## 1 Introduction  
Modified atmosphere packaging (MAP) has been established as an efficient method to preserve refrigerated fish and extend its shelf life. The application of such hurdles reduces the rate of fish product deterioration and spoilage caused by microbial growth. The application of MAP may result in a better retention of quality attributes and shelf life prolongation of fish, minimally processed fish products (e.g., marinated), and ready-to-cook commodities [1]. The most commonly used gases in MAP used for fish are oxygen (O\({}_{2}\)), carbon dioxide (CO\({}_{2}\)), and nitrogen (N\({}_{2}\)), as well as their concentrations in the package headspace, which depend on the specific fish product and the mechanism of spoilage that limits the shelf life of the final food product [2]. Microbial growth in food products is inhibited by CO\({}_{2}\), which is the most widely used gas for the MAP of fish [1]. The concentration of CO\({}_{2}\) has been reported to play a major role in the inhibition of microbial growth and thus may delay the growth of respiratory organisms, such as _Pseudomonas_ spp. and _Shewanella putrefaciens_[3]. The applicability of MAP on fish and its preservative effect have been reported in the literature, indicating a shelf life extension of several days, depending on species and storage temperature [4; 5; 6; 7; 8]. A significant diversification in the dominant spoilage bacteria in MAP fish is observed, which may be attributed to their geographical origination, as well as differences in water temperature and storage conditions [1; 3; 9; 10; 11; 12]. Although the importance of MAP technology in the fish industry is well established and several studies evaluate the effect of MAP on fish quality and shelf life, a small number of mathematical models have been developed in order to express the combined effect of storage temperature and headspace composition on the growth of spoilage bacteria. The effect of CO\({}_{2}\) on the growth kinetics for _Photobacterium phosphoreum_ and _Shewanella putrefaciens_ was quantified and modeled for MAP cod [13]. The results showed that the microbial spoilage of packed cod stored with various concentrations of CO\({}_{2}\) was accurately predicted from the effect of CO\({}_{2}\) on _P. phosphoreum_ growth in model substrates. The temperature behavior of the natural microflora on red mullet was examined in another study by [PERSON] et al. [14]. The growth of the spoilage bacteria _Pseudomonas_ spp., _S. putrefaciens, Brochothrix thermosphacta_, and lactic acid bacteria was modeled as a function of temperature and the concentration of CO\({}_{2}\) in MAP. Combined models were developed and comparatively assessed based on polynomial, Belehradek, and Arrhenius equations. The effect of storage temperature and CO\({}_{2}\) concentration on the growth of _Carnobacterium matraromaticum_, _Serratia proteamaculans_, _Yersinia intermedia_, and _Shewanella baltica_, as well as on the growth of a mixed culture of the four species, has also been investigated [15]. These species were identified as the organisms responsible for spoilage in MAP mackerel fillets. A modified Arrhenius model has been reported by [PERSON] et al. [16] that describes the lactic acid bacteria growth in MAP gilthead seabream fillets, and its applicability was validated at different storage conditions (0-15 \({}^{\circ}\)C and 20-80% CO\({}_{2}\)) [17]. Such mathematical models may predict microbial growth and consequently the shelf life of the studied MAP fish product as a function of packaging and refrigerated storage conditions. Under this context, predictive models for MAP fish products may enable the selection of appropriate MAP conditions in order to achieve adequate shelf life extension and minimize food waste and costs.