^{-1}
, site quality (
^{-1}
,

• The management schedules favoring merchantable timber production are not the same that favor C sequestration.

• For planted teak, the objectives of maximizing timber production and carbon sequestration are in conflict because the thinning schedules that maximize financial gains from C sequestration reduce economic gains from timber and vice versa.

• With actual timber teak and market C prices, optimal
^{W}
^{C}

• For C prices under 40 $US MgC optimizing simultaneously for timber production and C sequestration is the best option, as additional although sub-optimal revenues can be obtained from C payments.

• Lengthening the rotation, avoiding thinnings, or reducing their intensity increase carbon storage in planted teak, although, under the analyzed scenarios, after 120 yr. almost all carbon has been re-emitted to the atmosphere.

^{W}, NPV

^{C}, NPV

^{T}

_{p}

_{ob}, V

_{ub}

_{r}

Funding agencies/Institutions | Project / Grant |

Consejo de Desarrollo Científico, Humanístico, Tecnológico y de las Artes (CDCHTA), Universidad de Los Andes, Mérida, Venezuela | FO-748-17-01-B |

Given its high value as a precious tropical timber and its decline in natural forests, teak (

Commercial teak forest plantations must be managed intensively to obtain maximum profitability, however, an increasing awareness of society in environmental issues implies the need of reaching a trade-off between economic and environmental benefits. Today, many countries and private companies are investing in commercial teak plantations; however, there is a strong concern on global climate change, especially after the Paris 2015 Climate Change Conference, which raised the interest in planted forests as providers of environmental services, e.g., carbon sequestration. Planted forest for producing durable solid timber products can play an important role in carbon sequestration, as a large proportion of fixed C remains stored as solid, large size pieces of wood for long time after harvest. Thus, it should be appealing for planted teak forest managers to consider the additional potential benefits of producing timber and simultaneously providing environmental services such as C storage.

Within the frame of the intensive management of planted teak, managing the stand's carrying capacity and optimizing the planting density, thinning, and pruning schedules is crucial for producing high quality timber in large logs with a high proportion of heartwood, as these have much higher value for the international markets.

Most knowledge on the effect of initial spacing and thinning schedules in teak growth and yield come from field trials based on permanent plots subjected to several combinations of spacing and thinning schedules, and from growers’ experience and judgement. The latter is difficult to generalize; whereas, the former is limited by the number of testable combinations and circumscribed to specific sites. Mathematical models can integrate information from these experiences allowing generalization of growth responses and financial results to a large number of combinations including those for which no experimental studies exist. Moreover, models allow the assessment of the weight of intervening variables in the magnitude of observed changes in the biological, financial, and environmental outputs. Mathematical models for analyzing responses to thinning schedules include stand density diagrams (e.g.,

Our objective was to develop and implement an optimization model integrating a growth and yield model with a heuristic optimization technique (genetic algorithms,

1,600 trees ha
^{-1}
that are common for teak management in Venezuela, and other countries in Latin America and Africa.

The system represents planted, even aged teak stands managed with the primary purpose of producing solid merchantable timber and, in addition, storing carbon. Stands may differ in site quality, initial spacing, and rotation age (20 or 25 yr.). We developed a model that looks for combinations of thinning schedules (number, age, and intensity) that maximize the stand's financial benefits. The model comprises three modules: 1) a stand growth and yield model (
^{W}
^{C}
, or both simultaneously (

The growth and yield module consists of a whole-stand model based on a system of differential equations describing the dynamics of the main state variables; e.g. top height (
^{2}
ha
^{-1}
), and stand density (
^{-1}
). The model projects growth in basal area, height,
_{p}
) of the best sites for teak average 37.5 m
^{2}
ha
^{-1}
(
_{p}
. For
_{p}
is 37.5, 34, and 30 m
^{2}
ha
^{-1}
, respectively. Quadratic diameter (

The mortality submodel has three components: a) density-independent mortality due to factors other than tree competition (e.g. drought, pests, and weeds); b) density-dependent mortality due to intraspecific competition; and c) removal of trees by thinning and final harvest. Density-independent mortality occurs only for trees between 0 and 3 yr.-old with decreasing probability. Density-dependent mortality is a decreasing exponential function of stand density. Estimates of equations' coefficients came from permanent plots remeasured from 2 to 32 yr.-old established in the western plains of Venezuela.

The model predicts the instantaneous change in stand quadratic diameter and the proportion of harvested trees with respect to removed basal area depending on a thinning selectivity coefficient
_{s}
, where
_{s}
= 1

for systematic thinning,
_{s}
< 1 for thinning from below, and
_{s}
> 1 for thinning from above (
_{ob}
) and underbark (
_{ub}
) volumes in m
^{3}
from stem base up to 5-cm diameter at tree top (

This module represents the yearly dynamics of stand carbon capture and emissions due to growth and death of above and belowground biomass. Carbon emissions come from the decomposition of branches, stumps, stems, and wood from dead or harvested trees throughout the stand rotation; plus decomposition of harvested forest products and wood losses from processing. Net carbon sequestration is the difference between carbon stored in biomass and carbon emitted to the atmosphere. Total above and belowground stored C was calculated from the total stand overbark volume using the conversion and expansion factors obtained by

where
_{i}
= removed biomass in period
_{k}
= the fraction of removed total biomass from category
_{k,i+j}

A
_{Tk}
= anthropogenic time for category
_{k}
= annual decomposition fraction for category

where
_{Tk}
= decomposition time of category

For each use category, emission and decomposition stop when a very tiny fraction (< 0.01 MgC ha
^{-1}
) is emitted. Thus, a small fraction of biomass will remain without further decomposition, i.e., soil organic carbon (

Seven carbon compartments were considered: 1) roots, 2) deadwood, 3) branches and stumps, 4) bark and debris, 5) short-term duration products (small poles for fencing), 6) midterm duration products (struts and large poles), and 7) long term duration products (sawn wood). Information on decomposition and anthropogenic times are from

Optimization module

This module determines the thinning schedule that

maximizes

We developed a constrained optimization model that maximizes an objective function
^{T}
) of the cash flows through the rotation for a stand whose objectives are producing timber and sequestering carbon simultaneously:

where
^{W}
= the net present value of the cash flows of timber (wood) from thinning and final harvest occurred through the stand life:

and
^{C}
= the net present value of the cash flows due to positive net C storage through the stand life:

where
_{i}
= establishment and maintenance costs in yr.
_{i}
= benefits in yr.
_{c}
= carbon price (US$ Mg
^{-1}
C),
_{i}
= carbon fixed in yr.
_{i}
= carbon emitted in yr.
_{i}
= indicator variable (I
_{i}
= 1 if
_{i}
>
_{i}
, I
_{i}
= 0 otherwise). There are three maximization options for
^{W}
only, maximizing
^{C}
only, or maximizing both values simultaneously:

considering the following decision variables:
_{j}
= number of yr. from planting (age = 0) to first thinning (
_{j}
= intensity of thinning

_{i}
and
_{i}
are basal areas (m
^{2}
ha
^{-1}
) at the beginning and end of yr.
_{i+1,i}
= current annual increment in yr.
_{i}
= removed basal area by thinning in yr.

We designed a heuristic procedure based on genetic algorithms (

The data for growth and yield came from a network of permanent and temporal plots established on teak plantations in the western plains of Venezuela remeasured two or more times between 1.8 and 32 yr.-old. Initial spacing varied from 2.0 × 2.0 to 4.0 × 4.0 m and thinning schedules comprised from 0 to 4 thinnings varying in intensity, age, and intervals of execution. Establishment, management, harvest, and operation costs are shown in

The model, implemented in Visual Basic 2015, comprises the growth & yield, carbon sequestration, and optimization modules. The program generates the best thinning schedules to optimize separately for timber production or carbon sequestration or for optimizing both objectives simultaneously. Inputs are site quality, initial spacing, rotation age, and desired number of thinnings, timber prices differentiated by diameter categories, carbon prices, establishment, maintenance and harvest operations costs, and interest rates. Outputs are optimal thinning schedules (age and intensity of thinnings),
^{T}
^{W}
, and
^{C}
. Soil expectation value (

where

Optimal schedules are accompanied by the corresponding stand information on density, average tree diameter, basal area, dominant/average height, and merchantable volume on an annual basis. Outputs from carbon dynamics include storage, emissions, and annual C flows from stand initial conditions till 120 yr. after harvest considering standing trees, short, medium, and long term forest products, and wood debris from thinnings and final harvest.

We determined thinning schedules for two optimization criteria: A) maximizing the
^{W}
^{C}
); and B) maximizing the financial benefits associated with C sequestration only (maximize
^{C}
). For each criteria 60 scenarios were defined combining
^{-1}
), thinning schedules (0 to 4 thinnings from below;
_{s}
= 0.9), and harvest age (
_{0}
= 0 yr. at planting, initial

(1 cm). Initial stand height = 0.5 m.

The model was set to execute 50 runs for
^{-3}
and C price = 10 US$ Mg
^{-1}
C (equivalent to

2.72 US$ MgCO
_{2}
where 1 MgC = 3.67 MgCO
_{2}
), commonly used in financial analysis including C sequestration (

We carried out a sensitivity analysis to determine the effects on the optimal solution (thinning schedule and maximum for the objective function) when assumed inputs (independent variables) were changed. Each input was changed within a given range and the other parameters kept fixed. The following parameters were varied: a) growth rate (
_{r}
) at intervals of ±1%, (e.g., increases attributable to favorable climate conditions); b) thinning and harvest costs between ±10 and ±50% (base value =14.24 US$ m
^{-3}
) at 10% intervals; c)

5, 8, 12, 14 %, base 10%); d) C prices (0, 20, 30, 40, 50, 100, 150, and 200 US$ Mg
^{-1}
C, base US$ 10); and e) ratios of timber prices per cubic meter among diameter classes. Teak timber prices depend largely on log size and age, as large logs with a high proportion of heartwood are preferred by the market (e.g. furniture, plywood). For young teak plantations, log dimension is a valid surrogate of wood quality. Four situations were considered: 1) all diameter classes have the same price in US$ m
^{-3}
(i.e., no premium for large diameter logs); 2) logs with diameter ≥ 25 cm are worth twice the price of logs 10 ≤ d ≤ 25 cm; 3) logs with diameter ≥ 25 cm are worth three times the value of 10 ≤ d ≤ 25 cm logs; and 4) logs with size d ≤ 10 cm have no value (

For the optimization criterion A (simultaneous maximization of
^{W}
and
^{C}
), the largest
^{-1}
(US$ 14,542) and the
^{W}
^{C}
less than 3.5% (^{-1}
) was only slightly lower (US$ 14,318), but with a small increase in
^{C}
(4.2% of
^{T}
). The scenario (
^{-1}
) had a considerably lower
^{-1}
always had the largest
^{C}
is optimized; the highest
^{C}
= US$ 763 is for scenario
^{-1}
, and
^{-1}
,
^{C}
^{W}
, at base conditions, is very large when compared to the optimized
^{C}
(^{C}
, the
^{-1}
. In this case,
^{C}
is even larger than
^{W}
.

The thinning schedule with the best
^{W}
and
^{C}
for
^{-1}
,
^{-1}
,

46.2%

The optimal number of thinnings in
^{-1}
), in 50% of scenarios the best schedule is two thinnings. In contrast, with 1,111 trees ha
^{-1}
, in 50% of scenarios, the model indicated that the best schedule includes four thinnings. For 1,600 trees ha
^{-1}
, 75% of prescribed scenarios consisted of three intensive thinnings (33, 31, 52%

Overall, larger final diameters were reached for

^{-1}
, and four thinnings; whereas, the lowest diameter (30.3 cm) was reached for
^{-1}
, harvest age = 20 yr. and two thinnings.

When only C storage was optimized, all scenarios showed no thinning schedules (^{-1}
,

R = 25, and the lowest
^{-1}
,

The curves for simulated
^{W}
^{C}
) show a high contrast respect to the curves with the best

In addition to determining optimal
^{C}
and
^{W}
^{C}
(

Until harvest ages, most C remain stored in standing trees for both scenarios until harvest age. When maximizing only for
^{C}
, at age 25, just before harvest, C stored in standing trees peak at approximately 143 MgC ha
^{-1}
with only a small amount as debris from natural mortality (^{W}
^{C}
, the maximum stored C peaks around 13 years (94.1 MgC ha
^{-1}
) with 73.4 MgC ha
^{-1}
in standing trees, and the rest in various products (^{-1}
remain stored, from which 55.6 is C in standing trees, and the rest in various products and debris. After peaking, in both cases C is emitted to the atmosphere till about 120 yr. when most C has been released (^{W}
^{C}
(^{-1}
. This volume is comprised mainly by short and medium duration products (
^{-1}
) of C stored in long duration products. Afterwards, the remaining C is slowly released until 120 yr. when most of it has been reemitted in both scenarios, remaining only a small fraction that never decomposes or it is incorporated into the soil as organic C (

The sensitivity analysis for the model using as base the scenario with the maximum
^{-1}
,

_{r}
_{r}
varies ±1%.

^{-1}
for each change of ± 10% in harvest costs.

^{-1}
,

^{-1}
, the optimal thinning schedules did not change and the
^{-1}
the optimal solution changes by delaying the age and reducing the number or intensity of thinnings, and increasing the

As expected, plantations growing on
^{-1}
, the best thinning schedule is the same, no matter how much C is stored, indicating that C sequestration is not essential for optimizing the thinning schedules, because its weight in the objective function is not significant as compared to the timber prices (53-400 US$ m
^{-3}
). Thus, the optimal management schedules obtained for timber production and carbon sequestration (

20-30 yr. rotations. Also, results agree with executing a first intensive thinning (40-60%) at ages 3-6 yr. (

For teak plantations, the objectives of maximizing timber production and carbon sequestration are in conflict because the thinning schedules that maximize financial gains from C sequestration reduce economic gains from timber and
^{C}
will be lower than when maximizing only for C sequestration, but
^{W}
will be much higher, generating larger economic benefits, but keeping the environmental benefits of C fixation.

The management schedule affects the C storage capacity of planted teak. Increasing rotation length, higher initial spacings, and fewer thinnings with lower intensity or no thinning, stored more C and generated larger benefits independently of site quality. These results agree with those from

In the analysis of C flows for a stand along the rotation under the model assumptions and scenarios, the average annual rate of C sequestration varied between 3.1 and 4.8 MgC ha
^{-1}
yr.
^{-1}
depending on the management schedule. These values agree with those reported for teak by the
^{-1}
yr.
^{-1}
representing a fixation rate of 4 MgC ha
^{-1}
yr.
^{-1}
. Also, they agree with those of
^{-1}
yr.
^{-1}
for tropical plantations.

For a 20-yr. rotation, the model estimated between 55.7 and 77.0 MgC ha
^{-1}
of C stored in standing trees depending on the thinning schedule and site quality. For a 25-yr. rotation this value fluctuated between 67.2 and 87.1 MgC ha
^{-1}
.
^{-1}
and 89.5 MgC ha
^{-1}
for stands harvested at ages 20-25 respectively. Observed differences with our results are due mainly to the thinning schedule chosen by these authors (4, 8, 12, 18, and 24 yr. with remaining trees of 556, 333, 200, 150, and 120 trees ha
^{−1}
and initial stocking of 1111 trees ha
^{−1}
) which differ from schedules generated by our model.

When the only objective was maximizing
^{C}
(
^{-1}
,
^{-1}
yr
^{-1}
, and the amount of C stored in standing trees at final cut was 143 MgC ha
^{-1}
. This result agrees with those of
^{-1}
). It is important to notice that for the scenario that optimized
^{W}
^{C}
a larger amount of C than for the scenario
^{C}
remained stored until 80 years because it was contained in long duration products.

The sensitivity analysis showed that optimal schedules and
_{r}
by 2 % reduced the age of the first thinning to age 3; with an intensive thinning of 50 % intensity at age 16. On the other hand, reducing
_{r}
by 1% reduced the number of thinnings to three. Changing the relative timber prices also affected optimal schedules and

According to the above arguments, our model generates reasonable and consistent results under the imposed assumptions and constraints, making it useful for analyzing the potential of planted teak forest for storing C in biomass during and after the harvest as long duration forest products, as well as analyzing the effect of thinning schedules and rotation age for timber and C sequestration.

Additional economic benefits to timber production can be obtained by accounting for C sequestration in teak plantations without substantial changes in the optimal schedules that maximize
^{W}
. In contrast, if the main objective was to maximize the benefits from C sequestration, moderate, infrequent, and late thinnings will be needed to reduce emissions. This leads to a much lower total