Model  Photobacterium phosphoreum: Microbial spoilage model for fresh MAP fish 
Reference  Dalgaard, P., Mejlholm, O. and Huss, H.H. (1997a). Application of an iterative approach for development of a microbial model predicting the shelflife of packed fish. Int. J. Food Microbiol. 38, 169179 
Primary growth model  Logtransformed 3parameter Logistic model 
Secondary growth model  Polynomial model (quadratic) and squareroot model 
Factor(s) in model  Temperature and %CO_{2} 
Product validation studies 

Range of applicability 

Photobacterium phosphoreum is the specific spoilage organism (SSO) that limits shelflife of fresh marine fish when stored in modified atmosphere packaging (MAP). P. photobacterium typically grows without a lag phase and the logtransformed 3parameter Logistic model (Eqn. 1) is appropriate as a primary growth model. 
Primary growth model: 
Eqn. 1 
In eqn. 1, N_{t} (cfu/g) is the concentration of P. phosphoreum at time t, N_{0} (cfu/g) the initial concentration of P. phosphoreum, N_{max} the maximum concentration (cfu/g) and m_{max} the maximum specific growth rate (h ^{1}). 
Figure 1. Logtransformed Logistic model fitted to data for growth of P. phosphoreum in naturally contaminated cod fillets stored at 0^{o}C in an atmosphere with 100% N_{2}. As indicated by the arrows, sensory spoilage was observed some time after P. phosphoreum reached its maximum cell concentration (Dalgaard et al. 1997a) 
The end of shelflife for MAP cod fillets has been observed four generation times (t_{gen} = Ln(2)/µ_{max}) after the inflection point (t_{i}) of the Logistic growth model (See Figure above). Consequently, a particular minimal spoilage level was not identified. However, the inflection point is the time when N_{t} is equal to N_{max}/2 and shelf life can be calculated by the shelflife criterion shown below (Eqn. 2): 
Eqn. 2 
Shelflife is calculated from the initial concentration of P. phosphoreum and from its maximum specific growth rate (m_{max}). The initial numbers of P. phosphoreum can be determined in fresh fish by a specific conductance based method (Dalgaard et al., 1996) or by a quantitative realtime PCR (qPCR) method (Macé et al 2013).
Eqn. 3
Eqn. 4 
Figure 2. Observed and predicted growth of Photobacterium phosphoreum in fresh MAP cod fillets (Dalgaard et al. 1997a) 
The effect of temperature and CO_{2} on the maximum specific growth rate (m_{max}) of P. phosphoreum in MAP cod fillets can be predicted by a quadratic polynomial model (Eqn. 3). A squareroot model (Eqn. 4) is used for MAP plaice and MAP salmon. These secondary models allow growth of P. phosphoreum to be predicted in fresh fish stored in modified atmospheres with CO_{2}/N_{2} gas mixtures. See e.g. the Figure above for growth of P. phosphoreum in fresh MAP cod fillets. In fact, observed and predicted m_{max}values from 11 storage trials with MAP cod resulted in bias and accuracy factor values of 0.98 and 1.19, respectively, and this shows that the model predicted growth rates accurately (Dalgaard, 1999). In addition, in product storage trials the model only underestimated shelflife by 9% on average (See Table just below). 
Observed and predicted shelflife of MAP cod fillets stored at constant and at varying temperatures
Initial storage temp.  0^{o}C 
0^{o}C 
0^{o}C 
5^{o}C 
Final storage temp.  0^{o}C 
5^{o}C 
10^{o}C 
0^{o}C 
Winter experiments  
Observed shelflife, days  15.8 
8.2 
6.4 
9.3 
Predicted shelflife, days  13.9 (12 %)^{a} 
8.1 ( 2 %) 
6..1 ( 4 %) 
8.5 ( 9 %) 
Summer experiments  
Observed shelflife, days  16.8 
9.2 
5.9 
11.8 
Predicted shelflife, days  14.7 (13 %) 
8.0 (13 %) 
5.4 ( 8 %) 
10.3 (13 %) 