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Modelling the response of mildew to fungicide on the leaf

Modelling the response of mildew to fungicide on the leaf. BBSRC Collaborative Programme SRI and University of Portsmouth. Diffusion model. finite difference approximation leaf consists of homogeneous layers with different properties solubility diffusion flow. Diffusion model - leaf.

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Modelling the response of mildew to fungicide on the leaf

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  1. Modelling the response of mildew to fungicide on the leaf BBSRC Collaborative Programme SRI and University of Portsmouth

  2. Diffusion model • finite difference approximation • leaf consists of homogeneous layers with different properties • solubility • diffusion • flow

  3. Diffusion model - leaf • finite difference model with up to 7 layers

  4. Diffusion model - leaf • simpler 3 layer model • deposit initially in top of cuticle

  5. Probit analysis • want tolerance distribution (proportion control as function of conc.) for the response of E. graminis to Dinocap • experiment in agar medium counting germination for different concentrations • (results of Chowdhury)

  6. Probit analysis - experiment

  7. Probit transformation

  8. Probit analysis • can now use weighted linear regression • mean corresponds to a probit of 5 and 1/slope is the std. dev. • mean = -4.1, std. dev. = 1.48

  9. Germination • calculate concentrations after 72 hours from a single deposit • use tolerance distribution at this fixed point in time to calculate expected response • compare to experimental data

  10. Germination D = 5x10-14 m2s-1 time = 72 hours

  11. Germination D = 7x 10-14 m2s-1 time = 72 hours

  12. Germination • results compare well especially with D = 5 x 10-14 m2s-1 which is similar to the diffusion coefficient of Permethrin in a leaf cuticle (3 x 10-14 m2s-1) • reduced control at the source may be explained by the tolerance dist. being applied at 72 h by which time the source’s concentration has fallen

  13. Infection - sensitivity • 50 ng of pesticide in a 500 mm wide line spread across a 10 cm long leaf 3/4 of the way • concentrations recorded at 21 positions along the leaf every 12 hours for 40 days for logP = 1,3,5 and with or without flow towards the tip

  14. Infection: sensitivity analysis • apply the tolerance distribution • values of the mean of -3, -4.1 and -5.2 • values of std. dev. of 1, 1.5 and 2

  15. Infection - example logP = 3, with flow of 5 x 10-6 ms-1 in body of leaf mean and s.d. of tolerance distribution as calculated

  16. Effect of position on leaf

  17. Effect of time

  18. Effect of flow

  19. Effect of partition coeff.

  20. Effect of tolerance mean

  21. Effect of tolerance s.d.

  22. Interaction: mean - s.d.

  23. Interaction: flow - logP

  24. Conclusions • Good fit with germination experiment • Importance of log P • The model could help in the design of fungicide treatments

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