Modeling self-thinning of unthinned Lake States red pine stands using nonlinear simultaneous differential equations

Forest management demands thorough knowledge of ecological systems. Tree interaction dynamics are one component of these ecological systems. Developing growth models which incorporate ecological "laws" such as the self-thinning rule can lead to better understanding of the laws, to better understanding of what is still unknown, and to what is in need of refinement. To this end a system of simultaneous differential equations incorporating logical, linked hypotheses regarding growth and mortality is proposed and fit to data from red pine (Pinus resinosa Ait.) plantations in the Lake States (Minnesota, Michigan, and Wisconsin). Using this modeling framework it appears that stand initiation history has a large impact on the level of the self-thinning boundary for red pine growing in the Lake States. Stands with initially high density exhibited lower self-thinning boundaries than stands with lower densities. Site quality (as measured by site index) chiefly affected the rate at which stand dynamics progress. Higher quality sites progressed through stand development at faster rates than did sites with lower quality.