A simple production function model for variable density growth and yield modeling

Abstract

This paper proposes a logarithmic–reciprocal yield function that improves upon the function proposed by Nautiyal and Couto (J. C. Nautiyal and L. Couto. 1982. Can. J. For. Res. 12: 452–458) by allowing forest crops starting with different stocking levels to eventually approach the same volume and peaking of the current annual increment (CAI) at different ages of the stands. The function is then used to fit yield data generated from Smalley and Bailey's study (Smalley, G. W., and R. L. Bailey. 1974. U.S. For. Serv. Res. Pap. SO–96) that shows wobbles in CAI and changes in yield as a result of changes in planting density. The basic model is then expanded by incorporating site index to account for local differences in productivity. Finally, compatible growth functions that can be estimated with log differences in yield instead of instantaneous growth are also derived.