113 Research Article Received: 7 February 2008 Revised: 21 May 2008 Accepted: 4 June 2008 Published online in Wiley Interscience: 16 September 2008 (www.interscience.wiley.com) DOI 10.1002/ps.1647 Modelling binary mixtures of herbicides in populations resistant to one of the components: evaluation for resistance management Bertrand Jacquemin, Jacques Gasquez and Xavier Reboud * 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. CONCLUSION: 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. c  2008 Society of Chemical Industry Keywords: herbicide resistance; herbicide mixture; simulation; evolution of resistance 1 INTRODUCTION Weeds remain a major economic problem in many crop cultures. Up to now, their control in industrialised countries has relied mainly upon the use of herbicides. However, many weed species have developed herbicide resistance, and most herbicide families are now affected. 1 Facing this situation in their own fields, growers may be tempted to maintain the usual herbicide molecule (herbicide A) for which resistance has been detected but in combination with another mode of action (herbicide B) for which resistance has not yet been detected and which is thus effective in controlling the population. This habit would clearly differ from the usual ‘mixture strategy’ developed to cope with resistance selection. Indeed, the strategy of mixtures of active ingredients has been theoretically designed to prevent the selection of resistance. 2–5 This preventive property of the mixture strategy assumes that, if no resistance has so far developed in the treated population, the selection of resistance relies on the avoidance of both selection pressures. Therefore, the individuals that cope with both selection pressures can survive. In an untreated population, as the probability of finding the characteristics that confer resistance to one of the two active ingredients is low, the frequency of double-resistant individuals is even lower, as it corresponds to the product of the two resistance frequencies. In this paper, such a situation that reduces the probability of resistance selection will be called the ‘susceptible mixture’ (SM) strategy. Whenever resistance is already present, growers shifting to herbicide mixtures would thus clearly violate the assumption of the SM strategy, as the resistance frequency to one of the two herbicides would already be high. The term ‘resistant mixture’ (RM) strategy will refer to the voluntary use of a herbicide mixture when the resistance to one of the two mixed herbicides is already known to be frequent in the population. During 30 years of weed science experience and discussions with growers or technicians, the authors have been able to observe that an RM strategy is quite commonly practised and even tends to increase with the reduced availability of new active ingredients ∗ Correspondence to: Xavier Reboud, UMR1210, INRA, Universit´ e de Bourgogne, ENESAD, Biologie et Gestion des Adventices, BP 86510, 21065 Dijon Cedex, France. E-mail: reboud@dijon.inra.fr UMR1210, Biologie et Gestion des Adventices, INRA, 21000 Dijon, France Pest Manag Sci 2009; 65: 113–121 www.soci.org c  2008 Society of Chemical Industry