Evaluating Douglas-fir and western hemlock volume growth in response to thinning and fertilisation

Data

The thinning treatments ranged from controls (0% removal) up to 50% removal. All but two of the thinned plots (one for each species) were thinned to maintain the thinning ratio (mean diameter of removed stems over the mean diameter of stems before thinning) at 0.8 – 0.9 (Darling and Omule 1989; Stone 1994). The other two thinned plots were thinned to 746 stems per hectare (Stone 1994). Fertilisation was applied at rates of 225, 450, 675, or 900 kg/ha with prilled urea (46% nitrogen, Darling and Omule 1989). The application was done manually except for 43 Douglas-fir plots which were fertilised aerially.

The total age (yrs), total standing volume (m³/ha), and volume (m³/ha) removed through thinning were available for each species in the plot at each measurement. Only trees that had a diameter at breast height of 5.0 cm or greater were measured. Since only pure Douglas-fir and western hemlock stands were of interest, a plot was classified as being pure Douglas-fir (pure western hemlock) if it contained 80% Douglas-fir (western hemlock) by volume, averaged over all measurements. However, regardless of the species composition, the total volume of all species in the plot was analyzed. The site index (m at breast height age 50) was estimated from the height and age of the target species using the Bruce (1981) or Wiley (1978) height-age models for Douglas-fir and western hemlock, respectively.

Modelling

where SI = site index (m at breast height age 50), b_ij, i = 1, 2, j = 0, 1, . . ., 6 are model parameters, T is thinning intensity, F is fertilisation intensity, and ϵ is a random error term with the usual assumption that the ϵ are identically and independently distributed as N(0, σ²). Thinning intensity (T) is the volume (m³/ha) removed divided by the time (years) since the thinning. Fertilisation intensity (F) is the amount of fertiliser applied (kg/ha) divided by the time (years) since fertilisation.

Three significant modifications to Nishizono’s (2010) model and analysis were made: modifying the definition of thinning intensity, adding fertilisation, and analyzing the models as marginal or population average models (Diggle et al. 2002). These modifications are discussed more extensively in the Discussion section.

Mortality is not explicitly modelled. The dependent variable, standing live volume (V m³/ha), is net of mortality. Therefore, the model implicitly incorporates endemic mortality. If catastrophic mortality events such as massive windthrow or insect attack occur, then the models cannot be expected to give reasonable volume predictions. Since only endemic mortality was included in the model, data for which there was evidence of catastrophic volume loss was removed from the analysis data set.

Maximum likelihood estimation (procedure NLMIXED in SAS, SAS Institute Inc. 2004) was used to fit the model to the data. The variance was modelled as a power of the time since the last measurement (Pinheiro and Bates 2000), i.e., Var(ϵ_i) = σ² (t_i – t_i-1)^2δ. Serial correlation should not be an issue since volume is being projected for only one measurement interval. For each measurement in each plot, the standing volume (V_i m³/ha) was the dependent variable and the total age (t_i years) and the standing volume (V_i-1) and total age (t_i-1) from the previous measurement were independent variables in the fitting process, as well as the other variables in Equation 4. Consequently, the volume from the first observation for each plot was not used as a dependent variable since there was not a previous measurement to provide a value for V_i-1 and t_i-1. For all plots except one Douglas-fir plot, the thinning was done immediately after the plot was established. Therefore, the post-thinning volume (as opposed to the pre-thinned volume) was considered to be the observation for that year except for the one plot where the thinning was not done at plot establishment. For this plot, the pre-thinned volume was used as V_i for that year. The post-thinning volume was obtained by subtracting the volume removed in the thinning from the pre-thinned volume and it was used as V_i-1 for the next observation. Each species was analyzed independently from the other. Normal quantile-quantile (QQ) plots of the standardized residuals were made to check for normality and plots of the standardized residuals versus the fitted values and the years since the previous measurement (t_i – t_i-1) were made to check that the residuals were homoscedastic (Sen and Srivistava 1990).

Simulation

Modelling

Simulation

The results of the simulations for selected scenarios are discussed in the following section.

More productive sites (higher site index) have increased growth and yield

Site index is a measure of site productivity; better sites produce a greater volume of timber and the trees on the site are faster growing (Carmean 1975). Parameter b₀ increases and parameter b₂ decreases with site index for both species. As gleaned from the value of parameter b₀, the potential yield (asymptote) increases as site index increases. A graphical analysis (Figure 1) shows that growth also increases as site index increases even though parameter b₂ decreases. The models behave as expected with respect to site index.

The response to thinning depends on the thinning intensity

On a per tree basis, a heavy thinning will reduce competition more than a lighter thinning and hence the growth response is expected to increase as the thinning intensity increases (Pukkala et al. 2002). However, on a stand level the response is less clear because there are fewer trees to contribute to stand growth. Cañellas et al. (2004) found that Quercus pyrenaica growth increased with increasing thinning intensity but declined with the heaviest thinning. D’Amato et al. (2011) did not find any stand-level growth response to thinning of Picea glauca stands. For Pinus sylvestris stands, stand volume increment decreased as thinning intensity increased and the difference increased over time (del Río et al. 2008). To evaluate the fitted models, volume was plotted against age at 4 levels of thinning that occurred at age 30 assuming a site of medium quality (site index = 29 m) for both species (Figure 2). In absolute terms, the volume in the thinned stands did not approach the volume in the unthinned stands. That is, the volume lost in the thinning was not recovered through increased growth of the trees left on the site. However, on a relative basis, the thinned stands had proportionally more volume at the end of the 100 year simulation than was removed. That is, for Douglas fir, the volume lost when compared to the unthinned stands was 4%, 12%, and 23% for the 20%, 35%, and 50% removals, respectively. The volume lost for western hemlock was 9%, 19%, and 32% for the same levels of removal.

The effect of fertilisation on tree growth is relatively short-lived

Nitrogen (N) is the most limiting nutrient in Douglas-fir and western hemlock sites (Bennett et al. 2003; Chappell et al. 1991). Consequently, fertilisation with N is more common than fertilising with other nutrients. The period of time for which tree growth is elevated after fertilisation is variable but relatively short, e.g. 5 – 10 years (Bennett et al. 2003; Binkley and Reid 1985), although exceptions can be found (Binkley and Reid 1985). When fertiliser is applied at the time of thinning the maximum response is observed about 5 years after treatment (Snowdon 2002). It has been hypothesized that the length of time that a fertilisation effect is observed depends on the amount of fertilisation applied in relation to the amount of the nutrient on site before fertilisation (Miller 1981). These hypotheses can be evaluated with the models. For each species, sites at three levels of site index were fertilised with 450 kg/ha of N fertiliser at age 50. This level of fertiliser is generally the maximum that is economically feasible (Barclay and Brix 1985). The percent change in growth as compared to an unfertilised site with the same site index was plotted (part a of Figure 3 is for Douglas-fir; part b is for western hemlock).

Interaction between fertilisation and thinning

It may be of interest to determine whether the effects of thinning and fertilisation are additive or if there is an interaction between the two treatments (Miller et al. 1979; Zhang et al. 2005). This can be investigated with the models. The models for both Douglas-fir and western hemlock have significant interaction terms (parameters b₀₄ and b₂₄ for Douglas-fir, parameter b₀₄ only for western hemlock, Table 3). In a much smaller experiment, McWilliams and Thérien (1996) did not find any interaction between thinning and fertilisation in Douglas-fir. Simulation was used to investigate how this interaction term affects volume. Three site index levels were assumed with corresponding volumes at age 20 (Table 2) for each species. Thinning and fertilisation treatments (35% removal with 450 kg/ha urea fertiliser) were applied at age 30. The same scenario was applied with the interaction term removed from the model. The difference in volume is then due to the thinning/fertilisation interaction. The volume-age trajectories are plotted in Figure 4, parts a (Douglas-fir) and b (western hemlock). The effect of the interaction between fertilisation and thinning is slight for Douglas-fir (approximately 20 – 25 m³/ha at age 100 for low and medium sites, practically no difference for high sites) and virtually non-existent for western hemlock. Interestingly, though, the very slight effect of the thinning × fertilisation interaction for western hemlock is negative which is due to the negative estimated value of parameter b₀₄ in Equation 4. The lack of a significant interaction response for western hemlock (even though the parameter for this term is statistically significant) can be attributed to the small estimated value for parameter b₀₄ in Equation 4. When this parameter is multiplied by the thinning and fertilisation effects (T and F, respectively, in Equation 4), the term does not have a large effect on the asymptote, particularly as the thinning and fertilisation effects diminish over time.

Comparison to published yield tables

In this section, the models developed here (Equations 3/4 with appropriate parameters from Table 3) are compared to other published yield tables. For western hemlock, the comparison is made to yield tables published by Barnes (1962) and Taylor (1934). These tables are for fully stocked stands with a minimum diameter limit of 1.5 cm, making them approximately the same as the EP703 hemlock plots. However, both of these yield tables are for mixed species stands, and no thinning or fertilisation information is available. Barnes (1962) published yield tables for Oregon/Washington, Alaska, and British Columbia; the British Columbia tables were used in this comparison. At the same starting conditions at age 20, both the Taylor and Barnes yield curves are approximately the same for site index 25 and 29 stands. The western hemlock model predicts greater yields than these two yield tables at site index 25 and 29, but at site index 29 the yields are similar below age 60. At site index 34, the yields from Equations 3/4 and from Barnes’ yield table are almost identical (Taylor did not publish yield tables for site indexes greater than 32).

The fitted Douglas-fir model was compared graphically to published yield tables calculated using the Douglas-fir simulator (DFSIM) (Curtis et al. 1982). The DFSIM is a whole-stand growth and yield model developed specifically for Douglas-fir in the Pacific Northwest region of North America (Curtis et al. 1981). It is able to simulate natural and planted stands with pre-commercial and commercial thinning, as well as fertilisation. Four stand types were compared (natural, planted, planted and commercially thinned, natural with pre-commercial thinning and fertilisation) at three levels of site index (25.9, 32.0, and 38.1). These correspond to Tables 1, 2, 7, and 11, parts A, B, and C in Curtis et al. (1982). The simulations started at age 30. The starting volumes for the fitted model were taken from the corresponding tables in Curtis et al. (1982). A utilisation limit of 4 cm (1.6 inches) was used in the comparison when more than one utilisation limit was published. The commercial thinning and fertilisation treatments were applied at the same rate and age as in the published tables (Curtis et al. 1982). The thinning removed approximately 30% of the volume and the fertilisation was done with 225 kg/ha of N. The pre-commercial thinning in the fourth scenario was not modelled because the thinning was done too early for the fitted model to have any validity.

Figure 5 parts a – d show the results of the comparison. For natural stands (part a), there is good correspondence between the two models for the first 20 to 30 years after which the fitted model estimates higher volumes than those estimated by the DFSIM. The deviations between the two models increase with increasing site index. Curtis et al. (1981) had very little data for total ages greater than 60 years even in untreated natural stands. The plantation yield curves (part b) show similar yield projections over the longer term, but again the DFSIM yields are extrapolations beyond about total age 45 (Curtis et al. 1981). Unlike the natural stand yield curves, the differences between the two models decreases as site index increases. Part c shows that use of the DFSIM and Equations 3/4 lead to dissimilar volume predictions for thinning regimes. Both before and after thinning, volume growth rates are greater using the DFSIM model than for Equations 3/4 at all levels of site index, Figure 5c. As noted previously, a slight bias may be present in Equations 3/4 for thinned stands, but not to the extent that it would explain the differences in yield indicated in part c of Figure 5. The two models may be projecting different populations as there are no data for trees over age 45 in the DFSIM development data set. The fertilisation scenario (part d) shows good agreement between the two models, particularly at higher site indexes. The models developed here do not show as much fertiliser response as the DFSIM at the lower site index level.