A functional-structural model for radiata pine (Pinus radiata) focusing on tree architecture and wood quality

Abstract

Backgrounds and aims: Functional-structural models are interesting tools to relate environmental and management conditions with forest growth. Their three-dimensional images can reveal important characteristics of wood used for industrial products. Like virtual laboratories, they can be used to evaluate relationships among species, sites and management, and to support silvicultural design and decision processes. Our aim was to develop a functional-structural model for radiata pine (Pinus radiata) given its economic importance in many countries.

Methods: The plant model uses the L-system language. The structure of the model is based on operational units, which obey particular rules, and execute photosynthesis, respiration and morphogenesis, according to their particular characteristics. Plant allometry is adhered to so that harmonic growth and plant development are achieved. Environmental signals for morphogenesis are used. Dynamic turnover guides the normal evolution of the tree. Monthly steps allow for detailed information of wood characteristics. The model is independent of traditional forest inventory relationships and is conceived as a mechanistic model. For model parameterization, three databases which generated new information relating to P. radiata were analysed and incorporated.

Key results: Simulations under different and contrasting environmental and management conditions were run and statistically tested. The model was validated against forest inventory data for the same sites and times and against true crown architectural data. The performance of the model for 6-year-old trees was encouraging. Total height, diameter and lengths of growth units were adequately estimated. Branch diameters were slightly overestimated. Wood density values were not satisfactory, but the cyclical pattern and increase of growth rings were reasonably well modelled.

Conclusions: The model was able to reproduce the development and growth of the species based on mechanistic formulations. It may be valuable in assessing stand behaviour under different environmental and management conditions, assisting in decision-making with regard to management, and as a research tool to formulate hypothesis regarding forest tree growth and development.

Fig. 1.

Model structure. (A) The tree is a productive system, comprising operative units organized in axes that consist of subsystems starting from a branching point. Roots are treated as a single entity. The whole system receives energy and supplies for its functioning. System restrictions such as biomass balance, distribution and plant allometry ensure a harmonic growth. (B) Operative units consist of apical meristems, internodes and cones; each operative unit obeys its operational rules and generates internal products as net biomass and local architecture. (C) P. radiata presents three types of growth units: a vegetative growth unit with cataphylls zone (ca), needles zone (ne) and lateral and terminal vegetative meristems (am); a growth unit with male strobili (st) in the zone between cataphylls (ca) and needles (ne); and a growth unit with female strobili (co) as modified branches in the lateral meristems.

Fig. 2.

Main flowchart of the model.

Fig. 3.

Sketch of live foliar and structural biomass of growth units of the tree (b₁, b₂, b₃, b₄) on a given axis and total live biomass accumulated from each unit upwards (B₁, B₂, B₃, B₄). The biomass assigned to a certain growth unit i is the difference between the biomass assigned to B_i and the biomass assigned to B_(i+1).

Fig. 4.

Evolution of cumulated height and diameter at Los Alamos (A, E) and La Granja (B, F); average simulated height and data for Los Alamos (C) and La Granja (D), and simulated diameter and data for Los Alamos (G) and La Granja (H).

Fig. 5.

Histograms of simulated growth unit length (cm) and of the validation data for Los Alamos (A and B, respectively) and for La Granja (C and D, respectively).

Fig. 6.

(A, B) Main apex and lateral branches; (C, D) detail of the main apex; (E, F) close-up of an order 2 branch apex; (G, H) whorl of branches; and (I) two simulated 5-year-old trees from La Granja (left) and from Los Alamos (right). Margins of branches are not shown.

Fig. 7.

(A) Cumulative height and (B) diameter under initial stand densities of 400, 1100 and 1800 trees ha⁻¹ for an average tree. Effect of thinning at 5 years after planting on (C) height and (D) diameter; initial stand density was 1800 trees ha⁻¹ and after thinning was 800 trees ha⁻¹.

Fig. 8.

Sketch of widths of monthly rings for a stand density of (A) 1800 trees ha⁻¹ and of (B) 400 trees ha⁻¹. (C) Monthly wood profiles showing ring width peaks and depressions.

Fig. 9.

Wood density profile in a growth unit 1·3 m high: (A) based on monthly rings, (B) based on distance from the pith (mm). Measured data and fitted curves are shown.

Fig. 10.

Details of simulated slab and planks with knots. Fairly realistic monthly rings are observed.