Effect of Density on Mediterranean Pine Seedlings Using the Nelder Wheel Design: Analysis of Biomass Production

 Background: Forest resilience should be improved to promote species adaptation 20 and ensure the future of forests. Carbon stock is considered an indicator of 21 resilience, so it is necessary to determine forest carbon stocks and how to improve 22 them through forest management. The main objective of this study was to analyse 23 biomass production and distribution among the components of four-year-old Pinus pinaster and Pinus halepensis trees. Young trees from a Nelder wheel 25 experimental site were harvested and analysed. The effect of density could be 26 included in the biomass analysis thanks to the Nelder wheel design. We tested 27 densities from 1000 to 80000 seedlings/ha and analysed biomass by fitting 28 different equations: (i) linear regressions to analyse biomass production; (ii) 29 Dirichlet regressions to estimate the biomass proportions of each component and 30 (iii) allometric equations to predict the biomass content of each component. 31  Results: Results from this innovative approach showed that density was a 32 significant factor for Pinus halepensis . We observed a general increase of total 33 biomass at lower densities and this positive effect increased root biomass 34 proportion at the expense of aboveground biomass. Also, a new set of equations 35 was developed for estimating above- and below-ground biomass in young Pinus 36 pinaster and Pinus halepensis trees. 37  Conclusions: we note the importance of belowground biomass and its value in 38 total biomass production (approximately 20% of total biomass for both species). The effect density on biomass production was only significant for Pinus halepensis, the effect if biomass present study. proportion at the expense of aboveground biomass. Currently, this positive effect is especially important in promoting management to improve tree resilience.


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 Conclusions: we note the importance of belowground biomass and its value in 38 total biomass production (approximately 20% of total biomass for both species). 39 The effect of density on biomass production was only significant for Pinus 40 halepensis, but the effect of density would have been different if root biomass had 41 not been considered in the present study. Lower densities increased root biomass 42 High densities in mature stands generally cause competition for resources and reduce tree 67 growth, but competitive and facilitating effects can occur simultaneously in other phases 68 of stand development, such as seedling establishment. For example, seedlings might 69 compete with their own or other species for resources like water or light even as wind 70 velocity or transpiration are reduced by mutual shading or other species provide 71 protection against herbivores (Jactel and Brockerhoff 2007;Zamora et al. 2008;Uhl et al. 72 2015). Moreover, positive interactions can become negative as seedlings grow (Callaway 73 et al. 1996;Callaway and Walker 1997;Zamora et al. 2008;Uhl et al. 2015). Some 74 models predict that facilitation and competition interactions will vary across abiotic stress 75 gradients and that facilitation interactions will be dominant under stressful conditions, 76 though this is debated (Maestre et al. 2005(Maestre et al. , 2006Lortie and Callaway 2006). Therefore, 77 the net effect of intra-and inter-specific interactions among seedlings under high densities 78 is a key issue to analyse. 79 Most studies look at intra-and inter-specific interactions from a productive point of view,  (Thuiller 2003) 106 make it especially timelyto study how the selected species will behave together.

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One of the main issues in this kind of research is the experiment design. The most frequent 108 designs for analysing mixed stands consist of growing two species in varying proportions arcs, a tree is planted. This creates variable tree densities along the length of the spokes 117 within a single plot.

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The main objective of this study was to analyse biomass production and distribution 119 among the components of four-year-old Pinus pinaster and Pinus halepensis trees. Young 120 trees from a Nelder wheel experimental site were harvested and analysed. We expected 121 that: (i) biomass production would be different for Pinus halepensis and Pinus pinaster; 122 (ii) biomass production would be affected by density; (iii) the effect of density would be 123 different for each species.

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Experimental design 126 The present study was carried out in a density experiment following the design proposed 127 by Nelder (1962). The experimental site consisted of five Nelder wheelsfour permanent 128 and one temporaryin which 10 densities were tested: (Ruano et al 2021). The temporary 129 Nelder wheel plot was installed to obtain two seedling harvests for dry biomass analysis.

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The results of first harvest are presented here. Reforestation) for Pinus halepensiswere selected to avoid the site effect ( Figure 1).

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One of the most important parameters to obtain in the Nelder wheel plot was the 144 'rectangularity' proportion (Parrott et al. 2012). This is defined as a proportional 145 relationship between the arc length between spokes and the radial length between arcs, 146 where the numerator represents the arc length and the denominator represents radial 147 distance (Nelder 1962). Extreme 'rectangularity values can cause bias by creating an 148 unreasonably asymmetric arrangement of space around trees, so a rectangularity value of 149 1 was defined in the present experiment (Parrott et al. 2012).

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Ten densities were tested, ranging from 1000 to 80000 seedlings/ha (Table 1). Minimum 151 and maximum densities were also defined, to measure the effects of low and high fire in Pinus halepensis stands, which served to establish the maximum density at 80000 161 seedlings/ha in the present study. The same densities were tested for all seedlings of each 162 concentric ring and can be expressed in terms of stand density (trees/ha) or the 'growing 163 space' (m 2 /tree) available to each tree. In the present work, this will be referred to as 164 'growing space', which is related to stand density (Table 1) needles and thin branches (diameter smaller than 2 cm). The thinnest root fraction could 181 not be retrieved and there were no thick branches (diameter greater than 2 cm) on the 182 trees, so these elements were not included in the analysis. Samples of each fraction were 183 oven dried at 80 °C until constant weight was reached. Total biomass was defined as the 184 sum of the aboveground biomass (stem, thin branches and needles) and belowground 185 biomass (roots). The belowground/aboveground ratio was also calculated.

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The biomass production analysis was developed following the methodology of

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All compartment combinations between equations (5) and (7) were also tested.  (Table 2). Each biomass fraction was fitted individually 232 using the SAS 9.4 MODEL procedure of the SAS/STAT statistical program (SAS 233 Institute Inc. 2020). The different fractions were fitted as unique fractions in the analysis.

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The statistical parameters (the sum of squared estimated of errors (SSR) and the 235 determination coefficient (R 2 )) from the 13 models fitted for each fraction were then 236 compared to choose the best model. Weighted fitting using the inverse of the variance of 237 the residuals (σi 2 ) was applied to correct the heteroscedasticity problem (Parresol 2001).

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Exponent values of k were added to the fitting program. After fitting, the models were 239 again subjected to heteroscedasticity tests to verify their correctness. The best models for 240 each fraction were fitted simultaneously by the seemingly unrelated regressions method 241 (SUR) to guarantee the additivity of the system (SAS Institute Inc., 2020). The SUR  (Table 3 and Supplementary Figure 2). Pinus 253 halepensis seedling biomass was also higher, with 1504 g mean total biomass compared 254 to approximately 39 g for Pinus pinaster (Table 4). In both cases, needle biomass was higher than the other compartments, but root biomass was lower than the other 256 compartments for Pinus halepensis and branch biomass was lower than the other 257 compartments for Pinus pinaster ( Figure 2). This was reflected in 258 belowground/aboveground biomass ratio values of 0.23 for Pinus halepensis and 0.41 for 259 Pinus pinaster (Table 4 and Figure 3).  for the belowground to aboveground biomass ratio because the predictors were not 267 significant at all. In the case of Pinus pinaster however, equation (2) ln = 1 + 268 2 ln( ) + 3 ln ( ) showed better fit for all the biomass except the ratio. Once again, the 269 predictors were not significant and none of the equations was considered for this variable.

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In summary, basal diameter, total height and seedling growing space were better 271 predictors for estimating Pinus halepensis biomass, whereas basal diameter and total 272 height were better for Pinus pinaster. were considered for calculating fitted proportions ( For Pinus pinaster, basal diameter and total height were significant but growing space 306 was not. Fitted biomass proportions of each component are represented in Figure 5 307 considering minimum, average and maximum values for tree size (basal diameter and 308 total height) of harvested Pinus pinaster seedlings (Table 3). In general, higher sizes 309 increased biomass proportions for roots and thin branches but decreased needle and stem 310 biomass.

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Biomass components -SUR method 312 A system of compatible allometric equations for estimating biomass for tree components 313 was obtained for both species. Results of the individual models showed the best models 314 for each biomass fraction (roots, stem, needles and thin branches) of each species (Table   315   6).

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For Pinus halepensis, Model 9 gave the highest value of R 2 in total biomass, thin branches 317 and needles, while models 7 and 10 were the best for roots and stem, respectively.

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For Pinus pinaster, though the highest values of R 2 were obtained from Model 12 for thin 319 branches and root fractions, Model 10 for the stem, Model 13 for needles and Model 9 320 for total biomass; the best options for subsequent simultaneous fitting were Model 1 for 321 needles and stem fractions, Model 2 for thin branches and Model 7 for the root fraction.

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They were chosen because they had the smaller number of variables linked to the small 323 amount of data. Anyway, they have an appropriated biological behaviour.

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The results of the final simultaneous fitting and the statistics for bias and precision are 325 presented in Table 7. All parameters were significant at the 95% confidence level and all 326 models included basal diameter and total height as independent variables.

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Interest in biomass analysis for young trees is growing because natural regeneration densities along with lower root biomass at higher tree densities, but without the 353 decreasing effect for the crown. However, total, aboveground and belowground biomass 354 production were generally higher at lower densities. These minor differences between the 355 two studies may be due to age differences in trees; the earlier study included trees ranging 356 from five to 16 years old, while the present study looked only at four-year-old trees.

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Our results showed a general increment of total biomass for Pinus halepensis at lower proportions of around 20% allocated to stem biomass, less than 60% to crown biomass 406 with thin branches and needles, and around 20% to root biomass. Ruiz-Peinado et al.

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(2011) found differences between species, mainly for stem and crown biomass.    non-significant effect.