The quarter-power scaling model does not imply size-invariant hydraulic resistance in plants.
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Models, Biological↗
Biomedical subjects
Annikki Mäkelä
Publications and source records attributed to Annikki Mäkelä.
Carbon budget for Scots pine trees: effects of size, competition and site fertility on growth allocation and production.
Time series of carbon fluxes in individual Scots pine (Pinus sylvestris L.) trees were constructed based on biomass measurements and information about component-specific turnover and respiration rates. Foliage, branch, stem sapwood, heartwood and bark components of aboveground biomass were measured in 117 trees sampled from 17 stands varying in age, density and site fertility. A subsample of 32 trees was measured for belowground biomass excluding fine roots. Biomass of fine roots was estimated from the results of an earlier study. Statistical models were constructed to predict dry mass (DW) of components from tree height and basal area, and time derivatives of these models were used to estimate biomass increments from height growth and basal area growth. Biomass growth (G) was estimated by adding estimated biomass turnover rates to increments, and gross photosynthetic production (P) was estimated by adding estimated component respiration rates to growth. The method, which predicts the time course of G, P and biomass increment in individual trees as functions of height growth and basal area growth, was applied to eight example trees representing different dominance positions and site fertilities. Estimated G and P of the example trees varied with competition, site fertility and tree height, reaching maximum values of 22 and 43 kg(DW) year(-1), respectively. The site types did not show marked differences in productivity of trees of the same height, although height growth was greater on the fertile site. The G:P ratio decreased with tree height from 65 to 45%. Growth allocation to needles and branches increased with increasing dominance, whereas growth allocation to the stem decreased. Growth allocation to branches decreased and growth allocation to coarse roots increased with increasing tree size. Trees at the poor site allocated 49% more to fine roots than trees at the fertile site. The belowground parts accounted for 25 to 55% of annual G, increasing with tree size and decreasing with site fertility. Annual G and P per unit needle mass varied over the ranges 1.9-2.4 and 3.5-4.0 kg(DW) kg(-1), respectively. The relationship between P and needle mass in the example trees was linear and relatively independent of competition, site fertility and age.
Biomass↗
Bridging process-based and empirical approaches to modeling tree growth.
The gulf between process-based and empirical approaches to modeling tree growth may be bridged, in part, by the use of a common model. To this end, we have formulated a process-based model of tree growth that can be fitted and applied in an empirical mode. The growth model is grounded in pipe model theory and an optimal control model of crown development. Together, the pipe model and the optimal control model provide a framework for expressing the components of tree biomass in terms of three standard inventory variables: tree height, crown height and stem cross-sectional area. Growth rates of the inventory variables and the components of biomass are formulated from a carbon balance. Fundamentally, the parameters of the model comprise physiological rates and morphological ratios. In principle, the values of these parameters may be estimated by lower-level process models. Alternatively, the physiological and morphological parameters combine, under reasonable assumptions, into a set of aggregate parameters, whose values can be estimated from inventory data with a statistical fitting procedure.
Biomass↗
Analysis of biomass accumulation and stem size distributions over long periods in managed stands of Pinus sylvestris in Finland using the 3-PG model.
We tested the performance of a process-based model (PBM) in relation to long-term mensuration data from two sites in Finland where the stands were up to 90 years old and had been thinned at approximately 5-year intervals over the last 50 years. The PBM used was based on the 3-PG (Physiological Principles to Predict Growth) model developed by Landsberg and Waring (1997), with modifications in the biomass allocation routine, for which we used data and calculations by Vanninen (2003) to estimate the allocation coefficients and turnover rates. Site fertility was estimated in terms of known site-type characteristics. The model was evaluated in terms of stand development and its ability to simulate responses to thinning; stem numbers after thinning were specified at the dates when the thinning took place. Stand development in terms of basal area, volume and mean diameter at breast height, closely followed the measured characteristics of all stands. Foliage mass predictions were close to estimates obtained by an empirical method. The analysis shows that, under normal thinning regimes, a range of different thinning intensities can be adequately described using a simple multiplicative model relating the proportion of volume and foliage mass removed to the corresponding proportion of stem numbers. This model, together with stem allometry data, described the "growth" in mean diameter after thinning, which simply reflected the removal of the smaller trees. These results indicate that, with a single set of parameter values, 3-PG can provide good descriptions of the growth patterns of trees-in this case Pinus sylvestris L.-over long periods, including growth after repeated thinning. One of the outputs from the 3-PG model is mean stem diameter (B): we show that it is feasible to estimate stem size distributions, which changed considerably over the life of these stands, from B using the Weibull function. This shows that, given information about the Weibull parameters for particular species and cultural systems, it should be possible to use stem numbers and the B obtained from the 3-PG model to produce information about stem size distributions from simulated data.
Biomass↗
Acclimation of photosynthetic capacity in Scots pine to the annual cycle of temperature.
Coniferous trees growing in the boreal and temperate zones have a clear annual cycle of photosynthetic activity. A recent study demonstrated that the seasonal variation in photosynthetic capacity of Scots pine (Pinus sylvestris L.) could be attributed mainly to the light response curve of photosynthesis. The magnitude of the light response curve varied over the season while its shape remained constant, indicating that the two physiological parameters quantifying the curve-the quantum yield per unit internal carbon dioxide concentration and the corresponding light-saturated rate-remained proportional to each other. We now show, through modeling studies, that the quantum yield (and hence the light-saturated rate) is related to the annual cycle of temperature through a delayed dynamic response. The proposed model was tested by comparing model results with intensive measurements of photosynthesis and driving variables made from April to October in three shoots of Scots pine growing near the northern timberline. Photosynthetic capacity showed considerable acclimation during the growing season. A single model describing photosynthetic capacity as a reversible, first-order delay process driven by temperature explained most of the variation in photosynthetic capacity during the year. The proposed model is simpler but no less accurate than previous models of the annual cycle of photosynthetic capacity.
Acclimatization↗
Annual pattern of photosynthesis in Scots pine in the boreal zone.
To detect seasonal changes in photosynthetic rate in the field, a set of 18,000 photosynthetic measurements made between April and October on three shoots of Scots pine growing near the northern timberline was studied. The measurements were analyzed in the framework of an optimal stomatal control model of photosynthesis, in which irradiance (photosynthetically active radiation, I), air humidity and ambient temperature are driving variables. All driving variables were monitored concomitantly with gas exchange measurements throughout the growing season. The model has nine parameters, of which six were assumed to be constant over the growing season and were fixed based on previous information. The three variable parameters were the initial slope (alpha) and saturation value (gamma) of the light-response curve of carboxylation efficiency in the intercellular cavity, and the cost of transpiration (lambda), in carbon units, regulating the degree of stomatal opening. These parameters could not be estimated independently, nor could their values be satisfactorily found by standard nonlinear regression techniques. A Monte Carlo based simulation procedure was devised to analyze the best-fit parameters and their mutual correlations near the minimum of the residual sum of squares. This was accomplished by replacing the saturation value of the light-response curve with a linearity parameter that determined the shape of the curve. In the best fit solutions, only alpha and lambda varied from day to day, whereas the shape of the curve was constant (i.e., gamma was proportional to alpha). Both alpha and lambda showed consistent patterns from spring to autumn, but the seasonal variation was considerably greater for alpha than for lambda. The optimal stomatal control model with the seven fixed and two daily parameter values gave a good overall fit for photosynthetic rate over the season (PEV > 95%).
Models, Biological↗
Derivation of stem taper from the pipe theory in a carbon balance framework.
A dynamic tree growth model is described. The model derives the development of stem taper and vertical distribution of branch basal area from the pipe model, assuming that reuse of active pipes is regulated by foliage dynamics in a vertically explicit crown with a foliage distribution of constant shape. Based on empirical findings, the pipe model was modified slightly to allow the foliage/sapwood ratio to vary as a function of distance from the treetop. Growth was derived from carbon balance in a stand of different size trees that may shade each other. The model was applied to old and middle-aged trees growing in dense and sparse stands of Scots pine for which stand-level measurements are available as a chronosequence, but individual trees have been measured only once. Measured trees were compared with corresponding simulated trees for stem taper and vertical distribution of branch basal area. The results indicated that the pipe model assumptions, combined with a model of tree growth, are capable of producing realistic predictions of the vertical distribution of stem and branch diameter in trees of different sizes in the stand. A comparison of the results with a simple form of the uniform stress theory showed good agreement between the two models. However, a significant difference was found between the measured relative contribution of heartwood to total stem diameter and the predicted share of disused pipes in the stem. A possible explanation for this discrepancy is that the transition from sapwood to heartwood is gradual rather than abrupt as assumed in the model. A modification of the pipe model to incorporate a gradual transition is outlined.
Models, Biological↗
Process-based models for forest ecosystem management: current state of the art and challenges for practical implementation.
Recent progress toward the application of process-based models in forestmanagement includes the development of evaluation and parameter estimation methods suitable for models with causal structure, and the accumulation of data that can be used in model evaluation. The current state of the art of process modeling is discussed in the context of forest ecosystem management. We argue that the carbon balance approach is readily applicable for projecting forest yield and productivity, and review several carbon balance models for estimating stand productivity and individual tree growth and competition. We propose that to develop operational models, it is necessary to accept that all models may have both empirical and causal components at the system level. We present examples of hybrid carbon balance models and consider issues that currently require incorporation of empirical information at the system level. We review model calibration and validation methods that take account of the hybrid character of models. The operational implementation of process-based models to practical forest management is discussed. Methods of decision-making in forest management are gradually moving toward a more general, analytical approach, and it seems likely that models that include some process-oriented components will soon be used in forestry enterprises. This development is likely to run parallel with the further development of ecophysiologically based models.
Journal Article↗
Application of volume growth and survival graphs in the evaluation of four process-based forest growth models.
Volume growth and survival (VGS) graphs, which show volume growth rate and risk of mortality for individual trees (or tree size classes), have been proposed as a tool for assessing the validity of models that describe the development over time of tree size distributions within forest stands. We examined the utility of the VGS method in evaluating four process-based models. The performance of the models FORSKA, 4C, MORG, and PipeQual is analyzed against long-term data from a Scots pine stand in Evo, Finland, and the models FORSKA and 4C are also assessed with respect to data from a beech stand in Fabrikschleichach, Germany. Comparison of the measurement-based VGS graphs with those produced from the model-based data shows that although the models yield similar stand-level predictions, they can differ widely in their projections of individual tree growth and size distributions. Examination of the discrepancies between models and data in the context of the VGS graphs reveals several areas in which the models could be improved. We conclude that the method is useful in model evaluation, especially if used in combination with indicators of stand structure, such as the height/diameter ratio.
Journal Article↗
Volume growth and survival graphs: a method for evaluating process-based forest growth models.
We investigated the relationships within forest stands between tree size and (a) stem volume growth rate and (b) risk of mortality for individual trees. Values of both x and y variables were plotted relative to the largest value in the stand. We refer to the resultant presentations as relative volume growth and relative survival graphs (VGSs). A pair of VGSs can be produced readily from an individual-tree growth model. It can also be constructed from consecutive sets of field measurements. Comparison of VGSs derived from model and measurement data provides a test of the validity of the components of the growth model. We have analyzed VGSs based on measurement data for Scots pine (Pinus sylvestris L.) in central Finland and for beech (Fagus sylvatica L.) in southern Germany. The graphs based on measurement data varied as a consequence of differences in competition, stand management, and tree species. We analyzed the relationship between VGSs and stand dynamics using a simple growth model. We found that different features of the VGSs imply characteristic tree size distributions in subsequent years. Thus, we conclude that if the VGSs generated by a model do not correspond to those based on field measurements, the model cannot be relied on to reproduce the development of tree-size distribution correctly. Relative growth and survival graphs thus provide a tool for evaluating complicated growth models.
Journal Article↗
Needle and stem wood production in Scots pine (Pinus sylvestris) trees of different age, size and competitive status.
We studied effects of tree age, size and competitive status on foliage and stem production of 43 Scots pine (Pinus sylvestris L.) trees in southern Finland. The tree attributes related to competition included foliage density, crown ratio and height/diameter ratio. Needle mass was considered to be the primary cause of growth through photosynthesis. Both stem growth and foliage growth were strongly correlated with foliage mass. Consequently, differences in growth allocation between needles and stem wood in trees of different age, size, or position were small. However, increasing relative height increased the sum of stem growth and foliage growth per unit foliage mass, indicating an effect of available light. Suppressed trees seemed to allocate more growth to stem wood than dominant trees, and their stem growth per unit foliage mass was larger. Similarly, trees in dense stands allocated more growth to stem wood than trees in sparse stands. The results conformed to the pipe model theory but seemed to contradict the priority principle of allocation.
Journal Article↗
Optimal control of gas exchange.
A major difficulty in evaluating the optimization theory of leaf gas exchange under conditions of water deficit has been that of obtaining suitable experimental data. Mathematical solutions to three formulations of optimal stomatal control are presented which can be tested experimentally. First, it is assumed that the movement of stomata and changes in environmental factors are slow compared to changes in the internal CO(2) concentration. The optimization problem is solved under this assumption, and the procedures for testing the solution experimentally are described. Second, instantaneous stomatal response is postulated and the solution suggests that very rapid oscillations provide optimal CO(2) uptake. Third, variable stomatal dynamics are postulated and the mathematical solution shown to be similar to that of the second case. The second and third cases can also be tested empirically.
Journal Article↗