A model of the growth dynamics of forests was developed applying Bertalanffy growth
model (BGM) y=a[(1–e–bt)c] for individual trees. Based on linearized relationship with
diameter and height equation LnH=b0+LnD and volume equation V=b0Db1Hb2 mutually
compatible equations for diameter, basal area, height and volume were generated, adjusting
parameters a and c of BGM. Additionally, it was developed a methodology based on DBH
measurements in two occasions and the estimate value of parameter a to get the values of
parameter c and b of BGM. The data of the inventory of 1,061 trees over 40cm DBH of 67.5
hectares of tropical rain forest of Aquariquara Extractive Reserve, located in State of
Rondonia, Brazil, were used to test the developed model. These data were grouped in nine
maximum diameter (Dmax) classes. The tree survival was estimated based on the frequency of
trees by relative age class. The input and output of each tree was adjusted considering a closed
and stable population with replacement of a dead tree by the ingrowth of the same specie of
tree with 40cm DBH. Applying the model to such data and simulating the growth dynamics of
the forest in a time frame of 1500 years (T1 → 1,500), the difference of simulated annual
average, in relation to the observed values in the year T0 of the forest inventory was -2.09% in
age, -0.33% in height, -0.96% in diameter, -3.41% in basal area, -3.81% in volume and
+1.81% in merchantable trees value. The average values of T1→500, T501→1000 and T1001→1500
periods were equal for all variables by Kruskal-Wallis test (p=0.05). The simulation showed
that one hectare of this forest maintains a total stock composed of 15.72 120-year-old trees,
accumulated 4.35m2 of basal area and 37.98m3 wood volumes on average. The annual input
flow of the system was 0.3457 88-year-old trees which accumulated 0.0441m2 of basal area
and volume of 0.3265m3. The output of the system consists of 0.3459 132-year-old trees
totaling 0,1127m2 of basal area and 0.9911m3 in volume. The annual input and output rates
were, respectively, 2.20 and 2.20% in number of trees, 1.01 and 2.59% in basal area and 0.86
and 2.61% in volume. In addition, the simulation indicated that it is possible to sustain an
average annual production of 0.5528m3 of merchantable timber generating R$5.50 (about
US$1.49) annual income per hectare of forest. The simulation showed that the model
developed describes growth dynamics of tropical forest. However, it needs to be properly
adjusted based on real growth of each individual tree and flows of input and output of trees in
the system.
