An efficient class of tree network balanced designs for agroforestry experimentation

Abstract

The use of an appropriate design is a very important aspect of agroforestry experimentation. Since different species of trees may interact spatially, plots in agroforestry could be connected through network of trees which would create non-directional adjacency effects on a plot. Hence, there is a need to take the “direct effect of trees” and “tree network effects” on the crop into account when designing an agroforestry experiment. Tree network effect refers to the influence a tree exerts on the surrounding plots as a result of adjacency of the plots. In this paper, a class of network designs incorporating effects of trees from adjacent plots has been obtained. The characterization properties of the designs have also been studied. The designs are found to be variance balanced for the estimation of direct as well as network effects of trees. They are also highly efficient designs, and hence, are recommended for agroforestry experimentation with multiple tree species and a single crop.

Keywords:

• Adjacency matrix
• Agroforestry
• Canonical efficiency factor
• Fisher’s information matrix
• Network balanced designs
• SAS macro

Acknowledgments

P. T. Birteeb thanks University for Development Studies in Ghana for grant of study leave to enable him undertake this research. The provision of research facilities by the PG School of Indian Agricultural Research Institute, New Delhi, India is duly acknowledged. We would like to thank the editor and referees for valuable comments.

Additional information

Funding

The financial assistance received by P. T. Birteeb from Indian Council for Agricultural Research.