Biomathematics models to answer our research question


We have been working on this and we have submitted an abstract for the SETAC Europe Congress 2017. For me, Javier, it will be very enriching because I never attended to a congress of the Society of Environmental Toxicology and Chemistry


We add here the submitted abstract in case it interests you 🙂

Is rodenticide use disrupting the natural regulation of vole populations? A biomathematics modelling approach

Javier Fernandez-de-Simon1, Virgile Baudrot1, Michael Coeurdassier1, Xavier Lambin2, Patrick Giraudoux1,3

1Laboratoire Chrono-environnement UMR 6249 UBFC-CNRS, 16 Route de Gray, 25000, Besançon, France

2School of Biological Sciences, University of Aberdeen, Zoology Building, Tillydrone Avenue, Aberdeen AB24 2TZ, Scotland, UK

3Institut Universitaire de France, Paris, France
E-mail contact:

Abstract Anthropogenic activities modify ecosystems and as a result some ecological relationships are altered. For instance, many agricultural areas have followed a process of intensification. In these areas, voles frequently achieve pest levels through cyclic outbreaks reducing the food available for livestock and crop yields. Subsequently, some farmers respond using anticoagulant rodenticides to control voles. Thus, predators may be indirectly controlled by secondary exposure to rodenticides or by a reduction of food sources. Therefore, anticoagulant rodenticides might be acting analogously as a superpredator, interfering in the natural regulation of vole populations. Under what circumstances this may arise is not known. The objective of this study is to understand the interactions between an anticoagulant rodenticide (bromadiolone) to control vole populations and its indirect effects over vole specialist predators (stoats Mustela erminea and weasels Mustela nivalis) and a generalist predator of voles (the red fox Vulpes vulpes). We use a biomathematics modelling approach based on differential equations to explore several scenarios of this system. To study this we developed a model with two coupled dynamics: (i) the three studied animal populations, and (ii) their bromadiolone concentration. The four scenarios used are: Scenario 1, no bromadiolone use and no foxes; Scenario 2, bromadiolone use but no foxes; Scenario 3, no bromadiolone use but foxes; and Scenario 4, bromadiolone use and foxes. We observed the behaviour of the parts of the system until dynamics stabilisation. Our findings in Scenario 1 show a population decline of voles up to an equilibrium in relation to a mustelid numerical response. In Scenario 2, we found a quick decline of voles and mustelids, followed by their recovery. In Scenario 3, there were stable vole dynamics and small effect of predation over voles. In Scenario 4, we found a decline and delayed recovery of all species. The highest final vole densities appear in Scenario 3 and 4, with red foxes, which are affected by bromadiolone use but also behave as generalist predators with wider food spectrum and thus less exposure. They also feed on small mustelids, specialist predators of voles. The next steps of this study will be to model additional scenarios, using new parameters and sensitivity analyses. The future modelling results will be compared with field results in areas where bromadiolone showed red fox population decreases.

As you can see Virgile Baudrot, recently awarded with a PhD by the Université Bourgogne Franche-Comté, is providing a great input in this study. I am definitively learning a lot with him about biomathematics models and I strongly recommend reading this brilliant paper on functional responses that has been recently published:


Baudrot, V., Perasso, A., Fritsch, C., Giraudoux, P. & Raoul, F. (2016). The adaptation of generalist predators’ diet in a multi-prey context: insights from new functional responses. Ecology 97, 1832–1841.

If you are more interested on his research, you can also find him for instance in several internet sites:





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