Tef [Eragrostis tef (Zucc.)] is the most important cereal crop in Ethiopia covering 30% of the area and 20% of the total cereal production (CSA, 2015). It is an excellent source of essential amino acids, including lysine which is commonly deficient in cereal grain (Doris, 2002). It is gluten-free (Spaenij et al., 2005). However, tef has the lowest productivity as compared to the other cereal crops as the national average yield is meager, ranging between 1.28 and 1.58 t ha^-1 (CSA 2015).

Vertisols account for 23% of the cropland in Ethiopia and are the dominant soil type in the highlands where Jamma District of South Wollo Zone is located (Kamara and Haque, 1988). These soils are characterized by very low water infiltration rate or low saturated hydraulic conductivity and, therefore, are susceptible to waterlogging under high intensity rainfall conditions. Tef is the most important food crop in Jamma District (Getachew,  1991).  However,  tef  yield  in  the  District is below the national average, at least partly due to inadequate supply of plant nutrients (Stoorvogel and Smaling, 1990; Asnakew, 1994; Fassil and Charles, 2009; Tulema et al., 2005). In addition, the Ethiopia highland Vertisols tend to exhibit low total N mainly due to leaching and denitrification (Tekalign et al., 1988) limiting cereal production.

The current blanket fertilizer recommendation for tef and other cereal crops in Jamma District is to apply 64 kg N and 46 kg P₂O₅ ha^-1 (NFIU, 1992). Therefore, refinement of the previous fertilizer recommendations is essential from the basis of dynamic property of soils as a result of different natural and man-made factors.  However, nutrient fertilization recommendations must be based on crop yield optimization and profit maximization. Fertilization recommendations are usually based on results from field crop nutrient response trials which were lacking for Jamma District. The recent soil fertility assessment map produced by Ethiopian Soil Information System (EthioSIS) showed that in addition to N and P, K, S, B and Zn deficiencies are widespread in Ethiopian soils (EthioSIS 2014). Therefore, this research was conducted to develop a yield response curve of tef to fertilizer-N under adequate supply of all nutrients and determine the economically optimum N rate for tef.

Description of the study area

The study was carried out in 2014 and 2015 main cropping seasons in Jamma District of South Wollo Zone of the Amhara Region in Ethiopia. The district is situated within the geographical boundaries of 10° 06’ 24’’ - 10° 35’ 45’’ N latitudes and 39° 04’ 04’’ - 39^o 23’ 03’’ E longitudes and altitudinal ranges of 1428 - 2752 m above sea level (masl). The district receives a mean annual rainfall of 1130 mm   rainfall  with  approximately  60%  falling  in  July  and  August (Figure 1); with 10.3°C mean minimum temperature; and 21.6°C mean maximum temperature. The cropping season is from June to November. The soil type for the study sites is Pellic Vertisol with some of the physico-chemical properties mentioned in Table 1. The previous crop produced on the study sites had been wheat.

Treatments and experimental design 

The treatments comprised fertilizer-N at rates of 0, 23, 46, 69, 92, 115 and 138 kg ha^-1 with uniform application of 69/80/30/2/1 kg ha^-1 P₂O₅/K₂O/S/Zn/B. In addition, there was a zero fertilizer treatment and the recommended 69/46 kg ha^-1 N/P₂O₅. The randomized complete block design (RCBD) with three replications was used on each of three representative farmers’ fields in 2014 and 2015. The gross plot size was 3 x 3 m and 2 x 2 m was the harvested area for data collection.

Experimental materials and procedures

Tef variety with local name dega tef - DZ675 was planted in rows of 20 cm spacing at a seed rate of 10 kg ha^-1 on flat fine seed beds. Phosphorus, K and S fertilizers were band-applied at basal as triple super phosphate (TSP), muriate of potash (KCl) and calcium sulfate (CaSO₄) straight fertilizers, respectively. Fertilizer-N was applied as urea with 50% at planting and 50% at 45 days after planting. The micronutrients Zn as zinc sulphate (ZnSO₄) and B as borax (Na₂B₄O₇.5H₂O), each weighed in plot level, each dissolved in 16 L volume tap water in a knapsack sprayer were sprayed at foliage 45 and 60 days after planting, respectively.

Data collection

Fresh biomass yield was measured by weighing the total above ground biomass of the entire harvestable area. The dry biomass weight was obtained by drying a sample of plants, with seed panicles, in an oven at 105°C for 12 h and adjusting the fresh biomass weight into dry weight basis. Grain yield was determined from harvested grain weight and straw yield was calculated by subtracting the grain weight from the dry biomass weight. Harvest index was obtained by dividing the grain yield  by  the  dry  biomass weight. 

Data analysis

The collected data were subjected to analysis of variance (GLM procedure) using SAS software version 9.00 (SAS, 2004). The mixed model procedure was used for the combined analysis over the testing sites with treatments as a fixed variable and with site and replication as random variables. Treatment means separation was done with Duncan’s Multiple Range test (DMRT) at P ≤0.05. Simple non-linear regression analysis was run using SAS to determine the goodness of fit of the yield response curve to N. The farm-gate prices of Ethiopian Birr (ETB) 20, 2 and 23.9 per kg  for variable factors; tef grain, tef straw and N (derived from cost of urea, ETB 11.0 kg^-1), respectively, were used for partial budget analysis following the CIMMYT procedure (CIMMYT, 1988). The other factors were constant as they were applied uniform to all treatments. The mean grain and straw yields used in the partial budget analysis were adjusted to 90% of the measured yield. 

Yield response of Tef to N fertilizer

A highly significant (P≤ 0.01) grain and straw yield response to N was found at all testing sites in 2014 (Table 2). There was no significant difference in the response to fertilizer-N across testing sites. The grain yield was increased from 0.6 - 0.8 t ha^-1 to 1.3 - 1.4 t ha^-1 while the straw yield was increased from 1.6 - 1.8 t ha^-1 to 2.7 - 3.4 t ha^-1 by applying N₁₁₅. The significant yield response of tef to N was attributed to the low indigenous soil N supply (Table 1; Tekalign 1991). The results agree with other reports of tef response to fertilizer-N especially in the highland Vertisols (NFIU, 1993; Tekalign et al., 2001; Minale et al., 2004). The combined analysis of the yield data pooled over the testing sites in  2014  indicated that N had significant (P≤0.05) effect on the yield of tef with a mean maximum grain yield of 1.2 t ha^-1 and mean maximum straw yield of 2.9 t ha^-1 with N₁₁₅ and N₁₃₈ which were statistically at par with N₆₉ and N₉₂ (Table 4). However, treatments did not affect the harvest index (HI).  

Tef grain yield was increased with fertilizer-N at only one of the three sites in 2015 (Table 3). The lack of response for the two sites was attributed to these being newly cultivated fields which were previously range land had better soil fertility. Fertilizer-N application decreased grain yield at Site 6.  However, straw yield was increased at all testing sites in 2015. This result is supported by Alkamper (1973) and Legesse (2004) who concluded that straw compared with grain yield is more responsive to N while P encourages good tef grain production. The mean grain yield of 1.9 t ha^-1 in 2015 was above the then national average yield (CSA, 2015). Grain yield was not affected by N rate in the pooled analysis in 2015 (Table 4). The non-significant grain yield response to N and significant treatment by site interaction effect in 2015 was due to the non-significant grain yield response to N at two of the testing sites. The highest mean straw yield was 7.8 t ha^-1 with N₁₅₅ which was statistically at par with the straw yield from N₉₂ and N₁₃₈. The HI declined with increased N rate in 2015 due to relatively great straw compared with grain yield response to N rate.

Minale et al. (2004) and Alemayehu et al. (2007) recommended 60-80 kg N ha^-1 with 18-20 kg P₂O₅ ha^-1 for maximum tef production on Vertisols in Northwest Ethiopia. Application of 80 kg N ha^-1 plus 80 kg ha^-1 P₂O₅ with tef row spacing of 10 cm gave the highest tef yield (Kumela and Thomas, 2016) while Fissehaye et al. (2009) reported maximized tef grain yield with 69 kg N ha^-1 on Vertisols. In contradiction to these findings, Miller (2009) and Nosberg et al. (2009) stated that tef requires only 32 to 46 kg N ha^-1 and that excessive N rate results in increased lodging.

Wakene and Yifru (2013) showed that optimal N rates for tef in Ethiopia varied from 15-90 kg ha^-1 due to diversity in agro-ecology, climate and soil type and recommended 15-60 kg ha^-1 N for Nitisols, Luvisols, Fluvisols and Andosols, but 60-90 kg ha^-1 N for Vertisols. However, N fertilization for tef could be either omitted or reduced by half when the precursor crops are legumes (Tekalign et al., 2001; Alemayehu et al., 2010) or oil crops (Abedenna et al., 2006; Alemayehu et al., 2010).

Yield response function analysis

The mean grain yield response to N rate over two years fit a quadratic function. The adjusted R² = 0.25^** when the analysis was with plot data but 0.988 where the regression analysis was with overall N rate means (Figures 2 and 3). This generally agrees with tef responses reported for the central highlands of Ethiopia with Vertisols (Tekalign et al., 2001; Minale et al., 2004). Others have reported good fits of quadratic yield response to N fertilizer including for potato (Gilles et al., 2000), wheat (Cassman and Plant, 1992; Zhejun et al., 2014) and rice (Cassman and Plant 1992; Dobermann et al., 1992).

Economic analysis

The partial budget analysis showed that the highest net economic return of Ethiopian Birr (ETB) 30508 per ha with MRR of 236% was estimated from N₁₁₅ followed by the net economic return of 28971 ETB per ha and MRR of 288% from N₉₂ (Table 5). The dominance analysis showed that application of N₁₃₈ was dominated and thus was excluded from the analysis. The sensitivity analysis with the assumption of increasing fertilizer price and labor cost by 15% while decreasing grain and straw yields’ price by 15% also showed that the highest net economic returns were obtained from application of N₁₁₅ and N₉₂. However, the highest value to cost ratio (VCR) and highest benefit to cost ratio (BCR) of 10.9 and 5.2, respectively, in the first scenario and 8.1 and 2.9, respectively, in the second scenario were obtained from application of N₄₆ (Table 5). Using the yield response function determined, the profit-maximizing optimal rate of N, calculated by setting the first derivative of the response function that is, GY  =  -0.0459N²  +  11.929N  + 750.81 to the price ratio of the fertilizer-N to the grain price, that is, (ETB 23.9/ETB 20) was found to be 23.9/20 = -0.0918N + 11.929; N = 117 kg ha^-1 for scenario 1, while in the case of scenario 2, 27.5/17 = -0.0918N + 11.929; N = 112 kg ha^-1. Therefore, for the financially constrained farmers seeking maximum profits with least fertilizer costs, application of 46 kg N ha^-1 is recommended. However, for the farmers without financial constraints seeking for maximum net economic returns, application of 92-117 kg N ha^-1 is recommended. This result is supported by previous studies by Tekalign  et  al. (1996) and Wakene and Yifru (2013) who recommended application of 60-90 kg N ha^-1 on Vertisols in the highlands of Ethiopia.

The result revealed that quadratic response curve was the best fitting curve for the mean grain yield response of tef to application of N. The highest net economic returns and highest marginal rate of returns were obtained with 115 and 92 kg N ha^-1. However, the highest VCR and highest BCR were found with 46 kg N ha^-1. The profit-maximizing optimal rate of N using the yield response function determined in the study was found to be 117 kg N ha^-1 in scenario 1 and 112 kg N ha^-1 in scenario 2. However, taking the limited resource endowment of small holder farmers in the Jamma District in to consideration, 46 kg N ha^-1 is recommended for financially constrained farmers seeking maximum profits with least fertilizer costs, while 92-117 kg N ha^-1 is recommended for farmers without financial constraints seeking maximum net economic returns with higher investment.

The authors have not declared any conflict of interests

The authors appreciate Ethiopian Agricultural Transformation Agency (ATA) for funding the study and providing technical support during the course of the research and also like to extend their gratitude to Sirinka Agricultural Research Center for providing facility, vehicle and other logistic support for the study.