Incidence forecasting of new invasive pest of coconut rugose spiraling whitefly (Aleurodicus rugioperculatus) in India using ARIMAX analysis K.ELANGO*, S. JEYARAJAN NELSON and P.DINESHKUMAR1

Coconut (Cocos nucifera) is one of the most important crops in tropical areas. It is usually referred as ‘tree of heaven’ or ‘kalpavriksha’ because it provides more useful and diverse product to the people. Coconut is grown in more than 93 countries in the world in an area of 12 million hectares, with an annual production of 59.98 million tonnes of nuts. India occupies third position in the world level with an annual production of 10.56 million tonnes of coconuts. In India, Kerala, Tamil Nadu, Goa, Karnataka, Maharashtra, Orissa, West Bengal and Assam are the major coconut producing states in India. India consumes 50% of annual production for their culinary and religious purpose, 35% used as copra, 2% for manufacturing of value added products, 11% for tender uses and 2% for seed purpose. More than 900 species of pests are associated with coconut palm. This includes both invertebrates and vertebrates. Of these, red palm weevil, (Rhynchophorus ferrugineus Olivier) rhinoceros beetle (Oryctes rhinoceros L.) and coconut black-headed caterpillar (Opisina arenosella Walker) are the most important devastating insect pests of coconut in major coconut-growing areas of India (Kumara et al., 2015). In Tamil Nadu, the incidence of rugose spiraling whitefly, A. rugioperculatus (Hemiptera: Sternorrhyncha: Aleyrodidae) on coconut was first observed in Anaimalai block, Coimbatore during August, 2016 (Sundararaj and Selvaraj, 2017). Rugose spiraling whitefly (RSW) is a new invasive pest and also polyphagous which is likely to expand the host range as the species becomes more established. The RSW has been reported in India from Tamil Nadu, Karnataka, Kerala and Andhra Pradesh (Sundararaj and Selvaraj, 2017). It mainly infests coconut palms and other broad-leaved hosts in its native range. The pest is somewhat superficially similar in its habits and general appearance to spiralling whitefly A. disperses, which itself is an invasive pest that came to India in the mid-1990s. RSW causes stress to the host plant by removing water and nutrients and also by producing honeydew, which covers the lower leaves and results in the growth of sooty mold. Although sooty mold is not a plant disease, its presence on the upper surface of the leaf can potentially reduce photosynthesis of the plant. Influence of weather parameters on rugose spiralling whitefly incidence is lacking, which is essential for developing management strategies. Current studies showed that though the infestation was recorded throughout the year, it was found ABSTRACT

low in rainy season, moderate during post rainy season and high in summer. Therefore, weather parameters also play an important role in the rugose spiralling whitefly incidence in coconut trees. The population buildup of any insect is very intimately related with the weather parameters (Boopathi et al., 2014). Forecasting enables to prevent outbreaks and epidemics of rugose spiralling whitefly incidence. Hence, this study also aimed at proposing a prediction model to use management practices well in advance

Population dynamics of coconut rugose spiralling whitefly
The population density of A. rugioperculatus on five-year-old coconut trees was assessed from 2017 to 2019.
An earlier report by Elango et al. (2019)  the bottom matured five fronds were selected, and from each frond, five leaflets were marked for taking observations on population dynamics of RSW as per the methodology of Elango and Nelson (2020). Weekly observations were made in selected leaflets of the coconut tree, and the number of nymphs of A. rugioperculatus per leaf was noted on these leaflets

Weather parameters
The population RSW of (dependent variable) recorded on coconut were correlated with weather factors (independent variable) viz., maximum temperature (X 1 ), minimum temperature (X 2 ), maximum relative humidity (X 3 ), minimum relative humidity (X 4 ), and total rainfall (X 5 ) obtained from Agro Climate Research Centre (ACRC), Coimbatore for the entire study period. Totally 82 observations are collected from the 40 th SMW for 2017 to 14 th SMW of 2019. Multiple regression analysis was also performed with weather parameters.

Correlation
Simple correlation was performed using SPSS 16.0 statistical package to associate the incidence of A. rugioperculatus with various biotic factors.

Time series modeling
Along with the insect data, the above-mentioned climatological variables are also collected for the same time interval. So, Multivariate time series is employed for predicting the number of A. rugioperculatus nymphs per plant in the coconut.

Correlation studies of population density of A.
rugioperculatus It was found that the infestation was low during the rainy season, moderate during post rainy season and high in summer. RSW population density was high during first week       rugioperculatus (Josephrajkumar et al., 2018). Elango and Nelson (2020) also reported that prolonged dry spell is the main reason for proliferation and quick dispersal of the rugose spiraling whitefly in Tamil Nadu. In case of A. dispersus also the population density was positively correlated with maximum temperature and negatively correlated with relative humidity on guava (Mallappanavar, 2000;Mani and Krishnamoorthy, 2000).

ARIMAX modelling
Augmented Dickey-Fuller (ADF) Test and autocorrelation function (ACF) were used to test the stationarity of the insect population. From the Table 2, The t-statistic value of the Augmented Dickey-Fuller Test for the actual data shows that the data is non stationary ( -0.869). So, the first differenced data was taken and tested for stationarity. The t-statistic of the ADF test in the Table 2 shows that it is non stationary (-3.013). Again, the second differenced data was taken and test for stationarity. The ADF t-statistic value (-4.923) shows that the second differenced data is stationary. Fig. 1 shows the ACF values of the second differenced data which confirmed that it is stationary. Using the ACF and PACF values as showed in Fig. 1 and 2, the optimum lags for the Moving average and auto regressive polynomials (p, q) were selected.
All the climatic variables were used with various combinations to fit the ARIMAX model. The parameter estimates of the fitted models and its significance were calculated. On the basis of minimum corrected Akaike information criterion (AICc) and Schwartz-Bayesian criterion (BIC) values, best 10 ARIMAX model was selected and presented in the Table 3. Among the fitted models, ARIMAX (0,2,1) with Maximum temperature have the least AICc and BIC values.
For validating the selected model, the normality of the residuals was tested. The simple residual plot in the Fig. 3 suggests that the residuals may be normal. To test that, Normality test such as Box-Pierce test and Box-Ljung test were used. The statistics of these two tests are presented   (Fig. 4) is an added evidence for the residuals' normality. Fig. 5 which represents ACF of the residuals shows that none of the autocorrelation is significantly different from zero. From these evidences, we can conclude that the proposed ARIMAX model (Fig. 6) is the good fit and an appropriate model for the forecast of the insect population. Chattopadhyay (2021) stated that the management of weather and climate risks in agriculture has become an important issue due to climate change. Aishwariya et al. (2007) stated that whiteflies are present throughout the year in South India, with high population in summer (March-June) and low ones in winter (October January). Nymphal population was low in June to July and reached peak in November at Shimoga with this information, ARIMAX model was used to study the behavior of whitefly along with the abiotic factors. Only Maximum temperature has a significant impact with the whitefly population whereas the other abiotic factors were not significantly influencing the pest population.

CONCLUSION
ARIMAX model developed, it might be possible to predict a A. rugioperculatus incidence, since it is a new invasive pest of coconut in India. This model will further help to assess the incidence and population surge of rugose spiraling whitefly for its timely adoption of control measures by the growers. The model may further enables to prevent outbreaks and epidemics of rugose spiraling whitefly incidence in coconut ecosystem.