Forest Growth Modelling

Forest management planning relies heavily on mathematical models that involve time. Concerns about climate change and ecosystem services have highlighted the limitations of traditional growth and yield prediction tools. Modern dynamical system theory provides a framework for a flexible representation of varying environments, as well as of responses to intensive silviculture and natural disturbances. Emphasis changes from trying to directly model functions of time to modelling rates of change. The fundamental concepts are introduced here in a non-technical manner. The theory is illustrated with a recent whole-stand growth model for even-aged stands, but it is noted that it applies to any system that evolves over time. It is shown also how a modular approach can improve balance and efficiency in the development of such models.
Keywords: modelling, stand dynamics, system theory, system dynamics, forest growth and yield, thinning, hybrid models

The objective of this work was to study aspects of the dynamics, such as growth and yield of a representative sample of upland Tropical rainforest, experimentally managed over 30 years, aimed mathematical modeling of the experiment using a Model of Growth and Yield by Diameter Distribution. The study area is situated in the Tropical Forest Experimental Station, from National Institute of Amazon Research (EEST / INPA), about 90 km distant from the urban center of Manaus - AM, Brazil. The data came from Project BIONTE (Forest Biomass and Nutrients) started in 1980, based on 12 permanent plots of 1 ha, annually measured of all individuals with DBH ? 10 cm, between the years 1990 and 2008. The area was explored in 1987 and 1988 under different intensities of cutting, being demarcated experimentally at random block design with sub-plots in which silvicultural treatments, were applied with 6 treatments and 3 repetitions. Of these treatments, four were used: T0 = Witness or control, T1 = 25% of basal area explored between august and september 1987, T2 = 50% of basal area explored between october and november 1987, T3 = 75% of basal area explored between september and november 1988. To apply the model to the forest, all species of the experiment were classified into two groups, pioneers and non-pioneer species, according to their ecological characteristics, as well as biomathematics models were employed to express the dynamics of survival (recruitment and mortality), basal area, sum of diameters, and the productive capacity of each treatment and ecological group. The probability density function of Weibull was used as the basis for modeling the diameter distribution, as well as other already developed models that estimate the volume of trade and fresh biomass was used in the prognosis of these variables and the production of carbon stock per unit area for each treatment. The dissertation was divided into chapters aimed better understanding of each process applied in this work and its results. The first bleach on the theoretical background and its influence on the manuscript. The second presents a new method of productivity classification from the Pioneer Species Diametric Variation. The third model shows the survival, recruitment and mortality of pioneer species and all species per hectare. The fourth, and last, present the modelling of basal area dynamics and the sum of the diameters, as well as the model of growth and yield for the forest under analysis, and its efficiency in growth projection for the year 2009. The results and efficiency of the method are in their respective chapters.

The aim of this book is to give a contemporary review of tree growth modelling and represent our own results in this field. We demonstrate that the growth inhibition can be a result of a systemic level effect, which can be seen in a whole-tree physiological model which includes submodels for the processes of photosynthesis, mineral nutrition, respiration, phloem and xylem transport, and growth of roots, stems, and leaves. 

The parts 1, 2 and 3 represent the review and analysis of existing models, beginning with simple growth formulas and then concentrating in contemporary dynamic (ecophysiological) models which contain many state variables and tens of parameters. The analysis of these models is given by the main components of growth process.

Part 4 deals with the most important problem of causal tree growth analysis – the reason of growth cessation (self-inhibi­tion) of too big tree. The arguments are given, showing the inadequacy of explanations which are based on Pütter-Bertalanffy equation. In the fig. 4.5 the numerical scheme of carbon balance for whole tree is represented, based on the experimental results of Estonian researchers.

In part 5 the description of our model PUU-1 is given. It contains 9 state variables (see List of symbols), 6 driving variables (table 6.1) and 43 parameters (table 6.3). The model enables to analyze both seasonal and ontogenetic dynamics of evergreen tree growth. The summary of all equations of the model is represented in ch. 5.9.

Part 6 deals with identification of the model: getting initial values of state variables and values of parameters and driving variables. More than half of them are based on the measu­rements made by Estonian researchers in Picea abies, others are taken from literature.

Part 7 gives the results of numerical experiments with our model – analysis of sensitivity of model variables and parameters, examples of growth dynamics, including numerical experi­ments with fertilization. The model fits satisfactorily with measured data. The comparison of calculated tree ring dynamics with dendrochronological data shows great perspectives in applying dynamical growth models of whole tree in dendrochronology, as well as in growth analysis and prediction, including situations
and problems which arise in agroforestry.

The most important theoretical result of our modelling is connected with self-inhibition of growth in tree ontogeny. It is shown, that self-inhibition of growth is taking place even without any aging factor, only because of size effects, which are mostly connected with changes in tree water exchange and trans­ port of assimilates (supplying of roots with assimilates becoming worse according to monotonous growth of cambium area). In the last chapter (7.6) the perspectives of tree growth modelling are discussed.

Since its inception the Forestry Department has undertaken static inventories of the forest reserves qnd most recently of the off-reserve lands within the highforest zone and commerciql NTFPs. The paper briefly desuibes the purpose, design ønd achievements of each of these, These data have been used to explore a wide range of forest management issues. Strategic questions that hqve been addressed sre the determination of the AAC, the derivation of yield quotas and the calegorisation of species according to the degree of over-exploitation. Manøgement planning has benefited qs the data has been used as a guide to the identification of protection areas qnd as background information for the preparation of harvesting schedules. The dqta has also been used to prepare regeneration profiles for nearly alt the larger tree species and thereby provide a significant contribution to our understanding of forest ecologt. Attention is drøwn to the weqlth of information contained in static inventory records and the considerable scopeforfurther analyses is highlighted.

Contents: 1. Introduction--2. Whole Stand Models--3. Size Class Models--4. Single-tree and Tree List Models--5. Data Requirements--6. Constructing Growth Models--7. Forest Site Evaluation--8. Diameter Increment--9. Mortality and Merchantability--10. Regeneration and Recruitment--11. Model Evaluation and Re-calibration--12. Implementation and Use--13. Future Directions.

This study developed dbh-crown diameter prediction model for naturally grown Triplochiton scleroxylon (K. schum). Eight models for predicting crown diameter using diameter at breast height were tested for the species in Onigambari Forest Reserve, Nigeria. Data were obtained from all available T. scleroxylon tree species (dbh ≥ 10cm) measured on eight 25m x 25m temporary sample plots established using systematic line transects sampling technique. One linear and seven non-linear functions were selected as candidate functions to model the relationship. Regression analysis result showed that there were statistically significant (P > 0.05) and strong (R 2 > 0.50) relationship between dbh and crown diameter variables for all the models used. The results of the study showed that 104/ha stands of the species were available presently in the study area with mean dbh and crown diameter of 37.60cm and 18.50m respectively. The dbhcrown diameter relationship was best described by Cubic model , R 2 = 0.879, Coefficient of variation = -6.44x10 -16 and MSE = 0.226. This study showed that dbh can adequately predict the crown diameter very well the relationship as explained by cubic function can further be used to evaluate and estimate the stand volume and basal area in this forest.

This paper describes the development of top height model for stands of Azadirachta indica. The algebraic difference form of the Chapman-Richards equation is first fitted to the interval data of height-age data pairs resulting in an anamorphic system. Polymorphic site index curves were also developed using Ek's extension of the Chapman-Richards function. Secondly, some commonly used models were compared for their goodness-of-fit and predictive ability in describing allometric relationships between volume, diameter and age. It has been observed that, in general, Chapman-Richards function may be used to model the relationships between these growth parameters.

Some concepts that may be useful for the study of forest stands through mathematical models are discussed. A set of examples to illustrate these ideas is included. Application to stand model formulation of an approach based on the concept of dynamical system or multistage process, as used especially in Control Theory, is described. This approach involves the specification of a state vector which describes the system at a given time, and the specification of a transition function which determines the changes of state. Furthermore the need for multidimensional state vectors is pointed out.

Decisions on natural forest production management are based on sustained yield principles because forest management focuses on sustainability of standing stock rather than sustainability of ecology and social aspects. Diameter increment is an important factor for measuring income of management unit and understanding field standing stock. This study aims to construct a model based on diameter class and tree species group. The study uses a statistical model of permanent sampling plots data. The results show that current anual increament (CAI) is 1.3 cm-1-1 yr at 10–20 diameter class and 0.78 cm yr for diameter class larger than 40 cm. CAI of commercial groups are higher than it of non-commercial groups. Meanwhile, CAI for Dipterocarpaceae and Myrtaceae families are higher than those for Burseraceae, Fagaceae, Guttiferae and Lauraceae families. The model for all tree species is CAI = – 0.028D 2.19e , and for each tree species group is different. ABSTRAK Kajian riap pertumbuhan di hutan alam telah dilakukan dan masih berlangsung untuk memperoleh suatu model dugaan yang mampu menjelaskan pertumbuhan yang sebenarnya. Penggunaan metode penduga riap pertumbuhan masih merupakan alat utama pengambilan keputusan dalam manajemen hutan alam produksi. Keputusan manajemen hutan alam produksi dewasa ini masih berada pada prinsip kelestarian hasil. Hal ini dikarenakan unit manajemen masih memandang kelestarian hutan dari keberadaan pohon dan keberlangsungan pemanenan setiap tahunnya. Kajian riap berdasarkan jenis dominan perlu dilakukan sebagai alat pengukur pendapatan perusahaan dan sekaligus untuk membantu pemahaman potensi tegakan tinggal. Penelitian ini bertujuan untuk menduga riap pertumbuhan diameter berdasarkan kelas diameter dan kelompok jenis. Metode yang digunakan dalam penelitian ini adalah membangun model statistik dari data PUP. Hasil penelitian menunjukkan bahwa CAI 1,3 cm/tahun pada kelas diameter 10–20 dan 0,78 cm/tahun pada kelas diameter terbesar 40 cm ke atas. CAI kelompok jenis komersil lebih besar dibandingkan kelompok jenis non-komersil. Sementara itu, CAI famili Dipterocarpaceae dan Myrtaceae le-bih besar dibandingkan famili Burceraceae, Fagaceae, Guttiferae dan Lauraceae. Model penduga CAI untuk semua – 0,028D jenis di Pulau Buru adalah CAI = 2,19e. Untuk masing-masing kelompok jenis pohon memiliki bentuk persamaan yang berbeda. Namun demikian, model ini perlu dikaji lanjut di lapangan untuk menguji keterandalannya sebagai alat penduga pengaturan hasil. Kata kunci: Kelas diameter, kelompok jenis, model riap

RESUMEN Los ecosistemas forestales se caracterizan por una gran complejidad en la que distintos elementos bióticos y abióticos interactúan en varias escalas temporales y espaciales de formas muy diversas. Una manera de reducir la complejidad con la que se trabaja en gestión e investigación forestal es el desarrollo y utilización de modelos ecológicos que representen los procesos y elementos ecológicos más importantes del ecosistema. Todos los modelos son simplificaciones de la realidad, pero tanto si son modelos complejos o sencillos es importante seguir unas técnicas que permitan asegurar la calidad y confianza en la representatividad de los modelos utilizados. En este artículo se describen los pasos a seguir en el desarrollo de un modelo ecológico. Cada pasos es clave para conseguir un modelo útil para el objetivo requerido. Los distintos pasos en la creación de modelos serán ilustrados con un ejemplo de modelo aplicado a la gestión e investigación forestal en España. Palabras clave: modelos ecológicos, calibración de modelos, modelos conceptuales, evaluación de modelos, análisis de escenarios.

A whole-stand survival model is presented, that is parsimonious and well-behaved when extrapolated, making it particularly useful in data-poor situations. It is argued, on biological and system-theoretical grounds, that a suitable differential equation for the mortality rate should contain number of trees and top height on the right-hand side, avoiding age, mean diameter, or basal area. Following Eichhorn’s hypothesis, site quality can be neglected by modelling rates relative to height growth. The proposed model is dN/dH = −aN b H c , where N is number of trees per unit area, H is top height, and a, b and c are parameters to be estimated. The equation can be integrated to predict mortality between any two points in time. Satisfactory performance is demonstrated with a white spruce data set from British Columbia. It is shown that the model generalizes concepts of relative spacing, and mortality models for radiata pine and Douglas-fir used by Beekhuis in New Zealand in the 1960’s. Asymptotic behaviour is related to the 3/2, Reineke, and relative spacing self-thinning laws. Limitations of the self-thinning theories and relationships among their various forms are discussed.
Keywords: survival, growth and yield, relative spacing, self-thinning

Carbon allocation plays a key role in ecosystem dynamics and plant adaptation to changing environmental conditions. Hence, proper description of this process in vegetation models is crucial for the simulations of the impact of climate change on carbon cycling in forests. Here we review how carbon allocation modelling is currently implemented in 31 contrasting models to identify the main gaps compared with our theoretical and empirical understanding of carbon allocation. A hybrid approach based on combining several principles and/or types of carbon allocation modelling prevailed in the examined models, while physiologically more sophisticated approaches were used less often than empirical ones. The analysis revealed that, although the number of carbon allocation studies over the past 10 years has substantially increased, some background processes are still insufficiently understood and some issues in models are frequently poorly represented, oversimplified or even omitted. Hence, current challenges for carbon allocation modelling in forest ecosystems are (i) to overcome remaining limits in process understanding, particularly regarding the impact of disturbances on carbon allocation, accumulation and utilization of nonstructural carbohydrates, and carbon use by symbionts, and (ii) to implement existing knowledge of carbon allocation into defence, regeneration and improved resource uptake in order to better account for changing environmental conditions.

For the first time the trans-Eurasian additive allometric mixed-effects model of tree biomass components (stems, branches, needles and roots) is designed using the database unique in terms of its volume in a number of 900 model trees of five species of Picea spp. taken on sample plots within species from natural habitats in Eurasia. The problem of double harmonization of the model was first solved, in the structure of that two approaches are combined, both in ensuring the principle of additivity of biomass components and in involving into the model the block of dummy variables localizing it along eco-regions of Eurasia. Trivial model involving the dummy and numeric (stem diameter at breast height and the tree height) variables in allometric equations without additivity components gives biomass estimates harmonized according to eco-regions but differing by the absolute value of the mass components only. The fundamental distinction and advantage of the developed model of double harmonization is that unlike of trivial mixed-effects model, it provides compatibility and difference by eco-regions not only of absolute values of biomass components, but also of their ratios, i.e. reflects regional traits of biomass component structure.

Mast fruiting represents a synchronous population behaviour which can spread on large landscape areas. This reproductive pattern is generally perceived as a synchronous periodic production of large seed crops and has a significant practical importance to forest natural regeneration in order to synchronize cuttings. The mechanisms of masting are still argued and models of this phenomenon are uncommon, so a stochastic approach can cast significant light on some particular aspects. Trees manage to get synchronized and coordinate their reproductive routines. But is it possible that trees get synchronized by chance, absolutely random? Using a Monte Carlo simulation of seeding years and a theoretical masting pattern, a stochastic analysis is performed in order to assess the chance of random mast fruiting. Two populations of 100 trees, with different fruiting periodicity of 2-3 years and 4-6 years, were set and the fruition dynamic was simulated for 100 years. The results show that periodicity itself cannot induce by chance the masting effect, but periodicity mathematically influences the reproductive pattern.

Forest inventory studies in the Amazon indicate a large terrestrial carbon sink. However, field plots may fail to represent forest mortality processes at landscape-scales of tropical forests. Here we characterize the frequency distribution of disturbance events in natural forests from 0.01 ha to 2,651 ha size throughout Amazonia using a novel combination of forest inventory, airborne lidar and satellite remote sensing data. We find that small-scale mortality events are responsible for aboveground biomass losses of B1.28 Pg C y À 1 over the entire Amazon region. We also find that intermediate-scale disturbances account for losses of B0.01 Pg C y À 1 , and that the largest-scale disturbances as a result of blow-downs only account for losses of B0.003 Pg C y À 1 . Simulation of growth and mortality indicates that even when all carbon losses from intermediate and large-scale disturbances are considered, these are outweighed by the net biomass accumulation by tree growth, supporting the inference of an Amazon carbon sink.

This paper describes the development of top height model for stands of Azadirachta indica. The algebraic difference form of the Chapman-Richards equation is first fitted to the interval data of height-age data pairs resulting in an anamorphic system. Polymorphic site index curves were also developed using Ek's extension of the Chapman-Richards function. Secondly, some commonly used models were compared for their goodness-of-fit and predictive ability in describing allometric relationships between volume, diameter and age. It has been observed that, in general, Chapman-Richards function may be used to model the relationships between these growth parameters.

El desafío actual en el manejo forestal es la planificación de suministros sostenibles de madera y otros valores forestales, a la vez que se preserva la integridad del ecosistema forestal. En conse-cuencia, el uso de modelos basados en la simulación de procesos ecológicos se hace cada vez más necesario. Un tipo de modelos especialmente adecuado para su aplicación en la gestión forestal sos-tenible son los modelos híbridos, que compaginan la robustez y fiabilidad de los modelos estadísti-cos tradicionales de crecimiento basados en compilaciones de datos de campo con la flexibilidad otorgada por los modelos mecanicistas que simulan procesos ecológicos y la influencia de las con-diciones ambientales en los mismos. Los modelos híbridos, por lo tanto, modifican observaciones históricas reales de crecimiento con el conocimiento actual de los procesos fisiológicos que causan ese crecimiento. Estos modelos tienen aplicaciones diversas y en este artículo se mencionan tres apli-caciones del modelo FORECAST en Cuba, China y Canadá. Además, estos modelos pueden combi-narse de forma modular con otros modelos para realizar simulaciones múltiples de varios valores ecológicos y socioeconómicos, o usarse de forma secuencial para crear meta-modelos.

Site-index ideas are reviewed, stressing conceptual foundations and issues that are frequently misunderstood. The structure of site-index models is explained first within a traditional deterministic context. When variability due to environmental fluctuations and observational errors is introduced, it is found that difficulties of procedure and interpretation appear. Overlooked differences in the definitions of site index implicitly used by various authors can cause confusion. The relationship between growth functions and differential equations is also examined. Rational parameter estimation requires a clear model for the error structure, and a general formulation is offered. The article ends with a brief review of several site modelling methods in terms of the concepts previously exposed.

The regeneration of forest resources is one of the main objectives of modern forest management. The present thesis aims to identify detailed features of the regeneration process and the characteristics of sapling interaction. The research involved evaluation of regeneration structure, dimensional differentiation of saplings, spatial pattern analysis - sapling aggregation and species association,  and sapling competition using distance-dependent methods. A new distance-dependent dimensional differentiation index (IDIV) and a new geometrical criterion for selecting neighbouring competitor saplings were created and applied. Appropriate methods and techniques were identified for investigating regeneration and computer technology was used intensively. Nine stand-alone software programs were produced in order to achieve the objectives of the thesis.

A theory-influenced dynamical stand growth model formulation described well the behavior of thinned and unthinned loblolly pine plantations. A simplification containing few free parameters performed as well as a fully parametrized version. It seems particularly well suited to situations where available data is scarce. The stand model can be interfaced to additional climate, nutrition and carbon cycling modules for studying the effects of a changing environment.

How long would it take for forests to recover their original productivity following continuous intensive management if they are left untouched? This issue was explored using the model FORECAST, calibrated and validated for coastal Douglas-fir stands on Vancouver Island (western Canada). Three types of forest management (production of timber, pulp, and biomass) were simulated, being different in utilization level and rotation length (stem-only and 75-year rotation for timber production, whole-tree and 30-year rotation for pulp/fibre, and whole-tree and 15-year rotations for biomass production). Management was simulated for 150 years, followed by several cycles of natural growth without management ending with a stand-replacing windstorm with a return time of 200 years. Productivity-related ecological variables in previously managed stands were compared to natural forests. Stands developed after management for timber would quickly reach values similar to non-managed forests for tree and understory total biomass, stored carbon, available nitrogen and soil organic matter (SOM). However, intensive management regimes designed for fibre and biomass production would cause a decrease in SOM and nutrient availability, increasing understory biomass. As a consequence, stands recovering from intensive management would need at least two stand-replacing events (400 years) to reach a productivity status similar to non-managed stands. Stands developed after management for biomass would take much longer, up to 600 or 800 years to recover similar values of SOM and understory biomass, respectively. Current fertilization prescriptions will likely be not enough to stop a quick drop in forest productivity associated with intensive management. Intensifying forests management to achieve short-term objectives could produce a reduction of stand productivity that would influence tree growth for very long time (up to several centuries), if such management is continuously implemented at the same stand. Some of these effects could be reduced if one rotation of intensive management (for pulp or bioenergy) is followed by a rotation of management for timber, or leaving the forest without management for an equivalent time.

Forest ecosystems are typical examples of socio-ecological systems. However, in terms of modelling, the social aspect has been given far less attention than the ecological aspect. In this study, we modelled the impact of economic and social factors on the occurrence of harvesting. This harvest model was then integrated into an individual-based model of forest growth designed for large-area forecasts. The resulting socio-ecological model was then used to produce volume predictions for two regions of France. Among the economic factors, the annual stumpage prices in interaction with the species proved to be a significant predictor of harvest occurrence. Simulating different stumpage price evolutions made it possible to predict supply curves for the two regions. Projections until 2060 showed that increases in stumpage prices will be detrimental to standing volumes in both regions. Integrating the demand for wood products into such socio-ecological models in forestry would be a major improvement.

How long would it take for forests to recover their original productivity following continuous intensive management if they are left untouched? This issue was explored using the model FORECAST, calibrated and validated for coastal Douglas-fir stands on Vancouver Island (western Canada). Three types of forest management (production of timber, pulp, and biomass) were simulated, being different in utilization level and rotation length (stem-only and 75-year rotation for timber production, whole-tree and 30-year rotation for pulp/fibre, and whole-tree and 15-year rotations for biomass production). Management was simulated for 150 years, followed by several cycles of natural growth without management ending with a standreplacing windstorm with a return time of 200 years. Productivity-related ecological variables in previously managed stands were compared to natural forests. Stands developed after management for timber would quickly reach values similar to non-managed forests for tree and understory total biomass, stored carbon, available nitrogen and soil organic matter (SOM). However, intensive management regimes designed for fibre and biomass production would cause a decrease in SOM and nutrient availability, increasing understory biomass. As a consequence, stands recovering from intensive management would need at least two stand-replacing events (400 years) to reach a productivity status similar to non-managed stands. Stands developed after management for biomass would take much longer, up to 600 or 800 years to recover similar values of SOM and understory biomass, respectively. Current fertilization prescriptions will likely be not enough to stop a quick drop in forest productivity associated with intensive management. Intensifying forests management to achieve short-term objectives could produce a reduction of stand productivity that would influence tree growth for very long time (up to several centuries), if such management is continuously implemented at the same stand. Some of these effects could be reduced if one rotation of intensive management (for pulp or bioenergy) is followed by a rotation of management for timber, or leaving the forest without management for an equivalent time.

Atmospheric pollution levels in China are increasing quickly. Experience from other polluted regions shows that tree growth could be affected, but long-term effects of N deposition and soil acidification on Chinese forests remain mostly unknown. Soil acidification and N deposition were simulated for Chinese fir plantations in Southeast China. A factorial experiment combined four levels of rain pHs (2.5, 4.0, 5.6 and 7.0), four N deposition rates (1, 7.5, 15 and 30 kg N ha -1 y -1 ) and two site qualities (poor and rich sites), managed for 3 consecutive 20-year rotations. Results indicate atmospheric pollution effects are not immediate, but after 1 to 2 rotations soil acidification effects could reduce ecosystem C pools significantly (-25% and -11% in poor and rich sites, respectively). N deposition rates above 15 kg N ha -1 y -1 could offset some of the negative effects of soil acidification and led to more ecosystem C (19 and 28 Mg C ha -1 more in poor and rich sites than in low N deposition). However, at high N deposition rates (>15 kg N ha -1 y -1 ), N leaching losses could greatly increase, reaching 75 kg N ha -1 y -1 . Moderate N deposition could increase tree biomass production and soil organic mass, resulting in increased ecosystem C, but these gains could be associated to important N leaching. Atmospheric pollution could also result in the longterm in nutrient imbalances and additional ecological issues (i.e. biodiversity loss, eutrophication, etc.) not studied here.

A general framework is proposed for the formulation and simulation of spatially explicit individual-based models of plant communities. A software implementation, siplab, was developed using the R statistical programming language. The scheme is a synthesis that encompasses many approaches from
the literature, making possible to compare and combine their different components. Relationships between plant growth and various competition or assimilation indices are discussed, together with the choice of state variables and statistical issues in growth equations. Modelling is extended to deal with environmental heterogeneity, specified as a given resource distribution in the plane. Plants exert competitive pressure over
resources at each point, represented by size- and distance-dependent functions that emulate or generalize similar concepts used in existing models. The partitioning of resources where these functions overlap is parameterized in a way that includes the one-sided fully asymmetric allocation of tessellation models, as well as a continuum of symmetric and asymmetric resource sharing alternatives. Finally, the plant
resource uptake is integrated over space, with an optional size- and distance-dependent plant response or efficiency weighting. The framework and software permit conducting simulation studies where results are less dependent on any specific model structure.
Keywords: individual-tree, spatially explicit, growth, competition, asymmetry, R, siplab

Los análisis de sensibilidad son una herramienta importante para comprender el funcionamiento de los modelos ecológicos, así como para identificar los parámetros más importantes en su funcionamiento. Además, los análisis de sensibilidad pueden utilizarse para diseñar de forma más efectiva planes de muestreo de campo dirigidos a calibrar los modelos ecológicos. En los estudios de ecosistemas forestales, el análisis cuantitativo de la parte subterránea es mucho más costoso y complicado que el estudio de la parte aérea, en especial el estudio de la dinámica de producción y descomposición de raíces gruesas y finas de los árboles. En este trabajo se muestra un ejemplo de análisis de sensibilidad del modelo forestal FORECAST a parámetros que definen la biomasa, longevidad y concentración de nitrógeno en las raíces de los árboles. El modelo se calibró para simular dos rodales de pino silvestre (Pinus sylvestris) en los Pirineos de Navarra. Los resultados indican que la tasa de renovación de raíces finas es el parámetro más influyente en las estimaciones del modelo de crecimiento de los árboles, seguida de la concentración de N en las mismas, siendo la relación biomasa subterránea/total el parámetro al cual el modelo es menos sensible. Además, el modelo es más sensible a los parámetros que definen el componente subterráneo de la biomasa arbórea cuando simula un sitio de menor capacidad productiva y mayor limitación por nutrientes.

Subjective a priori grouping of tropical rain forest species for growth prediction may be unreliable because 1) there may be hundreds of species, many comparatively uncommon, the ecology of which may not be well known, 2) species within the same genus, may have significantly different growth patterns, and 3) growth rate may not provide a reliable indication of mortality. Growth models can retain the species identity of each simulated tree, but some aggregation is necessary to enable estimation of increment and mortality functions. An objective approach aggregated 100 rain forest tree species into ten groups to enable efficient estimation of mortality functions. This strategy provided better predictions than a previous subjective grouping. Annual survival probabilities were predicted from tree size, stand density and site quality using a logistic equation fitted by maximum likelihood estimation. Additional species with insufficient data for analysis were subjectively assigned to these ten equations. Several strategies were investigated; the best approach for these species seemed to be to employ the equation which served the greatest number of species. The increment pattern did not provide a good basis for assigning such species to equations, and this suggests that different groupings may be necessary to model the various components of tree growth.

Upaya pencegahan perubahan iklim yang disebabkan karena emisi gas rumah kaca sedang menjadi salah satu kegiatan yang dibicarakan saat ini. Perusahaan dibidang kehutanan merupakan salah satu perusahaan yang memberikan peran besar dalam peningkatan emisi gas rumah kaca di atmosfer, termasuk PT. Bina Sejahtera. Salah satu upaya yang dapat dilakukan oleh PT. Bina Sejahtera untuk menurunkan emisi karbon ini adalah dengan meningkatkan serapan kabondioksida. PT. Bina Sejahtera harus memiliki dokumen penurunan emisi, guna mengetahui besarnya simpanan karbon maupun serapan karbon dioksida.  Tujuan dari pemodelan ini adalah membuat model dinamika simpanan karbon di PT. Bina Sejahtera sehingga melalui model tersebut dapat dibuat skenario yang digunakan oleh PT Bina Sejahtera untuk memilih sistem silvikultur yang lebih tinggi dalam menyerap karbon untuk digunakan dalam pengelolaan hutan pada tahun ketiga. Batasan dari model dinamika sistem yang dikembangkan terfokus pada hal-hal yang terkait dengan simpanan karbon  dalam PUP TPTI dan PUP TPTJ teknik SILIN serta data luasan sistem silvikultur TPTI maupun TPTJ di areal IUPHHK-HA PT. Bina Sejahtera.

Vanclay, J.K., 1991. Aggregating tree species to develop diameter increment equations for tropical rainforests. For. Ecol. Manage., 42: 143-168. Pairwise F-tests provided an efficient approach for aggregating large numbers of species into a manageable number of groups for developing diameter increment functions. The first stage of the two-stage procedure identified the number of groups required and the species defining these groups; the second stage aggregated all the remaining species into the most appropriate group. Although there is no guarantee that this leads to an optimal solution, empirical results suggest that the outcome is near optimal. This approach is readily automated and computationally efficient. An analysis of diameter increments of 237 species from the rainforests of north Queensland indicated 41 species groups, each with increment functions significantly different at P<0.01. These provided a substantially better model than the previous model based on subjectively formed groups.

Individual-tree growth models are often used to describe forest stand development and response to silvicultural treatments. Although ideal as research tools, incomplete information on initial conditions can make them unreliable and awkward to use for forest management decision-making. At least for even-aged single-species stands, whole-stand models are an attractive alternative. There may be doubts, however, about the ability of these simpler models to reproduce the behaviour of managed forest stands. To explore this issue, stand-level approximations to TASS, a highly detailed mechanistic individual-tree distance-dependent growth model, are investigated. It is shown that a two-dimensional state space, implicit in stand density management diagrams and self-thinning theories, is insufficient for describing the predicted growth of thinned stands. TASS predictions, however, can be approximated by a relatively simple dynamical whole-stand model using three state variables.
Keywords: stand dynamics, self-thinning, aggregation, state-space, Douglas-fir,
thinning.

An equation depending on two shape parameters includes many of the sigmoids found in the literature as special cases. The formulation facilitates the analysis and description of model properties, and can be used to enhance the generality of software and statistical procedures. Some of the models obtained may be new. The relationship between growth curves and differential equations is discussed; the non-uniqueness of the differential forms has not been generally recognized.
Keywords: Growth and yield models, growth curves, differential equations, Burr distribution, Box-Cox transformation, Richards, logistic.

Trends in growth and productivity of European forests are studied. A retrospective analysis of height growth across Europe over the twentieth century found positive trends, which were substantiated by a literature review. The review  addresses both observed (20th century) and projected (21st century) trends and discusses underlying causes and uncertainties. A main focus of this report is on the tree species Norway spruce, Scots pine and European beech.

Different types of models have been developed and applied to address various problems and issues in forestry. This paper reviews modelling trends in four areas, namely, forest management planning and decision-making, forest dynamics and growth projection, forest landscape and spatial models and participatory forest management models. The first type includes decision models generally structured as optimization models applied to forest planning. These models evolved from single objective to multiple objectives with spatial ...

Masting is the highly variable and synchronous production of seeds by plants. Masting can have cascading effects on plant population dynamics and forest properties such as tree growth, carbon stocks, regeneration, nutrient cycling, or future species composition. However, masting has often been missing from forest models. Those few that simulate masting have done so using relatively simple empirical rules, and lack an implementation of process-based mechanisms that control such events. Here we review more than 200 published papers on me-chanistic formulations of masting, and summarize how the main processes involved in masting and their related patterns can be incorporated in forest models at different degrees of complexity. Our review showed that, of all proximate causes of masting, resource acquisition, storage and allocation were the processes studied most often. Hormonal and genetic regulation of bud formation, floral induction, and an-thesis were less frequently addressed. We outline the building blocks of a general process-based model of masting that can be used to improve the oversimplified functions in different types of forest models, and to implement them where missing. A complete implementation of masting in forest models should include functions for resource allocation and depletion, and for pollination, as regulated by both forest structure and weather in the years prior to seed production. When models operate at spatio-temporal scales mismatched with the main masting processes, or if calibration data are not available, simulation can be based on parameterizing masting patterns (variability, synchrony, or frequency). Also, observed masting patterns have the potential to be used as "reality checks" for more process-based forest models wishing to accurately reproduce masting as an emergent phenomenon.

This study aimed to evaluate the ecological and successional aspects of a subtropical forest fragment by projection of the diameter distribution of different ecological groups, using transition matrix model. Based on measurements of 2009 and 2012 of all trees above 10 cm of DBH, projection of the diameter distribution as well as analysis of forest dynamic were made for three species groups: Pioneer; Non Pioneers, and the whole forest. Simulations of the dynamics of the groups were made until 2027 after method validation. The projection method was adherent in all cases, with higher precision when using the 5cm class interval. The analysis made indicated a gradual substitution tendency of the pioneer species, suggesting a successional advance in the forest fragment under study, as well as an efficiency of the projection method for dynamics analysis of the ecological groups studied.

Subtropical planted forests are rapidly expanding. They are traditionally managed for intensive, short-term goals that often lead to long-term yield decline and reduced carbon sequestration capacity. Here we show how it is possible to increase and sustain carbon stored in subtropical forest plantations if management is switched towards more sustainable forestry. We first conducted a literature review to explore possible management factors that contribute to the potentials in ecosystem C in tropical and subtropical plantations. We found that broadleaves plantations have significantly higher ecosystem C than conifer plantations. In addition, ecosystem C increases with plantation age, and reaches a peak with intermediate stand densities of 1500-2500 trees ha 21 . We then used the FORECAST model to simulate the regional implications of switching from traditional to sustainable management regimes, using Chinese fir (Cunninghamia lanceolata) plantations in subtropical China as a study case. We randomly simulated 200 traditional short-rotation pure stands and 200 sustainably-managed mixed Chinese fir -Phoebe bournei plantations, for 120 years. Our results showed that mixed, sustainably-managed plantations have on average 67.5% more ecosystem C than traditional pure conifer plantations. If all pure plantations were gradually transformed into mixed plantations during the next 10 years, carbon stocks could rise in 2050 by 260.22 TgC in east-central China. Assuming similar differences for temperate and boreal plantations, if sustainable forestry practices were applied to all new forest plantation types in China, stored carbon could increase by 1,482.80 TgC in 2050. Such an increase would be equivalent to a yearly sequestration rate of 40.08 TgC yr 21 , offsetting 1.9% of China's annual emissions in 2010. More importantly, this C increase can be sustained in the long term through the maintenance of higher amounts of soil organic carbon and the production of timber products with longer life spans.

Individual-based and aggregated models for forest stands are
compared. This is followed by a brief review of research on mathematical analysis of complex simulation models, and the derivation of simpler analytical approximations. Finally, a statistical top-down approach is demonstrated, with a three-dimensional state space model that approximates stand development predicted by the TASS tree-level simulator.

The capacity of rainforests to recover from logging disturbance is difficult to model due to the compounding interactions between long-term disturbance effects, natural dynamics, site characteristics and tree species regeneration strategies. The aim of this study was to develop a quantitative model using over three decades of data from stands subjected to various levels of disturbance ranging from natural, through increasing intensities of tree removal to intensive logging. Data for trees &gt;10 cm diameter at 1.3 m above the ground (dbh) in subtropical rainforest of north-east New South Wales, Australia were used. Botanical identity of trees at species level, species-specific shade tolerance and size at maturity were used to classify 117 species into five groups. These groups include the emergent and shade tolerant main canopy species, shade tolerant mid canopy species, shade tolerant understorey species, moderate shade tolerant species, and shade intolerant tree species. Multileve...

In the climate change era, forest managers are challenged to use innovative tools to encourage a sustained provision of goods and services. Many decision support tools (DSTs), developed to address global changes in forest management practices, reflect the complexity of the scientific knowledge produced, a fact that could make it difficult for practitioners to understand and adopt them. Acknowledging the importance of knowledge transfer to forestry practitioners, this study describes a user-centric decision support software tool, aiming to assess forest management and climate change impacts on multiple ecosystem services (ESs) at a stand level. SORTIE-ND, a spatially explicit tree-level simulator for projecting stand dynamics that is sensitive to climate change, is encapsulated into the decision support tool and used as the simulation engine for stand development. Linking functions are implemented to evaluate ecosystem services and potential risks, and decision support is provided in form of interactive 2D and 3D visualizations. Five main components were identified to delineate the workflow and to shape the decision support tool: the information base, the alternative generator, the forest simulator, the ecosystem services calculator, and the visualization component. In order to improve the interaction design and general user satisfaction, the usability of the system was tested at an early stage of development. While we have specifically focused on a management-oriented approach through user-centric interface design, the utilization of the product is likely to be of importance in facilitating education in the field of forest management.

Forest inventory studies in the Amazon indicate a large terrestrial carbon sink. However, field plots may fail to represent forest mortality processes at landscape-scales of tropical forests. Here we characterize the frequency distribution of disturbance events in natural forests from 0.01 ha to 2,651 ha size throughout Amazonia using a novel combination of forest inventory, airborne lidar and satellite remote sensing data. We find that small-scale mortality events are responsible for aboveground biomass losses of ~1.7 Pg C y-1 over the entire Amazon region. We also find that intermediate-scale disturbances account for losses of ~0.2 Pg C y-1, and that the largest-scale disturbances as a result of blow-downs only account for losses of ~0.004 Pg C y-1. Simulation of growth and mortality indicates that even when all carbon losses from intermediate and large-scale disturbances are considered, these are outweighed by the net biomass accumulation by tree growth, supporting the inference of an Amazon carbon sink.

Subtropical planted forests are rapidly expanding. They are traditionally managed for intensive, short-term goals that often lead to long-term yield decline and reduced carbon sequestration capacity. Here we show how it is possible to increase and sustain carbon stored in subtropical forest plantations if management is switched towards more sustainable forestry. We first conducted a literature review to explore possible management factors that contribute to the potentials in ecosystem C in tropical and subtropical plantations. We found that broadleaves plantations have significantly higher ecosystem C than conifer plantations. In addition, ecosystem C increases with plantation age, and reaches a peak with intermediate stand densities of 1500–2500 trees ha 21. We then used the FORECAST model to simulate the regional implications of switching from traditional to sustainable management regimes, using Chinese fir (Cunninghamia lanceolata) plantations in subtropical China as a study case. We randomly simulated 200 traditional short-rotation pure stands and 200 sustainably-managed mixed Chinese fir – Phoebe bournei plantations, for 120 years. Our results showed that mixed, sustainably-managed plantations have on average 67.5% more ecosystem C than traditional pure conifer plantations. If all pure plantations were gradually transformed into mixed plantations during the next 10 years, carbon stocks could rise in 2050 by 260.22 TgC in east-central China. Assuming similar differences for temperate and boreal plantations, if sustainable forestry practices were applied to all new forest plantation types in China, stored carbon could increase by 1,482.80 TgC in 2050. Such an increase would be equivalent to a yearly sequestration rate of 40.08 TgC yr 21 , offsetting 1.9% of China's annual emissions in 2010. More importantly, this C increase can be sustained in the long term through the maintenance of higher amounts of soil organic carbon and the production of timber products with longer life spans.

This study examined the relative importance of soil, stand development and climate hypotheses in driving productivity for a species that is widely distributed in North America. Inventory plots, 3548 of such, either dominated by aspen or made up of species mixture of which aspen occurs in dominant canopy position were sampled along a longitudinal gradient from Quebec to British Columbia. Site index (SI), was used as a measure of productivity, and soil, climate and stand attributes were correlated with site index in order to determine their effects on productivity. Results show a decline in productivity with high moisture deficit. Soil humus correlates significantly with SI but does not sufficiently capture differential rates of litter deposition and decomposition effects over the long-term. Consequently, aspen composition, stand ageing, and stand structural changes dominate variability in productivity. Within the context where deciduous cover has being increasing, there are implications for forest productivity.