*2.4. Calculations*

N and P2O5 accumulation in each biomass component were calculated as follows:

$$\mathbf{\color{red}{Nacc}}\_{i} = \mathbf{\color{red}{Ncomc}}\_{i} \times \mathbf{dw}\_{i} \tag{1}$$

$$P\_2\text{O}\_5\text{acc}\_i = P\text{conc}\_i \times \text{dw}\_i \times 2.29\tag{2}$$

where "Nacc*i*" and "P2O5acc*i*" are, respectively, the N and P2O5 accumulation (kg ha−1) in the "i" biomass component of the crop (i.e., crop residues or marketable product); "Nconc*i*" and "Pconc*i*" are, respectively, the N and P concentration (g 100 g d.m−1) in the "i" biomass component of the crop; and "dw*i*" is the dry matter (kg ha−1) in the "i" biomass component of the crop. The N and P2O5 accumulation in the total aboveground biomass of each crop was calculated as the sum of the accumulation in crop residues and marketable product.

The N budget (kg N ha−1) at the level of single crops was estimated according to the following equation:

$$\text{N}\_{\text{budget}} = (\text{N}\_{\text{fert}} + \text{N}\_{\text{rain}} + \text{N}\_{\text{min}} + \text{N}\_{\text{fix}}) - (\text{N}\_{\text{acc}}) \tag{3}$$

where "Nfert" is the amount of N supplied by mineral and organic fertilizers (kg N ha−1) applied to the single crop; "Nrain" is the amount of N supplied by rainfall that occurred in the growing period of the crop (kg N ha−1), assuming that the mean N concentration in rain water is 3 mg N kg−1; "Nmin" is the amount of N originated by the mineralization of the soil organic N in the first 30 cm of depth in the growing period of the crop (kg N ha−1), assuming that the organic N content is 1.10 mg N kg−<sup>1</sup> soil, the bulk density of the soil is 1.46 kg dm−3, and the mineralization rate accounts for 2 g 100 g<sup>−</sup><sup>1</sup> year<sup>−</sup>1; "Nfix" is the amount of N fixed from the atmosphere through symbiotic N2 fixation of legume cover crops (i.e., red clover, pigeon bean, field pea, and red cowpea), assuming that the percentage of N derived from N2 fixation on total N accumulated in the aboveground biomass of legumes is 80% and that there are no di fferences in the mineralization rate of legume cover crops managed as living/dead mulches or as green manures; and "Nacc" is the N accumulation in total biomass of the crops.

To assess the N use e fficiency and to test whether N represented a limiting factor for crop yield in all the three systems, N surplus [33], N utilization e fficiency (NUtE) [34], N Recovery E fficiency (NREac) [35], and Partial Factor Productivity (PFP) [36] were calculated as follows:

$$\text{Nsurplus}\_{\text{ti}} = \text{Nérct}\_{\text{i}} - \text{Nacc}\_{\text{ti}} \tag{4}$$

$$\text{Nsurplus}\_{yi} = \text{Nérct}\_{i} - \text{Nacc}\_{yi} \tag{5}$$

$$\text{NU} \text{t} \text{E}\_{i} = \text{Y}\_{i} \text{Nacc}\_{ti} \tag{6}$$

$$\text{NREac}\_{i} = \text{Nacc}\_{ti} \text{Ninput}\_{i} \tag{7}$$

$$\text{NREac}\_{\%} = \text{Nacc}\_{li} \text{Nfert}\_{i} \tag{8}$$

$$\text{PFP}\_{i} = \text{Y}\_{i} / \text{Ninput}\_{i} \tag{9}$$

$$\text{PFP}\_{\text{fi}} = \text{Y}\_{i} / \text{Nfert}\_{i} \tag{10}$$

where "*N f erti*" is the N supplied as fertilizers (kg N ha−1) to the "i" crop; "*Ninputi*" is the total N input (kg N ha−1) of the "i" crop; "*Naccti*" is the N accumulated (kg N ha−1) in total aboveground biomass of the "i" crop; "*Naccyi*" is the N accumulated (kg N ha−1) in the marketable product of the "i" crop; and "*Yi*" is the fresh weight of the marketable product of the "i" crop (Mg ha−1).

## *2.5. Statistical Analysis*

Data normality was assessed using the Shapiro–Wilk test. Other tests consisted of the Student's t-test to verify that the mean error was not significantly different to zero, the Breusch–Pagan test for homoscedasticity, and the Durbin–Watson test for autocorrelation.

All the dependent variables except for N use efficiency parameters were modelled in a linear mixed model using the extension package lmerTest (tests in the linear mixed effects models) [37] of R software [38]. We analyzed first the agronomic performances of each crop species (i.e., savoy cabbage, fennel, spring lettuce, and summer lettuce) separately in terms of fresh marketable yield (Y), dry matter of marketable yield (dwy), dry matter of residues (dwr), total aboveground dry matter (dwt), harvest index (HI), total aboveground dry matter of weeds (dww), mean fresh weight of marketable product unit (MFW), mean diameter of marketable product unit (MD), N concentration in marketable yield (Nconcy) and in residues (Nconcr), N accumulation in marketable yield (Naccy), residues (Naccr) and total aboveground biomass (Nacct), P concentration in marketable yield (Pconcy) and in residues (Pconcr), P2O5 accumulation in marketable yield (P2O5accy), and residues (P2O5accr) and total aboveground biomass (P2O5acct). For these dependent variables, the cropping system and the year were the fixed factors whilst the block and the year were the random factors. The year was also tested as a fixed factor to test the effect of interannual variability on the dependent variables.

The agronomic performances of each cropping system at the level of entire crop sequence were analyzed separately for each field by summing the performances of each crop grown in the field over the entire experimental period (2014–2017). The global performances of the cropping systems were tested either including or not the contribution of cover crops in order to assess how they could lead to different performances in the systems. Cover crops affected only dry matter and nutrient parameters related to weed biomass (dww), crop residues (dwr, Naccr), and total crop aboveground biomass (dwt, Nacct). When analyzing these parameters as dependent variables, the cropping system, the inclusion/exclusion of cover crops and the field (i.e., F1 or F2) were the fixed factors and the block was the random factor. The field was considered as a factor as, in the crop sequence, there were slight differences in the number of occurrences of a single crop in the single field (Table S7). In the case of the analysis of parameters related to the crop marketable product (dwy, Naccy, and P2O5accy), the cropping system and the field were the fixed factors and the block was the random factor. The effect of cover crops was not considered for these variables as they resulted from the sum of the marketable yield or the N accumulation in marketable yield of the vegetable crops and thus were not affected by the contribution of cover crops. Fitted correlations among the slopes were set. The analysis of variance was run.
