Yields gap evaluation of wheat grown in Piedmont plain and Floodplain soils of Bangladesh through compositional nutrient diagnosis (CND) norm

Mineralnutrient stress is one of the major yield gap factors, especially in floodplain and piedmont plain soil. The compositional nutrient diagnosis (CND) provides a plant nutrient imbalance index in statistical distribution patterns, which is important for adjusting the soil-plant systems specific fertilization for maintaining sustainable soil fertility. This study calculated the CND norms of wheat (Triticum aestivum L.) and identified optimum wheat yield target of high-yielding subpopulation in farmers' fields. It also categorized the most yield limiting nutrient(s) for wheat grown. Popular high-yielding wheat was grown in 62 farmers' fields, maintaining farmers' nutrient management plan (FP) and improved nutrient management plan (INM). Nutrient composition analysis was done from 62 young foliar composite samples, collected at 7th leaves stage (vegetative stage).The CND generic model gave 3.47 Mg ha–1 as minimum cutoff yield of the high-yield subpopulation. Nitrogen was identified as the core yield limiting nutrient for wheat in piedmont and floodplain soils. However, the yield limiting nutrients for wheat grown in the studied are were established the following series: N > S > K, Mg >P, Ca and Mn >Fe >B >Zn respectively. The CND generic model, allowed us to suggest thatN, P, K, Mn, B were the factors discriminating high- from low–yielding subpopulation in piedmont plain and floodplain soils of Bangladesh.

showed that available K concentration of floodplain and piedmont plain soil store < 0.1 meq/100 g soil and mean annual balance of P was found -1 to -9 kg ha -1 Panaullah et al., 2006). Besides, less conspicuous deficiency symptoms of P and K in wheat co mpared to the symptoms of N and S retain farmers fro m applying these fertilizers. Therefore, understanding of mult i-environ mental soil nutrient dynamics and nutrient absorption, transport accumulat ion in p lant tissue is essential, to improve the nutritional value of the plant and reducing the yield gap (Mattos et al., 2003;Vargas et al., 2013).
Leaf analysis is a good tool to monitor, evaluate and adjust agricultural fertilization programs to reduce the yield gap  (Bates, 1971), Diagnosis and Reco mmendation Integrated System (DRIS) (Walworth and Sumner, 1987), and Co mpositional Nutrient Diagnosis (CND) (Parent et al., 1994). A mong these methods, CND approaches, calculate nutrient balance considering all foliar nutrient elements and their interactions and dry mass of plants, provide greater accuracy of diagnosis (Cunha et al., 2013). For selecting suitable nutrient norms, an arbitrarily yield cutoff value is needed for defining a high yield subpopulation (Kh iari et al., 2001). Parent and Dafir (1992) and Parent et al., (1994) proposed the X 2 distribution function to define a CND threshold value for nutrient imbalance when relat ing yield and the cu mulative variance ratio function for each nutrient. The CND approach has a robust mathemat ical basis to define a minimu m y ield target useful for discriminating between high and low yield subpopulations for identifying specific element related yield gap. Thus, the CND approach is applicable for solving nutrient imbalance prob lems in specific physiographic unit soil (Khiari et al., 2001).
In Bangladesh, wheat (Triticum aestivum L.) is common ly grown in rice-wheat cropping patterns during the "rabi" season from October to March. It is the reg ion's second most important food security crop after rice (Debnath et al., 2011;Krupnik et al., 2015). The consumption of wheat is increasing due to increase in food diversity in the country.
Currently, per capita wheat demand is a 17.3 kg year -1 , which is approximately 20% of rice consumption. With 3% more protein than rice, wheat makes an important contribution to per capita protein intake at 4.3 g day -1 (FAOSTAT, 2014). Production of wheat is increasing day by day, although the country still impo rts significant quantities of wheat to meet the rapid ly growing domestic demand.
Nutrient constraints present in Bangladesh soil become prime yield limit ing problem in wheat growing areas especially p iedmont and floodplain soils . Ho wever, a b ig knowledge gap is detected in the area of demarcating nutrient based yield gap in the farmer's field of Bangladesh.
Although several nutrient diagnosis approaches were identified for nutrient balance in relation to yield of conifer seedling, onion, garlic, pepper, potato and fruits (Parent et compositional nutrient diagnosis (CND) norms of wheat (Triticum aestivum L.) and identifies optimu m wheat yield target of high-yielding subpopulation in farmer's fields and nutritional interaction between high and low yielding subpopulation. Moreover, it also categorizes the most limit ing nutrient(s) that should be applied to reduce the yield gap of wheat in the region.

Experimental data
This study was conducted based on the data acquired fro m .

Theory of the CND approach
To calculate the preliminary co mpositional nutrient diagnosis norms, we used the CND approach, which has The nutrient proportions become scale invariant after they have been divided by the geometric mean ( G) of the d + 1 components, including Rd (Aitchison, 1986), as follows: Row-centered log rations are computed as follows: and VN+ Vp+ VK + ..+ VRd = 0 Where, VXis the CND row-centered log ratio exp ression for nutrient X. The sum of t issue components is 100%, as in equation (1), and the sum of their row-centered log ratios including the filling value must be zero, as in equation (5).
Thereafter, the database is partitioned between two subpopulations using the Cate-Nelson procedure, once the observations have been ranked in a decreasing yield order (Khiari et al., 2001). At each iteration, the group A comprises n1 observations, and the group B co mprises n2 observations for a total of n observations (n = n1 + n2) in the whole database. For the two subpopulations, the variance of the CND VX value must be computed. The variance rat io for component X can be estimated as: Where1(Vx) is the ratio function between two subpopulations, for nutrient X at the ith iteration (i=ni-1) and the Vx is the CND row-centered log ratio exp ression for nutrient X.
The cumu lative variance rat io function is the sum of variance ratios at the ith iteration from top. The cumulat ive variance ratio function F C i (VX) can then be computed (Khiari et al., 2001) as: is partition nu mber and n is total number o f observations (n1+n2). The denomination is the sum o f variance ratios across all iterations and thus is a constant for nutrient X.
The cumulative function F c 1 (Vx) related to yield (Y) shows a cubic pattern: The inflection point is the point where the model shows a change in concavity. It is obtained by delving equation [8] twice: The infection point is then obtained by equating the second derivative of equation (10) to zero. Thus the solution for the yield cutoff value is -b/3a. The h ighest yield cutoff values across nutrient expressions (N, P, K and S) were selected to ascertain the minimu m y ield target for a h igh yield subpopulation. CND norms were co mputed using means and standard deviations corresponding to the row-centered log ratios VX of d nutrients for high-yield specimens.

The CND norms of nutrients
The CND norms were derived fro m high yielding sub-population and low-yield ing sub-population farmer's field yield of wheat. Nutrient concentrations that were transformed into row-centered log rat ios were used for the derivation of CND norms. There was however a significant difference in the mean ro w centered log rat ios for the high and low-yielding sub populations, suggesting that the yield difference is due to nutritional disorder (Nkengafac and Ejolle, 2014). These obtained nutrient norms helps to nutrient assessment in wheat grown in Pied mont and Floodplain soil. Yield depended database shown that for nitrogen the cutoff yield was 3.47 Mg ha -1 indicates commensurate to a reasonable good yield for wheat (Tab le 1).
Thus, it is most likely that N was the most limit ing nutrient of yield, as this was evidenced by a significant negative correlation between N and yield (data not shown) when considering low performance observations. However, the cutoff yield for F c i (VS), F c i (VK) were 3.45 and 3.39 Mg ha -1 respectively also matching to a reasonable good yield for wheat (Table 1). This trends suggests that K and S also limited the yield of wheat considered as experimental unit, which can be interpreted as insufficiency of this nutrient,  However, these study identified that some of mo lar nutrient ratio beco me mo re important for wheat production in  (Table 3).
A symmetric skewness was observed in P/ Ca mo lar rat io (Table 4) and with a significant level of the F value (Table   3). This negative relat ionship may result fro m higher act ivity of P in the soil solution due to forming higher solubility of P minerals, especially on soils having lower exchangeable Ca2+, and thus increase P uptake by plants ( Barł óg, 2014).
There is no robust physiological exp lanation for the antagonism between N and Mg. This negative interaction has been found in corn leaves by Dara et al., (1992). The ratio between these two nutrients was not prominent to differentiate high-and lo w-yield datasets using the F-test (Table 3).
In contrast, the symmetric skewness between Ca and P was found to discriminate between h igh-and low-yield subpopulations as shown by the F test (Table 3). This finding is disagrees with report of Parent et al. (1994) who had reported the antagonistic effects of these two nutrients.
These trends may be happened due to the sandy and or silty soil type of these areas with lo w cation exchange capacity.
Another important molar ratio was the K/Ca ratio (Tab le 4).
This positive interaction was also useful to differentiate high from low-yield subpopulations ( Table 3).
The P/K ratio appeared significant to discriminate high and low-y ield subpopulations (Table 3). Su mner and Farina (1986) found that the K-P interaction was important in the forage sorghum production, indicating that the balance between K and P is important.
The N/P rat io, as evidenced by a symmetric skewness between N and P (Table 4)  A symmetric skewness was observed in N/K mo lar rat io (Table 4) and with a significant level of the F value (Table   3), was the most discriminating ratio between the low -and high-yielding subpopulations. These trends may be happened due to continual cultivation of wheat-rice cropping, application of lesser K fertilizer than crop removal in the pied mont soils. Under dose of K fert ilizer application create a negative K balance in ricewheat cropping . These results agreed with findings of Saleque et al., (2008) indicat ing that soils of the study area had low (0.06 -0.11 cmol kg -1 ) soil exchangeable K.
Moreover, Timsina et al., (2006) reported that with continual cropping and low application of K fertilizer create a negative K balance in ricewheat cropping pied mont and floodplain soils of Bangladesh. However, the interpretation of interactions identified by diagnostic techniques, as the mu ltivariate CND approach could help in overco ming some of the drawbacks of the classical approaches.

V. CONCLUSION
Generic approach to select a minimu m y ield target for the high yield subpopulation was found effective for a small