Table 2). The calcium concentration in oil palm plantation that nutrients were applied the soil was at optimum to high level in most far below the required doses; as leaf of the oil palm plantation of the study area. discolourations were observed. Furthermore, This result is might be due to high CEC level according to Miransari and Mackenzie (2010), in the soil, on one hand, and the pH values evaluation of spatial variability can be used for which could have induced low amount of soil optimum fertiliser application recommendation calcium on the other hand. In addition, the as it suggests appropriate nutrients based on strong bonding between Ca and clay (Plaster, deficiency level in the soil. This can contribute 2009) in the soil protects the nutrient against suitably to enhanced tree crops’ productivity. leaching process. This could have increased Knowledge of spatial dependency and Ca concentrations in the soil. distribution of soil properties is crucial for It was noticed from the present study that natural resource evaluation and environmental nutrient deficiency in the oil palm plantation management of un-surveyed locations (Behera varied according to the soil types. This et al., 2015). In contrast with our findings, corroborate Shukla et al. (2014), who Tesfahunegn et al. (2011) and Behera et al. mentioned also that cropping systems and (2015) reported best fit Gaussian model for anthropogenic activities could induce low Ca total nitrogen and total phosphorus assessment, level in a field. spherical for exchangeable K+, exponential for Soils under the oil palm plantation in the exchangeable Ca2+ and Mg2+ in Mai-Negus study area were deficient in total N, available catchment (north Ethiopia) and southern P and exchangeable K+. This could be due to plateau of India, respectively. This is probably the type of fertilisers (most growers apply urea due to the evolution of nutrient levels in the +KCl). Our results are in line with those of soil from one sampling point to another, in both Rendana et al. (2016), who found N, P, K and study area. However, the best fitted model is Mg deficiencies in the oil palm plantation in the one which better estimates the variables India which could have been caused by with a positive variance. The criteria used to factors including water erosion, pH and classify the spatial dependence variables were fertiliser application. the percentage of nugget/sill ratio. With respect to these criteria, our findings showed strong Spatial distribution of nutrient deficiency and moderate spatial dependence for N, P, K, status. Our findings showed different nutrient Mg and Ca (Fig. 3). Strong spatial dependence distribution in the soil of the oil palm plantation of soil properties observed in our study could of the study area. This can affect the oil palm be due to intrinsic factors, such as soil yield at some point inside each plantation. mineralogy, whereas, the moderate spatial However, traditional practices of fertilisation dependence is the consequence of both 154 N.S. KINDOHOUNDÉ et al. intrinsic and extrinsic factors such as palm leaves; nutrient deficiency might occur anthropogenic activities as mentioned by in leaves as consequence of nutrient Behera et al. (2015). unbalance, which will limit the effect of oil The ranges estimated for (Fig. 3) are likely palm fertiliser management based only on soil to be landscape dependent and could be nutrient deficiency map. In fact, nutrient explained by the distance through distinct soil deficiency maps have been developed in types. Thus, soil samples separated by Indonesia and were very useful in the sit- distances closer than the range are spatially specific fertiliser development for oil palm related; whereas those separated by greater production improvement. Because of limited distances than the range are not spatially budget, this study did not take into account all related. Our findings showed higher range regions of oil palm production in Benin and, values for P, with great differences between therefore, we suggest extending this study to ranges of soil properties in the study area. other regions in order to have a global overview Behera et al. (2015) stated that large range on soil nutrients distribution in oil palm values of a soil property indicate that soil production. We strongly believe that this study properties measured were influenced by natural is a starting point for the improvement of the and anthropogenic factors, over greater fertiliser generally recommended to farmer’s distances. Several authors reported similar large oil palm. differences between range values of soil characteristic when attempting to map CONCLUSION variations (Tesfahunegn et al. 2011; Foroughifar et al. 2013). This study has shown N, P and K deficiency in the farmer’s oil palm plantation in most of Reliability of the nutrient maps for the soils. Strong to moderate spatial decision making. The mapping of soil dependency were observed for N, P, K, Mg nutrients in the farmers’ oil palm plantations and Ca. Soil of the oil palm plantations are is a key method of assessing soil micro heterogeneous, and present micro variability, variability, to address a suitable site-specific which should be taking into account for fertiliser recommendation. The heterogeneity fertiliser application. It is also suggested that observed in the soil nutrient contents in the fertiliser application in the oil palm plantation farmers’ oil palm plantation, was used to design should be site specific, considering soil analysis mineral deficiency map (Fig. 5), which results. indicated soil homogeneity inside a zone. This is crucial for planning appropriate soil fertility REFERENCES management strategies in the oil palm plantations, to achieve optimal yields. 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