Tree survival and maximum density of planted forests – Observations from South African spacing studies

The observations

Direct assessment of the potential density, and of the development towards that elusive state, requires densely stocked unmanaged and sufficiently large field plots that are enumerated regularly during long observation periods. A rare example of such an elaborate experiment is the Correlated Curve Trend (CCT) spacing study established by O’Connor ([1935]) in South Africa. The CCT experiment is a classic spacing trial designed to predict yields from plantations of various species of pine and eucalyptus for a wide range of densities, varying between extremely dense (2965 stems per ha) and free growth (124 stems per ha). Additional file 1: Table S1 shows details of the eight experiments used in this paper, and a map with their locations in South Africa.

The original objective of the CCT study was to predict yields from plantations of various species of pine and eucalypt for a wide range of planting densities. Most of the experiments were established between 1936 and 1938 and several detailed descriptions of the CCT design were published during the past 70 years (see for example Craib [1939]; Marsh [1957]; O’Connor [1960]; Burgers [1976]; Van Laar [1982]; Gadow [1987]; Bredenkamp et al. [2000]). Some relevant details of four spacing trials each for Pinus patula and P. elliotti are presented in Additional file 1: Table S1. The altitudes range from 53 m.a.s.l. (Kwambonambi) to 1400 m.a.s.l. (Nelshoogte), the mean annual temperatures from 15.9°C (Weza) to 21.8°C (Dukuduku) and the mean annual precipitation from 830 mm (Weza) to 1463mm (MacMac).

Soil depths and geology were also assessed in each of the eight experiments. With a depth of 120-150 cm the soils are deep in all experiments. Humic soils on granite are encountered in the MacMac and Nelshoogte experiments, sandy soils in Dukuduku and Kwambonambi and red apedal dystrophic soils in Entabeni on basalt. The mean height of dominant trees at age 20 (SI20) is lowest for P. elliottii at Dukuduku (17.0 m) and highest for P. patula at MacMac (24.3 m). Further details are presented in Additional file 1: Table S1.

The typical CCT experiment consists of 18 plots, covering 0.081 ha each. Nine of the 18 plots were left unthinned, the other nine were subjected to various thinning regimes. The treatment details for plots 1-8, and a map of the CCT spacing study Nelshoogte, are presented in Additional file 2: Table S2.

The unthinned experiment, known as the Basic Series, provides information about the growth of unthinned stands for a wide of range of planting densities. In the other, known as the Thinned Series, the response to various thinning regimes may be assessed. Eight nominal stand densities, ranging from 124 to 2965 stems per hectare, were established in plots 1 to 8 of the basic series. In order to avoid suppression by competing herbaceous flora, all plots were initially planted at 2965 stems per hectare and then thinned ‘in advance of competition’ until the nominal stocking was achieved (for further details of the trial design refer to Bredenkamp [1984] and Gadow and Bredenkamp [1992], p. 55 et sqq.). In this study only the results from several basic series are used.

Data from the CCT experiments are suitable for analysing tree survival in response to forest density and tree age. Additional climate and soil data have become available more recently, allowing a more detailed analysis of environmental effects.

Methods to describe maximum density

This section introduces three specific approaches for analyzing maximum density and tree survival. We define the rate of survival as the ratio $\frac{N_2}{N_1}$ while mortality may be expressed by $\frac{N_1-N_2}{N_1}$.

Maximum density

Limiting line and site index

The limiting line was fitted to the CCT experiments listed in Additional file 1: Table S1 and the parameter estimates for the eight datasets are listed in Additional file 3: Table S3. Not surprisingly, the value of a₁ deviates considerably from the constant -1.605 proposed by Reineke ([1933]). Previous studies have shown that the exponent may assume a wide range of values, depending on tree species and site conditions (Gadow [1986]). The relationship between the intercept (coefficient a₀) and the site index is shown in the graph on the right of Additional file 3: Table S3.

The value of the intercept, which is the most important indicator of maximum density, is increasing with increasing site index. This is apparent in both species. The relationships between site index and a0 are:

$\mathit{Pinus}\mathit{elliottii}:{\mathrm{a}}_0=‐464924+64472*\mathrm{S}\mathrm{I}20\left({\mathrm{R}}^2=0.79,\mathrm{n}=4\right)$

(8)

$\mathit{Pinus}\mathit{patula}:{\mathrm{a}}_0=‐2542807+142609*\mathrm{S}\mathrm{I}20\left({\mathrm{R}}^2=0.88,\mathrm{n}=4\right)$

(9)

The results of relationships (8), (9) are based on four experiments for each of the two species. The database is limited. Nevertheless, to our knowledge, this is the first time that an estimate of maximum density could be related to site index. The range of site indices (17-24 m and 20-24 m) is relatively broad and covers a wide range of the growing sites where the two species are found in South Africa. The dramatic effect of the environment on the maximum density of the same species can be seen in Figure 1 which shows the limiting line fitted to Pinus elliottii MacMac using the 0.975 percentile data.

The limiting lines for the Pinus elliottii experiments in MacMac and Kwambonambi are also shown in Figure 1, with the log transformed variables. The lines are almost parallel and the difference between the intercepts in terms of maximum surviving trees for a given mean diameter is considerable. For example, for a quadratic mean dbh of 30 cm the maximum number of live trees is estimated at N_max = 781116.5 ⋅ 30^− 2.09 = 639 per ha in Kwambonambi and at N_max = 1063674.8 ⋅ 30^− 2.04 = 1032 in MacMac. Kwambonambi supports only 67 percent of the MacMac maximum and the difference between the two sites, given a quadratic mean dbh of 30cm, is 1032-639 = 393 P. elliottii trees per ha. The growing conditions are very different. Considerably more trees are able to survive on the cool mountain site at MacMac than on the warm subtropical sandy site at Kwambonambi.

Nilson’s sparsity

The parameters of Equation 3 can be estimated using data from fully stocked, unthinned trials, again using specific percentile values and the R library quantreg. The relations are presented in Figure 2 and the corresponding equations are:

$\mathrm{Lmin}=0.4044+\mathrm{D}*0.0870\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{all}\mathit{Pinus}\mathit{elliottii}\mathrm{experiments}$

(10)

$\mathrm{Lmin}=0.4178+\mathrm{D}*0.0980\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{all}\mathit{Pinus}\mathit{patula}\mathrm{experiments}$

(11)

The four coefficients are highly significant, and surprisingly similar. The relationship between the minimum average spacing and average tree size is assumed to be linear, at least up to the point when the tree size does not increase sufficiently, but mortality continues. It appears that, after reaching an average dbh of about 60 cm, the trees start dying, not as a result of competition-induced self-thinning, but possibly because of other factors, such as failing defence mechanisms and reduced ability to survive pathogen attacks.

Shvidenko et al. ([2006]) describe the development of the number of trees per ha and the average tree diameter for fully stocked Pinus sylvestris forests in the forest tundra and northern taiga ecoregions in the European part of Russia. These data show a linear relation between L and D up to the age of 200 years. For the CCT data of the two pine species, the relationships appears to be linear up to a mean diameter of about 60 cm.

Tree survival

Survival functions (Equation 7) were fitted to different planting densities of the two pine species in each of the four CCT experiments listed in Additional file 3: Table S3. Figure 3 presents examples of the fitted functions involving Pinus elliotti with four different planting densities of the CCT experiments MacMac and Kwambonambi.

The parameter estimates of the 32 survival functions are presented in Additional file 4: Table S4. The scale (b) and shape (c) parameters of the Weibull distribution are linear functions of the number of planted trees per ha and may be estimated using the following linear models:

$\ln \left(\mathrm{c}\right)=\mathrm{AC}+\mathrm{B}\mathrm{C}*\ln \left(\mathrm{number}\mathrm{of}\mathrm{planted}\mathrm{trees}\mathrm{per}\mathrm{ha}\right)$

(12)

$\ln \left(\mathrm{b}\right)=\mathrm{AB}+\mathrm{B}\mathrm{B}*\ln \left(\mathrm{number}\mathrm{of}\mathrm{planted}\mathrm{trees}\mathrm{per}\mathrm{ha}\right)$

(13)

The four parameters of these two equations are listed for each of the 8 experiments in the last two columns of Additional file 4: Table S4. These results show that the Weibull function is suitable for estimating individual tree survival for both species and planting densities between 2965 and 741 trees per ha.

This relationship is potentially useful in that it permits estimating the lifetime distribution for a range of planting densities. The probability of tree survival and tree mortality is affected by the planting espacement and as expected, the probability of tree survival is increasing with decreasing number of planted trees per unit area. The peaks of tree mortality occur earlier, and this effect is longer lasting, in the higher planting densities. These characteristic differences are notable for both species and the entire range of ages. It was also possible to relate the Weibull parameters to site index using the following linear equations with both Pinus patula and P. elliottii data combined:

$\mathrm{c}=‐1.611+0.2336\left(\mathrm{S}\mathrm{I}20\right)$

(14)

$\mathrm{b}=110.46-2.813\left(\mathrm{S}\mathrm{I}20\right)$

(15)

The slope coefficients were significant in both equations, but the intercept was only significant in equation (15). Interestingly, the response of the two species does not appear to be different. However, it must be pointed out again that the database is too limited to draw general conclusions about the relationship between site index and Weibull parameters.

Nilson’s sparsity

Nilson ([2006]; see also Hilmi [1957]) argues that the most simple and logical relation is expected between variables of the same dimension, which is not the case in the Reineke model (Equation 1). For this reason, and because of its simpler form, Equation (3) was thought to be preferable when compared with Equation (1). A general discussion on the assumption of linearity of Nilson’s sparsity is not possible, because the CCT material does not cover the seedling stage and stands older than about 60 years. The tables published by Shvidenko et al. ([2006]) for Russian Pinus sylvestris forests on site quality II show that Nilson’s sparsity is linear up to the age of 180 years. However, the available material shows that the assumption of linearity cannot be confirmed for the Pinus patula CCT studies. Considering the culmination of diameter increment of Russian P. sylvestris and the much faster growing P. patula in South Africa one might expect that a deviation from linearity, should it signify a general, species independent pattern, could be induced at much higher ages in P. sylvestris. It is known that stem diameter scales well with crown extension and thus light competition and that these relations are very species specific, at least for conifers, which might affect the relationship.

Development of density over age

The maximum density of a planted forest is usually unknown because of the high cost to obtain empirical observations that permit a credible analysis of that elusive natural phenomenon. In addition to the observations about maximum density, the CCT experiments provide information about the development of forest density. The development of relative spacing, the average distance between the trees divided by the dominant height, is shown in Figure 4.

The minimum relative spacing (RS) in the Pinus elliottii experiment MacMac is 0.0752, observed at age 24. The minimum RS in the P. patula experiment MacMac is 0.095, observed at age 18. The maximum basal areas are 56.6 m²/ha at age 28 for P. patula MacMac 83.6 m²/ha at age 24 for P. elliottii MacMac.

The nelder design

Maintaining a series of large field plots over long periods of time is expensive. One attempt to reduce such high costs is the design proposed by Nelder ([1962]). The compact Nelder design consists of a number of spokes of an imaginary wheel with trees planted at different radial distances, at the intersection of circular arcs and linear spokes (Barry [2013]). Parrot et al. ([2012]) discuss various aspects of the Nelder design which allows the effects of different planting densities to be examined in a single experiment. The experimental unit in a Nelder design is the individual tree and research usually involves to relating the available growing area of each tree to growth rates or tree architecture (Gaul and Stüber [1996]; Mabvurira and Miina [2002]; Aphalo and Rikala [2006]). According to Affleck ([2001]) the analysis of Nelder experiments is problematic because the compact arrangement of trees may result in significant correlations among neighbouring variables. Hall ([1994]) notes that seedling survival is a primary concern when establishing Nelder plantings because a major drawback of the Nelder design is the sensitivity of the analysis to tree mortality (see also Stape and Binkley [2010]).

The compact Nelder design, although having a cost advantage, only presents observations about the relationship between available growing space, tree growth and tree architecture. The Nelder wheel does not provide information about maximum density and the analysis is usually limited to the juvenile stage (Gaul and Stüber [1996]). As mentioned before, data about the maximum density of planted forests are very scarce because the cost of maintaining a series of unthinned, densely-stocked and sufficiently large field plots over long periods of time may be exorbitant. The CCT experiments represents, therefore, a valuable source of information for the analysis of maximum density and tree survival. Surprisingly few studies have used these unique datasets.

Risk and uncertainty

This contribution is part of a thematic series on risk and uncertainty. It is therefore appropriate to relate the results to the overall topic. The scientific analysis of risk and uncertainty in the context of natural hazards had its beginning at the turn of the 18^th century, when catastrophic events were no longer considered simple acts of destiny, but as relations of causes and effects (Weiss [2001]). Plantation forest ecosystems have become an important strategic resource in a number of countries. Many industrial plantations are re-established after clearfelling and never thinned, especially those grown on short rotations and for maximum biomass, and their development resembles that of the unthinned CCT series. This study, therefore, contributes to a better understanding of tree survival and maximum density which are the key factors required for estimating risk and uncertainty. The risk of tree mortality is not constant, but varies with tree species, planting density, tree age and growing site. For estimating that risk, therefore, continuous long-term observation on different sites and with varying planting densities, as provided by the unthinned CCT series, are essential. Because of the particular risks involved in overaged plantations, such observational studies should be maintained as long as possible, preferably beyond the age of natural tree longevity.