Modèle d’interaction entre Campagnols Microtus arvalis et prairie permanente
Authors: Yu O. , Vergne Y. , Gounot M. 
Published: November 2022

A mathematical model is proposed to quantify the interactions between a population of field voles Microtus agrestis and a meadow, on a yearly basis.
It includes a model of the population dynamics of the voles when food is not limited, the seasonal variations of climate and food quality being taken into consideration. The standard energy requirements of individual voles for growth, reproduction and maintenance being known, it becomes possible to estimate the potential energy requirements of the vole population. On the other hand, the assessment of the available food resources is dependent on a reliable estimate of the primary production of the meadow, which cannot be accuretely measured (the usual methods commonly result in underestimates). Mathematical models are even less adequate. Furthermore, it would also be necessary to take into account the feeding behavior of the voles, their preference for certain plant species, the amount of food wasted by the animals and the variable use of space by voles. Digestibility of the plant material, which varies from one species to another, and also seasonally, must also be taken into account. However, when the coefficients of digestibility of the various food items, their calorific value and their selectivity coefficients are known, it becomes possible to estimate the amount of plant material necessary to balance the energy needs of the vole population. When food production does not meet the needs of the vole population, the adjustment of demand to supply is made by a decrease in the body weight of the voles and, when necessary, by a subsequent increase in their mortality rate (first the 0-1 month age cohort, and then the adults), until a new equilibrium is reached.
No comprehensive set of data being available to test our model, we had to make use of both the incomplete set of data resulting from our own field study on Etalans (Doubs, eastern France), and of data borrowed from the literature. The demographic parameters of the vole population are based upon our trapping programme at Etalans. The percentage of the various food items consumed by the voles is based upon the analysis of their stomach contents. The digestibility coefficients are borrowed from the literature. Both the primary production and the amount of food wasted have been estimated empirically. The amount of plant material produced has been partitioned between plant species, in proportion to their seasonal cover percentage. Two vegetation clippings were made, one in June and the other in September, resulting in a reduction of the available plants biomass for the corresponding months.
On the basis of these data, we have calculated the monthly consumption of the various plant species by the voles (for males, non pregnant females and pregnant females separately). On this basis, the trophic impact of the vole population at various seasons has been estimated. This impact is very important for some species (e.g. Daucus carota, Taraxacum officinale, Medicago sativa, Anthoxanthum odoratum). A simulation of the population dynamics of the vole population has also been made ; it fits reasonably well with the results of our trapping programme in Etalans.
The proposed model can also be used to assess the threshold at which food is no longer a limiting factor for the vole population, and also to identify the critical periods of the yearly cycle. Sensibility analysis emphasizes the important role of the sex-ratio in influencing the dynamics of the vole population.