• formind2.0;
  • logging scenarios;
  • plant functional types;
  • simulation;
  • tropical forest


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  • 1
     Reliable data on the growth and yield of logged-over forest, to determine sustainable cutting cycles, are widely missing for the tropics.
  • 2
     We used the process-based model formind2.0 to analyse the growth and yield of logged-over forest in Venezuela under different logging scenarios over a period of 240 years, and compared results with unlogged stands. The performance of the model was evaluated with a detailed stability and sensitivity analysis.
  • 3
     In the absence of further logging, the logged-over stand approached the stand structure of mature forest in terms of bole volume and basal area after about 50–100 years.
  • 4
     Thirty-year cutting cycles with conventional logging methods and net extraction volumes of 45 and 60 m3 ha−1 cycle−1 did not provide sustainable yields under either of two minimum felling diameters (35 and 50 cm) that were applied. Only the 60-year cutting cycle provided sustainable yields under conventional and reduced-impact logging, with the different minimum felling diameters and a range of net volumes extracted (30–60 m3 ha−1 cycle−1).
  • 5
     With the longest cutting cycle (60 years), bole volume recovered to levels similar to the mature unlogged stand, but the species composition was very different.
  • 6
     Scenarios with reduced-impact logging provided a significantly higher timber volume than under conventional logging. The conservation of forest resources will only be possible with long cutting cycles (at least 60 years) in combination with reduced-impact logging.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

The determination of sustainable cutting cycles and annual allowable cuts is crucial to forestalling further degradation of tropical timber resources. In Latin America, where extensive areas of natural forest have been granted to concession logging in the last few years (FAO 1997), little is known about the long-term dynamics of logged-over stands. The silvicultural system CELOS in Surinam is the only experiment to date giving a fairly comprehensive idea about the management tools needed to sustain timber production in natural forests (de Graaf 1986). However, the suggested cutting cycle of 20 years with a restricted net removal of 20 m3 ha−1 in the CELOS system is based on intensive post-logging treatments. Another long-term study on growth and yield in logged-over and untreated plots in the Brazilian Amazon revealed a low volume increment of timber species, indicating that short cutting cycles are unlikely to be sustainable (Silva et al. 1995, 1996).

Numerous forest models have been developed to bridge the gap between generally short-term empirical data on forest dynamics and the need for reliable long-term yield prediction. Vanclay (1989, 1994), for example, simulated logged-over forest in North Queensland, Australia, with stand models based on tree density and basal area. Kürpick, Kürpick & Huth (1997) used the gap model formal to simulate the stand development of logged-over Malayan dipterocarp forest. Process-based models, simulating physiological processes under changing environmental conditions, are another approach to forest modelling (Landsberg & Gower 1997). The formix model and its successor formix3, which were successfully tested in Malayan dipterocarp and peat swamp forest, respectively (Bossel & Krieger 1991; Huth, Hahn-Schilling & Bossel 1994; Huth, Ditzer & Bossel 1998; Ditzer et al. 2000), combine the advantages of conventional forestry models with process-based models. formix was recently developed into the individual-orientated formind2.0 model, which provides more details about forest dynamics compared with its predecessor (Köhler & Huth 1998; Köhler et al. 2001).

In this study we tested whether prescribed cutting cycles at intervals of 30 years in Venezuela provide sustainable timber yields under the currently uncontrolled logging methods, by modelling a logged-over stand with formind2.0. We also tested whether controlled logging would allow cutting cycles to be shortened and still allow sustainable timber yields. Finally, we simulated the impact of different cutting cycles, logging methods and extraction volumes on the ingrowth and mortality of commercial species, and species composition. The results were compared with stands that have either never been logged or logged only once.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

Study site

The 7000-ha ‘Estación experimental’ of the Universidad de Los Andes is part of the ‘Reserva Forestal de Caparo’ located in the western Venezuelan plains (7°30′ N, 70°45′ W; elevation 100 m). The mean annual rainfall is 1750 mm, with a pronounced dry season from December to March (monthly precipitation < 50 mm). The average annual temperature is 24·6 °C. The soils are of alluvial origin and relatively fertile compared with other neotropical lowland areas (Hase & Fölster 1982). Intensive sedimentation by river flooding has resulted in a fine-scaled micro-relief, ranging from sandy levee sites to clay-rich depressions. Inundation of depressions lasts up to 9 months, depending on soil texture, relief and ground water level (Franco 1979). Levee sites, in contrast, are well-drained throughout the year.

The high forest of Caparo, naturally distributed on well-drained and poorly drained sites up to an inundation period of 6 months, is classified as ‘moist semi-deciduous’ (Lamprecht 1989). On both sites, the palm Attalea maracaibensis (Mart.) Burret (Arecaceae) and large tree Bombacopsis quinata (Jacq.) Dugand (Bombacaceae) are the predominant components of the forest in terms of basal area (Franco 1979; Kammesheidt 1994). A total of 53 tree and palm species ≥ 10 cm d.b.h. has been recorded, and both the well-drained and poorly drained sites are similar in stand structure and species composition (Kammesheidt 1994, unpublished data). The number of deciduous trees increases from well-drained to poorly drained sites (Franco 1979).

Logging started in the early 1970s. In the beginning, only B. quinata, Swietenia macrophylla King and Cedrela odorata L. (both Meliaceae) and Cordia thaisiana Agostini (Boraginaceae) were logged. Currently, more than 20 species are logged (L. Lugo, personal communication). The shift from few to many merchantable species and increasingly mechanized logging has resulted in an increase in the level of damage on residual stands compared with stands logged in the 1970s. Although logging is carried out by a local sawmill owner under the supervision of university staff, no efforts have apparently been made to reduce the impact of logging on residual stands. About one-third of the individual logging unit (100 ha) is actually affected by logging; in this third, on average 10 trees with a standing bole volume of 66·5 m3 ha−1 are removed (Kammesheidt 1998). No post-harvest treatments are carried out.

Data set

The data base for modelling was an inventory of logged (5, 8 and 19 years after timber harvest) and unlogged stands (hereafter mature forest; MF) made in late 1991. The actual logged area was delimited (27–37 ha per 100 ha logging unit). Thereafter, 30 plots of 400 m2 (1·2 ha in each of the logged stands) were put at systematic distances along transect lines using tape and compass. In MF (total area approximately 30 ha), 25 plots were established in the same way. In all stands, a roughly equal number of plots was laid out on well-drained and poorly drained sites, respectively. Trees and palms ≥ 10 cm d.b.h. were measured; seedlings and saplings were sampled in subplots nested in the major sampling unit. Results refer to the stand 5 years after logging (LG5) because it represents a damage level, judged by the proportion of landings in the overall area logged, between those of the other two logged stands (Kammesheidt 1994).

Species grouping

Shrub, tree and palm species (total number 127 spp., species list available online at were assigned to 12 different plant functional types, based on successional status and maximum height at maturity (Table 1), following an approach developed for rain forest in Malaysia (Köhler, Ditzer & Huth 2000). The successional status of species was determined by their gap association at the juvenile stage, spatial pattern and ability/inability to persist in closed mature forest as adult individuals (Kammesheidt 2000, unpublished data). Similar functional groups are defined by Swaine & Whitmore (1988), Manokaran & Swaine (1994) and Thomas & Bazzaz (1999).

Table 1.  Autecological characteristics of plant functional types (PFT) in the Caparo forest, Venezuela. Height and d.b.h. range at maturity. Height group (HG) and successional status (SS). Total number of species (N) in the different PFT. Relative abundance of trees (10 cm d.b.h.) in the mature forest (MF) and the stand 5 years after logging (LG5)
Plant functional typeHeight (m)d.b.h. (cm)PFT indexHGSSNMF (%)LG5 (%)
Mid-successional shrub spp. 1–10 2–10 11218
Late successional shrub spp. 1–10 2–10 213 7
Small early successional spp.10–1510–25 321 3 2·9
Small mid-successional spp.10–1510–25 42211 3·7 2·7
Small late successional spp.10–1510–25 52317 0·3 4·6
Medium-sized early successional spp.15–3020–35 631 2 1·013·1
Medium-sized mid-successional spp.15–3020–70 73211 6·0 9·9
Medium-sized late successional spp.15–3020–70 8332617·414·2
Large mid-successional spp.30–4060–150 9421614·9 8·3
Large late successional spp.30–4060–15010431215·6 9·1
Small palm sp. 1–10 5–101154 1
Medium-sized palm spp.15–3010–501264 341·035·1

Description of the model

formind2.0 is an individual-orientated forest growth model (Köhler & Huth 1998; Köhler et al. 2001) to simulate stand development under certain scenarios, for example different cutting cycles. The model includes tree growth, competition, mortality and regeneration. The main processes including improvements on former versions are described below; functional relationships are found in Table 2.

Table 2.  Description of parameters used in the model, including functional relationships
Environmental parameters
kLight extinction coefficient
I0Light intensity above canopy
SDDay length
SSLength of wet/dry season
Establishment parameters
DSInitial diameter of seedlings
ISsMinimal light intensity for germination
NSsIngrowth rate of seeds into seed pool
Mortality parameters
MBBasic mortality rate
MSMortality rate of seeds
MDjSize-dependent mortality rate (MD = MD0 – MD0/MD1 × d)
WProbability of a dying tree to fall
Tree physiognomic parameters
DMMaximum diameter
cPCrown length fraction
τFraction of stem wood biomass to total above-ground biomass
h0h and h1hHeight =f(diameter) (h = d/(1/h0h + d/h1h))
γjForm factor =f(diameter) (γ = γ0 × exp(γ1 × dγ2))
fjCrown diameter =f(diameter) (dc = (f0 + f1 × df2) × d)
ljLeaf area =f(diameter) (l = l1 × d + l2 × d2 + l3 × d3)
LAIMMaximal leaf area index of single tree
Biomass production parameters
PMPhotosynthetic capacity in light response curve
αPhotosynthetic efficiency in light response curve
ρStem wood density
r0l and r1lRespiration =f(biomass) (Rm(Bi) = r0l × B2/3 + r1l × Bι)
RGSpecific growth respiration rate
mLeaf transmittance
gConversation factor gCO2 to godm
Spatial structure

The model describes tree competition in patches. These patches have sizes typical of natural gaps created by the fall of large trees (= 400 m2; van der Meer & Bongers 1996). The model follows the gap approach (Botkin, Janak & Wallis 1972; Botkin 1993; Shugart 1998) and is therefore spatially non-explicit. Tree positions of falling trees are determined randomly within single patches. In contrast to most gap models, formind2.0 simulates a shifting stand mosaic. Thus, several contiguous patches (5 × 5 patches ha−1, each 20 × 20 m2 in size) are simulated simultaneously (Smith & Urban 1988; Urban et al. 1991).

Tree growth and competition

Within a single patch, the model calculates stand development based on cohorts of trees belonging to the same plant functional type. A cohort i is characterized by the number of trees Ni and by the size of one representative tree. Using allometric relationships, the size of a tree can be expressed in terms of its above-ground biomass Bi, height hi or diameter at breast height di. A form factor is applied that takes the difference from an idealistic cylindrical stem into account. Tree height is calculated from diameter. The crown projection area f is calculated from the proportionality of stem diameter to crown diameter dc (Rollet 1978; Poker 1993). Crown length is proportional to tree height (Burgess 1961; Poker 1993), using a constant factor. Leaf area l is a function of diameter but is corrected to avoid unrealistically high values of the leaf area index, LAI = f/l, which should not exceed a certain value, LAIM (Ashton 1978). The bole volume is calculated by the stem wood fraction τ, wood density ρs, and the geometrical relation of a truncated cone from biomass Bi. Using these allometric relationships, the distribution of individual tree crowns and their leaf area in the canopy are calculated in horizontal canopy layers of 0·5 m.

The growth of an individual tree is based on its carbon balance. Calculations include photoproduction of the trees and assimilate losses due to respiration, litter-fall and fine root decay. Within a patch, the light attenuation Ii downwards in the canopy is calculated from light intensity above the canopy I0 and the light extinction coefficient k with respect to the absorption of tree crowns. The dependence of specific photosynthetic productivity Pi on irradiance is modelled using a Michaelis–Menten type light response curve. Photoproduction P̃i is calculated from the tree’s leaf area and its specific productivity Pi by integrating down the canopy of the tree in question (Monsi & Saeki 1953). Differences between wet and dry season y are considered in terms of different light intensity I0y, the different length of daily photo-active period SDy, and the different length of seasons SSy. We assume an increasing limiting effect of water transport deficiencies with increasing tree height. Actual productivity is calculated by applying a size-dependent limitation factor q(di) according to the equation q(di) = 1 − (1 − qDM) × ([di/DM])2, where DM is the maximum diameter of trees and qDM is the limitation factor at maximum tree height (corresponding to the ageing factor cs of Landsberg, & Waring 1997). With the condition of no tree growth at maximum diameter, qDM can be calculated from the parameter set. Assimilate losses are estimated in relation to tree biomass (Kira 1978; Yoda 1983). Losses are composed of root decay, litter-fall and respiration of tree organs and leaves. We distinguish between a biomass-dependent maintenance respiration Rm(B) and growth respiration RG (Ditzer et al. 2000). This leads to our main growth equation:

  • image(1)

Water balance is not included in the model. The calculation of tree growth is performed in annual time steps.

Competition is modelled in terms of competition for light as described above, and competition for space as described below concerning mortality.


Mortality is modelled on an annual basis at a basic rate MB. To this is added a diameter-dependent mortality MD, which is zero above a threshold diameter dt = MD1. Thinning is assumed to occur in dense patches. Mortality is modelled as a stochastic event. Senescent trees (≥ 10 cm d.b.h.) die and fall with the probability W. They knock down smaller trees in neighbouring patches and create gaps. The number of trees NF destroyed from the total number Np in the target patch p is calculated from the crown projection area fF of the falling tree relative to patch size A (NF = Np[(fF)/A]).


Seed germination depends on minimal light intensities IS on the forest floor. It is assumed that intact forest surrounding the simulation area provides a constant seed input NS. Incoming seeds are added to a seed pool, which takes into account the variance in the length of dormancy (MS) between plant functional types (Garwood 1983, 1989).

Parameters and initial conditions

Table 3 contains the parameters used for the simulations. Data on the light environment are drawn from Veillon (1989) and L. Kammesheidt (unpublished data). Most allometric relations (h = f(d)/(cP) are based on data derived from Kammesheidt (1994, unpublished data). The form factor γ, leaf and crown area to diameter relations are taken from measurements of Kato, Tadaki & Ogawa (1978) and Kira (1978) in Pasoh, Malaysia. Data on the photosynthetic response of plant functional types to different light levels are given in Oberbauer & Strain (1984). The wood density of species was determined at the Institute of Wood Technology and Wood Biology of Göttingen University, Göttingen, Germany. Parameters for respiration processes (r0s and r1s) were investigated using parameter variation to gain realistic diameter increment values for different size classes and light conditions. Mortality and ingrowth rates correspond to typical values found in the literature (Swaine 1989; Condit, Hubbell & Foster 1992; Carey et al. 1994; Phillips & Gentry 1994; Condit, Hubbell & Foster 1995a,b; Silva et al. 1995; van der Meer & Bongers 1996). Mortality M is correlated to the diameter growth rate gd and maximum size DM such that ω=DM/gd× M is roughly constant. Otherwise the number of large trees would be overestimated (ω << 1) or only small trees would occur (ω >> 1) (Chave 1999).

Table 3.  Parameter estimates for the simulation of the Caparo forest, Venezuela. Parameters with subindex vary according to season (y), successional status (s), potential height (h) (corresponding to SS and HG in Table 1) or different functional coefficients (j)
  1. *p, photons; c, CO2.

Environmental parameter
k   0·7     
I0ywet, dryµmol(p) m−2 s−1816·01005·0    
SDywet, dryh 12·0  12·0    
SSywet, dry  0·67   0·33    
Establishment parameter
DS m  0·01     
NSss = 1–4ha−1 year−1500 2002550  
ISss = 1–4fraction of I0y  0·05   0·01 0·01 0·01  
Mortality parameter
MBs,hs = 1; h = 1–6year−1  0·00   0·12 0·08 0·00  0·00  0·00
MBs,hs = 2; h = 1–6year−1  0·06   0·05 0·035 0·03  0·00  0·00
MBs,hs = 3; h = 1–6year−1  0·05   0·04 0·03 0·025  0·00  0·00
MBs,hs = 4; h = 1–6year−1  0·00   0·00 0·00 0·00  0·01  0·01
MSss = 1–4year−1  0·1   0·5 1·0 1·0  
MDjj = 0–1year−1, m−1  0·4   0·2    
W   0·40     
Tree physiognomic parameter
MMs,hs≠ 1; h = 1–6m  0·10   0·25 0·70 1·50  0·10  0·50
MMs,hs = 1; h = 2–3m    0·25 0·35   
cP   0·358     
τ   0·7     
h0hh = 1–6cm m−1  1·63   1·63 1·41 1·50  0·22  0·22
h1hh = 1–6m−1 19·9  19·935·745·4325·7325·7
γjj = 0–2–, cm−1, –  2·575  −1·409 0·0358   
fjj = 0–2–, –, –  0·132   0·933−0·6615   
ljj = 1–3m cm−1, m cm−2, m cm−3  3·197   0·0684−0·000379   
LAIM   2     
Biomass production parameter
PMss = 1–4µmol(c) m−2 s−1 27·7  11·3 6·8 6·8  
αss = 1–4µmol(c) µmol(p)−1  0·043   0·043 0·043 0·043  
ρss = 1–4todm m−3  0·24   0·69 0·69 0·75  
r0ss = 1–4todm3/2  0·20   0·06 0·05 0·04  
r1ss = 1–4  0·60   0·02 0·015 0·04  
RG   0·25     
m   0·1     
g godm gCO2−1  0·63     

From data sets of the two stands chosen for simulations (MF and LG5), 25 patches (of 400 m2 each), randomly chosen in the case of LG5, were clustered to form the initial data set for 1 ha. The functional groups were then aggregated into different cohorts regarding their diameter (d.b.h. class of 5 cm). To minimize stochastic effects in tree mortality, each simulation was performed for an area of 25 ha.

The model was written in the programming language C++. Simulations were run on a PC (400 MHz, system Linux), taking on average 9 s to simulate the growth of 1 ha of rain forest over 100 years.

Stability and sensitivity analysis

The performance of the model was evaluated using a stability analysis of the long-term model dynamics. This involves a comparison of field data from the mature stand (MF) with the dynamic model output, assuming long-term stability in tropical mature forests (Whitmore 1988) without climate or evolutionary changes. Stability indices were calculated by averaging the values of 28 result variables [leaf area index LAI; succession stages (GAP phase: no trees with h ≥ 15 m in patch; BUILDING phase: trees with h ≥ 15 m in patch; MATURE phase: trees with h ≥ 30 m in patch), basal area BA; bole volume V of the whole stand; relative basal area of the different plant functional types; successional status; height groups; total (N) stem number; and stem number as a function of the diameter in four size classes (N0–30, N30–60, N60–90, N90)] over the last 100 of 240 simulated years and normalizing them with their initial values (Huth & Ditzer 2001). A stability index of 1·0 corresponds to a stable variable, whose long-term average value is identical to field data.

The sensitivity of 28 result variables (the same as for the stability analysis) to parameter variations was investigated by varying the 60 parameters in Table 3 within their realistic range (values found in the literature and within physical boundaries). Seven simulations over 4 ha and 100 years in the mature stand were performed for each varied parameter, including one simulation with the standard value. Mean values (v) of the chosen result variables were averaged over the seven simulations. The coefficient of variation (CV) from the resulting average (a) was chosen as an indicator to find out whether the individual variable responded sensitively (CV = 1v − a1/a × 100).

Logging scenarios

On the basis of the logging practices in the study area documented by Plonczak (1989) and Kammesheidt (1994) and data from the literature (Hendrison 1990), the following logging scenarios were simulated. (i) During conventional logging, one-third of the area was converted into roads and log-landings; this involved complete removal of the residual stand. Beside damage during felling that destroyed an area proportional to the crown projection area of the cut tree, 55% of trees in the felling area were killed in the log removal operation. (ii) By applying reduced-impact logging, landing areas diminished to 12% and the log removal damage was limited to 25%. If possible, trees were felled into existing gaps under both logging scenarios. In the initial phase after logging (years 1–10), mortality was two and three times higher than the normal rate found in mature forest for reduced-impact and conventional logging, respectively. Cutting cycles of 30, 40 and 60 years, respectively, with three net harvest volumes (30, 45 and 60 m3 ha−1 cycle−1, respectively), applying a minimum felling diameter (MFD) of 35 and 50 cm, were simulated. The simulation time was 240 years and the simulated area comprised 25 ha. To obtain the given net volume, 30% harvest loss had to be added to the logged volume, corresponding to gross volumes of 43, 65 and 86 m3 ha−1 cycle−1, respectively. From all medium-sized and large, mid- and late successional species at MFD, trees were randomly chosen for logging until the target harvest volume was reached. Early successional species are not merchantable and did not attain a diameter ≥ 35 cm (Kammesheidt 2000). In the case of understocking (if harvestable standing volume is lower than the target gross volume for logging), logging was suspended for one cutting cycle and, hence, timber yield was unsustainable.

Data analysis

The G-test was applied to test for differences in the proportion of successional groups in bole volume between logging scenarios. The z-test was used to compare the means of ingrowth and mortality, and bole volume between different logging methods and the unlogged and once-logged stand (Fowler, Cohen & Jarvis 1998). Two-way anova was employed to test for differences in bole volume prior to logging within and between different logging scenarios.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

Model evaluation

The results of the stability analysis of a mature forest are shown in Fig. 1. Most of the general variables (GEN) were stable, with stability indices between 0·85 and 1·0, except for those relating to the proportion of forest in the gap and building phase. In fact, the initial stand comprised no area in the gap phase, keeping this value at zero and influencing directly the proportion of forest in the building phase. Relative basal areas were stable in plant functional types, with different successional status and different maximum heights. Only the relative basal area of successional stage 1 (SS1) and height group 2 (HG2) showed relatively unstable values (1·7 and 2·8, respectively). For the individual plant functional types (PFT), the forest was more stable for plant functional types with larger trees and higher absolute values in basal area. PFT3 was not found in the initial site and therefore its stability index was zero. PFT4, PFT5 and PFT7 were unstable, with values between 2·2 and 3·2. In the stem diameter distribution, different diameter classes were stable, total stem number N declined to 80%, while the number of large trees (N90) increased by 50%.


Figure 1. Stability index for the simulation of a mature forest stand. A stability index of 1·0 corresponds to a time-averaged stable variable. The simulations were run over 240 years in an area of 25 ha; stability was analysed over the last 100 years (mean ± SD). Result variables are classified according to their level of information: GEN, general information refers to total leaf area index LAI, successional stages (GAP phase: no trees with h ≥ 15 m in patch; BUILDING phase: trees with h ≥ 15 m in patch; MATURE phase: trees with h ≥ 30 m in patch), basal area BA and bole volume V of the whole stand; PFT, relative basal area of the different plant functional types; SS, relative basal area of the different successional stages; HG, relative basal area of the different height groups; ND, stem number as function of diameter (N, all trees) for trees between 0 and 30 cm d.b.h. (N0–30), 30 and 60 cm d.b.h. (N30–60), 60 and 90 cm d.b.h. (N60–90) and above 90 cm d.b.h. (N90). For the stability analysis only trees ≥ 10 cm d.b.h. are considered. Consequently, PFT1, PFT2, PFT11, HG1 and HG5 are omitted.

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In the sensitivity analysis, the parameters were grouped according to the different parts of the model to which they belonged (Fig. 2). The results showed that the behaviour of the forest was sensitive to the number of trees in the gap phase (GAP), the relative proportion of early successional species (SS1) and the number of trees ≥ 90 cm (N90). Their values varied throughout nearly the whole parameter range (CV > 50%). The model was also moderately sensitive to the proportion of some plant functional types (PFT3–PFT7) over a wide range of parameter values. In contrast, the model was not sensitive to the following parameters: the total leaf area index (LAI), proportion of forest in mature phase (MATURE), total basal area (BA), total stem number (N) and, with some exceptions, total bole volume (V), and relative share of mid- and late successional species (SS2, SS3). The parameter values for the initial diameter of ingrowing seedlings DS, and various mortality rates MB, generated sensitive responses over the whole range of result variables. The parameters of the mortality module had a greater influence on the simulation results than those of other modules.


Figure 2. Analysis of the sensitivity of 28 result variables describing the state of the forest (for abbreviations see Fig. 1). The result variables were grouped into five groups: general structure (GEN), abundance of species groups (PFT), successional groups (SS), abundance of trees in different height classes (HG) and diameter classes (NG). Each parameter was varied within the given range. The grey scale of boxes indicates how sensitive a certain result variable reacts to variations in a model parameter (for abbreviations see Table 3). Black: high sensitivity (CV > 50%); grey: medium sensitivity (10% < CV ≤ 50%); white: low sensitivity (CV ≤ 10%). The calculation of CV is explained in the text. All simulations were made for a mature forest of 4 ha (simulation time t = 100 years).

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Stand development in the absence of logging

The logged stand (LG5) approached the stand structure of mature forest in terms of both basal area and bole volume after about 50–100 years (Fig. 3). In the equilibrium phase, mid-successional species dominated over late successional species in both stands. Early successional species disappeared before the equilibrium phase was reached. In both stands, palm species formed a constant high proportion of the basal area. The slight decline of the bole volume and basal area in mature forest over the simulation period indicated that stand structure was crowded at the time of sampling and thinned thereafter.


Figure 3. Development of the basal area (m2 ha−1) and bole volume (m3 ha−1) in unlogged (a, c) and logged stands (b, d) by plant functional types over a simulation period of 240 years in 25 ha for trees ≥ 10 cm d.b.h. Total (solid bold line), early successional spp. (solid line), mid-successional spp. (broken dotted line), late successional spp. (broken line), palm spp. (long broken line).

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Yield prediction under different logging scenarios

With conventional logging and a MFD of 35 cm and a 30-year cutting cycle, logging would not take place two and four times, respectively, over a simulation period of 240 years, if the net volume extracted (NVE) was either 45 or 60 m3 ha−1 cycle−1 (Table 4). All other logging scenarios with a MFD of 35 cm provided a merchantable volume in any of the individual cutting cycles. Conventional logging methods with a MFD of 50 cm and a 30-year cutting cycle were unlikely to be sustainable, even with low NVE of 30 m3 ha−1, because the overall volume prior to logging was on average only slightly higher than the minimum level of 43 m3 ha−1 needed as gross volume (Table 4 and Fig. 4). An extension of the length of cutting cycle to 40 years, but otherwise unchanged conditions, led to a significant increase in commercial stock (z = 37·1, P < 0·01). By applying reduced-impact logging, timber harvest had to be suspended less often.

Table 4.  Bole volume of trees ≥ 35 (50) cm d.b.h after and prior to logging applying different logging scenarios (CON, conventional logging; RIL, reduced-impact logging) over a simulation period of 240 years. Minimum felling diameter (MFD) either 35 or 50 cm. Values for the mature forest (MF) are given as reference. If the individual gross bole volume was not reached, logging was omitted. Mean values and standard deviation for bole volume after/prior to logging were taken from the different number of logging events (n = 4–8). Mean annual bole volume increment was averaged over the simulation period
Logging methodCutting cycle (years)Net volume extracted (m3 ha−1 cycle−1)Bole volume (m3 ha−1)Times logging omittedMean annual bole volume increment (m3 ha−1 year−1) mean ± SD
After loggingPrior to logging
Mean ± SDRangeMean ± SDRange
MFD = 35 cm; trees ≥ 35 cm d.b.h.
MF    250 ± 14231–274 0·0 ± 1·2
CON3030 33 ± 16 21–71 77 ± 16 65–1163·5 ± 5·9
CON3045 43 ± 34  0–90109 ± 34 65–15723·2 ± 5·3
CON3060 60 ± 17 29–71147 ± 18116–15943·2 ± 5·0
RIL3030 93 ± 11 71–101138 ± 11116–1472·7 ± 2·4
RIL3045 54 ± 5 45–61121 ± 6112–1283·3 ± 2·4
RIL3060 25 ± 5 14–30112 ± 5101–1173·8 ± 2·6
CON4030 79 ± 12 70–105125 ± 12115–1513·0 ± 4·8
CON4045 44 ± 18 30–84111 ± 18 97–1513·5 ± 5·3
CON4060 19 ± 20  6–64106 ± 20 93–1513·6 ± 5·5
RIL4030119 ± 7105–127165 ± 7151–1722·3 ± 2·2
RIL4045 89 ± 4 83–94157 ± 5150–1622·8 ± 2·3
RIL4060 64 ± 3 59–67151 ± 3146–1553·2 ± 2·3
CON6030133 ± 9123–146178 ± 9168–1912·2 ± 4·0
CON6045108 ± 9100–123176 ± 9168–1912·6 ± 4·0
CON6060 80 ± 13 72–103169 ± 13161–1912·9 ± 4·2
RIL6030152 ± 4146–156199 ± 5191–2021·8 ± 2·1
RIL6045128 ± 3123–131196 ± 3191–1992·1 ± 2·0
RIL6060109 ± 4103–113196 ± 4191–2022·4 ± 2·1
MFD = 50 cm; trees ≥ 50 cm d.b.h.
MF    208 ± 12192–232 0·0 ± 1·3
CON3030  5 ± 4  2–16 49 ± 5 44–621·8 ± 1·9
CON3045 70 ± 4 67–77138 ± 4135–14542·2 ± 3·1
CON3060 45 ± 7 39–57134 ± 7127–14542·4 ± 3·4
RIL3030 51 ± 16 16–65 96 ± 16 62–1112·1 ± 1·8
RIL3045 31 ± 19 17–77 99 ± 19 84–14512·4 ± 1·7
RIL3060 42 ± 29  2–72130 ± 30 88–16132·2 ± 2·2
CON4030 27 ± 8 19–45 72 ± 8 64–901·6 ± 1·8
CON4045 58 ± 41 10–104124 ± 42 75–17122·0 ± 2·8
CON4060 52 ± 33  5–77139 ± 35 90–16531·8 ± 2·9
RIL4030 66 ± 10 45–75112 ± 11 90–1211·7 ± 1·4
RIL4045 39 ± 9 23–46106 ± 9 90–1142·1 ± 1·5
RIL4060 27 ± 32  5–91114 ± 33 90–18012·1 ± 2·0
CON6030 98 ± 4 93–104144 ± 4138–1501·9 ± 2·9
CON6045 71 ± 7 65–82139 ± 7133–1502·2 ± 3·2
CON6060 45 ± 10 37–62133 ± 10126–1502·4 ± 3·4
RIL6030119 ± 10104–131165 ± 10150–1771·6 ± 1·9
RIL6045 91 ± 6 82–97160 ± 6150–1651·9 ± 2·0
RIL6060 69 ± 5 62–74157 ± 5150–1632·1 ± 2·1

Figure 4. Development of bole volume (m3 ha−1) for a range of logging scenarios by plant functional type over a simulation period of 240 years in 25 ha for trees ≥ 10 cm d.b.h. The subheadings indicate logging conditions (method, cycle in years, intensity in m3 ha−1 cycle−1) with: RIL, reduced-impact logging; CON, conventional logging. Minimum felling diameter was 50 cm. Total (solid bold line), early successional spp. (solid line), mid-successional spp. (broken dotted line), late successional spp. (broken line).

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In logging scenarios with a sustainable timber supply over the 240-year simulation period, differences in bole volume after logging, corresponding to the different net volumes extracted, diminished until the next cutting cycle (Table 4). This trend was largely due to the higher increment in bole volume with increasing NVE in most scenarios. However, within-group differences in the 40-year cutting cycle prior to logging remained significant (F2,30 = 8·9, P < 0·01), while differences were non-significant in the 60-year cutting cycle for both MFD applied (F2,30 < 1·8, P > 0·05). Differences between logging methods and NVE prior to logging were significantly different in all scenarios (F1,30 > 31·4, P < 0·01).

Even under the longest cutting cycle with reduced-impact logging and a low timber extraction of 30 m3 ha−1, the average bole volume prior to logging was significantly lower compared with mature forest for both diameter limits (z > 44·0, P < 0·01).

Ingrowth and mortality

Regular logging operations kept the stand under all logging scenarios in a building phase, indicated by the fact that ingrowth dominated over mortality (Table 5). Ingrowth was significantly higher than mortality in trees ≥ 50 cm d.b.h. under all logging scenarios (z > 2·6, P < 0·01), while no significant differences were found in trees ≥ 35 cm d.b.h. (z < 1·4, P > 0·05). Differences in ingrowth rates between logging methods were non-significant, except for trees ≥ 35 cm d.b.h. in the 40-year cutting cycle (z = 2·36, P < 0·05). Although annual ingrowth and mortality were higher under conventional logging, significant differences between logging methods were found in only a few cases. Overall, the rate of ingrowth and mortality declined with longer cutting cycles irrespective of logging methods. However, even under a 60-year cutting cycle and reduced-impact logging, ingrowth and mortality were significantly higher than in both mature forest and LG5 (z > 2·82, P < 0·01).

Table 5.  Average annual ingrowth and mortality (%) of trees ≥ 35 or 50 cm d.b.h., respectively, in unlogged (MF), one-time (LG5) and several-times logged stands under different logging scenarios over a simulation period of 240 years. Minimum felling diameter (MFD) either 35 or 50 cm. Logging methods are designated as either conventional (CON) or reduced-impact logging (RIL). Data are mean ± SD of time-averaged values of scenarios with different extraction intensities (n = 3)
Logging methodCutting cycle (years)IngrowthMortality
MFD = 35 cm; trees ≥ 35 cm d.b.h.
MF 2·7 ± 0·52·7 ± 0·3
LG5 3·0 ± 2·52·8 ± 2·6
CON306·2 ± 9·75·6 ± 9·9
RIL305·1 ± 3·54·3 ± 4·5
CON406·0 ± 9·45·5 ± 9·8
RIL404·5 ± 2·93·9 ± 3·8
CON604·5 ± 7·04·4 ± 7·1
RIL603·8 ± 2·63·5 ± 2·8
MFD = 50 cm; trees ≥ 50 cm d.b.h.
MF 1·6 ± 0·81·6 ± 0·5
LG5 2·3 ± 2·81·7 ± 0·6
CON305·7 ± 7·93·5 ± 9·1
RIL304·6 ± 4·32·6 ± 3·6
CON404·8 ± 7·33·1 ± 7·6
RIL404·4 ± 4·82·5 ± 3·4
CON604·1 ± 5·12·9 ± 6·8
RIL603·3 ± 3·22·2 ± 2·5

Successional groups of species

Logging methods had a significant influence on the proportion of different successional groups in bole volume (G > 6·6, P < 0·05) (Table 6). The extension of the length of cutting cycles resulted in a decline in the proportion of early successional species and an increase in late successional species under both conventional and reduced-impact logging. This was also illustrated by the development of these successional groups of species along the 240-year simulation period (Fig. 4). Over the whole simulation period, the proportion of successional groups in LG5 did not differ from those in the mature forest (G = 2·4, P > 0·05), whereas the bole volume was significantly lower (z = 13·1, P < 0·01). Reduced-impact logging kept the standing stock in any of the cutting cycles and MFD on a significantly higher level than conventional logging (z > 1·83, P < 0·01). Within the same logging method, the lower MFD applied led to a significantly lower standing stock in short cutting cycles (z > 3·2, P < 0·01), except for reduced-impact logging with a 40-year cutting cycle. Only with the longest cutting cycle and reduced-impact logging, did differences in species composition with LG5 decline to a non-significant level (G = 4·0, P > 0·05). The mean bole volume of all logging scenarios was significantly lower than in both LG5 and mature stand MF (z > 9·0, P < 0·01).

Table 6.  Proportion (mean ± SD) of plant functional types summarized into successional groups [early (1), mid (2) and late (3) successional spp.; ≥ 10 cm d.b.h.] in bole volume (m3 ha−1, mean ± SD) in unlogged (MF), one-time (LG5) and several-times logged stands under different logging scenarios over a simulation period of 240 years. Minimum felling diameter (MFD) either 35 or 50 cm. Logging methods are designated as either conventional (CON) or reduced-impact logging (RIL). Data are mean ± SD of time-averaged values of scenarios with different extraction intensities (n = 3)
Logging methodsCutting cycles (years)m3 ha−1Successional groups (%)
MF 270 ± 14 1 ± 056 ± 444 ± 2
LG5 235 ± 39 3 ± 456 ± 642 ± 2
MFD ≥ 35 cm d.b.h.
CON30144 ± 4429 ± 1857 ± 1714 ± 12
RIL30154 ± 3610 ± 570 ± 1221 ± 10
CON40144 ± 3928 ± 1856 ± 1616 ± 14
RIL40176 ± 38 7 ± 468 ± 1225 ± 10
CON60179 ± 4415 ± 1363 ± 1522 ± 13
RIL60201 ± 42 5 ± 465 ± 1130 ± 9
MFD ≥ 50 cm d.b.h.
CON30161 ± 4520 ± 1461 ± 1419 ± 13
RIL30172 ± 37 8 ± 468 ± 1225 ± 11
CON40173 ± 4716 ± 1365 ± 1519 ± 12
RIL40181 ± 40 7 ± 468 ± 1225 ± 10
CON60179 ± 4515 ± 1363 ± 1523 ± 13
RIL60200 ± 42 5 ± 465 ± 1230 ± 9


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

This study involved a two-step approach to forecast growth and yield of logged-over forest, consisting of testing the model under undisturbed conditions and then simulating logging scenarios.

Model performance under undisturbed conditions

Although the structure and species composition of mature forest shifts continuously on a small scale (Wiens 1999), we believe that a stability analysis is worthwhile to evaluate model performance. In fact, all forest growth models known to the authors (e.g. Liu & Ashton 1995) implicitly accept a so-called potential natural vegetation (PNV), which represents the steady-state as a product of model structure and parameterization. None of them has tested the PNV in detail against field data of mature forest. The critical point of the stability test was whether the site we categorized as mature forest was representative. In a few aspects, the mature forest lacked this representativity. For example, no area was in the gap phase and consequently early successional species were rare. However, a field inventory represents only one condition in space and time. A comparison of the field inventory with the time-averaged model output suggests that those missing that represent mature forest have a minor influence on the quality of the model results. For instance, the time-averaged fraction of gap area in mature forest or the proportion of early successional species showed small differences to initial values (Table 6). Two further trends need to be discussed: the relatively low stability indices (< 1) of most general variables (Fig. 1) and the relatively high stability indices of PFT4–PFT7. The latter results from the fact that the initial species composition was fairly distinct from the averaged modelled one. Field data of a larger sampling area might be needed to reflect the accuracy of the modelled composition of plant functional types. From our model analysis, we know that recruitment is the most important factor for species composition and needs to be modelled in more detail in future applications. The relatively low stability indices of most of the general variables could be explained by the missing gap phase. The initial data set suggests that the analysed mature forest is a well-structured stand showing high values in basal area, bole volume and leaf area index. The stability index of most of the variables in Fig. 1 showed changes below 15%, indicating that the model and its parameterization is stable and a suitable tool for further analysis of logging scenarios in the Caparo forest.

The sensitivity analysis was undertaken within a realistic range of parameter values. This implies that the response of the result variables to parameter changes should not be too sensitive. The results showed low sensitivity for most parameter variations. The sensitivity of the model to variations in the mortality parameters raises the question of whether these values were chosen properly. However, simulated mortality rates in the mature forest are within the range observed in other neotropical forests (Condit, Hubbell & Foster 1992; Carey et al. 1994).

Logging scenarios

Net timber volumes in the range of 30–60 m3 ha−1 cycle−1 assumed in the scenarios for the second and subsequent cutting cycles may be perceived as high, bearing in mind the traditionally low intensity of wood removal in Latin America compared with South-East Asia (Plumptre 1996). In fact, the first cutting cycle is selective, focusing on the most valuable species, i.e. B. quinata, S. macrophylla and C. odorata, in areas where they occur clumped, resulting in low harvest volumes, in reference to the whole logging unit. As individuals of these species are found rarely below the MFD (Plonczak 1989; Kammesheidt 1994, 1998), logged-over stands are composed of potential commercial species with a considerably lower market value (Centeno 1995). Further depletion of the most valuable species might result in an increase of log prices of formerly unlogged or rarely logged species. However, even an increase of log prices for less acceptable species would hardly offset the loss of valuable timber species so that a higher volume must be harvested to keep the cost–benefit ratio of the first cutting cycle. To include all species above the legal size in the present logging scenario is reasonable because this is being done already in other concession areas in the western plains of Venezuela (J. Duque, personal communication). Also, the currently applied MFD of 50 cm for medium-hardwood species, most of them with a mid-successional status constituting the bulk of commercial volume, might be reduced if sawable logs above this size should become scarce. Overall, harvest volume and MFD may vary within the range given in this study depending on the composition of commercial volume in the individual logging unit.

Unlike other neotropical regions, some empirical data on long-term growth and yield are available to evaluate our results. An average annual bole volume increment of 3·8 m3 ha−1 year−1 (SD = 4·2; trees ≥ 10 cm d.b.h.) for the 30-year cutting cycle with conventional logging is a conservative growth rate compared with Veillon’s (1985) mean figure of 4·4 m3 ha−1 year−1 (SD = 0·5) measured in a stand 15–32 years after light logging. The basal area increment in the first 10 years after logging over the simulation period under conventional or reduced-impact logging with a 30-year cutting cycle and a removal of 30 and 60 m3 ha−1 cycle−1, respectively, was 0·3 and 1·1 m2 ha−1 year−1. Lozada (1998) found similar basal area increment rates in the first 10 years in experimentally cut stands with a basal area removal of 20–84%. By simulating 240 years, early successional species accounted on average for 83–95% of the basal area increment at any initial phase (1–10 years) after logging at 30-year intervals. Lozada (1998) found a mean percentage of 45. This suggests that shortening cutting cycles over a longer period of time will result in early successional species becoming predominant.

Ingrowth and mortality declined with increasing length of cutting cycles (Table 5). In the 60-year cutting cycle with reduced-impact logging, both parameters reached average values in the range of 2·2–3·8%, which is similar to turn-over rates of trees ≥ 30 cm d.b.h. in old-growth forest in Panama (Condit, Hubbell & Foster 1992). In our simulations we assumed a continuous input of seeds. This might have been too optimistic in the case of short cutting cycles. In combination with a low MFD, at least some commercial species will be harvested before they have attained their reproductive stage. Thus, stand composition will either shift to common species capable of early reproduction or overall regeneration will decline.

We simulated the spatial pattern of disturbance associated with logging. Differences between logging methods in terms of area damaged could be even more pronounced taking into account that cut trees are expected to fall swiftly to the ground if vines are cut well before logging, as assumed in our model. Conventional logging methods do not consider vine cutting; this results in tree tangles that extend the canopy gap area (Johns, Barreto & Uhl 1996). Vine cutting may become an even more important measure in logged-over stands because these areas support a proliferation of lianas (Kammesheidt 1999). With reduced-impact and conventional logging, respectively, 23–35% and 50–73% of the simulated area was damaged (i.e. log-landings, felling and skidding areas), corresponding to a basal area removal of 2·5–5 m2 ha−1 cycle−1. In contrast, Hendrison (1990) found, in Suriname, with a basal area removal of 4 m2 ha−1 cycle−1, that 22% and 36%, respectively, of the forest area was damaged under controlled and uncontrolled logging. The much higher damage level with conventional logging in Venezuela highlights the careless logging methods in the study area.

The data for the simulations were derived from both well-drained and poorly drained sites. The latter sites might show a slower rate of tree establishment and lower diameter increment rates than the well-drained sites owing to different soil water availability in the rainy and dry season. This may result in a different speed of succession and it would obviously be of interest to explore this further. The simulations were also made under the assumption of no disturbance other than logging and gap creation owing to tree fall. However, fire is a real hazard because of the considerable increase in fuel mass after logging (Nepstad et al. 1999), which is easily inflammable during the pronounced dry season. Particularly short cutting cycles with conventional logging methods leave large tracts of open forest, increasing the susceptibility to fire. This also requires further investigation.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

Both the stability and sensitivity analyses showed that formind2.0 simulates the stand dynamics of Caparo forest within realistic limits. The model’s capability to simulate the spatial heterogeneity of stands with high resolution makes the model useful for simulating growth and yield of logged-over forest. Whether cutting cycles identified as sustainable in terms of timber yield are economically viable in the long run will strongly depend on species composition and log quality of merchantable trees. Reliable forecasts to this end will offer new challenges to forest modelling.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

We thank F. Hapla, Göttingen University, who determined the wood density of selected tree species. H. Bossel, J. Chave, A.R. Watkinson and an anonymous referee provided helpful comments on the manuscript. P. Köhler was funded by the Otto-Braun-Foundation of the University of Kassel.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
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Received 23 December 1999; revision received 2 February 2001