Mortality estimation
for individual-based simulations of phosphine resistance in lesser grain borer (Rhyzopertha dominica) Dr. Mingren Shi Dr. Michael Renton biosecurity built on science Cooperative Research Centre for National Plant Biosecurity
Background Lesser grain borer
It is the most serious primary pest of stored grain in Australia
The evolution of resistance is a major challenge to the grain industry biosecurity built on science
Background Importance of mortality estimation Computer simulation models can provide a relatively fast, safe and inexpensive way to judge and weigh the merits of various management options. biosecurity built on science
Background previous modelling  survivorship was not explicitly included in the model  a simple single gene model was used. because adequate data were not available biosecurity built on science
Two-locus model and nine genotypes  Resistance to phosphine is an inherited trait  Two alleles on each of these two loci that govern the trait of resistance - dominant (susceptibility) alleles - recessive (resistance) alleles biosecurity built on science
Nine genotypes 2nd gene 1st gene
s homo suscpt
h hetero
s
ss Both homozygous susceptible hs 1st hetero& 2nd homo susceptible rs 1st homoresistant & 2nd homo- suscpt
sh 1st homo suscpt & 2nd heterozygous hh Both heterozygous
h
r
r homo resist
sr 1st homo suscpt & 2nd homo- resist hr 1st hetero& 2nd homo resistant rh 1st homo rr Both resistant &2nd homozygous heterozygous resistant biosecurity built on science
Data for 5 strains Insects have been purified strains Each strain a single genotype Collins et al (2002 & 2005) - 3 strains QRD14 (ss), QRD569 (rr), 14x569 (hh)
Daglish (2004) – 3 strains
QRD14 (ss), QRD369 (rs), 14x569 (hs)
It is the time now to estimate mortalities for the five available strains biosecurity built on science
Probit models Data - Collins et al. (2002) Fixed exposure time 48hr & Different concentrations Different mortalities Strain QRD14 (ss) Strain Comb F1 (hh)
Model - 2-parameter probit model Y=a+b log(Ct
Y - probit mortality, the inverse CDF (~N(0,1) ) value + 5 C – PH3 dose or concentration (mg/l) t - exposure time (hours)
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Probit models Strain QRD569 (rr) Data 1- Collins et al. (2002) [ t = 48hr] Data 2- Collins et al. (2005)
Different concentrations & fixed 99.9% mortality ďƒ Different times LT99.9: days to achieve 99.9% mortality
Model - 4-paramter probit model
Y=a+b1log(t)+b2log(C)+b3log(t)log(C) biosecurity built on science
Probit models
Data - Daglish (2004) Different concentrations & Exposure times
to achieve fixed 50% or 99% mortality Strains: QRD14 (ss), QRD369 (rs), QRD369Ă—QRD14 (hs)
Model - 4-paramter probit model Y=a+b1log(t)+b2log(C)+b3log(t)log(C)
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Probit models Fit the data sets very well:
LC50 values for the 5 genotypes
The predicted values are very close to the observed values for all the 5 genotypes The predicted values for ss using Collins’ data & Daglish’s data are the same as the observed value – 0.0017
LT99.9 values for genotype rr
The predicted values are very close to the observed values
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Daily probit mortality values for 5 strain at C=[0.01,1.0] mg/l
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Construct a probit model for other 4 genotypes x: x=sh, sr, hr, rh Use
a 2-parameter probit model Y = a + b log(Ct) Assumed b(x) = estimated slope b(hh) a(x) can be found from the estimate LC50(x) - LC50(y) values for the 5 strains are already known - Resistance factors f50(y) for those can be obtained from LC50(x)=0.0017 f50(x) (0.0017= LC50(ss) ) biosecurity built on science
Construct a probit model Estimation of f50(x) for x=sh, sr, hr, rh Assumed that ln[f50(x)] for the nine genotypes can be expressed in terms of k, d1, d2, s1 & s2 s
2nd gene 1st gene
h
r
s
0
d2s2 (x2)
s2
h
d1s1
ln f (hh)
d1s1+s1+ k(d1s1)s2 (x1) s2+s1+ks1s2
=ln f(hs) r
s1
d2s2+s1+k s1 =ln f(rs) (d2s2) (x3)
=ln f (rr)
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Estimation of f50(x) for x=sh, sr, hr, rh s
2nd gene 1st gene
h
r
s
0
h
d1s1 ln f (hh) =ln f(hs)
d1s1+s1+ k(d1s1)s2 (x1)
r
s1
s2+s1+ks1s2
=ln f(rs)
d2s2 (x2)
s2
d2s2+s1+k s1 (d2s2) (x3) st
=ln f (rr)
nd
s1, s2 - strength of the 1 (2 ) gene st nd d1, d2- dominance of the 1 (2 ) gene k - synergism between the two genes biosecurity built on science
Construct a probit model Estimation of f50(x) for x=sh, sr, hr, rh
There are 5 variables: x1, x2, x3, s2, k But only 4 expressions (5 strains – ss) Another condition is required:
We knew f(sr) < f(rs) s2 < s1 assumed s2 [=ln f(sr)]= ps1, with p = 0.5 Solve s2 = 0.5 s1 = 0.5 ln f(sr) Solve k, x1, x2 and x3 successfully biosecurity built on science
Construct a probit model
Estimate parameter a(x): x=sh, sr, hr, rh Probit model Y=a+b log(Ct) Concentration LC50(x)=0.0017 f50(x) C Time t = 48 h Parameter b(x) =b(hh) Probit motality value Y CDF(Z=z)=0.5 z=0 Y=0+5=5
Insert C,t,b(x) and Y to model a(x)
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Fitted parameters for nine genotypes Genotype a b ss 15.032386 9.229083 sh 10.854928 5.913329 hh 7.954711 5.913329 rh 1.682448 5.913329 sr 7.043248 5.913329 hr 3.944565 5.913329 Genotype a b1 b2 b3 hs 11.284676 3.776399 6.964954 –1.010451 rs –10.413046 15.575413 0.047656 4.701759 rr –12.232356 10.386287 3.101974 1.190773 biosecurity built on science
Daily probit values
at C=[0.01,1] mg/l for 9 genotypes
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Daily survival rates
at C=[0.01,1] mg/l for 9 genotypes
ss, sh, sr, hs, hh
hh, hr, rs, rh, rr biosecurity built on science
Strengths and applications No previous models have included mortality predictions that vary with concentration, exposure time, and genotype and based on extensive experimental data in the way we have here Our model based on extensive data sets This allows us to accurately predict mortality of the lesser grain borer - under a variety of phosphine treatments - with different concentrations and exposure times biosecurity built on science
Applications (1) These results provided survival rates for our two-locus model - to investigate management tactics - found that extending exposure duration is a much more efficient control tactic than increasing the PH3 - e.g. a PH3 treatment of 0.53 mg/l × 7 days is often used. It may be better to instead use an equi-toxic treatment concentration“0.17 mg/l × 14 days”. biosecurity built on science
Applications (2) ď&#x201A;§ Also used results to compare the differences between one- and twolocus models - importance of basing resistance evolution models on realistic genetics - over-simplified one-locus models run the risk of not correctly identifying tactics to minimise the incidence of pest infestation. biosecurity built on science
Applications (3) Also used results to investigate the impact of dose consistency and immigration rate on population increase and resistance evolution ď&#x201A;§ Achieving a consistent fumigant dose is the key factor - In avoiding evolution of resistance - In maintaining control of populations
ď&#x201A;§ The dose achieved is very inconsistent, there is always a problem regardless of immigration rate. biosecurity built on science
Extension and Adoption ď&#x201A;§ Our project includes industry researchers and is supported by the National Plant Biosecurity CRC ď&#x201A;§ Results from this study will have a clear route to extension and adoption
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Thank you Coauthor and/or Supervisor: Dr. Michael Renton Dr. Patrick J. Collins
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