Minimum nutrient input requirement Minimum nutrient input requirement

In our approach to assess long-term nutrient input requirements it is postulated that the annual application rates of macro-nutrients (N, P, K) should at least be equal to total nutrient uptake in the aboveground crop biomass (grain and stover) at  a given target yield, YT. In this way, the minimum input requirements (A, kgnutrient ha-1) are equivalent to the uptake requirements (U, kgnutrient ha-1) of the crop at the target yield.

The nutrient uptake for a given YT is calculated using selected principles of the QUEFTS model (Janssen et al., 1990). These include (1) a coefficient to express physiological efficiency of each nutrient (kg grain per kg uptake of the nutrient in total crop biomass) (Table 1 – we used medium values); (2) balanced nutrition implying that overall efficiency is best served if the different nutrients are taken up in optimum stoichiometric ratios to one another; (3) both physiological efficiency and nutrient uptake ratios (N/P/K) are constant up to a given relative target yield (YT/Yw), here 0.62; and (4) beyond this point the N-use efficiency decreases non-linearly as the target yield approaches the yield ceiling Yw as a result of extra nutrient uptake. This decline is defined by linear decreases of both derivatives dY/dU and dU/dA from their initial values (valid up to YT/Yw=0.62) to zero at the yield ceiling (YT=Yw). In contrast to N, the physiological efficiency of which decreases for YT/Yw exceeding 0.62, no accumulation of P or K in crop biomass is presumed beyond the 62% point, and therefore the input requirements of P and K are constant per kg grain produced.

The above implies a course of agronomic N use efficiency (N-AE, kg grain per kg nutrient applied) versus relative yield that starts at 52 kg kg-1 which is maintained for yields up to 62% of Yw, and then declines to reach ca. 46 kg kg-1 for yields representing 80% of Yw. Yields are expressed at 15.5% moisture. (This corresponds to N-AE = 50 kg kg-1 at 12% moisture, which implies that 20 kg of N input is needed per ton of maize grain produced.)

This approach to minimum nutrient input requirement assumes that other management factors are optimal so as to avoid yield limitations other than due to water (in rainfed conditions), while yield reducing factors (weeds, pests and diseases) are well-controlled.

In a steady-state equilibrium (soil nutrient pools are constant) the annual nutrient losses are – by definition - equal to the difference between nutrient input and offtake, i.e. to the nutrient surplus. This means that in crops where  only the grains are harvested and all crop residues are retained on the field, the postulated condition (input equals uptake in aboveground biomass) implies that the annual nutrient loss is equal to the amount of the nutrient contained in crop residues. This approach is suitable for long-term calculations where soil nutrient pools adapt to a given input regime.

One may argue that these minimum N input requirements are a very optimistic (i.e., ‘low') estimate of actual N input requirements. This is certainly true for a system where all residues are harvested, as our approach then implies that all added fertiliser N is either taken up by the crop or substitutes N taken up from the soil pool, at any ratio between these two. That implies zero N losses via volatilisation (NH3), denitrification (N2 and N2O), or leaching (nitrate). In contrast, for a system where all residues are returned to the soil, the proposed minimum N input requirement implies that annual N losses are equivalent to the amount of N in the stover, and this may be achievable for N provided highly efficient management. For P and K the crop-soil system is less ‘leaky' than for N, and sustaining target yields at the stated minimum input requirements will be easier, except on P-fixing soils. In summary, our minimum N,P,K requirements can be seen as a well-defined target, presuming highly efficient management, no soil mining of nutrients and low losses to the environment. The given values indicate the minimum amounts of macro-nutrients that are likely needed on the longer term to achieve a defined target yield. When using the minimum input requirements, it should be born in mind that currently, actual agronomic nutrient efficiencies might be much lower due to sub-optimal management, and therefore nutrient losses to the environmental also higher than implicated here.

For a more comprehensive description of quantifying minimum nutrient input requirements and balanced nutrition, see Ten Berge et al., 2019.

*These parameters are consistent with those of For other examples of analyses of yield-uptake relationships or the use of balanced nutrition, see e.g. Witt et al. (1999) for rice and Setiyono et al. (2011) for maize.

Table 1: Internal or physiological nutrient use efficiency, IE (kg grain per kg crop nutrient uptake) of cereals for macronutrients N, P, K for cereals, assessed from different literature sources. Superscripts for maximum accumulation (acc), maximum dilution (dil), or medium dilution (med).  Values were converted to standard moisture content.




(kg grain yield/kg nutrient)


(kg grain yield/kg nutrient)


(kg grain yield/kg nutrient)










Ludemann, Cameron et al. (2022),

















e.g. Ansari et al., 2011; Fofana et al., 2008; Muehlig-Versen et al., 2003; Samaké, 2003; Sangare et al., 2002; Van Duivenbooden, 1992

















 e.g. Baishya et al., 2015; Mosaad et al., 2018; Ockerby et al., 1999; Suriyakup et al., 2007; Van Duivenbooden, 1992; Zhang et al., 2010

















 e.g. Dixit et al., 2005; Duhan, 2013; Gordon et al., 1998; Han et al., 2011; Sahrawat et al., 1995; Van Duivenbooden, 1992

















e.g. Abate et al., 2011; Baishya et al., 2015; Chuan et al., 2013; Jan et al., 2014; Van Duivenbooden, 1992; Yadav et al., 2005; Zhan et al., 2016












Actual nutrient input

Actual nutrient input is defined as the sum of mineral fertilizer, manure and atmospheric deposition (in case of nitrogen).

Data on mineral fertilizer input per country and crop were obtained from Ludemann et al. (2022). In case the country was not present in that database, mean mineral fertilizer input across all cropland for that country from the FAOSTAT cropland nutrient budget was used as a proxy for fertilizer input per crop. For both manure and deposition data we also used data from the FAOSTAT cropland nutrient budget; this database provides only nutrient inputs as an average for all crops – it is not crop specific.

Manure data used from the FAOSTAT cropland nutrient budget has a few known limitations (Ludemann et al., In Press). This includes the fact that international imports/exports of livestock manure are not accounted for and manure was apportioned to cropland and non-cropland using the same coefficients as used to apportion mineral fertilizer to cropland and non-cropland (Ludemann et al., In Press). While this may give some indication of proportion of manure applied to cropland, it is not based on surveys of flows of manure. These limitations could result in nutrient inputs through manure being grossly overestimated for countries such as Belgium, Ireland, Montenegro and the Netherlands



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