Prey-predator models are frequently developed to investigate trophic webs and to predict the population dynamics of prey and predators. However, the parameters of these models are often implemented without empirical data and sometimes chosen arbitrarily. Furthermore, when the sensibility of the model to its parameter values is tested, only a few parameters are tested and different prey-predator models (in terms of predation function structure, for example) are rarely compared. Here, we propose a method to compare four prey-predator models for two populations and select the more biologically plausible one to model a simplified agricultural trophic system, including one predator compartment (the red fox Vulpes vulpes) and one prey group compartment (small mammals). These models are based on various Holling functional responses for the predation interaction and take the prey intrinsic growth into account through a Verhulst logistic function. Most parameters values (like attack rates or growth rates) were calculated from field data or based on literature review. Uncertainty quantification is a recent trend that has gained popularity in engineering fields. In this vein, we used Sobol indices to conduct parameter exploration around mean parameter values to investigate and compare the model dynamics responses. Our first results showed that under our assumptions, the two most relevant models for our study case are the saturated Holling I and II models. Furthermore, we were able to discriminate which were the most sensitive parameters in each model. These first encouraging results open the way for the next step, which will be to adapt this model construction to more complex prey-predator systems, with several predator and/or several prey compartments.