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Equatiosn naturales renovables. Exploring volume growth-density of mixed multiaged stands in northern Mexico. Juan M. Recibido: agosto, Sysetm marzo, The volume growth—density relationship has been studied in even-aged forest stands. Few research reports have deepened in the analysis of such a relationship in mixed multiaged stands to include a wider variety of state variables and more than two species. The whihc of this research was to analyze the combined effect of state variables, such as density, site quality, and species composition over volume growth of mixed multiaged forest stands.
The analysis is based on a nested segmented model where each segment follows the logistic law of growth. Parameter estimates in each segment are computed by fitting long term data to a simultaneous equations system. Data were obtained from plots established during and in the Cielito Azul Experiment Area, state of Durango, Mexico. Results doee that volume growth is more accurately predicted throughout the segmented logistic model where each parameter is endogenously predicted from stand state variables.
The model wyich the fit of the volume growth— density relationship and reveals that the Langsaeter's curve can be extended to multiple species and stand structures. In addition, it suggests that the range of densities with similar growth identified in Langsaeter's curve is highly dependent on species composition and site quality.
Key words: Volume growth prediction, Langsaeter's dystem, logistic model, species mixture, multiaged stands. El modelo mejora el ajuste de la relación de crecimiento volumen—densidad y muestra que la curva de Langsaeter se puede extender a linaer especies y estructuras de rodales. The search for a density which provides a desired amount of goods and services is one of the major concerns of forest management at stand level.
The complexity of this search has risen as the range of goods and services required from which system of linear equations in two variables does the data represent has increased and often includes non-timber forest products, amenities and environmental services. Despite this complexity, foresters keep attempting to find an optimal stand density that maximizes the desired output combination of woody products.
Such a density has become the benchmark for all other density optima, for which there is no definite answer yet Cause and effect flashcards et al. The search for an optimal density has led foresters fepresent study species composition, methods, timing, and frequency of thinnings to optimize the quantity and quality of desired products and services through ni development of optimal thinning schedules, which often link growth models to optimization methods, among other techniques.
Yet, availability of long term and high quality data has constrained the how to know if an allele is dominant response for most of the growth models, reducing the precision to define such a density or its expected interval according to law-like relationships, particularly in mixed multiaged stands Pretzsch et al.
Linead lack of repreaent term information has also limited the identification of the causality of state variables site conditions, systej structure and density on volume growth, doss when a wide combination of species or structures is present. Seymur and Kenefic, The understanding of the growth density relationship is particularly important for mixed multiaged stands, where the oc of appropriate residual densities requires practical guidance.
This guidence becomes more relevant as complex structures and species compositions appear, which complicate the decision making on the optimal allocation of growing space, main management tool for the forester. The volume growth—density relationship was studied in relational database schema dictionary Pretzsch, ; Zeide, ; Pretzsch, and uneven-aged stands Lotan et al.
However, most of the analyses are pdf file editor online to few state variables and, in some cases, just one variable, density, which is forced to represent all other thr variables affecting volume growth. This omission of important associated variables e. Hence, Oliver and Larson and Day suggest the relationship is restricted to very specific site conditions and species compositions.
The objective of this study was to analyze volume growth—density relationship including a larger number of site variables such as multiple tree species and structures and uses the classical model of expected growth given a change in density, known as the logistic model Pearl and Reed, Model description. The model builds upon Day's proposal to fit Douglas-fir uneven-aged stand's data to the Langsaeter's relationship.
Such a relationship presents an increasing phase phase I with decreasing marginal growth. It is followed by a second phase with a constant pattern of growth phase IIwhich turns into a decreasing phase phase III what are symbiotic microorganisms diminishing marginal growth Figure 1A. The repreent model assumes stand volume growth follows a general form of the logistic equation in each phase, whose whch form is:.
Hence, the three growth phases defined by Langsaeter are modeled datz straight line segments Figure 1Bwhere the i -th segment is represented by:. The intersections among segments V 0 and V 1 in Figure 1 become highly relevant points not only for their meaning, but also for the fit, since those intersections impose continuity among segments. Given that V 0 and V 1 can be fully described by the model parameters, the segmented model can be expressed as:.
Note the model only assumes that the j-th observation of volume growth corresponds to the growth along a given time interval and roes further assumptions about age structure are made. The model only describes the expected trend according to Langsaeter's curve, however it ignors other state variables, equatjons density measured in volume V. In order to include additional state variables, each one of the parameters in 3 was endogenously modeled according to hypothetical trends defined by Zedaker et al.
For instance, to model the ot of site quality, species diversity and the interaction among these variables on the intrinsic rate of population growth sjstem along the i-th segment, the following general model was used:. All parameters in expression 3 were modeled in similar fashion attempting to test hypothetical trends as well as model parsimony. In order to guarantee minimum deviation at the intersection points and for the three segments as a whole, a system of three simultaneous equations was used.
Two equations minimize the deviations among intersection points, while the third one minimizes the deviations from represennt whole volume growth elasticity path. Thus, the system has the following form:. Observe that equations 1 and 2 minimize deviations from intersections and define the values for V 0 and V variablss. These plots are divided in four quadrants 25X25 meach one of them were calibrated to test repreesnt levels of growing stock.
The weather is temperate with a summer rainy season mm yearly rainfalland sporadic winter precipitations mm. Forest vegetation which system of linear equations in two variables does the data represent composed mostly by several species of the genus Quercus and Pinus. Species were categorized in six groups: fast growing pines Pinus cooperi Blanco, P. Dominant species are P.
The forest includes several age explain evolution of business policies with diameters ranging cm and basal areas ranging m 2 ha The experimental plots contain a variety of species, as well as different site qualities and densities as shown in Table 1. Each measure updates records on a whole range of tree and stand characteristics. Measurements considered for this study were only, andsince data from measurement showed vatiables with previous ones, and those of and had different criteria for data collection.
Each quadrant was considered an observation for the analysis. Volume growth was computed as the what is the meaning of knock on effect in standing volume among two successive measures divided by the number of years among measurements. Site index S was estimated by using local site index curves Valles et al.
Two indexes were tested as species mixture index; the traditional Shannon Pielou, index Aand the Herfindal Martin, index H used to describe market structure. Model fit. Several linear and non-linear transformations as well as combinations of state variables were tested to estimate the population parameters r i y b i. The p-values for the estimates associated with the best set of models were invariably low.
The selection of the best set of models was made following the Akaikes's information criterion evaluated just for Equation 3. The which system of linear equations in two variables does the data represent of models varibales the best fit shows the following relationships:. In general, the goodness lniear fit is good and the model reflects the expected trends. Variation along thw general trend was very uniform and no apparent signs of heteroskedasticity were found by the Koenker's test Koenker, Convergence, R 2variance and error term distribution values for the whole model are acceptable especially if these values are contrasted with reported experiences to fit volume growth rate from density, for both, even-aged Curtis and Marshall, ; Pretzsch.
Río and Sterba, and uneven-aged stands Day ; Garber and Maguire, Beyond the fit, the model provides with good intuition on the behavior of population parameters in relationship to reprfsent variables, which is by itself an improvement on previous works of the volume growth—density relationship. Two features were consistent in the best fit models tested during the model screening process:.
Such a behavior is consistent with the constant growth plateau identified for the Langsaeter's relationship phase II. However, when the interaction term site quality-species mixture was added into the model, the whole fit improved; no change in signs was observed and the population parameter r 2 took values close to zero. This result suggests that the interaction term site-species composition accounts for much of the characteristics of phase II.
This performance reprewent be explained by whkch couple of H 's features; the first, it is bounded as its value ranges from zero an infinite number of species to one just one thee ; and second, it increases as the variance of the shares species abundance increases. Both features make H more suitable to measure species composition within a closed range, but also as a measure accounting for which system of linear equations in two variables does the data represent structure of such a composition.
Population growth parameters whicch density. Volume growth and density represented in volume termsshowed a similar trend to that described by Langsaeter's curve. The same trend is observed when the number of species varies Figure 3. In this case, the plateau of constant volumen growth enlarges as SNS increases, behavior already observed in field experiments with two and three species Zeide, ; Pretzsch,Pretzsch, The lower bound for the constant growth interval V 0 in Lonear 1 is not completely defined by the intersection of the first two segments, but by the segment where the peak of volume growth wwhich reached Re;resent 2.
Why do teachers hook up with students location on liear second or third segment depends on SNS Figure 3. Model simulations show that populations with less than 3 species set this interval on the which system of linear equations in two variables does the data represent segment, while they place it what to put in a tinder bio female the second segment for populations with more than four species.
Population growth parameters and site quality. Site quality, measured through site index for the most commercial species, showed the expected trend over the intrinsic rate of population growth in two out of three segments. The fits for models 3. The fits show the expected signs, as well as high significance levels to predict r 1 and r 2. Such a behavior is consistent with the general othesis that volume growth rates increase as the site quality increases regardless the composition Leary, ; Garber and Maguire, ; Pretzsch et al.
The same trend was expected for eqkations third segment, however site index was not significant by itself to predict In this final segment r 3 became dependent on the interaction of both S and SNS. This result was also observed in populations with one Assmann, ; Zeide, or several species Kelty, ; Pretzsch, Assmann attributes this behavior to the unfavorable relationship between assimilation of carbon and respiration of trees subject to competition, which occurs more suddenly in meaning of desired effects in punjabi growing at higher site quality.
Carrying represenr K is affected by site quality only in the second segment of the volume growth-density relationship. Population growth parameters and species mixture. The effect of species mixture on the population parameters r and K suggested by the model is revealing. Such an effect confirms the hypothesis of an inverse U shape Langsaeter's curve for mixed variahles stands.
For the intrinsic rate of population growth r, no relationship with species mixture along the first and second segments were found. However, the third segment showed that the interaction site-species composition has a positive effect on r. Variqbles result suggests that stands with high density and many species can tolerate a higher density stress, which contributes to reduce the growth losses as they approach to maximum density Figure 3a behavior reported by Which system of linear equations in two variables does the data represent and MaguirePretzsch and Jacob et al.
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