title: Modelling binary mixtures of herbicides in populations resistant to one of the components: evaluation for resistance management.
abstract: BACKGROUND
  Herbicide mixtures are commonly proposed to delay the selection of herbicide resistance in susceptible populations (called the SM strategy). However, in practice, herbicide mixtures are often used when resistance to one of the two active ingredients has already been detected in the targeted population (called the RM strategy). It is doubtful whether such a practice can select against resistance, as the corresponding selection pressure is still exerted. As a consequence, the effect of mixtures on the evolution of an already detected resistance to one of the herbicides in the combination remains largely unexplored. In the present work, a simple model was developed to explore further the necessary and sufficient conditions under which a binary RM strategy might stabilise or even reduce resistance frequency.
  
  
  RESULTS
  Covering the hypothetical largest range of parameters, 39% of 9000 random simulations attest that the RM strategy might theoretically reduce resistance frequency. When strong enough, high genetic cost of resistance, negative cross-resistance between the herbicides associated in the mixture and reduced selection differential between resistant and susceptible plants can counterbalance the resistance advantage to one of the two applied herbicides. However, the required conditions for an RM strategy to ensure resistance containment in natural conditions seldom overlap with experimental parameter estimates given in the literature.
  
  
  CONCLUSIONS
  It is concluded that the sufficient conditions for an RM strategy to be effective would rarely be encountered. As a consequence, the strategy of formulating mixtures with herbicides for which resistance has already been detected should be avoided.
authors.affiliation: UMR1210, Biologie et Gestion des Adventices, INRA, 21000 Dijon, France.
authors.forename: Bertrand
authors.initials: B
authors.lastname: Jacquemin
authors.forename: Jacques
authors.initials: J
authors.lastname: Gasquez
authors.forename: Xavier
authors.initials: X
authors.lastname: Reboud
mesh_terms: D005075:Biological Evolution; D053209:Herbicide Resistance; D006540:Herbicides / Q000494:pharmacology*; D008954:Models, Biological; D006109:Poaceae / Q000187:drug effects* / Q000235:genetics / Q000502:physiology
chemical_list: D006540:Herbicides