1. Aakriti Sharma and Pragya Adhikari
Analysis of Phenotypic Data of Bacterial Spot Disease Resistance of Tomato Using Bayesian Approach
Aakriti Sharma and Pragya Adhikari
Bacterial spot is one of the most important diseases of tomato in North Carolina and many other States, caused by multiple bacterial species and physiological races within the genus Xanthomonas, with distinct geographical distribution of each species and races. There is no any commercial bacterial spot resistant cultivar so far. Therefore, we screened 10 different tomato genotypes (NC1CS, HI7998, HI7981, NC1CELBR, NC30P, NC84713, NC714, PI270443, FLA7060, NC22L) in the phytotron using random block design with nine replications, to select potential parents to develop mapping population. Tomato plants were inoculated with race T4 of Xanthomonas as this race is expected to be predominant in North Carolina. The disease score was recorded after a week of inoculation in terms of percentage of canopy affected.
Introduction
FLA 7060 was the most susceptible (highest mean) and PI was the most resistant among 10 genotypes (lowest mean) (Table 1).
The credible set of PI genotype is not overlapped with other genotypes, except NC22L (Figure 2), thus significantly vary from other genotypes.
Results
Figure 1. Convergence diagnostics.
Objective
Our objective is to analyze a model in a Bayesian perspective to identify significant suitable parents that show resistance to bacterial spot disease. In addition, we are also interested in comparing the results obtained from the Bayesian approach with the frequentist approach.
Mean
Quantiles
2.50%
97.50%
alpha
tau
NC1CS
HI 7998
HI 7981
NC1CELBR
NC 30P
NC84713
NC 714 PI
FLA 7060
NC 22L
Table 1. Posterior summary of the regression parameters.
Contrast
p-value
NC714-NC1CS
NC1CELBR-NC22L
NC84713-NC1CS
NC1CELBR-FLA7060
2.00E-07
PI NC1CS
NC714-FLA7060
NC1CS-HI7998
3.00E-07
NC84713-FLA7060
NC1CS-HI7981
NC30P-HI7998
4.60E-06
NC714-NC22L
NC714-NC30P
NC84713-NC22l
1.20E-05
PI NC30P
PI NC1CELBR
1.80E-06
NC30P-HI7981
NC1CELBR-HI7998
Table 2. Genotypes showing significant differences using frequentist method (Tukey-Test).
Bayesian linear regression with uninformative prior was used to determine the response of the plant genotype to the disease. The significant genotypes were determined from the 97.5 % credible sets. The data consisted of 10 different genotypes and each genotype had 9 replications. The response is the susceptibility or resistance capacity of a particular genotype to the disease. Here we are interested in estimating the significant genotypes that are resistant to the disease.
Model Specification
Y[i,j]~dnorm(alpha + beta[j], tau)
where, Yij is the response of the genotypes to the disease. The prior distributions for parameters alpha, beta and tau were considered to be uninformative prior, which assumes no information about the parameters and hence shrinks more towards the data.
beta[j]~dnorm(0,0.0001)
alpha~dnorm(0,0.0001)
tau~dgamma(1,0.0001)
The effects of different genotypes on bacterial spot disease was analyzed using MCMC algorithm of bayesian inference. The model was fitted in R using JAGS and MCMC sampling. The first 1,000 iterations were discarded as burn-in samples and the next 1,00,000 were generated for estimating the posterior of the model parameters with thinning intervals of 10. The convergence diagnostic (trace plot and autocorrelation plots (Figure1).) confirmed us that the MCMC algorithm was producing a reliable output for the final model.
Frequentist analysis
The model we fitted is: Yij = µ + βi + ԑij
where, i is the indicator for each genotype and j for each replication within a particular genotype. The effect βi represents how the ith genotype varies from the overall mean.
Methods
Using Bayeisan approach, among 10 genotypes, PI was found to significantly vary from other genotype, and was also the most resistant genotype. Therefore, this genotype can be crossed with any other genotypes to develop mapping population.
NC22L was also significant and showed some level of resistance.
NC1CELBR and NC30P turned out to be insignificant, and therefore would not be used for developing mapping population.
This result is similar to that obtained from frequentist approach analyzed using ANOVA and TUKEY test.
Due to the use of uninformative prior, the result is more shrinked towards the data rather than the prior.
This selection approach is useful to plant breeders that allows them to select the best parents that are disease resistant, and develop new resistant hybrids, which ultimately benefits the farmers resulting a maximum crop yield.
Conclusions
Figure 2. Plot showing relative effect of genotypes to the disease.