Strategies to maximize the wood production in Amazon forest

3 Background: This study aimed to develop a procedure to determine which logging 4 diameter would achieve optimal wood production by species, aiming to support 5 sustainable management of the Amazon forest. Two main methodologies of analysis by 6 species were combined: probability density function (PDF) and growth modeling. The 7 growth models were used to derive the volume increment curves at the individual tree 8 level. To detect the points of maximum annual increment in volume at the population 9 tree level we used PDF with adjusted growth equations. 10 Results: The population maximum annual volumetric increments occurred in smaller 11 diameters compared to that of the individual-level. When combining shorter cutting 12 cycles with the population biological rotation point considered as the minimum cutting 13 diameter (MCD), we observed higher annual increments in volume than that achieved 14 using the Brazilian law criteria (MCD = 50 cm) or other MCD tested. 15 Conclusion: The procedure proposed may be used by forest managers and forest law- 16 makers, aiming to maximize sustainable wood production in the Amazon forest. 17

. The management must be carefully planned and be 25 consistent with the initial natural forest structure (e.g., density, diametric distribution, 26 growth, mortality, and regeneration) of the species of interest (Seydack et al., 1995;27 Bick et al., 1998). 28 According to Seydack (2012), a challenge for forestry scientists is to combine modeling 29 and simulation tools to understand tropical forest dynamics, enabling production 30 maximization. Minimum cutting diameters (MCD) should be defined for all commercial 31 species, representing a powerful tool in maximizing increment for tropical forests under 32 management as in the Amazon region. 33 Knowledge of the natural forest balance allows identification of the ideal moment of 34 intervention and its production potential (Bick et al., 1998). The forest balance equation 35 depends on how tree increment occurs over time. Studies of species growth at 36 individual-level, structure, and reproductive biology are the basis for defining the 37 management guidelines that guarantee sustainability for wood production in tropical 38 forests (Vanclay, 1989 Forest growth goes through youth, maturity, senescence, and stagnation phases. Its basic 40 unit is the tree, which has a distinct sigmoidal growth pattern, tending to a biological 41 limit (Odum, 1988). Trees that were established decades ago will grow within the 42 ingress criteria for classes with larger diameters, will stagnate or eventually die. Thus, a 43 diametric distribution of natural forest is the result of several tree establishments over 44 different periods. 45 Diametric distribution is a useful factor to describe the forest properties since the 46 diameter is easily obtained and correlated with other variables such as volume, which 47 defines the economic value of the forest area (Bailey;Dell, 1973). Diameter is widely 48 used in the forest sector to assess the effect of environmental and anthropogenic 49 disturbances (Kohyama, 1986;Coomes et al., 2003;Wright et al., 2003;Bettinger et al., 50 2009;Hossain et al., 2015), to describe successional patterns (Kohyama, 1986;Wright 51 et al., 2003;Wang et al., 2009) and for the prediction of the future stock of a stand (De 52 Liocourt, 1898; Meyer, 1952;Carvalho, 1981;Condit et al. , 1998;Bettinger et al., 53 2009;Hossain et al., 2015;Orellana;Figueiredo Filho, 2017). However, future stock 54 projection is difficult for tropical forest due to its great diversity (Orellana, Figueiredo 55 Filho, 2017). Moreover, information about individual species distribution pattern is 56 scarce. 57 Describing forest growth trajectory requires long-term information when permanent 58 plots are used as data source (Bick et al., 1998). The successive measurements can make 59 it difficult or even imply a failed simulation, due to the time spent to replicate a 60 structure that represents the initial diametric classes up to the biological diameter limit Most studies of the species forest growth in the Amazon basin were carried out with 63 permanent plots (Silva, 1989;Higuchi, 1996 legislation (Silva, 1989(Silva, , 1997Higuchi, 1996). However, in some species less than one 66 individual per hectare occurs in Amazonian primary forest structure, especially when 67 considering trees with commercial dimensions (Miranda,  Brazil, permanent plots monitored for more than 40 years are rare. These periods are 73 short compared to the age of commercial trees, which are rarely less than 100 years old 74 (Brienen;Zuidema, 2006a;Schöngart, 2008;Rosa et al., 2017). 75 Growth series obtained by dendrochronology became more popular as an alternative to 76 permanent-plot data to supply the demand for information and growth models of species 77 (Brienen, 2005 analysis is a fast and reliable tool for assessing tree age, determining its growth rates 80 over the life cycle, and identifying growth differences between species (Groenendijk et 81 al., 2017;Rosa et al., 2017). 82 This study aimed to develop a procedure based on the diametric structure and growth 83 models to set the minimum cutting diameter (MCD) for optimal wood production. MAI v were calculated, following the same procedures. 185

Obtaining growth curves in volume of the population of each species 186
To obtain growth in volume per unit area for the population of each species over time, 187 individual growth curves in volume were associated with the PDFs. It was assumed that 188 a species diametric distribution follows the same pattern that occurred in the past 189 (Gotelli, 2008;Lundqvist, 2017).

Management simulations 213
The projection method by diametric class (Alder, 1995)

236
The matrices were built from the 30-cm dbh class, for every 5 years (t), until reaching 238 the desired cutting cycle. We considered the wood volume of trees with a dbh higher 239 than the MCD the volume to be harvested (H k ). The following data were used: 240 After obtaining the final diametric structure of the projection matrix by diametric class, 261 the number of trees was converted into volume (applying the taper functions previously 262 described) to obtain the total wood production in the considered period. This production 263 was divided by the cutting cycles, in order to proportionally compare the production of 264 the tested MCD and cutting cycles. 265 266

Diametric structure 268
When testing the adherence of general probability density functions (PDFs) adjusted to 269 the measured density distributions for each species and for each forest compartment, the 270 majority of tested PDF fitted (  The fitted height/dbh model showed satisfactory statistics and residual distribution for 296 all species (Fig. 3). The species that reached the highest commercial heights were E. 297 uncinatum and H. excelsum. The largest commercial height range occurred before 298 reaching 60-cm dbh, ranging from 6.5 to 10.9 m. After 60-cm dbh, the commercial 299 heights tended to stabilize, ranging from 10.9 to 13.4 m.

Diametric increment in dbh classes 307
The mean increment by dbh class and passage time are shown in Fig. 4 and 5. Apuleia 308 leiocarpa presented an initial increase in dbh increment, and a decrease for the upper 309 diameter classes (Fig. 4A), characterizing the U shape for the passage time (Fig. 5A). 310 Erisma uncinatum, H. excelsum, and T. burserifolia showed a higher increase in the 311 upper classes (Fig. 4 B, C and D), assuming a decreasing passage time (Fig. 5 B, C  annual increment in volume (CAI v ) when considering the available data (Fig. 7 A, B  342 and D). The maximum CAI v for H. excelsum was estimated at approximately 245 years 343 (Fig. 7C)

Growth by species population 363
The maximum CAI v and biological rotation ages of the population volume (Table 3; Table 2). Those ages were reached for diameters within the stem samples. There was 366 therefore no need for the extrapolation of the volume growth equations that was 367 required for the individual diameter growth (Fig. 7). 368 369

378
In the secondary y-axis: dbh = diameter at 1.30 m above ground level (cm), obtained from the growth 379 equation.

Minimum cutting diameter (MCD) and cutting cycle simulations 382
The MCD criteria determined by the biological rotation age of the population and with 383 short cutting cycles (10 years) (  Considering the MCD defined by the population's biological rotation age, the annual 398 volumetric production decreased for the four species as the cutting cycle increased (Fig.  399   9). 400 Most of the probability density functions (PDFs) (Table 1) fitted to data in each forest 408 compartment. Thus, a single PDF per species was fitted at the Sinop microregion (Fig.  409 2). Fitting only one PDF per species across the microregion suggests the existence of 410 similarities in the species diametric structure in the typology, contrasting to the claim 411 that ecosystems are chaotic and disordered (O'Hara, 2014). According to this same 412 author, ecosystems are not deterministic or ordered, due to the occurrence of repeated 413 disturbances on small scales, which prevent the forest from being homogeneous over 414 time. However, for Larson (1992), the occurrence of environmental or anthropic 415 disturbances combined with the genetic variation of mixed forest does not imply that 416 forest development patterns cannot be discerned. 417 Also, the micro-region's pattern agrees with the demographic equilibrium theory, which 418 states that the diameter distribution balance may be scalar (Muller-Landau et al., 2006). 419 The forest structure is regulated by general principles of growth, mortality (Wang et al., 420 2009) and ecological succession (Oliver, 1992). 421 Even in distant or geographically isolated regions, species with resembling 422 physiological and morphological characteristics can have a similar population structure 423 (Oliver, 1992). This occurs because the structures repeat over time in the forest (Gotelli, 424 2008  However, several studies have found that some forest types and many individual species 434 may not follow such a negative exponential model (Condit et al., 1998;Dawkins;435 Philip, 1998;Nyland, 2002;Pascal, 2003;Braz, 2010;Braz et al., 2014;Hossain et al., 436 2015), as occurred for three of the species in this study (Fig. 2 A, B and C). An over-stocked upper stratum may have its regeneration constrained due to inadequate 455 access to light by trees in the lower canopy (Yegang;Jinxuan, 1988;Lamprecht, 1990;456 Felfili, 1997;Nyland, 2002;Bettinger et al. 2009). In such cases, some species may 457 need a longer time scale to regenerate (Felfili, 1997). Over time, this factor de-458 characterizes both the negative exponential structure (Braz, 2010;Bettinger et al., 2009) 459 and the whole forest increment (Dawkins;Philip, 1998). 460

Production modeling at individual tree level 461
Commercial height is an essential dendrometric variable for modeling production 462 forests since it is used for volume prediction (Lappi, 1997). Fitting parameters for the 463 commercial height/dbh ratio (Fig. 3)  According to Alder (1995), in natural forests the initial growth of trees is slow, followed 468 by a phase of higher increments until it reaches its maximum. After that maximum 469 point, growth reduces until stagnation. Apuleia leiocarpa, E. uncinatum and T. 470 burserifolia followed this pattern (Fig. 4 A, B and D and 5 A, B and D), while H. 471 excelsum maintained constant growth during five diameter classes, not exceeding 0.5 472 cm year -1 , except in the 65-cm class (Fig. 4C). The constant growth of H. excelsum until 473 larger sizes is a feature of late and emerging secondary species (Silva et al., 1985), 474 whose crowns extend above the canopy average level. These functional groups have 475 several micro-habitats during their ontogenesis (Clark; Clark, 1992). They are 476 characterized as partial sciophytes, shade-tolerate in the early development stages. 477 However, they require a high degree of illumination to overcome the intermediate stages 478 to maturity, increasing its growth during canopy opening (Maciel et al., 2017). 479 The decreasing tendency of passage time (Fig. 5 B (Fig. 5A). 489 The biological rotation and maximum CAI v ages ( Fig. 7; Table 2) were consistent with 490 the increment by diameter class (Fig. 4). Apuleia leiocarpa, an initial secondary species, 491 reached biological rotation and maximum CAI v ages in smaller diameters, while H. logging happens before the maximum CAI v or after the maximum MAI v , the volumetric 498 production will be inefficient. In this case, the species would not have reached or would 499 have passed their optimal growth (Schöngart, 2008;Braz;. Therefore, 500 knowing the maximum CAI v and MAI v per species is essential for sustainable forest 501 management in the Amazon forest. Volumetric population growth 508 The maximum CAI v estimated from the population increment curves occurred for 509 diameters lower than 50 cm for A. leiocarpa, H. excelsum, and T. burserifolia, and at 510 64-cm diameter for E. uncinatum (Table 3; Fig. 8). The dbh when biological rotation 511 age occurs, at which CAI v and MAI v curves intersected, was around 50 cm for A. 512 leiocarpa, H. excelsum, and T. burserifolia, while for E. uncinatum this occurred at 86 513 cm. Erisma uncinatum has increased growth (Fig. 4) Table 2). The inclusion of the number of trees per diameter class anticipates the 530 culmination since it indirectly represents the population mortality and survival rates 531 (Assmann, 1970;Rubin et al., 2006). As trees increase in size, the number of trees 532 decreases due to mortality, causing a deceleration in the gross wood production, even 533 though the remaining trees become larger (Seydack, 2000;Lundqvist, 2017). Therefore, 534 even if individual trees are growing, the total production per unit area will decline much 535 earlier (Assmann, 1970). 536 According to Seydack (2000) the population demographic factors of commercial species 537 are essential to determine the optimal parameters for forest management. In the natural 538 forest structure, the available stock of trees by diameter class is a crucial factor for yield 539 projection in terms of the number of trees, basal area and volume (Ong;Kleine, 1996), 540 since they indicate survival by diameter class. The recovery time of the wood volume in 541 a post-intervention cycle is related to the species-specific growth, and also to the 542 number of trees in the smaller diameter classes to the intervention diameter (Brienen;543 Zuidema, 2006a). Therefore, methods based on the inflection point age at the population 544 level are recognized for being more accurate in predicting maximum volume yield in a 545 natural forest than methods that consider only the individual tree growth. 546 Volumetric production using different management criteria 547 The increments (m³ ha -1 year -1 ) of each species were, in general, compatible with other 548 studies carried out in the Amazon, using permanent plots ( (Table 4), 550 considering the cutting cycle and MCD of the Brazilian forest law (Brasil, 2006). 551 The cutting cycles and alternative MCD from those defined in Brazilian forest law 552 produced higher volumetric increment for the 4 studied species, similar to that obtained 553 by Groenendijk et al. (2017) in tropical rainforest in Cameroon. Erisma uncinatum 554 produced approximately seven times higher wood volume (ha -1 year -1 ) applying short 555 cutting cycle (10 years) and MCD 70% larger (86 cm) than the Brazilian mandatory 556 MCD (50 cm). Erisma uncinatum presented the highest yield gain with the alternative 557 MCD and cutting cycles, due to the higher number of trees and growth in dbh classes 558 above 50 cm ( Fig. 2 and 7). All results, especially those of E. uncinatum, showed the 559 potential of maximizing the forest management yield considering population 560 characteristics at the species level. The ideal MCD can increase volumetric increments, 561 even without silvicultural treatments, and so should be considered to increase 562 management productivity (Avila et al., 2017). 563 The MCD defined by the dbh of the biological rotation of the population produced 564 higher annual increments for the four species, especially for shorter cutting cycles 565 (Table 4). It is important to consider the optimal population increment rate instead of 566 average growth data. This was previously considered by Ong and Kleine (1996) and 567 Bick et al. (1998) when studying natural forests in Malaysia. These authors obtained the 568 population growth from zero using permanent plots and simulations of forest production 569 and found the maximum sustainable yield population, defining optimum logging rates 570 and cutting cycles. Glauner et al. (2003) pointed out that the underlying principle of 571 management is to improve the forest condition, converting its stock to an optimum level 572 of increment of the commercial species. 573 In this study the dbh of the maximum CAI v (lowest among those tested as MCD) 574 produced the lowest volume increments considering the tested cycles (Table 4). 575 According to Bick et al. (1998), the harvested volume of two cycles must oscillate in the 576 population growth curve between a lower and an upper limit of the maximum yield 577 volume (i.e., the age of maximum CAI v ). These authors recommended an MCD above 578 the dbh of maximum CAI v . Our results are consistent with these recommendations, 579 since the yield was higher when the logging was carried out at an age after the 580 maximum population CAI v , such as the biological rotation age. 581 When considering only the individual tree growth curve to define the logging 582 parameters we observed that the MCD was always higher, although the volumetric 583 increments were lower, except for A. leiocarpa (Table 4). Contrary to the statement of 584 Sebbenn et al. (2008) and Lacerda et al. (2013), the excessive MCD increase does not 585 always imply higher forest productivity for all species. As mentioned, after reaching 586 their productivity peak the trees grow at moderate rates and the mortality is high. Slow 587 growth trees should be logged before dying, through selective logging of mature trees of 588 declining vigor (Seydack, 2012;Lundqvist, 2017). 589 The cutting cycles must be long enough so that remaining trees reach the MCD 590 (Seydack et al., 1995). However, it cannot be too long, to ensure the trees' potential 591 growth and forest economic sustainability (Mattioli et al., 2015). The simulations 592 revealed that long cutting cycles resulted in smaller volumetric increments for all 593 species (Fig. 9), reaching a loss higher than 60% compared to the 10-year cutting cycle, 594 considering the same MCD (defined by population biological rotation). Therefore, 595 increasing the cutting cycle indefinitely (Sebbenn et al., 2008) represents a technical 596 error in a productive forest . Moreover, increasing the cut cycle 597 requires long-term investment (Glauner et al., 2003), which is difficult in unstable 598 political-economic environments (Groenendijk et al., 2017). On the other hand, short 599 cutting cycles require logging planning, following the reduced-impact logging 600 standards. 601 Suitable cutting cycles depend on economic considerations (Bick et al., 1998)  Modifications of the standard diametric structure by species can be combined with 612 growth models for inferring tropical forest dynamics, as done in this study. The 613 diametric distribution should support wood production planning and be the basis for 614 monitoring forest logging. 615 The optimum population minimum cutting diameter (MCD) of a species can 616 significantly increase the volumetric increment and the total wood volume, maximizing 617 the forest production under management. After determining the MCD, the best cutting 618 cycle must be defined according to economic analysis, which will specify the best 619 intervention time for the productive forest. 620 The methodology for species-level MCDs proved to be a useful tool and superior to the 621 fixed parameters defined in the Brazilian law or the methodologies that consider only 622 the individual tree growth. The procedure provides higher reliability for the maximized 623 wood production. The ideal MCDs based on dendrochronology substantially reduces 624 costs and time spent collecting data for forest modeling. 625 626 Availability of data and materials 627 The data that support the findings of this study are available from Embrapa Florestas 628 and Elabore Projetos e Consultoria Florestal but restrictions apply to the availability of 629 these data, which were used under license for the current study, and so are not publicly