The onion data set comprised 13 N fertilization trials conducted in Histosols of south-western Quebec, Quebec, Canada, between 2003 and 2006. Meteorological data were obtained from the Hemmingford station, Quebec (Latitude: 45˚4.200'N; Longitude: 73˚43.200'W; Altitude: 61 m). The length of the growing period averaged 120 d. The onion was irrigated during dry periods.

Plots were 3 to 8 rows in width and 6 to 8 m in length. Fertilizers were applied broadcast before sowing or in 2 split applications. There were four N rates up to 180 kg N ha⁻¹ including a control treatment without N, allocated to three randomized blocks. Harvest date depended on the number of days required to meet commercial standards. Yields were measured in two central rows of 3 m in length. Plant density of cultivars Bastille, Fortress, Arsenal, Genesis, Frontier and Hamlet at harvest averaged 245,863, 325,650, 382,979, 449,173, 477,205 and 501,774 plants ha⁻¹, respectively. Bulbs were classified as follows (Ø = diameter): extra-large (Ø > 76.3 mm), large (Ø 57.3 - 76.3 mm), medium (Ø 44.5 - 57.3 mm), small (Ø 31.8 - 44.5 mm), and discarded (too small, evidence of rot).

Soil samples were collected in the spring before fertilizer application and composited by block (three sub-sam- ples per sample). Soils were cleaned from roots and woody particles, air-dried to constant weight and sieved to < 2 mm before analysis. Soil pH was determined in a 0.01 M CaCl₂ using a 1:4 soil to solution volumetric ratio [28] . Total C and N were determined by combustion using CNS-Leco 2000 [29] . Organic matter content was estimated assuming 58% C content. Elements were extracted using the Mehlich-3 method [30] and quantified by ICP-OES.

The compositional space S of C and N analyses was described as follows [21] :

where was computed by difference between 100% and analytical results (%C, %N) and c indicates closure of the simplex to the unit of measurement (here, 100%). Compositional data are relative to each other and thus inter-related. As inferred from Equation (1), any change in a given concentration (by adding more N for example) must affect the proportion of other components. Due to redundancy among components, there are D-1 degrees of freedom in a D-parts composition [31] . The ilr allows reducing D parts to D-1 orthogonally arranged variables. The D-1 ilr coordinates are computed as follows [22] :

where i varies between 1 and D-1, and are the numbers of components in group at numerator and group at denominator, respectively, is geometric mean across components in and is geometric mean across components in. We selected the following two isometric log contrasts or balances between C, N and as follows: C () vs. N () representing the C/N ratio and the contrast between C and N () and () representing the dilution of C and N in the residual soil mass. For example, a soil containing 46.61% C and 2.09% N returns the following ilr values:

Balance indices were computed as distances between a given composition and a reference one, as follows across results of Equations (3) and (4):

where and are the mean and standard deviation of a reference soil subpopulation defined using independent data from highly mineralizing Histosols (> 1 kg NO₃-N ha⁻¹∙d⁻¹) in USA and Europe [32] . Reference ilr values (mean ± standard deviation) were computed as 1.899 ± 0.173 for and −1.391 ± 0.192 for (Table 1). Because ilrs are orthogonal to each other, an STN index is computed as Mahalanobis distance () across results of Equations (5) and (6) as follows:

To separate low-from high-N mineralizing Histosols, we selected the critical value of 5.5, computed as half the maximum value of 11 for net nitrification [32] . Net N immobilization was assumed to occur for values >11, high-N net mineralization for values <5.5, and low-N mineralization for intermediate values (>5.5 and <11). Approximately halving or doubling a critical value is suggested to build soil fertility classes in view of interpreting soil test results to make fertilizer recommendations [33] .

Analysis of variance of marketable yields was conducted using the MIXED procedure using SAS version 9.2 for Windows [34] . Meta-analyses were conducted using Excel and formulas for random mixed models in [35] . The response ratio (RR) was computed as follows:

The variance of RR was computed as follows [35] :

where

where

where

where is the pooled within group standard deviation, and are the numbers of observations in treatment and control, respectively (here,), and are treatment and control means, respectively, and and are standard deviations for treatment and control, respectively, computed as the square root of error mean square () plus the term variance for the block effect () which takes into account the standard error () (Gaétan Daigle, professional statistician, University Laval, personal communication). Size effect in meta-analysis was declared significant at P < 0.10 for possible inclusion into the response model.

Rainfall from May to August was higher in 2003 and 2006 compared to 2004 and 2005 (Figure 1). Climate was driest in 2005, especially in May and August. Irrigation was applied at need. However, the effect of climate on the response ratio could not be tested due to the limited number of N trials. Hence, STN was the only factor retained to build subgroups of onion response to added N.

The soils covered a large spectrum of C and N concentration values and other properties (Table 2). Total soil C varied from 222.7 to 507.4 g C kg⁻¹ while total N ranged between 11.6 and 25.3 g N kg⁻¹ compared to 310 to 530 g C kg⁻¹ and 19.0 to 40.0 g N kg⁻¹ in [32] (Table 1). Organic matter varied between 12.9% and 29.4% and the soil C/N ratio between 18.9 and 29.3. Soil pH (CaCl₂) varied from 4.5 to 6.7 therefore pH_H2Ovaried from 4.7

to 7.1 using the conversion equation of [28] , within ranges reported by [28] and [32] for Quebec Histosols. The values ranged between 1.1 and 19.6, hence reaching beyond the limit of 11 for net N immobilization suggested by [32] .

There were 9 sites in the STN group and 4 sites in the group (Table 3). Onion response to added N was smaller in the compared to the group. In the, onion response to N was significant at the 0.10 level adding 60 kg N ha⁻¹. The onion crop in the group was responsive to added N at the 0.10 level of significance adding 180 kg N ha⁻¹. The scanned a much larger range up to nearly 20 in the STN group (Table 2) but the latter group could not be further partitioned due to the small number of observations.

Although references [13] and [14] provided no soil analyses enabling to relate STN to added N, additions of 0 to 56 kg N ha⁻¹ without significant yield response supported our results if such trials had been conducted on Histosols showing. Indeed, reference [13] conducted their trials on a “well-drained and well-de- composed muck” at the Agriculture and Agrifood Canada experimental farm (Ste-Clotilde, Quebec) where STN as was found to be 2.5 in 2004 and 2.6 in 2005 in our study. The trials of reference [14] have been conducted on 2-m deep Elba “muck” soil containing 80% organic matter. A Cornell University survey report [36] indicated that recommended N should not exceed 56 kg N ha⁻¹ in “Elba” deep mucks containing ≈80% organic matter while discharging up to 37 NO₃-N L⁻¹ into waterways, an extremely high value.

On the other hand, in a Nova Scotia experiment on the Caribou bog where N was applied at rates of 0, 90, 180 and 270 kg N ha⁻¹, reference [37] found that maximum onion yield of 50.5 Mg ha⁻¹ was obtained with 180 kg N ha^-1 for a ripening acid sphagnum peat soil cultivated five years after reclamation. In comparison, a maximum yield of 37.2 Mg ha⁻¹ was obtained with 270 kg N ha⁻¹ on a newly broken Histosol of similar origin. Although reference [37] did not provide soil C and N analyses, a former soil survey of the pristine Caribou bog [38] where their trial was conducted indicated that the upper soil layer made of the brownish fibrous mossy peat contained

0.91% of total N and 46% of total C (i.e., organic matter content = 79.3%), returning a value of 28.5, far beyond the upper limit of the model in Figure 2. Onion response was consistent with the peat ripening process where N concentration increases in the upper layer [39] resulting in lower values, hence less N requirement.

Reference [39] reported that Histosols showing C/N ratio of 29 could release 77 - 98 kg N ha⁻¹ yr⁻¹; more ripened soils showing C/N ratios of 23 - 24, 170 - 493 kg N ha⁻¹ yr⁻¹ while muck soils with C/N ratio of 18 could release 99 - 186 kg N ha⁻¹ yr⁻¹. The pattern of soil N mineralization capacity thus appeared to be quadratic. Indeed, total N and the C/N ratio could be effective STNs where content varies little such as in high-C peat materials [1] [17] [18] . Otherwise, is a more suitable STN where Histosol compositions vary more widely within the limits of soil properties outlined in Table 1.

Significant (P < 0.10) trends of crop response to added N for treatments showing the highest RR (Table 3) in

^ns, ^a: not significant and significantly different from BRR = 1 at the 0.10 level according to t test, respectively. Yield_t and Yield₀: yields of treatment with added N and control (zero N), respectively.

each STN class were selected to build a provisory N requirement model, i.e. 60 and 180 kg N ha⁻¹ for the values of 3.16 (1.14 to 5.08) for the high-N mineralizing STN group and 10.55 (5.83 to 19.65) for the low-N mineralizing STN group, respectively.

Although there were only two soil fertility classes based on, the relationship between onion N requirements and STN was modelled under the following assumptions 1) N requirements → 0 kg N ha⁻¹ where values → 0 because there was no response to added N in the trials of references [1] and [13] (hence the probability of no response to added N is real); 2) onion responded significantly to 60 kg N ha⁻¹ where averaged 3.16, a value close to 56 kg N ha⁻¹ obtained by [14] for high-N mineralizing soils; 3) onion responded significantly to 180 kg N ha⁻¹ where averaged 10.55. Onion response to added N appeared to be linearly related to as STN index as shown in Figure 2. No R² value is presented because the meta-regression uses group means rather than individual data points. Variation about each group mean are indicated by confidence intervals (P = 0.05). The apparent close fit between and the N rate indicated that could be an appropriate STN index to adjust N fertilization to the Histosol capacity to supply N to the crop. There is some evidence for N requirements beyond 180 kg N ha⁻¹ in a sphagnum bog of unknown composition [37] . The present empirical model that relies on a Quebec data set and meta-analysis should not be extrapolated to situations beyond the limits of application without additional experimentation where both soil test and crop response are reported. More robust and site-specific N recommendation interpolating models could be developed for the onion crop in Histosols through research collaboration to enhance the size of data set that include climatic data and soil classification.

Bulb quality could also be considered in N management because onion flavor [40] [41] and susceptibility to diseases [9] and bulb rot [42] may be affected by N excess. Moreover, an oversupply of nitrogen during the growing period may promote excessive top growth resulting in bulb expansion and splitting, while late-season applications may promote top growth, delay maturity, and favor diseases [36] . Because rapid growth rate of seeded onion may not occur until 5 - 6 weeks after emergence, a PSNT test [15] may be further investigated as complementary diagnostic tool to allow seasonal adjustment of N fertilization to soil N supply capacity as defined by STN and to N leaching through rainfall and irrigation.