borne pathogen competing with the natural microflora in food using mathematical models. Breidit and Fleming 1998 modeled the competitive growth of Listeria monocytogenes and Lactococcus lactis by modeling the concentration of lactic acid produced and the pH of vegetable broth. Gimenez and Dalgaard 2004 also developed a competition model for L. monocytogenes and lactic acid bacteria. Le Marc et al. 2009 developed a competition model by introducing the concept of critical population density for lactic acid bacteria against a competing bacterium S. aureus . These models seem to be specific to the species of concern, and do not generally address a number of microbial species. Dens et al. 1999 proposed a microbial competition model with the Lotka-Volterra LV model, a very wellknown and general model for the description of competition between two species in ecology. However, their studies were just mathematical simulations without biological evidence. Liu et al. 2006 studied interactions of microorganisms on pork with a modified LV model. They showed the parameter values of microbial
IntroductionThere are several relationships among microbial species in the environment, including mutualism, competition, commensalism, and amensalism Bailey and Ollis, 1986 . Among these relationships, competition would be the most common for interacting microbial species, because all microbial species need nutrients and space for growth. Food and food materials such as vegetables, fish, and meat, which are often contaminated with natural microflora from the soil, the sea, and domestic animals, are thought to be ecosystems for microbes. Thus, when a species of concern such as Salmonella or Staphylococcus aureus contaminates food with other non-harmful microorganisms, mathematical models that could describe and predict the growth of the species of concern and others in the food would be a useful tool for microbial food safety.Many researchers have studied the growth of a food- A novel competition model developed with the new logistic model and the Lotka-Volterra model successfully predicted the growth of bacteria in mixed culture using the mesophiles Staphylococcus aureus, Escherichia coli, and Salmonella at a constant temperature in our previous studies. In this study, we further studied the prediction of the growth of those bacteria in mixed culture at dynamic temperatures with various initial populations with the competition model. First, we studied the growth kinetics of the species in a monoculture at various constant temperatures ranging from 16 to 32 . With the analyzed data in the monoculture, we then examined the prediction of bacterial growth in mixed culture with two and three species. The growth of the bacteria in the mixed culture at dynamic temperatures was successfully predicted with the model. The residuals between the observed and predicted populations at the data points were <0.5 log at most points, being 83.3% and 84.2% for the two-species mixture and the three-species mixture, respectively. The present study showed tha...