Stand Growth ©

A knowledge of stand growth or increment is one of the most important requirements for intelligent forest management. Estimates of stand growth are needed to decide the health of the forest, the volume of material that can be harvested (yield) without violating the sustainability of the forest, the allowable cut, where the cut will be made and the trees which will comprise it.

In assessing stand growth, we need to consider each of the following components:

  1. Regeneration and other non-measurable trees;
  2. Accretion - the sum of the individual increases in size of the trees of measurable size present at the commencement of the growth period;
  3. Ingrowth - the quantity of trees entering the measurable stand since the previous assessment;
  4. Mortality - the quantity of trees lost through death;
  5. Drain - the quantity of trees harvested during the growth period.
Bounded plots (fixed-area plots of square, rectangular or circular shape) are most commonly used to assess all five components. Sometimes the same size of plot is used for all five: occasionally, different sizes are adopted. Normally, whatever method is adopted, too many small trees and too few larger ones are assessed, which is a situatuion inversely proportional to value. One should allocate optimumly for each size of tree. Obviously, point sampling in which the probability of selection is proportional to size is particularly appropriate in this situation.

Productivity (= accretion + ingrowth + mortality) is a measure of site capability and the degree of utilisation of the site. Thus, a site measured in terms of parameters such as temperature, rainfall, physical and chemical soil properties, etc., can describe the capability of that site but the productivity of a crop on it refers only to that crop in the given circumstances and not to the inherent qualities generally of the site.

A forest manager, will be particularly concerned with the capacity of the forest to grow, i.e. with its increment, because the likely future condition of a stand can be forecast using past increment data and projecting the present sizes (techniques called STAND PROJECTION). The past increment is determined from periodic measurement or, with trees having annual rings, from stem analysis, and is expressed in one of two ways:

The purpose of the distinction is to allow a choice in projecting a stand table. Suppose we have two trees with DBHOB as follows:
               TREE A         TREE B
     1972           30 cm          25 cm
     1977           38 cm          30 cm
then, the projected DBHOB increment of a 30 cm tree for the next 5 years (1977+) could be either: The decision as to which of the two expressions to use for projection purposes is a silvicultural one - it must be related to the condition of the stand and its growth behaviour.

When the trees in a stand are identified individually (i.e. numbered or tagged) it is a simple matter to determine the DBHOB increment of each tree or diameter class in the stand. A problem arises, however, when the trees are not identified. In these instances, the only data available are the two stand tables, one at the beginning and the other at the end of the increment period.

The standard or classical method of deriving increment data for stands in which the trees are not identified is rarely used in Australia.

The terms MAI, CAI and PAI (discussed with reference to the growth of individual trees), are also used with stands.

Increment in DBHOB

The relationships between tree diameter and diameter increment and between tree diameter at the beginning and end of a period are variously linear or curvilinear with correlations either positive or negative, the sign of the correlation depending on the growth habits of the species, stand structure and stand age. Linear relationships with a high positive correlation have been demonstrated for P. radiata at Kowen, but in native mixed species forests, e.g. Pine Creek State Forest (Coffs Harbour District), curvilinear relationships are frequently found.

A decrement in dbhob between one inventory and another is not unusual. It may be due to operator error in measurement at either measure but it can be real, e.g.

            	Natural                        	Artificial
            	Annual or periodic shedding    	Climbing by students
            	Abrasion by adjacent plants   	Abrasion by logging equipment
            	Wild fires
For species that shed their bark annually, it is wise to standardise the time (month) of measurement to eliminate variation due to this cause.

Increment in Height

Estimates of height increment are essential in silviculture and management, e.g.
  1. study of growth patterns of stands and effects of site on these patterns;
  2. study of stand response to treatment, e.g. fertilising, drainage, pruning;
  3. projection of diameter and height for estimates of future volume.
If the trees are identified individually, the height increment of each is determined directly. If they are not identified, the procedure is more complex. One method based on compiling stand height curves and applying Prodan's method for determining increment for the coming period is described by Carron (1968, p. 161).

Increment in volume

Volume increment is determined directly as the difference in the estimate of volume between any two assessments. It is essential that the method used to assess volume is the same at both assessments and that mortality and removals are allowed for in calculating the increment.


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 plot information is by far the most satisfactory on which to base yield tables.

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.

There are three main types of yield table, viz. normal, empirical and variable density.

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.

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:

Variable Density Yield Table

The limitations listed above for normal and empirical yield tabls 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:

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.

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:

  1. 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).
  2. Within site classes, stratify the forest into age and density sub-classes.
  3. 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.
  4. Stratify the data based on site class assigning a class to each plot.
  5. Check the stocking of each plot for abnormality and reject any atypical plot.
  6. 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.
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.Such an equation for natural slash pine in Florida accounted for 94% of the variation in yield (Bennett, 1966) . 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 ingrowth.

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 easlily 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 volumne 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:
  1. determining present stand condition (usually by inventory);
  2. 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:
  3. 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:
  1. 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.
  2. 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 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 volume and which can be projected readily and reliably.

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 outputf 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.


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Editor Cris Brack ©
Last Modified DateFri, 9 Feb 1996