## 3 Results and Discussion
### One-Step Analysis of Competitive Growth
The results of the tests (Supplementary Figure S2) indicated that this isolate appeared to be sensitive to lactic acid or competition in general since it reached MPD in the stationary phase in less than 4 logs (3.38 \(\pm\) 0.40 log CFU/mL) and the increase in population in less than 1 log (0.65 \(\pm\) 0.27 log CFU/mL). The production of organic acids has a major impact on the quality of the final products during the cheesemaking process. Acidification is usually achieved by the production of lactic acid through the fermentation of lactose by LAB [48, 53]. The pH changes in our study followed a sigmoidal behaviour throughout LAB growth but with a delay of approximately 6 to 10 h. This trend is consistent with those reported by [PERSON] et al. [48] when analysing the antimicrobial activity of the LABs against some potentially pathogenic bacteria used as indicators, including _S. aureus_. As LAB growth progressed to the exponential and stationary growth phase, a rapid and significant drop in pH (pH \(\leq\) 5.3) was observed in the second phase. The parameters estimated for the H-GD model are presented in Tables 2 and 3 for both _E. coli_ and _S. aureus_ isolates in co-cultures, respectively. Except for the facts described above, the data in Table 2 pointed out that the competition coefficients \(I_{\mathrm{EL}}\) (Equation (2)) in the H-GD model showed a similar growth reduction (<60%) for both isolates of _E. coli_ compared with their original capacity as individual species in milk [19]. On the other hand, the competitive effect of LAB on _S. aureus_ isolates was stronger and strain-dependent. The coefficients \(I_{\mathrm{SL}}\) in Table 3 were significantly lower and different for isolates 2064 and 14733. Thus, they confirmed the higher sensitivity to non-specific inhibition caused by LAB that was found for isolate 14733. Figure 2: Co-culture growth of LAB Fresco, _S. aureus_ 14733, and _G. candidum_ in milk at 15, 18, and 21 \({}^{\circ}\)C (without and with 1% NaCl, respectively). The continuous lines represent the growth predicted values by the H-GD model and the dots represent the experimental values (\(\blacksquare\) LAB, \(\blacktriangle\) Sa, \(\bullet\) Gc). The results in Tables 2-4 showed that the tertiary H-GD model successfully described the competitive growth between species in milk at temperatures related to the ripening conditions of artisanal cheesemaking. The global _RMSE_ values for all cases are lower than 0.33 log CFU/mL, which is well within the range of normal experimental error. A dominant level of inoculum (approximately 10\({}^{6}\) CFU/mL) of a starter culture favoured the growth of LAB in milk (the competition coefficient \(I_{\rm LP}\) is greater than one in almost all cases and was able not only to induce an early stationary state in _E. coli_ (isolates BR and PS2) and _S. aureus_ (isolates 2064 and 14733) for cases without and with 1% NaCl addition but also subsequently reduced their population. LAB growth of the LAB slightly suppressed the growth rate of _G. candidum_ of its original ability as a single species in milk. The reduction coefficients of the growth rate of _G. candidum_\(k_{\rm Ge}\) were within the region 0.710-0.995. Naturally, their values were lower for the cases with NaCl addition (Tables 2 and 3). To conclude the experimental findings, except for _L. monocytogenes_, the four decisive populations of cheese fermentation and ripening can be ranked according to their ability to compete with each other. Taking into account two isolates of _S. aureus_ and _E. coli_, _S. aureus_ showed less competitive behaviour, followed by _E. coli_. However, _G. candidum_, with its ability to assimilate lactic acid produced by LAB appears to be an independent player in co-cultures. Finally, it was confirmed that after proper milk acidification, LAB is (and should be) a dominant and stable population that, depending on the time, may control other undesirable microbial populations.