*2.3. Calculations*

The phosphorus accumulation was calculated by multiplying the content of this element in individual parts of the plants by the weight of these organs.

Based on the phosphorus accumulation in the total above-ground biomass of the plants, the relative yield (RY) (Equation (1)) and the total relative yield (RYT) (Equation (2)) were determined [66]:

$$\text{RY}\_{\text{B}} = \text{Y}\_{\text{BM}} / \text{Y}\_{\text{BP}} \text{ and } \text{RY}\_{\text{R}} = \text{Y}\_{\text{RM}} / \text{Y}\_{\text{RP}} \tag{1}$$

$$\text{RYT} = \text{RY}\_{\text{B}} + \text{RY}\_{\text{R}} \tag{2}$$

The relative competitive capacity for phosphorus in mixed seedings was expressed as the competitive equilibrium index (Cb) (Equation (3)) [67]:

$$\text{Cb} = \ln[(\text{Y}\_{\text{BM}}/\text{Y}\_{\text{RM}})/(\text{Y}\_{\text{BP}}/\text{Y}\_{\text{RP}})] \tag{3}$$

where: RYB—relative barley yield, YBM—barley in mixture yield, YBP—barley yield for single-species sowing, RYR—relative rye-grass yield, YRM—rye-grass in mixture yield, YRP—rye-grass yield for single-species sowing, ln—natural logarithm.

In the additive pattern, RY < 1 indicates competition, RY > 1 indicates positive interactions, and RY = 1 no interactions. If RYT > 1, this indicates partial complementarity in resource acquisition by the mixture components, positive interactions between species, or incomplete resource acquisition by species in single-species seedings, while if RYT = 2, there are no competitive interactions between species in the mixture, as the resource acquisition by each species in the mixture is the same as in the single-species sowing [60].

The competitive equilibrium index Cb indicates which of the species is more competitive. The experiment calculated Cb for barley in relation to Italian rye-grass. If the species are equal competitors, then Cb = 0, if barley is a better competitor than rye-grass, then Cb > 0, and if rye-grass is a better competitor than barley, then Cb < 0.

#### *2.4. Statistical Analysis*

The results were subjected to the analysis of variance (ANOVA). The statistics were calculated separately for each growth stage and for individual plant parts. Homogeneous groups were identified by Duncan's test at *p* < 0.05. Using correlation coefficients, the relationship between the phosphorus accumulation and its content in the organs of plants and their above-ground biomass (the leaves, stems and spikes) was presented. The correlation coefficients were calculated separately for barley and rye-grass, based on the results from all objects (irrespective of the water supply of the plants). It was also checked as to whether the RY and RYT values differ significantly from the unity, and the Cb values from zero, using the t-Student test [60]. Statistical analyses were carried out using the STATISTICA software (data analysis software system), version 12, StatSoft [68].

The results in the tables are means for the three cycles (years) of the experiment.
