Dr. Mex Peki DOF - PNG University of Technology
YIELD TABLE
Definition of Yield Tables
tabulation indicating the volume of wood per unit area of forest to be expected at different ages of the trees
The term yield is used in forestry with a number of qualifiers e.g. annual, intermediate, final, sustained, financial. Each has a special connotation for management. In this course, we shall use yield in a very general sense implying the accumulation of increment available at a particular time for a particular purpose, e.g. the total amount of wood capable of being harvested at a certain time.
A yield table is essentially a tool of long term planning. It is a type of growth or 'experience' table which lists expected productivity/volumetric yield for a given age, site or crop quality and sometimes other indices such as density. Thus, yield tables usually refer only to even-aged stands.
Data to prepare such tables may be obtained from:
permanent sample plots;
temporary sample plots;
stem analysis.
Permanent sample plot information is by far the most satisfactory on which to base yield tables.
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What the yield tables show
The Forest Yield tables present values for all the main growth and yield variables for a sequence of stand ages. There are two table formats. The first format is for displaying yield tables involving thinning as part of the management
prescription. The format is designed to show results for both standing trees and thinnings. The second format is for displaying yield tables for unthinned stands, and only shows values for standing trees and a summary for volume lost to mortality.
Yield tables for thinned and unthinned stands display values for:
stand age
top height
number of trees per hectare
mean diameter at breast height (dbh)
basal area per hectare
mean volume per tree
volume per hectare
per cent mortality (applies to unthinned stands only)
mean annual increment (MAI).
What the yield tables show continued
Yield tables for thinned stands display values for standing trees and thinnings separately and also show cumulative production of basal area and volume. For unthinned stands, values for
cumulative volume production are not displayed and values for mean annual increment are based on standing volume rather than cumulative volume, i.e. not including volume effectively lost due to mortality.
When displaying a yield table, the values for number of trees, basal area and volume are normally expressed for a stand area of one hectare so that they represent per-hectare results.
However, a different stand area can be specified in Forest Yield if
required, in which case, values will be displayed that relate to the
specified area.
Limitations of the yield tables
The yield tables are designed mainly for application to even- aged silvicultural systems. They have limited application to forest stands with more complex structure and silvicultural practice, for example uneven-aged stands of trees – this is a subject of ongoing research and development.
A characteristic stand growth pattern and a particular management prescription have been assumed in the construction of each yield table. Any deviation from the
assumed growth pattern or management prescription will result in different stand characteristics compared with predictions.
Direct comparisons of the results for an actual stand with predictions from a yield table may not be meaningful because it is inevitable that the growth of an individual stand will vary in some way from the patterns assumed in a yield table.
However, the trends of growth which are given in a yield table can be used to estimate the probable development of any particular stand.
PURPOSE OF YIELD TABLE
The main purpose of yield tables is to provide estimates of present yield and future increment and yield.
The tables may be presented in tabular or graphical form or
in the form of a regression equation relating yield to age,
site and stand density.
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TYPES OF YIELD TABLES
There are three main types of yield table, viz.
1. Normal,
2. Empirical and
3. Variable density .
TYPES OF YIELD TABLES CONTINUED
1. Normal Yield Table
A normal yield table is based on two independent variables, age and site (species constant), and applies to fully stocked (or normal) stands.
It depicts relationships between volume/unit area together with other stand parameters and the independent variables. 'Normal' is an unfortunate term as fully stocked stands are rather unusual.
Since only two independent variables are involved, normal yield tables are conveniently constructed by graphical means. The density variable is held constant by attempting to select sample plots of a certain fixed density assessed as full (or normal) stocking. Because it is difficult to describe precisely and recognise full stocking, generalized subjective descriptions are used which leave much to the judgment of the individual in choosing samples.
The data presented in normal yield tables are averages derived from many stands considered to be fully stocked at the time they were sampled.
Example of Normal Yield table
TYPES OF YIELD TABLES CONTINUED
2. Empirical Yield Table
In contrast to normal yield tables, empirical yield tables are based on average rather than fully stocked stands. This simplifies the selection of stands for sampling. The resulting yield tables describe stand characteristics for the average stand density encountered during the collection of field data. Normal and empirical yield tables essentially have the same limitations, namely:
the difficulty of locating fully stocked stands or representative average stocked stands from which to collect the basic data;
stocking may not have always been 'fully stocked' or 'average';
the problem of selecting correction factors to apply to stands
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TYPES OF YIELD TABLES CONTINUED
3. Variable Density Yield Table
The limitations listed above for normal and empirical yield tables led to the development of techniques for compiling tables with three independent variables, stand density being included as the third variable: hence the term variable density yield tables. Basal area/unit area, mean diameter or stand density indices are used to define the density classes. Such yield tables are particularly useful for abnormal stands e.g. abnormal due to early
establishment problems, insect and fungal attack, drought, fire, fluctuating demands for produce, etc. However, they still have limitations (which apply also to normal and empirical tables), namely:
no confidence limits are attached to trends;
extrapolations are made outside and beyond thinning regimes and ages sampled;
volume functions used are mostly two-dimensional and of regional application;
volumes are computed for normal trees only and no account is taken of malformation and other such factors affecting recoverability;
usually, no account is taken of the pruned component of a stand.
Yield Table Compilation
The first essential in yield table construction is to adequately sample the area to be served by the table.
Ideally, the sample should include at least one plot in every cell of the table which the stands are capable of filling.
Acceptable results are only achieved if the sample plots are uniformly distributed with respect to the independent variables being tested.
If they are not, unreal effects may be introduced during
interpolation and/or extrapolation of relationships.
Yield Table Compilation Continued
Stands abnormally affected by destructive agencies (fire, insects, disease, etc.) should be excluded from sampling. Attention should be confined to stands having no other factors measurably affecting growth other than those being evaluated, i.e. age, site and stand density. A common procedure is as follows:
If not already done, classify the forest into areas of
different productivity (S.Q. or S.I. classes - site is one of the independent variables in the yield table).
Within site classes, stratify the forest into age and density sub-classes.
Sample stands in each site-age-density cell for the various dependent variables to be included in the table, e.g. in each plot, measure dbhob of every tree and stand height and calculate volume of the plot in some objective way.
Stratify the data based on site class assigning a class to each plot.
Check the stocking of each plot for abnormality and reject any atypical plot.
Establish the relationships between the dependent variables and age within site classes, and harmonise. For two independent variables, this can be done by subjective graphics.
Yield Table Compilation continued
Mathematical analysis is needed if three independent variables are involved. Simple regression models sometimes satisfactorily express the relationship between cubic yield and the age/site/density combinations covered by the sample data.
Basal area per unit area proved to be the most highly significant variable in the regression accounting for 53% of the total variation removed by the equation.
Stocking density (trees per unit area) was much less effective.
Stand density is the dominant factor affecting yield in older
stands where volume increase is primarily through diameter
growth. It is much less dominant in younger stands where
yield is materially influenced by height growth and/or
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Leech and Ferguson (1981) examined the yield of unthinned stands of P.radiata in the lower south east of South Australia and compared the yield predicted from the graphically compiled curves of Lewis et al. (1976) with that from a range of non-linear growth models they had formulated, the best being a conditioned form of the periodic annual increment (PAI) Mitscherlich model. Although they found no significant difference between the predictions, the mathematical model was preferred because it was easily updated and prediction of yield was facilitated.
The exponential form of the Mitscherlich growth curve has been widely used in forestry. A form of this equation for total volume growth is:
YA = YM - b EXP^ (-pA) where A is age, YA is yield at age A, YM is a constant; the asymptotic maximum yield, and b and p are coefficients. Such a model is non-linear in form and needs an iterative
programme to fit the best set of YM, b and p coefficients to the data. Non-linear models of a sigmoid shape have been used to define mathematically Douglas fir site yield curves in British Columbia (Nokoe 1980) . However, Leech and Ferguson pointed out that yield of P. radiata is modelled commonly to a merchantable volume limited by a specific top diameter under bark (10 cm in South Australia; 7.5 cm in Gippsland) which may mean that the early point of inflexion of the sigmoid curve is before
merchantable volume growth commences.
The PAI form of the Mitscherlich model favoured by Leech and Ferguson (op. cit.) was conditioned to pass through the quantity, total yield at age 10 years (Y10). This was termed "site potential" and set the curve for a particular site quality of given Y10. The form of the model was:
YA = Y10 [1 - EXP (-p(A - A0))] --- [1 - EXP (-p(10 - A0))] where A0 is the age at which volume to 10 cm top diameter first occurs. This model has no point of inflexion but approaches a limiting value as age approaches infinity.
Forecasting using yield tables
As mentioned earlier, estimation of yield is one of the main purposes of a yield table. If the rotation is not yet complete, the history of growth to the present can be compiled and presented in yield table form. Likely future yield is then predicted by extrapolating the relationships of the stand variables on age and site. Such forecasts, however, should be limited to short periods (approx. 5 years).
For a species in its second rotation, the yield table of the first rotation can be used for long term forecasting provided there has been no change in site productivity. If a change in productivity is detected, it is essential before applying the yield table to ensure that the growth trends of the various site classes are not affected.
Reliable growth functions for many commercially important tree species have now been established which permit tree and stand growth to be simulated under a wide range of conditions. As a consequence,
estimating forest yield in future will mostly involve an initial inventory and then growth simulation using established growth functions.
Stand Projection
Stand projection is a direct method of estimating stand growth based on an analysis of a given stand from measured variables. It involves:
determining present stand condition (usually by inventory);
forecasting increment in the future period based on increment in the past period (determined from permanent sample plots or stem analysis of individual trees) and adjusting for factors such as mortality and ingrowth:
adding future increment to the present condition of the stand.
The method can be used for projecting diameter, height, basal area and volume and, unlike yield tables, can be applied to any kind of stand, even-aged or uneven-aged. Provided drastic changes in growing conditions have not occurred, stand projection can be based on past increment in two ways: By assuming that future growth will equal past growth: This linear extrapolation leads to overestimates for many growth parameters because rate of growth tends to decelerate with age. For this reason, linear extrapolation is of little use in predicting future diameter. The premise, however, is useful for predicting basal area growth and frequently volume growth which proceed linearly for the major portion of the life of a tree i.e. the central section of the cumulative growth curve is extended. Note: A constant basal area increment implies a gradually decreasing diameter increment with time.
By assuming that future growth will follow the trend established by past growth: Suppose, for example, that records of past growth indicate a curvilinear trend. Future growth may then be estimated by extrapolating this trend. The procedure outlined may be used with little danger for short term predictions but is unreliable for long term predictions.
Stand Projection continued
Stand tables are commonly used in stand projection. Growth prediction is accomplished by separately projecting each diameter class of the stand table using a technique called Stand Table Projection.
This technique predicts future diameters and so basal area growth. Stand table projection is much less successful for projecting volume because time changes in the height/dbh relationship and form are rarely taken into account properly.
If reliable growth functions are available, an alternative to
projecting stand volume is to forecast future volume from the
growth equations using as independent variables those stand
characteristics (e.g. dbh and height) which are correlated with
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Modelling growth
In managing plantations, which is far more capital intensive than in natural forests, it is important to select the best set of silvicultural regimes which satisfy the various constraints on demand and resources.
Thus, the traditional management approaches using yield tables described earlier have been superceded in most developed countries by growth and yield simulation models.
These mathematical models permit estimates of growth to be predicted and management strategies to be optimised by computer. However, the final decision still rests with the manager (who must interpret the output and determine which strategies are feasible and ecologically and socially acceptable).
Optimisation models can be developed for both even and uneven aged forests once the basic growth and yield simulation models have been formulated. These models can be very helpful for regional and national planning.
Furthermore, if the forests are managed under multiple goals and for multiple products, optimisation models can be developed using goal programming.
References cited
Clutter, J.L., Forston, J.C., Pienaar, L.V., Brister, G.H. and Bailey, R.L. 1983.
Predicting Growth and Yield. Chp. 4 in 'Timber Management: a Quantitative Approach.' John Wiley & Sons, New York.
Prodan, M. (1968). Forest Biometrics. Pergamon Press, Oxford.
Smith, J.H.G. and Kozek, A. (1984). New non-linear models can improve estimates of growth and yield. Commonw. For. Rev. 63(1): 41- 45.
Carron, L.C. 1968. An Outline of Forest Mensuration with Special Reference to Australia. Aust. Nat. Univ. Press. 224 p.
Bennett, F.A. 1966. Construction and use of volume and yield tables. In T.D. keister (ed.), 'Measuring the Southern Forest'. Louisiana State Univ.
Press, p. 17-29.
Leech, J.W. and Ferguson, I.S. (1981). Comparison of yield models for unthinned stands of radiata pine. Aust. For. Res 11: 231-245.
Nokoe, S. (1980). Non-linear models fitted to stand volume-age data compare favourably with British Columbia Forest Service hard-drawn volume-age curves. Can. J. For. Res. 10: 304-307.
