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Stand and Tree Dynamics of Uneven-aged Ponderosa Pine
Abstract
A system of algebraic difference equations is presented for projecting, at the stand level, number of pole trees, survivor number of merchantable trees, and survivor basal area. Ingrowth is indirectly derived from projection equations that estimate the total change in the number of pole trees. The individual tree growth equation and mortality function are consistent with the stand level projection equations. The ingrowth diameter distribution is modeled with a parameter recovery method for the Uniform distribution. The species of ingrowth trees are predicted from equations that are a function of habitat series and cumulative ratios of trees per acre by species. For. Sci. 40(2):289-302.
... This trend was consistent with the actual survey results (Figure 2). was used for the average tree diameter in the research of tree growth, having a better performance than the arithmetic mean diameter [51,52]. Curtis et al. [53] explained the difference between the average and the arithmetic mean diameter in detail and their respective applicable scenarios. ...
The relative growth rate (RGRnv) is the standardized measurement of forest growth, whereby excluding the size differences between individuals allows their performance to be compared equally. The RGRnv model was developed using the National Forest Inventory (NFI) data on the Daxing’an Mountains, in Northeast China, which contain Dahurian larch (Larix gmelinii Rupr.), white birch (Betula platyphylla Suk.), and mixed coniferous–broadleaf forests. Four predictor variables—i.e., quadratic mean diameter (Dq), stand basal area (G), average tree height (Ha), and altitude (A)—and four different methods—i.e., the nonlinear mixed-effects models (NLME), three nonlinear quantile regression (NQR3), five nonlinear quantile regression (NQR5), and nine nonlinear quantile regression (NQR9) models—were used in this study. All the models were validated using the leave-one-out method. The results showed that (1) the mixed coniferous–broadleaf forest presented the highest RGRnv; (2) the RGRnv was negatively correlated with the four predictors, and the heteroscedasticity reduced significantly after the weighting function was integrated into the models; and (3) the quantile regression models performed better than NLME, and NQR9 outperformed both NQR3 and NQR5. To make more accurate predictions, parameters of the adjusted mixed-effects and quantile regression models should be recalculated and localized using sampled RGRnv in each region and then applied to predict all the other RGRnv of plots. MAPE% indicates the mean absolute percentage error. The values were stable when the sample numbers were greater than or equal to six across the three forest types, which showed relatively accurate and lowest-cost prediction results.
... Another category of disaggregation methods involves proportional allocations that can be applied to either growth or yield. In the proportional yield method, predicted tree basal area is adjusted to match predicted stand basal area (Clutter and Allison 1974, Clutter and Jones 1980, Pienaar and Harrison 1988, Nepal and Somers 1992, McTague and Stansfield 1994, 1995. The proportional growth method involves adjusting predicted tree basal area growth to match predicted stand basal area growth (Campbell et al. 1979, Moore et al. 1994, tree volume growth to match stand volume growth (Dahms 1983, Zhang et al. 1993, or tree diameter growth to match stand diameter growth (Leary et al. 1979). ...
Background
Different types of growth and yield models provide essential information for making informed decisions on how to manage forests. Whole-stand models often provide well-behaved outputs at the stand level, but lack information on stand structures. Detailed information from individual-tree models and size-class models typically suffers from accumulation of errors. The disaggregation method, in assuming that predictions from a whole-stand model are reliable, partitions these outputs to individual trees. On the other hand, the combination method seeks to improve stand-level predictions from both whole-stand and individual-tree models by combining them.
Methods
Data from 100 plots randomly selected from the Southwide Seed Source Study of loblolly pine (Pinus taeda L.) were used to evaluate the unadjusted individual-tree model against the disaggregation and combination methods.
Results
Compared to the whole-stand model, the combination method did not show improvements in predicting stand attributes in this study. The combination method also did not perform as well as the disaggregation method in tree-level predictions. The disaggregation method provided the best predictions of tree- and stand-level survival and growth.
Conclusions
The disaggregation approach provides a link between individual-tree models and whole-stand models, and should be considered as a better alternative to the unadjusted tree model.
... Dans cette optique, c'est d'ailleurs avant tout la désagrégation qui a été utilisée pour prédire l'évolution de caractéristiques détaillées du peuplement à l'aide d'un système dynamique reposant sur des caractéristiques agrégées du peuplement (Ritchie & Hann, 1997). Les niveaux connectés par les modèles désagrégatifs sont le niveau distribution et le niveau peuplement (figure 5.2), ou le niveau arbre et le niveau peuplement (Pienaar & Harrison, 1988;Zhang et al., 1993;Dhôte, 1994;McTague & Stansfield, 1994;Somers & Nepal, 1994). ...
La modélisation de la dynamique des forêts naturelles tropicales peut reposer sur deux niveaux de description : l'arbre ou la distribution en taille des arbres au sein du peuplement. Mes travaux ont porté essentiellement sur le lien entre ces deux niveaux de description, que ce soit d'un point de vue théorique ou appliqué. La théorie de l'agrégation permet ainsi de basculer du niveau détaillé de l'arbre au niveau agrégé de la distribution. Lorsque les interactions entre arbres ne sont pas dépendantes des distances, l'agrégation est asymptotiquement parfaite. Dans le cas contraire, il est essentiel de pouvoir modéliser la relation rétro-active de la dynamique sur la répartition spatiale des arbres. La méthode des moments apporte alors une solution approximative à la question de l'agrégation. La question peut également être abordée dans le sens inverse (désagrégation), le modèle de dynamique étant vu comme un algorithme de simulation d'un processus ponctuel marqué (la marque étant la taille des arbres). Ces questions se transposent pour traiter le cas de la diversité spécifique propre aux forêts tropicales. La théorie de l'agrégation peut à nouveau être mise en oeuvre pour regrouper les multiples espèces en groupes ayant des caractéristiques de dynamique communes.
The focus of this chapter is on modeling methods that have been developed specifically for application to uneven-aged forests. The basic frameworks of whole-stand, diameter-distribution, size-class, and individual-tree modeling structures have been adapted to stand types that are age indeterminate. The most common approaches to modeling uneven-aged forests include: (i) whole-stand models based on elapsed time from specified initial conditions, (ii) models that produce size class information from continuous distributions, (iii) size-class models that rely on discrete distributions (stand table projection and matrix models), and (iv) models that aggregate individual tree values for stand-level estimates. Matrix models, which are a type of size-class model, are well suited to modeling uneven-aged forests; hence they are described in detail in this chapter.
New functions are presented for spruce-fir survivor growth, ingrowth,and mortality using a data set of Continuous Forest Inventory plots exclusively from the spruce-fir forest type in east-central Arizona. The individual tree diameter squared growth model is validated at the tree and stand level with an independent data set. Individual tree mortality is modeled for any projection interval with a logistic function. Ingrowth dynamics is modeled at three levels of resolution; the stand level, species level, and the diameter class level. Ingrowth trees are distributed to diameter classes using the Uniform distribution.
Growth and yield simulators may be characterized with regard to the aggregation structure employed. Individual-tree simulators are an example of a passive aggregation approach. Whole-stand models represent an active aggregation structure. Of particular interest is the disaggregative modeling approach, which employs elements of both individual-tree and whole-stand simulators. The apparent resolution of the disaggregative model is at the tree-level; however, the functional resolution is at the stand level. Disaggregation may be achieved with either additive or proportional allocation of growth. Additive allocation may not ensure positive individual-tree projections of growth. Either may be constrained so as to maintain symmetry between the whole-stand projection of growth and the aggregate of predicted tree growth. Traditionally, the disaggregative approach has seen the application of very simple structures for allocation of growth depending on tree dimension alone. However, the concept may be generalized to include traditional individual-tree growth equations constrained so as to act as an allocation of predicted stand growth.
The colonial history of North America presents a contrast between Mexico and the two predominantly English-speaking countries, the United States and Canada. In Mexico, indigenous and other local communities own considerable forested lands, a consequence of the Mexican Revolution of the early twentieth century. In the United States, forest land is now primarily in private or federal hands, while in Canada forest land is primarily managed by the provinces. In all three countries, traditional knowledge had little effect upon forestry until the end of the twentieth century. In Mexico and the United States, the central government retained control over forested lands ostensibly held by communities. Policy changes in those two countries have decentralized control to indigenous peoples, and their ideas have started to affect forestry. In Canada, although traditional management of lands in remote regions persisted until the middle of the twentieth century, provincial policies have generally been displacing indigenous control; First Nations knowledge, which has survived well in some areas, is only recently being applied to forest management, and in only a few examples.
A functional approach is proposed for comparing the development of individual red pine (Pinus resinosa Ait.) trees which had been growing under different intensities of competition from ages 13 to 43. Growth rate measures, based on absolute growth rate, relative growth rate and the ratio of absolute growth rate to crown width, were obtained from the differentiation of a cumulative growth function. Individual tree data were obtained from stands of the same age, but with different initial spacings: 1.5 x 1.5 m, 2.4 x 2.4 m, and 4.3 x 4.3 m. The Chapman-Richards function represented adequately the growth trends of individual trees. While cumulative growth indicated a fairly consistent pattern, that is, the bigger the tree initially, the bigger it remained, absolute growth rate was not related to tree size. Some of the smallest trees had the greatest absolute growth rate. Relative growth rate was more informative on the effect of competition. Before competition became severe, small trees had greater relative growth rates than large trees, and the effect of competition was to reverse this trend. The ratio of absolute growth rate to crown width indicated that the ability of trees to occupy the aerial growing space was not related to tree size.
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