Time series application for quantification of Alternate Bearing Intensity (ABI) in mango (Mangifera indica) cv Langra

Abstract

The alternate bearing intensity (ABI) in mango (Mangifera indica L.) cv Langra, a distinct alternate bearer was statistically appraised through application of time series methods by subjecting yield data of one hundred trees growing under uniform cultural conditions at Central Institute for Subtropical Horticulture, Lucknow, Uttar Pradesh, over five years (2007-11). They were considered as 100 time series of short duration and arranged in 100 × 5 matrix for appraisal. The lag-one autocorrelation was calculated from the residual yield data obtained by removing year and tree effects. The quantification of ABI separately also by applying ‘I’ value and time series methods to the same set of data clearly brought out the limitations of ‘I’ value quantifying ABI as a descriptive statistic that sans inference test for significance thus, accounted for less than 60 percent of actuality vis a vis time series, attributable due to eliminating of trends generating a series of non-negative values by ignoring asymmetrical phase changes, an exclusive nature of a crop like mango. In the present analysis, higher precision of time series approach in quantification of ABI is largely by taking into account, the yield residuals and hence was found more efficient as compared to ‘I’ value. The autocorrelation was found negative and highly significant implying, distinctiveness in manifestation of alternate bearing rhythm. This analysis besides confirming strong and distinct alternate bearing tendency of Langra trees, provides a precise approach for quantification of ABI. The results of the present investigation could eventually lead to development of predictive models of yield in cv Langra as a component of decision support to empower growers for optimizing inputs management for sustained Langra mango tree health. In this paper, we present a simple but precise methodology to quantify alternate bearing intensity in Langra through autocorrelations that take into account unexplained components of alternate bearing phenomena.