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Modelling the response of mildew to fungicide on the leaf

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Probit analysis. want tolerance distribution (proportion control as function of conc. ... mean corresponds to a probit of 5 and 1/slope is the std. dev. mean ... – PowerPoint PPT presentation

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Title: Modelling the response of mildew to fungicide on the leaf


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 sources 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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