Methods for using an integro-differential equation as a model of tree height growth

1987 ◽  
Vol 17 (5) ◽  
pp. 353-356 ◽  
Author(s):  
David Hamlin ◽  
Rolfe Leary
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Tree Height ◽  
Analysis Data ◽  
Equation Model ◽  
Height Growth ◽  
Integro Differential Equation ◽  
Biological Interpretation ◽  
Linear Differential ◽  
Tree Height Growth

An integro-differential equation model of tree height growth is developed, together with a biological interpretation of its coefficients. The integro-differential equation is reduced to a second order linear differential equation with constraints on its initial conditions. Because of the constraints, fitting of the differential equation is best accomplished using a multipoint boundary value approach. An example using stem analysis data is presented. The model fit the data well and was montonically increasing with an upper asymptote, although several other curve forms are possible.

scholarly journals Modeling Effects of Overstory Density and Competing Vegetation on Tree Height Growth

2008 ◽  
Vol 54 (1) ◽  
pp. 107-122
Author(s):  
Christian Salas ◽  
Albert R. Stage ◽  
Andrew P. Robinson
Keyword(s):  
Habitat Type ◽  
Predictor Variable ◽  
Tree Height ◽  
Height Growth ◽  
Tree Age ◽  
Individual Tree ◽  
Vegetation Control ◽  
Index Site ◽  
Linear Differential ◽  
Tree Height Growth

Abstract We developed and evaluated an individual-tree height growth model for Douglas-fir [Pseudotsuga menziesii (Mirbel) Franco] in the Inland Northwest United States. The model predicts growth for all tree sizes continuously, rather than requiring a transition between independent models for juvenile and mature growth phases. The model predicts the effects of overstory and understory vegetative competition on height growth. Our model requires attained height rather than tree age as a predictor variable, thereby avoiding the problems of site index. Site effects are introduced as a function of ecological habitat type, elevation, aspect, and slope. We used six data sets totaling 3,785 trees in 314 plots. The structure of the data and the model indicated the need for a mixed-effects, nonlinear modeling approach using maximum likelihood in a linear differential equation with a power transformation. Behavior of the model was analyzed using a state-space approach. Our results show that both overstory and understory density affect height growth, allowing a manager to make informed decisions about vegetation control.

Genetic resistance to western gall rust in jack pine and its relationship with tree height growth

2015 ◽  
Vol 45 (8) ◽  
pp. 970-977 ◽  
Author(s):  
Y.H. Weng ◽  
P. Lu ◽  
Q.F. Meng ◽  
M. Krasowski
Keyword(s):  
Growth Traits ◽  
Tree Height ◽  
Jack Pine ◽  
Height Growth ◽  
Progeny Testing ◽  
Gene Effects ◽  
Individual Tree ◽  
Improvement Programs ◽  
Heritability Estimates ◽  
Tree Height Growth

Developing resistance to western gall rust (WGR) is important for maintaining healthy and productive jack pine plantations. In this study, we estimated genetic parameters of resistance to WGR and its relationship with tree height growth, based on data collected from three second-generation full-sib progeny testing series of jack pine planted in New Brunswick, Canada. Results indicated that (i) resistance to WGR in jack pine was controlled by both additive and dominance gene effects, with the latter playing a greater role; (ii) narrow-sense heritability estimates for resistance to WGR were low (mean = 0.05; series range = 0.00∼0.09), and broad-sense heritability estimates were moderate on an individual-tree basis (mean = 0.53) and considerably higher on the full-sib family mean basis (mean = 0.87); (iii) additive genetic correlation between tree height growth and WGR incidence was low (≤0.06) in two series and only slightly higher and favorable (–0.19) in one series, suggesting that selection on growth traits would not negatively affect WGR resistance; and (iv) mid-parental additive genetic and dominance effects on WGR were empirically correlated (>0.65), indicating that incorporating breeding for WGR resistance into current jack pine tree improvement programs with a seed orchard approach could partly capture the benefit from dominance effects. Although genetic gains in WGR resistance could be realized through various breeding and deployment schemes, it appeared that rapid improvement could be achieved through backward selection on full-sib family means.

Site Index Curves for Loblolly Pine Plantations on Cutover Site-Prepared Lands

1985 ◽  
Vol 9 (3) ◽  
pp. 166-169 ◽  
Author(s):  
Ralph L. Amateis ◽  
Harold E. Burkhart
Keyword(s):  
Differential Equation ◽  
Pinus Taeda ◽  
Loblolly Pine ◽  
Analysis Data ◽  
Site Index ◽  
Height Growth ◽  
Pine Plantations ◽  
The South ◽  
Stem Analysis ◽  
Natural Range

Abstract Stem analysis data collected from dominant and codominant loblolly pine (Pinus taeda) trees in cutover, site-prepared plantations were used to develop site index curves. The data were collected over much of the natural range of loblolly pine. A separable differential equation which expresses height growth as a function of both height and age was used to develop the site index curves. These site index curves should be applicable to loblolly pine plantations on cutover, site-prepared lands through much of the South.1

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