1021-B1

A Mathematical Model for Predicting the Growth of Eucalyptus Globulus under Agroforestry Plantation

M. S. Malik^[1], C. Surendran and K. Kailasham

Abstract

A mathematical model is proposed for predicting the changes in growth of industrial agroforestry plantations under intercropping, weeding and fertilizer practices. The model also enabled the prediction of the growth, growth rate and felling period of Eucalyptus globulus under agroforestry system. The model was applied to growth data of a four-year pulpwood plantation of E. globulus under agroforestry practices with intercrop of potato, beans, maize and also with silvicultural practices such as weeding and fertilizer treatments in the long-term agroforestry experiments conducted in Palani Hills of South India.

The growth period of E. globulus has been classified into three growth stages, namely the establishment stage, the vegetative stage and the felling stage. Based on the complete growth period observation, it was found that the establishment period was up to the second year, the vegetative growth stage covers from the third to the seventh year and the remaining period covers the felling stage for pulpwood plantation.

To estimate a single growth model for the entire growth period of eucalyptus the following models were tried: Gompertz curve, Hill curve, Logistic curve, Richards curve, Polynomial exponential curve, Cubic Polynomial curve and Gauss curve.

Among the growth models, the Logistic growth model was found suitable for estimation of growth at harvesting period. Eucalyptus with potato intercrop gave higher yield of pulpwood in all the trials. Eucalyptus has maximum growth at fourth year. Eucalyptus grown with compatible intercrops reached its maximum potential of active growth in the sixth year. It is also suggested that the present rotation of eight years can be reduced to six years achieving the same yield and saving two years, a boon to the tree grower.

Introduction

The potential role of forest plantations in compensating for some of the products and services lost by deforestation has once more been emphasized with recent publications of data from the FAO’s Forest Resource Assessment, 1990 (FRA, 1991). Intervention of agroforestry as an effective land management tool has become very appropriate in maximising productivity of plantation areas. Within the agroforestry system, recourse to develop plantations as a source of raw material for industries is simply termed as industrial agroforestry. The demand for forest products is increasing rapidly in India, as anywhere else in the world and the gap between their demand and supply is widening (Luna, 1989).

The forest policy of Government of India, 1988, however, indicates irrevocably that wood based industries should look to agroforestry farmers for their requirement of wood over and above the raw material allotment made by the State Forest Department a concession extended to industries to put up factories. Since the Forest Department plantation can supply only a part of the expanded requirement of the industries. Now industries are encouraging the farmers to grow the pulpwood especially eucalyptus as a monocrop at their own fields. Agroforestry intervention in this would afford seasonal income for a few years in the life of the plantation.

Among the plantation grown species, poplars and eucalyptus are the most promising raw materials for pulp and paper manufacture because of their fast rate of growth. Later, Eucalyptus globulus (blue gum) became very popular and its cultivation was extended over a large area in the Nilgiri’s and Pulney hills of South India. The wood based industries have large scale industrial agroforestry plantation in the hilly region, especially Eucalyptus globulus plantation for rayon pulp. In order to maintain sustained timber and crop production associated with high yields, it is necessary to look into the effects of continuous growth.

There is therefore, need to develop a growth model for prediction of yield.

Materials and methods

The model was applied to growth data of four years pulpwood plantation of E. globulus under agroforestry practices with intercrop of potato (Solanum tuberosum), beans (Phaseolus lunatus), maize (Zea mays) and also with silvicultural practices such as weeding and fertilizer treatments in the long term agroforestry experiments conducted in Palani Hills of South India.

The growth period of Eucalyptus globulus has been classified into three growth stages namely establishment stage, vegetative stage and felling stage. Based on the complete growth period observation, it was found that E. globulus establishment period was upto second year, the vegetative growth stage cover from second year to seventh year and remaining period cover the felling stage for pulpwood plantation. Hence to estimate its growth rate at every stage the splitted regression analysis has been used as detailed below:

For the present study the growth observations of Eucalyptus globulus with intercrop were available only upto 4 years and to estimate its growth at the end of the 7^th year the vegetative growth stage regression was used.

To estimate single growth model for the entire growth period of eucalyptus, the following models such as Gompertz curve, Hill curve, Logistic curve, Richard’s curve, Polynomial exponential curve, Cubic polynomial curve and Gauss curve were tried for the present observations (Meek et al. 1991). The growth models were

Out of the above growth models based on the predicting ability and correlation coefficient value, the logistic growth model found to be most applicable for the present data. The predicted growth (PGt), the growth rates (GRt) were estimated based on the logistic growth model for every year.

Results

Stage-wise linear regression (Table 1).

TABLE: 1 STAGE WISE LINEAR REGRESSION

Significant at 1% level (r = 0.684)

The complete growth period of Eucalyptus globulus was divided into 3 critical growth stage viz. establishment stage covering 0 to 24 months; vegetative stage between 24 to 84 months and felling stage beyond 84 months. The main objective of stage wise linear regression was to predict the growth and growth rate of E. globulus at 84^th months with intercropping, weeding and fertilization. The present study, the data available only upto 48^th months hence the linear regression for establishment stage and vegetative growth stage were estimated within available data.

To estimate the stage wise linear regression for the establishment stage 7 observations at 4 months interval were used. Estimated correlation coefficient was very high and it was significant at 1% level for eucalypt growth with intercropping, weeding and fertilization clearly indicated the goodness of fit.

The growth rate of E. globulus with intercrop of potato, beans and maize was 0.21, 0.11 and 0.05 m³ ha^-1 per months respectively which was higher than unweeded eucalypt. Potato had higher growth rate among intercrops, and silvicultural manipulation at establishment stage.

The state wise linear regression was estimated for vegetative stage. For this, 7 observations at 4-month interval were used. The result showed highly significant correlation coefficient of E. globulus growth with intercrops and silvicultural manipulation. At vegetative stage, the highest growth rate of eucalypt was obtained with potato intercrop followed by beans, weeding and least with unweeded eucalyptus. The growth rate of E. globulus with intercrops potato, beans, maize and weeding was 2.88, 2.60, 2.24 and 2.49 m³ ha^{- 1} per month.

Estimated logistic growth model (Table 2).

TABLE: 2 ESTIMATED LOGISTIC GROWTH MODEL FOR EUCALYPTUS GLOBULUS WITH INTERCROPPING, WEEDING AND FERTILIZATION

W + A/ [ 1 + exp (B + Ct_i) ]
Significant at 1% level (r = 0.684)

Seven growth models viz. Gompertz curve, Hill curve, Logistic curve, Richard’s curve, Polynomial exponential curve, Cubic polynomial curve and Gauss curve were tried to establish a single growth model. Logistic growth model was found suitable and it showed a goodness of fit for prediction of growth of eucalypts with intercropping, weeding and fertilization. Estimated correlation coefficient values for the entire growth model was greater than 0.9 (significant at 1% level) and indicated the goodness of fit. The estimated maximum growth of E. globulus for seven years with intercrop potato, beans and maize was predicted to be 190.5, 170.8 and 148.3 m³ ha^-1. The weeded and unweeded eucalyptus showed 155.1 and 128.1 m³ ha^-1 respectively. When fertilizers were introduced, biofertilizer application resulted in 138.2 and inorganic fertilizer in 141.9 m³ ha^-1.

This forecasts the advantages of manipulating the interspace between the moderately spaced wide rows of eucalyptus now planted at 3 meter x 3 meter.

Predicted growth of E. globulus (m³ ha^-1) (Table 3).

TABLE: 3 PREDICTED GROWTH OF EUCALYPTUS GLOBULUS WITH INTERCROPPING, WEEDING AND FERTILIZATION (M³ HA^-1)

This model provided the rate of growth of eucalypt for every year and also showed exponential growth rate before it reached the plateau. This would help to judge when the growth declined so that felling could be resorted to instead of retaining the crop in the field unnecessarily.

In the first year, barring eucalypt potato, all the other treatments showed least growth rate. During the second year, the intercrops accelerated the growth of eucalypt better than the silvicultural manipulations and the trend continued though upto sixth year.

With unweeded eucalypt always registering the lowest yields, the yields reached a plateau in the sixth year for all treatments and the annual increment was also decidedly low. Given the optimal conditions of growth and stocking of 80 per cent, an yield of 173.2 m³ ha^-1 in five years involving agroforestry manipulations is a distinct possibility.

Growth rate of E. globulus per mensem (m³ ha^-1) (Table 4)

TABLE: 4 GROWTH RATE OF EUCALYPTUS GLOBULUS WITH INTERCROPPING, WEEDING AND FERTILIZATION (M³ HA^-1) PER MONTH

The growth rate of eucalypt with potato was maximum as compared to all other treatments in the first year. In the second and third years, intercropping intervention accelerated the growth better than silvicultural manipulations, with unweeded eucalypt registering lowest values. During the fourth year, eucalypt with beans association showed fastest growth than all other combinations recording a highest rate of 7.05 m³ ha^-1 (84.6 m³ ha^-1 / year). However, in the fifth and subsequent years there was a sudden fall in the growth rate, in all the treatments involved, contributing poorly to the biomass of the main crop, the eucalypt.

This table indicates that the active growth of eucalypt, with or without treatments, in this particular location, is limited to a maximum of four-year and what is contributed between fifth and seventh year hardly justifies retention of the growing stock beyond fifth year.

Discussions

The stage wise linear regression provides a means for assessing growth effect of Eucalyptus globulus and intercropping, weeding and fertilization in different growth stages. From the table 1, it is clear that E. globulus growth was very fast under potato followed by beans in comparison with other treatments in the establishment growth stage. The same growth behaviour has been noticed in the vegetative growth stage also. So the stage wise linear regression clearly indicates the growth of E. globulus was sufficiently improved when grown with potato or beans as intercropping. Among the silvicultural management practices the growth of E. globulus is better with weeded conditions in the vegetative growth stage.

E. globulus growth followed a sigmodal growth trend. From the Table 2, estimated logistic growth model also reveals the same trend as observed in stage wise linear regression. The predicted maximum yield of E. globulus at the 7^th year is 190.5 m³ ha^-1 with potato and 170.8 m³ ha^-1 with beans which is much higher when compared with unweeded situation at the same period.

From the predicted growth of E. globulus with intercropping, weeding and fertilization (Table 3), the growth of Eucalyptus globulus is very fast during 3^rd and 4^th year as compared to rest of the period. The growth of eucalypt is much negligible during 6^th year and beyond. Hence, optimum felling period can be recommended at the sixth year itself. A similar observation was made by Shugart and Smith (1992) for optimizing growth period of boreal forest.

The growth rate of E. globulus with intercropping, weeding and fertilization indicates the same trend as in the case of predicted growth. The growth rate is very high in 3^rd and 4^th year when compared to remaining period in all the treatments. Moreover, the growth rate of E. globulus is much negligible from 6^th and 7^th year. Hence, the optimum felling period is six years and retaining E. globulus the tree beyond sixth year, increase in biomass is much negligible. The present simple model adopted over comes the complications of correlated errors that traditionally arise in the analysis of longitudinal data but avoids the sophisticated model specification of the stochastic models (Rennolls, 1995).

The concept of plantation forestry has been broadened. It is no longer adequate for models to be confined to regular spaced industrial plantations. As part of the shift to create or maintain, sustainable landscapes, trees are grown in a range of configurations and for purposes in addition to timber or fibre production strips, rows or wide spaced trees are increasingly being used for agroforestry application (Battaglia et al. 2002).

Conclusion

Among the growth models logistic growth model was found suitable for estimation of growth at 7^th year (i.e. harvesting period). Eucalyptus with potato intercrop gave higher yield followed by among the intercrops and other silvicultural manipulations. At 4^th year, Eucalyptus had maximum growth. Eucalyptus grown with compatible intercrops reached its maximum potential of active growth in 6th years. It also suggested that the present rotation of eight years can be reduced to six years, achieving the same yield and a saving of two years of in waiting, a boon to tree growers.

Literature cited

Battaglia, M., P.J. Sands and D. Mummery, 2002. Silvicultural decision support with a dynamic process based growth model. In: proceeding of International Conference on Eucalypt productivity. 10-15 November 2002. Tasmania, Australia, pp. 90-91.

FRA 1991. Second interim report on the state of tropical forests. Forest Resources Assessment 1990 project presented at 10^th World Forestry Congress, September 1991, Paris.

Luna, R.K. 1989. Plantation Forestry in India. International Book Distributor, Dehradun, India, pp. 173-186.

Meek, D.W. Hutmacher, R.B., Machey and Davis, K.R. 1991. Heteroscedasticity in whole plant growth curves developed from non-replicated data. Agron. J. 83: 417-424.

Rennolls, K. 1995. Forest height growth modelling. Forest Ecol. Manage. 71: 217-225.

Shugart, H.H. and Smith T.M., 1995. Modelling boreal forest dynamics in response to environmental change. Unasyle 170(43) pp. 30-38.