## 1 Introduction  
A wide range of interactions among microbial populations belongs to actual and challenging subjects of quantitative food microbiology, especially when the research results have applicable predictive potential. Experiments referring to the fate of populations in the background of ongoing fermentation and ripening may provide a substantial view to several questions that usually appear in the practice of artisan cheese. For example, we may ask whether bacterial starters are more suitable and effective against contaminants than naturally present LAB populations with their diversity, actual activity, and acidification ability. In predictive microbiology, two- and one-step approaches are usually applied to describe and predict growth, inactivation/survival, and interactions between microorganisms in foods with known environmental factors. First, the traditional two-step approach is based on the estimation of the pertinent kinetic parameters using a suitable primary model. Then, the effect of environmental conditions on these parameters is modelled using secondary models, and finally, their integration into a tertiary model enables the prediction of microbial behaviour over time [1; 2]. One-step data analysis is applied to construct the tertiary model directly with a combination of primary and secondary models, thus minimising global error [3]. For the co-culture description, various competitive/interaction models can be used. They are based on a semi-mechanistic approach, descriptive models such as Lotka-Voltera types, and models quantifying the \"Jameson effect\" [4; 5]. Both two- and one-step approaches can be implemented to study the competitive growth of microbial populations. In this work, the one-step approach is preferred to model and predict the growth of _E. coli_, _G. candidium_ and _S. aureus_, _G. candidium_ in the presence of lactic acid bacteria in milk. Except for _L. monocytogenes_, which is not the subject of this research, _E. coli_ and _S. aureus_ should be included as pathogenic bacteria considered a major safety issue for raw milk cheese. They are most often found in cheeses produced with raw milk and function as an indicator of hygiene deficiencies [6; 7; 8]. According to [PERSON] and [PERSON] [9], raw milk can become contaminated with _E. coli_ directly through animal faeces or indirectly through contaminated farm and dairy environments, equipment, and handling personnel. Although most _E. coli_ strains are harmless commensals, some are known to be pathogenic bacteria, causing severe intestinal and extraintestinal diseases in humans. _The presence of S. aureus_ in cheese is associated with post-secretory contamination and it is relevant as it may produce enterotoxins [10; 11; 12]. In general, the microbiota of artisanal cheese consists of complex assemblages consisting of not only prokaryotic but also fungal populations. As an example, the presence of _G. candidium_ has been linked to the microbial profile of several artisanal raw milk cheeses from various countries [13; 14; 15; 16]. Data on raw milk cheese quality and the prevalence of food-borne pathogens are well documented. However, there is less information in the literature on the in-depth knowledge of interactions between microbial populations [17; 18]. On the one hand, physiological studies contribute to a better understanding of the behaviour of the microbiota, but studies in predictive microbiology go one step further by modelling and simulating microbial dynamics over time. Therefore, both can provide reproducible complex patterns that give insight into the effect of varying processing environmental conditions on the cheese microsystem [19; 20; 21]. As for most artisanal cheeses, ambient temperatures from 15 to 21 \({}^{\circ}\)C are applied during fermentation and the early phase of the ripening processes [10; 22], our objective was to identify the microbial interactions between a starter culture of lactic acid bacteria, and isolates of _E. coli_, _S. aureus_, and _G.