Supplementary material
Development of the leaf blast infection ability model
Leaf blast of rice, caused by the pathogen Magnaportheoryzae, is an air-borne disease. Infection, latent period (time to sporulation and lesion development), and lesion growth characterize blast epidemics (Teng et al. 1991), whichmay have 7–8 monocycles per crop season in temperate agro-ecosystems and 10–15 cycles per crop season in the tropics (Kato 1974; Kingsolver et al. 1984). Temperature plays an important role in determining latent period,which thus affects inoculum concentration(Teng et al. 1991). Sporulation and lesion development aretermedinfection ability(Suzuki 1975; Kingsolver et al. 1984; Koizumi and Kato 1991;Ribot et al. 2008).For leaf blast, temperature thresholds for sporulationand lesion development have beenreported (Henry and Andersen1948; Kahn and Libby 1958; Sekiguchi and Furuta 1970; Yoshin 1979). Using these cardinal temperatures, an infection ability response curve can be developed, following the classic biological response curve (Reed et al. 1976) and a beta function (Yan and Hunt 1999; Guyaderet al. 2013). The resulting model can then be used with meteorological data to assess the likely spread of the diseasefor larger areas under rice cultivation in current and future climates. The infection ability model in the present study was constructed using cardinal temperatures (lower, upper, and optimum thresholds) for sporulation and lesion development. This supplement provides details about the development of the model and its validation.
Sporulation on artificial media
For sporulation, slants (rice leaf extract and sucrose agarin test tubes) were inoculated witha mycelial disk (0.4 cm) from five-day-old culture and kept in a biological oxygen demandincubator (attached with a black fluorescent light source emitting wavelengths of 350–390 nm) set at temperature levels 5, 8, 10, 13, 15, 18, 21, 25, 28, 32, and 36°C. For fluorescent light exposure to induce sporulation, the slants were kept 20 cm from the light source. Infrared thermography (AX8, FLIR, USA) was used toaccurately recordtemperature on the surface of the slants. Initiation of sporulation on the slants coincided with a change of the mycelial mat color to a light black tinge, which was then confirmed bymicroscopic observation. Mean time at each temperature from inoculationto the development of the black tinge was noted as sporulation time (h),whilethe reciprocal of the sporulation time was called the sporulation rate (r[T]SPh-1).
Lesion development on rice leaves
Rice seedlingsof the susceptible cultivar Pusa Basmati 1 (Division of Genetics, IARI, New Delhi) were raised in polypropylene pots (15×20 cm) filled with uniform soil mixtureat optimum moisture.About 40 days after sowingwhen the sixth leaf hadhalf emerged, rice plants were inoculated with pathogen spore suspension prepared following the standard method (Valentet al. 1991;Jia et al. 2003). Conidial suspensions of 105 conidia/mLwater containing 0.25% gelatin and 0.02% Tween 20were sprayed on leaves once with a fine atomizer. Leaves were prepared for inoculation by sprayingwith 0.25% gelatine and 0.02% Tween 20to promote adherence of conidia to the leaves. Negative controls receivedthissame gelatin and Tween 20 solution without spores. After that, plants were kept in fine mist chamber for 10 hat 27°C and then were transferred togrowth cabinets at temperature levels 19, 22, 24, 26, 28, 30, and 32°C. A positive checkwas maintained at 27°C to verify that inoculation and lesion development were normal. Observations at 27°C wereused to normalize the number of lesions in each temperature treatment. Incubation conditions includeddaily cycle of 14 h light (>95% RH) followed by 10 h of darkness (> 95% RH). The plants weremonitored hourly until characteristic and visible blast lesions were observed.
The numbers of lesions on leaves wererecorded untilno more lesionsappearedfor each temperature treatment. The effect of temperature on the average number of lesions per fiveleaves (in threereplications) wasanalyzed in a completely randomized design. The median time by which 50% of the lesions had appeared was estimated;the reciprocal of median time is termed the lesion development rate(r[T]LDh-1).
Model development
The model was constructed based on the cardinal temperatures (lower, upper, and optimum thresholds) for sporulation and lesion development, following a non-linear beta function (Yan and Hunt 1999;Guyaderet al.2013) as follows:
r(T) = Rmax*[(Tmax – T )/(Tmax – Topt )]*[(T – Tmin )/(Topt– Tmin)](Topt– Tmin )/(Tmax – Topt) .
This model was used to estimate the response of sporulation, r(T)SP,and lesion development,r(T)LD, to temperature T, with Rmax as their respective asymptotes.Tmax, Tmin,and Topt are the upper, lower, and optimum temperatures,respectively, for both sporulation and lesion development.The upper and lower thresholds where r(T) =0 indicates that sporulation or lesion development is assumed to be zero. Parameter estimates for Rmax, Tmin, Topt, and Tmax were determined following nonlinear iterative procedures,such as theLevenberg–Marquardt (L-M) analysis(Seber and Wild 1989; Madden et al.2007). Goodness-of-fit was evaluated by plotting and inspectingobserved and predicted values side-by-side. The statistical significance of the difference between the models (sporulationrate vs. lesion development rate) in terms of goodness of fit was assessed using the F-testdescribed by Motulsky and Ransnas(1987).
Validation of infection ability model
To validate the model, two locations were selected with representative temperature variation of the two rice-growing seasons, monsoon and winter. For the monsoon rice, the blast-susceptible cultivar Pusa Basmati 1 was transplantedinto a plot under Delhi climate conditionsand sized 2 × 1 m2 on July 2 and August 2,2014 and on July 5and August 5, 2015. For winter rice, transplanting was done on January 10 and February 10, 2014 and on January 15 and February 15, 2015 at Nandyal in the Kurnool district of Andhra Pradesh. In each plot of five rows, one plant in each row was inoculated 40 days after transplantingto evaluate the lesion development rate underdifferent temperature regimes. Spore suspension (105 conidia/mLwater) containing 0.25% gelatin and 0.02% Tween 20 was inoculated as described before. Inoculated plants were covered with polythene bags for 10 h to maintain relative humidity (RH) over 95%. For accurate measurement of hourly temperature and RH-hour, a calibrated Kestrel pocket weather tracker was kept inside the canopy. The experiment was conducted only when both temperature and RH-hoursexposure(over 15 h) were sufficient for infection (Kim et al. 1985). Lesion development was observed daily, and the time of 50%lesionsappearedwas recordedfor every plot. In the model, this time was predictedby integrating r(T);the modelled estimate wascompared with observed values. Model performance was assessed by calculating the root mean square error (RMSE) and Nash-Sutcliffe efficiency (NSE) toindicate how well the plot of observed versus predicted data fit the 1:1 line (Nash and Sutcliffe 1970). These are calculated as below:
whereXobs, iis the ith observation, Xmodelis the ith predicted value for the constituent being evaluated, Xobs, meanis the mean of the observed data, and n is the total number of observations. NSE values between 0.0 and 1.0 are generally viewed as acceptable levels of performance, whereas values <0.0 indicated unacceptable performance.
Cardinal temperatures and infection ability model
Temperature significantly influenced both sporulation andmycelialgrowth (p0.05). Mycelial growth was very slow at temperatures below 8°C and above 36°C.Sporulationoccurredafter160h of exposure to 15°C, at 69–70h of exposureto28–29°C,and at 130 h to34°C (Supplementary Table 1). Hourly fractions of the sporulation rate (h-1),estimated as the reciprocal of the latent period, increased significantly from 0.009259 at21°C, reachinga maximum of 0.014315 around 28°C beforesharply droppingto 0.007694 at 34°C.
Inoculated rice plants exposed to different temperatures(with RH95% for a fixed duration) showedsignificant (p0.05) differenceswith respect tothe duration of lesion development, which was 98.4–144 h in the temperature range of 24to 30°C. However, lesion development took 240 h and 168 h at 19°C and 32°C, respectively (SupplementaryTable 2).The lesion development rate (h-1) increased significantly from 0.004166at19°C to 0.010162 at 26°C beforedecreased to 0.006944 at 32°C.
Tmax, Tmin,and Topt for sporulationand lesion development were appropriated from the observed data on sporulation (SupplementaryTable 1) and lesion development rates (Supplementary Table 2) by fitting thebeta function.Parameter estimates from this model are given in Supplementary Table 3.
Model parameters Tmax, Tmin,and Topt for sporulationrate were determined to be 36°, 5°, and 28°C, respectively, with Rmax = 0.015 and the fitted temperature response curve as shown (SupplementaryFigure1). The inflection point [d2 r(T)/dT2=0] from the fitted model was estimated to be20°C, with maximum sporulation rate [d r(T)/dT=0] at 28°C. Thus, the model for sporulation was constructed as follows:
r(T)SP= 0.015*[(36-T)/8]*[(T-5)/23]2.875.
Similarly, Tmax, Tmin,and Toptfor lesion development were obtained, with model parameters, respectively,of34.1°, 7.9°, and 27.4°C, and with Rmax = 0.01.The fitted temperature response curve is shown in SupplementaryFigure 2. The model estimated the inflection point [d2 r(T)/dT2=0] for lesion development at 20.9°C, with a local maximum [d r(T)/dT=0] at 27.5°C. Thus, the model for lesion development was constructed as follows:
r(T)LD = 0.01[(34.1-T)/6.6][(T-7.9)/19.6]2.9697.
Overall, infection ability in terms of sporulation and lesion development was reached at a peak between 24 and 30°C. The data provide fairly good estimates, with small standard errors for Tmax and Topt.ForTmin, error was on the higher side. Although no direct observationswere obtained on lesion development for minimum and maximum temperature (and none ispossible because of experimental difficulties), the fitted curve was consistent with the lower and upper limits of the pathogen’s mycelial growth and sporulation. The Rmax, Tmax, Tmin,and Topt for sporulationand lesion development did not differ significantly, as indicated by an F-test (p0.05). Temperature response modelswere therefore similar for both processes.
For field validation, the lesion development rate model was considered. Low estimates of RMSE (1.20–3.30) and acceptable NSE values (0.0130–0.3624) indicated that the temperature-dependent model could predict the observed response of lesiondevelopment under field conditions (Supplementary Table 4).Hence, sporulation and lesion development rateare summarized into aninfection ability modeltoassess leaf blast incidence in both current and future climates.
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Supplementary Table1Mean time (h) for initiation of sporulationfor Magnaportheoryzae under different temperatures
Temperature (oC) / Hours* to initiation of sporulation (h) / Hourly sporulation rate (h-1)as reciprocal of initiation time for sporulation15 / 160.0±4.3 / 0.006251
18 / 122.2±2.2 / 0.008197
21 / 108.3±2.4 / 0.009259
23 / 92.0±2.5 / 0.010871
27 / 72.0±3.5 / 0.013929
28 / 69.2±2.9 / 0.014315
29 / 70.1±2.7 / 0.014304
32 / 77.0±3.1 / 0.012887
34 / 130.2±2.6 / 0.007694
CD (5%) / 3.61
Sem / 0.95
*Mean hour of four replications with ±SD
Supplementary Table2 Median time (h) for 50% blast lesion development on rice leaf inoculated with spore suspension (M. oryzae)under temperature levels
Temperature(0C) / Hour* for appearance of 50% lesion / Hourly lesion development rate (h-1) as reciprocals of median time for 50% lesion appearance19 / 240.0±2.6 / 0.004166
22 / 144.0±2.2 / 0.006944
24 / 115.2±1.6 / 0.008680
26 / 98.4±1.2 / 0.010162
28 / 100.8±1.8 / 0.009920
30 / 115.2±1.2 / 0.008680
32 / 144.0±2.1 / 0.006944
CD (5%) / 2.84
Sem / 0.88
. *Mean hour of four replications with ±SD
Supplementary Table3 Parameter estimates for the beta function [r(T) =Rmax*[(Tmax – T )/(Tmax – Topt )]×[(T – Tmin )/(Topt– Tmin)](Topt – Tmin )/(Tmax – Topt))] fitted* on data for sporulation (obtained from fixed temperature exposure of M. oryzaein artificial media) and lesion development (at fixed temperature exposure to inoculated rice plants for 50% of lesion appearance).
Model parameters / Estimates (95% Confidence interval ) / Standard errorsSporulation / Lesion development / Sporulation / Lesion development
Rmax / 0.015
( 0.012-0.170 ) / 0.010
(0.010-0.011) / 0.001 / 0.002
Tmin / 5.003
(-30.8-38.5) / 7.9
(-32.5-48.4) / 8.729 / 12.729
Topt / 28.0
(25.6-30.5) / 27.4
(26.3-28.5) / 0.676 / 0.346
Tmax / 36.0
(33.4-38.5) / 34.1
(32.6-35.4) / 0.924 / 0.424
R squared= 1- (Residual sum of squares)/(Corrected sum of squares) / 0.813 / 0.983
F-test for model comparison / P =0.121
*convergence of parameter estimates was reached in the iteration process (in 21 for sporulation and 18 for lesion development) of model fitting
Supplementary Table 4 Predicted and observed median time for 50% of blast lesion development on rice, expressed as hour under field conditions.
HourMonsoon rice (Delhi) / Winter rice (Nandyal AP)
2014 / 2015 / 2014 / 2015
40 DAI / 60 DAI / 40 DAI / 60 DAI / 40 DAI / 60 DAI / 40 DAI / 60 DAI
Predicteda / 124 / 156 / 124 / 151 / 158 / 168 / 151 / 158
Observedb / 131 / 172 / 137 / 142 / 168 / 174 / 160 / 168
Differencec / 7 / 16 / 13 / 9 / 10 / 6 / 9 / 10
95% Confidence intervald / 112.5-142.5 / 146.2-179.3 / 108.4-152.2 / 126.7-162.4 / 142.1-176.3 / 143.5-179.4 / 143.4-169.4 / 138.4-172.1
RMSEe / 1.7320 / 1.2018 / 2.8920 / 3.3021 / 1.2431 / 2.3355 / 2.9627 / 1.9148
NSEf / 0.0130 / 0.2778 / 0.0601 / 0.2607 / 0.1022 / 0.1054 / 0.0437 / 0.3624
aMedian hours for 50% lesion development calculated as sum of hourly rate from the time of inoculation using the model r(T) = 0.01[(34.1-T)/6.6][(T-7.9)/19.6]2.9697
bMedian hours for 50% lesion development during 2014 (n=9) and 2015 (n=11) under Delhi and Nandyal conditions.
c Difference in hours between predicted and observed median time.
dLower and upper limits of 95% confidence interval for observed median time for lesion development
eRMSEin hours between predicted and observed median time.
fNash-Sutcliffefficiency NSE) is the measure of relative magnitude of the residual variance to the variance of the errors obtained by the simple persistence model (Gupta et al., 1999).
Supplementary Figure 1Sporulation rate model (R2= 0.863) from the data generated based on artificial media, line indicates fitted beta function and dotsas observed fraction of sporulationrate inM. oryzaeunder different temperatures.
Supplementary Figure 2 Leaf blast lesion development rate model fitted (R2= 0.983) from the data generated under controlled experiment (on susceptible rice cultivar Pusa Basmati 1); line indicates fitted beta function and dots as observed lesion development rate.