• dose–response curves;
  • effective dose;
  • fungicide programmes;
  • multiplicative survival model;
  • Septoria tritici;
  • tebuconazole

A function was derived to predict fungicide efficacy when more than one application of a single active ingredient is made to a crop, given parameters describing the dose–response curves of the component single-spray applications. In the function, a second application is considered to act on that proportion of the total pathogen population which was uncontrollable at the time of the first application (represented by the lower asymptote of the dose–response curve for the first treatment), plus any additional part of the population which survived the first application as a result of a finite dose being applied. Data to estimate the single-spray dose–response curve parameters and validate predictions of two-spray programme efficacy were obtained from separate subsets of treatments in four field experiments. A systemic fungicide spray was applied to wheat at a range of doses, at one or both of two times (t1 and t2), in all dose combinations. Observed values of the area under the disease progress curve (AUDPC) for septoria leaf blotch (Mycosphaerella graminicola) were used to construct response surfaces of dose at t1 by dose at t2 for each culm leaf layer. Parameters were estimated from single-spray and zero-dose treatment data only. The model predicted a high proportion (R2 = 71–95%) of the variation in efficacy of the two-spray programmes. AUDPC isobols showed that the dose required at t2 was inversely related to the dose at t1, but the slope of the relationship varied with the relative timings of t1 and t2 in relation to culm leaf emergence. Isobols were curved, so the effective dose – the total dose required to achieve a given level of disease suppression – was lower when administered as two applications.