J. Hort. Sci. 
Vol. 1 (1): 64-67, 2006 

A statistical model for ascertaining the influence and reliability of weather parameters 
on incidence of blossom blight in mango (Mangifera indica L.) 

R. Venugopalan, R. D. RawaP and A. K. Saxena' 
Section of Economics and Statistics 

Indian Institute of Horticultural Research 
Hessaraghatta Lake Post, Bangalore-560 089, India 

E-mail: venur@iihr.emet.in 

ABSTRACT 
A statistical model was developed to study the influence and reliability of weatlier parameters on incidence of 

blossom blight in Mango {Mangifera indica) and subsequently to predict their incidence. Results showed that 
preceding week's weather variables viz., maximum and minimum temperature, evaporation, rainfall, morning 
and evening relative humidity and wind speed were found to collectively predict blossom blight incidence to the 
extent of 94.3 per cent. Further, as a measure of goodness-of-fit, the coefficient of determination (R̂ ) and mean 
squared error were used to evaluate the empirical model developed by using above variables. Validation test 
showed that the model developed using relative humidity at 07.30 h (X,), evaporation (X̂ ) and wind speed (X̂ ) 
(Y = 883.4 - 8.065 X, -11.506 X̂  -33.619 X̂ ) could predict the incidence to the extent of 75.7%. This model is 
useful in determining the role of climatic factors in disease appearance and progression and devising suitable 
management strategy. 

Keywords: Blossom blight, mango, coefficient of determination, climatic factors, model 

INTRODUCTION 

Mango {Mangifera indica L) is the most important 
fruit crop grown across various climatic and soil conditions 
in India. Although mango is grown in large area, the 
productivity is much lower than the world average. There 
are many biotic and abiotic stresses, which are responsible 
for the low productivity. Among the biotic factors, diseases 
like powdery mildew, leaf spot and blossom blight are the 
most serious on mango and account for the major losses. 
The pathogens such as, Colletotrichum glaeosporioides, 
Alternaria alternata and Pestalotiopsis mangiferae are 
responsible for blossom blight. These pathogens can cause 
disease singly or in combination depending upon the 
weather conditions. In India, the occurrence and importance 
of blossom blight disease was reported during 1992 (Rawal, 
1992). However, information on the influence of weather 
factors on disease outbreak is lacking. In view of this, a 
study was undertaken to find out the role of weather factors 
individually and in combination that lead to the disease 
incidence. Such work will be helpful to develop prediction 
equations so as to facilitate devising a suitable management 
strategy. 

MATERIAL AND METHODS 

Mango var. Totapuri orchards were surveyed 
during August to October 2005 (flowering period) to record 
the blossom blight disease initiation and its progression. 
Disease ratings were recorded at weekly interval by 
following 0-5 scale, where 0 = nil PDI; 1= 0> PDI d>10; 
2= 11>PDI<25; 3= 26>PDI<50; 4= 51>PDI<75 and 5 =e 
<76 Per cent Disease Intensity (PDI). Data thus recorded 
were converted to Percent Disease Index as per McKenny 
(1923). The weekly weather data such as maximum 
temperature (°C) (X,), minimum temperature (°C) (X^), 
relative humidity (%) (7.30 h) (X3); X4: relative humidity 
(%) (14.30 h), (X^), evaporation (mm) (X^), wind speed 
(Kph) (Xg), rainfall (mm) (X )̂ and number of rainy days 
(Xj) were collected from IIHR meteorological observatory 
for the same period. All the data were subjected to statistical 
analysis in order to assess the influence of abiotic factors 
on blossom blight incidence and subsequently for the 
development of disease prediction models as detailed below. 

In order to assess the degree of linear association 
of each of the weather variables on blossom blight incidence 
over a time period, linear correlation coefficient was worked 
out. Further, with a view to understand the role of weather 

'Division of Plant Pathology 

mailto:venur@iihr.emet.in


Venugopalan et al 

parameters on degree of disease incidence, a statistical 
model was developed. As a measure of goodness-of-fit, 
the value of the co-efficient of determination (R^) was 
calculated (Kvalseth, 1985) as illustrated below: 

A 

R^= 1-[I(Y,-Y)^ / [ I ( Y , - Y ) ^ ] 

where Ŷ  represents PDI during the time period t. 

However, inclusion of an additional independent 
variable into the selected candidate model always boosts 
the computed R- value. Hence, to ensure the statistical 
significance of the computed regression coefficients, these 
were subjected to r-test statistical analysis. Further, to test 
whether the regression models are robust against the basic 
assumption of regression approach, viz., independent 
variables should not be related among themselves, 
commonly known as the problem of multi-colinearity, 
Variance Inflation Factor (VIF) was worked out. A value 
of VIF exceeding 10 indicates the presence of strong multi-
colinearity among observations (Ryan, 1997). To select the 
significant weather parameters influencing the observed 
variability in blossom blight incidence, a step-wise 
regression procedure (Ryan, 1997), was employed as 
delineated below. 

In step-wise regression, the final regression equation 
was developed stage by stage. During each stage, making 
use of F test, an independent variable (weather factor) would 
enter into the equation if the significance level of its F value 
is <0.05, and would be removed if the significance level is 
>0.1. This process was continued until all the variables were 
exhausted and are found significant, resulting in the final 
equation comprising only the significant weather variables. 
Further, as we are dealing with a set of sample observations 
to take inference about the whole population under study 
(variability in blossom blight incidence over time), in 
general, it is essential to perform a detailed residual 
(difference between observed and predicted PDI) analysis 

(Venugopalan and Prajneshu, 1997) before flagging of the 
developed model for its universal validity. To this end, two 
important assumptions about the model generated residuals; 
viz. randomness and normality were tested by following one-
sample run test and Shapiro-Wilk test, respectively 
(Agostid'no and Stephens, 1986). 

RESULTS AND DISCUSSION 

Linear correlation coefficient analysis among 
weekly blossom blight incidence with preceding week's 
weather parameters were worked out and presented in Table 
1. Perusal of the results indicated the presence of highly 
significant correlation among blossom blight incidence with 
the averages of preceding week's weather variables viz., 
relative humidity at 14.30 h (r=0.60) and wind speed (r=-
0.69). Among the intra-class linear correlation coefficients 
based on preceding week's weather parameters, maximum 
temperature had shown a significant positive correlation 
with wind speed (r=0.65); relative humidity at 7.30h with 
evaporation (r=-0.82), with rainfall (r=0.79); relative 
humidity at 14.30h with wind speed (r=-0.88) indicating 
about the indirect effect of these factors on blossom blight 
incidence. 

As a next step, statistical model was developed by 
regressing weekly blossom blight incidence with all the 
weather parameters of preceding week. Perusal of Table 2 
indicates that the preceding week's weather variables were 
found to predict blossom blight incidence to the extent of 
94.3%. Though the model developed resulted in 
considerably high R^ value, some of the regression 
coefficients corresponding to weather parameters were only 
significantly related to blossom blight incidence as indicated 
by the t-test statistic value (being greater than 1.96). In 
addition to this, the model indicated the presence of strong 
multi-collinearity among weather variables as indicated by 
VIF (Variance Inflation Factor) value 23.18 (being >10 and 
eigen value being nearer to zero). 

Table 1. Correlation coefficient ( r ) among weekly blossom blight incidence and weather parameters 

Variable 
% damage (1) 
Maximum temperature (2) 
Minimumtemperature (3) 
RH 7hrs (4) 
RH 13hrs(5) 
Wind speed (6) 
Evaporation (7) 
Rain fall (8) 
No of rainy days (9) 

(1) 
1.00 

-0.37 
-0.41 
0.31 
0.60 

-0.54 
-0.69 
0.10 
0.3 1 

(2) 

1.00 
-0.22 
-0.11 
-0.41 
-0.12 
0.65 
0.09 

-0.50 

(3) 

-1.00 
-0.22 
-0.17 
0.25 

-0.02 
0.19 
0.35 

(4) 

1.00 
0.37 

-0.82 
-0.52 
0.79 
0.76 

(5) 

1.00 
-0.33 
-0.88 
0.05 
0.56 

(6) 

1.00 
0.40 

-0.58 
-0.51 

(V) 

1.00 
-0.13 
-0.69 

(8) 

1.00 
0.60 

Note: bold values are significant at 5% level 

J. Hort. Sci. 
Vol. 1 (1): 64-67, 2006 

65 



Mango blossom blight forecasting model 

Table 2. Results of statistical models with goodness of fit statistics 

Model type 
Full regression model 
(Ail weather parameters) 

Model using wind speed (X^), 
relative humidity 07.30 h (X,) 
evaporation (X,) and rainfall (X )̂ 
Optimised model wind speed (X^), 
relative humidity 07.30 h (X,) 
evaporation (X,) only] 

Y = 1866.4 
(18.3) 

-Stat -1.6 
Y = 1290.8 

t-stat 
Y = 8 8 3 . 4 -

t-.stat 

Statistical model (with Standard error of b̂ )) 
-31.1 X, -H30.4 X, -19.9 X, - 25.5 X^ 4-4.6 X,-21.52 X^-h3.64 X, -15.45 X, 

(20.3) (7.7) (4.8) (8.8) (33.7) (1.6) (8.03) 
1.5 -2.6 0.95 -2.87 -0.63 2.25 -1.9 

- 12.9X,-12.7X,-41.2X^ 4-1.57 X, 
(5.04) (3.98) (11.3) (1.27) 
-2.56 -3.2 .15 -3.67 

8.06X,-11.506 X,-33.619 X(, 
(3.3) (4.02) (9.84) 

-2.42 -2.86 -3.42 

RH%) 
94.3 

80.7 

75.7 

VIF 
23.2 

8.76 

3.56 

Note: Values parenthesis are standard error of regression estimates bi 

Accordingly, to eliminate this multi-coUinearity 
problem, step-wise regression models were developed and 
the results are presented in Table 2. The results indicated 
that only four variables viz., wind speed, relative humidity 
at 07.30h, rainfall and evaporation could explain the 
variability in blossom blight incidence to the extent of 80.7 
% as against 94.3% (when all weather variables included 
in the model). However, in another optimized model, rain 
fall was also eliminated, because the corresponding 
regression coefficient was not statistically significant as 
indicated by t-test statistical value 1.27 (being <1.96). 
Therefore, among all weather parameters tried, only three 
weather variables, viz. relative humidity at 07.30h, 
evaporation and wind speed could themselves collectively 
explain 75.7% of the variation in weekly blossom blight 
incidence, which is quite high while predicting a biological 
variable. Further, the regression coefficients corresponding 
to these variables in the final model were also statistically 
significant, as indicated by the t-statistic value, which in 

Table 3. Results of residual analysis for the optimized model 

Test criterion Residual Statistic Significance 
assumption tested value 

Run test 
Shapiro-wilk 

Randomness 
Normality 

0.0091 
0.931 

P<0.005 
P<0.005 

Table 4. Calculated per cent error variation for predicted blossom 
blight incidences 

Time in Date of 
Week observation 

Predicted blossom 
blight incidence 

(%) 

Error variation between 
observed and blossom 

blight (%) 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

J. Hon. 

12.8.05 
19.8.05 
26.8.05 

2.9.05 
9.9.05 

16.9.05 
23.9.05 
30.9.05 
7.10.05 

14.10.05 
21.10.05 

Sci. 
Vol. 1 (1): 64-67,2006 

16.44 
41.68 
56.67 
19.49 
45.78 
31.08 
57.48 
64.84 
86.50 
96.18 
92.63 

-7.76 
-25.60 
-27.30 
12.50 
-4.44 
20.92 
16.52 
10.48 
0.83 

-2.17 
6.03 

absolute value exceeded 1.96, the critical region value. Also 
the VIF value computed for this model was well inside the 
acceptable limit (3.56<10.0) which further strengthens the 
statistical validity of the optimized model. 

Before drawing final conclusion about the adequacy 
of the selected model, universal validity of the model was 
assessed by performing detailed residual analysis. The 
randomness assumption of the residuals tested using the 
one-sample run test resulted in the test statistic value as 
0.009, which being less than 1.96, is well inside the critical 
region of normal table at 5% level of significance. The 
normality assumption of the model generated residuals 
tested using Shapiro-Wilk test resulted in the test statistic 
value as 0.931, which being less than 1.96, is well inside 
the critical region at 5% level of significance (Table 3). 
These two results further ensured the universal validly of 
the developed model. A graphic representation of the 
adequacy of the fitted models is presented in Fig. 1. The 
per cent error variation between observed and predicted 
values ranged from 0.83 to 20.9 (Table 4). The approach of 
this study is to develop a reasonable prediction model for 
mango (cv Totapuri) blossom blight using reliable and 
dependable weather variables which have direct influence 
on blossom blight incidence. Further, validation of 
optimized model (the observed incidence values were 

Fig. 1. Statistical model for epidemiology of Blossom Blight in 
Mango (cv Totapuri) 

Time pariod Observed PDI 
Predicled PDI 

66 



Venugopalan et al 

compared to predicted values using optimized model), 
clearly indicated that the model could predict the incidence 
reasonably well. 

By using the model developed in the present study, 
it is possible to workout mango (cv Totapuri) blossom blight 
incidence with minimum available data viz., relative 
humidity at 07.30h, evaporation and wind speed. However, 
future studies to standardize variables for improving the 
precision of blossom blight incidence estimates will be 
envisaged with good variability in the data set. This model 
is useful in determining the role of climatic factors in disease 
appearance and progression and devising a suitable 
management strategy. Thus, we have used statistical 
modelling as a power tool for developing suitable disease 
forecasting models and also for optimizing factors 
influencing disease incidence. 

ACKNOWLEDGEMENTS 

The authors are grateful to the Director, Indian 
Institute of Horticultural Research, Hesseraghatta Lake PO, 

Bangalore , India for providing facilities to carry out the 
work. The authors also thank the anonymous referee and 
the editor for their critical suggestions which led to 
substantial improvement in the quality of the paper. 

REFERENCES 

Agostid'no R.B and Stephens. M.A. 1986. Goodness of 
Fit Techniques. Marcel Dekker, New York.576p 
Kvalseth, T. O. 1985. Cautionary note about R^ 
Amer. 5far., 39:279-85 

Mcknney, H. H., 1923. Influence of soil temperature and 
moisture on infection of wheat seedlings by 
Helminthosporium sativum. J. Agric. Res., 26:195-217 

Rawal, R.D. 1992. Ann. Rep. 1991-92. Indian Institute of 
Horticultural Research, Bangalore, India 204p 

Ryan, Thomas R 1997. Modem Regression Methods. John 
Wiley and Sons Inc., New York. 515p 

Venugopalan, R and Prajneshu. 1997. A generalized 
allometric model for determining length-weight 
relationship. Biometrical J., 39:733-39. 

(MS Received 3 April, 2006 Revised 12 June, 2006) 

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Vol. 1(1): 64-67, 2006 

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