Time series analysis of variation in abundance of selected cocoa insects and fitting of simple linear predictive models

Abstract

AbstractA plot of cocoa trees at the Cocoa Research Institute, Tafo, Ghana, was inspected weekly for the presence on each tree of 18 species of insects. The 306 consecutive weekly records of percentage of trees occupied by each species were subjected to time series analysis. Auto-correlation and partial auto-correlation functions were calculated for each series and used to identify simple autoregressive linear models to account for the serial correlation. It was found that all species needed a stabilizing autoregressive parameter of lag 1 and all but four a second autoregressive parameter of lag 2. Seasonal autoregressive parameters at lags 3, 4, 5, 7, 9, or 13 were needed for over half the species, either in addition to the parameter at lag 2 or in place of it. It is postulated that these seasonal parameters mimic generation cycles. Runs of the models using random inputs produced series which were close to the originals in general form. The models could be further refined by adjusting the fixed mean levels assumed by the models to take into account the effects due to the abundance of young extension growth on the trees and atmospheric moisture, as measured by afternoon relative humidity readings. Although the production of extension growth is cyclical it would seem that it does not induce the cyclical behaviour observed in some of the insect series. The peaks in the latter cycles are, however, reinforced when they coincide with peaks in extension growth.