Stand Growth ©

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.

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:

• Increment of the coming period, i.e. the increment put on trees of a certain size at the beginning of the period;
• Increment of the past period, i.e. the increment put on trees to make them a certain size at the end of the period.

               TREE A         TREE B
     1972           30 cm          25 cm
     1977           38 cm          30 cm

• 8 cm (38 - 30 cm) being the increment of a tree 30 cm in 1972 in the coming period of the past five years (1972-1977);
• 5 cm (30 - 25 cm) being the increment of a tree (30 cm in 1977) in the past period of five years.

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

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.

• acute physiological disturbance (disease, insect attack, etc.). Dying trees generally show a decrease in diameter approaching death;
• actual stem and bark shrinkage due to drought at the most recent measure;
• actual swelling of bark due to heavy rainfall at time of earlier measure;
• loss of bark due to natural or artificial causes:

            	Natural                        	Artificial
            	Annual or periodic shedding    	Climbing by students
            	Abrasion by adjacent plants   	Abrasion by logging equipment
            	Wild fires

Increment in Height

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.

Increment in volume

Yield

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.

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

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

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 of density other than normal or average.

Variable Density Yield Table

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

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.

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.

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. 

Forecasting using yield tables

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

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.

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 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

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

• 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.
• Smithers, L. 1949. A simplification of the continuous inventory method of calculating diameter growth. Can. Dom. For. Serv. Leaflet No. 31.
• Prodan, M. 1947. Der Starkezuwachs in Plenterbestanden Schweiz. Z.f.Forsstw., 98.
• 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.
• Lewis, N.B., Keeves, A. and Leech, J.W. (1976). Yield regulation in South Australia Pinus radiata plantations. Woods and Forests Dept., South Australia. Bull 23.
• 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.

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