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Supplementary Material Supplementary material Initial responses in growth, production, and regeneration following selection cuttings with varying residual densities in hardwood-dominated temperate rainforests in Chile Height and diameter functions, adjusted following the Stage’s model ([35]; equation S1). µ h=1,3+ α ∗(∗ ) [S1] Where: α, β, μ: parameters to be estimated; dbh: diameter at breast height (cm); h = total height (m). Table S1 Parameters and measures of goodness of fit and prediction of height-diameter functions in Llancahue (LL). n: number of samples. Parameter DA RMSE R2 Species n α β µ (%) (%) (%) Aextoxicon punctatum 69.33 5.35 0.41 0.08 14.42 87 30 Drimys winteri 32.04 4.46 0.59 -0.70 9.42 92 30 Eucryphia cordifolia 58.08 4.13 0.41 0.99 12.00 85 57 Laureliopsis philippiana 56.20 5.30 0.47 0.48 13.57 78 78 Long-lived intolerant 49.62 3.46 0.38 -0.08 14.58 72 16 Myrtaceae 147.06 4.81 0.25 1.48 16.87 75 30 Other species 44.48 4.61 0.43 0.53 17.92 70 31 Podocarpaceae 61.13 5.01 0.40 0.18 13.57 89 26 Proteaceae 31.32 2.82 0.43 -1.25 16.61 50 22 Notes: Long-lived intolerant: Nothofagus dombeyi, Weinmannia trichosperma; Myrtaceae: Amomyrtus luma, Amomyrtus meli, Luma apiculate;Podocarpaceae: Podocarpus salignus, Podocarpus nubigenus, Saxegothaea conspicua; Proteaceae: Gevuina avellana, Lomatia ferruginea, Lomatia dentata. DA and RMSE are measures of goodness of prediction: DA (Aggregated difference), RMSE (Root mean square error). R2 is a measure of goodness of fit (Coefficient of determination). Table S2 Parameters and measures of goodness of fit and prediction of height-diameter functions in Llancahue (LL). n: number of samples. Parameter DA RMSE R2 Species n α β µ (%) (%) (%) Aextoxicon punctatum 49.26 5.84 0.53 0.10 15.90 83 59 Eucryphia cordifolia 32.63 6.00 0.77 -0.22 19.43 76 83 Laureliopsis philippiana 38.75 4.87 0.57 -0.30 16.72 73 79 Long-lived intolerant 49.62 3.46 0.38 -0.08 14.58 72 16 Myrtaceae 30.17 3.67 0.55 -0.16 16.51 69 89 Other species 44.48 4.61 0.43 0.53 17.92 70 31 Persea lingue 27.16 4.51 0.67 -1.23 16.98 78 18 Proteaceae 27.51 3.51 0.58 -0.14 17.08 63 24 Notes: Long-lived intolerant: Nothofagus dombeyi, Weinmannia trichosperma; Myrtaceae: Amomyrtus luma, Amomyrtus meli, Luma apiculata; Proteaceae: Gevuina avellana, Lomatia ferruginea, Lomatia dentata; DA and RMSE are measures of goodness of prediction: DA (Aggregated difference), RMSE (Root mean square error). R2 is a measure of goodness of fit (Coefficient of determination). Table S3 Total stem volume functions used in the study [1]. Species Volume function RMSE (%) n V = −0.10377 − 0.0000099208 ∗ ( ∗H ) + 0.0009 ∗ Eucryphia cordifolia 22.2 34 () Nothofagus dombeyi = −0.001846 + 0.000037 ∗ ( ∗) Ni 50 = −0.2129 + 0.000014 ∗ ( ∗) + 0.000459 ∗ Aextoxicon 24.8 104 punctatum () Laureliopsis = 0.00003 ∗ ( ∗) −9.258∗10 ∗ ( ∗ 32.7 84 philippiana ) Drimys winteri V = 0.000007357 ∗ ( ∗) + 0.000371 ∗ () 26.3 117 V = 0.000025 ∗ ( ∗) + 1.40850 ∗ 10 ∗ Amomyrtus meli 23.5 99 ( ∗) − 1.28933 ∗ 10 ∗ ( ∗) Weinmannia V = −0.1052 + 0.00004606 ∗ ( ∗) + 0.0001776 ∗ Ni Ni trichosperma + 0.0002609 ∗ Proteaceae and V = 0.000025 ∗ ( ∗) 20.1 29 others species Luma apiculata V = 0.0381 + 0.4731 ∗ ( ) ∗ (−5.081 + 0.7704 ∗ ) Ni Ni V = 0.000028 ∗ ( ∗) + 7.0473 ∗ 10 ∗ ( ∗ Amomyrtus luma 17.5 49 ) −2.583∗10 ∗ ( ∗) Podocarpus sp V = 0.00004375 ∗ ∗ + 0.00009836 ∗ Ni Ni Saxegothaea V = (−9.915425 + 0.939798 ∗ LN(DBH ∗H) Ni 30 conspicua Dasyphyllum V = 0.000799 + 0.000033318 ∗ ( ∗) Ni 50 diacanthoides Persea lingue V = −0.041488 + 0.000448 ∗ () + 0.003063 ∗ Ni 22 RMSE (Root mean square error); * Ni = no information Table S4 Mixed-effect models for the effect of site and treatment on diameter increment. Functional Source of Response Beyond optimal model P Final model group variation Log(d) 0.0001* Diameter class 0.0001* =+ Site 0.2786 ( ℎ) + ℎ (2013) + All trees Treatment 0.8799 + ℎ ∗ Diameter class * + + ɛ 0.0001* Treatment * Site =+ Log(d) 0.0001* Log (pai in =+ ( ℎ) + ℎ (2013) + Diameter class 0.0001* diameter) Mid- + +ℎ∗ Site 0.0164* ( ℎ) + ℎ (2013) + (cm year-1) tolerant Treatment 0.3352 + ℎ ∗ ∗+ + ɛ Diameter class * + + ɛ 0.0001* Treatment * Site Log(d) 0.0001* Diameter class 0.0001* =+ Shade- Site 0.6215 ( ℎ) + ℎ (2013) + tolerant Treatment 0.5161 + ℎ ∗ Diameter class * 0.0001* + + ɛ Treatment * Site Notes: Log(d): Log (diameter of tree-i in the plot-j in 2013); Diameter class: diameter class of the tree-i in the plot-j in 2013 (5-≤20 cm, 20- ≤50 cm, 50-80 cm, >80 cm); site: LL or LR; treatment: HRBA or LRBA; Year: 2013 or 2018-19; P: p-values of the significant tests; αj: Random effect of the nested plots within the sites. Table S5 Mixed-effect models for the effect of year, height class, site and treatment on regeneration density. Functional Response Beyond optimal model Source of variation P Final model group Year 2.2e-16 * = + Height class 2.2e-16 * + ℎ + Site 0.0113* + + Shade- Treatment 0.5267 ∗ ∗ intolerant Year * Site * Treatment 2.2e-16 * + ℎ ∗+ Height class * Year 2.2e-16 * + ɛ =+ Year 7.2e-07 * =++ + ℎ + Regeneration Height class 2.2e-16 * + ℎ ++ + + density Site 0.0474* +∗ Mid-tolerant ∗ ∗ + (n ha-1) Treatment 0.3900 ∗ + ℎ ∗+ + Year * Site * Treatment 2.2e-16 * ℎ ∗+ ɛ Height class * Year 2.2e-16 * + ɛ Year 2.2e-16 * =++ Height class 2.2e-16 * + ℎ ++ Shade- Site 0.0100* +∗ tolerant Treatment 0.9176 ∗ + Year * Site * Treatment 2.2e-16 * ℎ ∗+ Height class * Year 2.2e-16 * + ɛ Notes: Site: LL or LR; treatment: HRBA or LRBA; Year: 2013 or 2018-19; Height class: (5-<50, 50-<100, 100-200 cm) of tree regeneration-i in the plot-j; P: p-values of the significant tests: αj: Random effect of the nested subplots within the plot and the sites. Table S6 Effect of site and treatment in the generalized linear model (ingrowth) and the linear model (Pai in basal area and volume). Functional group Response Model Source of variation P Site 0.3670 All trees = + Treatment 0.039* Site 0.5154 .1) Ingrowth density (n° ha Mid-tolerant = + Treatment 0.158 Site 0.3620 Shade-tolerant = + Treatment 0.082 Pai basal area (m2 ha-1 Site 0.0110* Stand level = + year-1) Treatment 0.0227* Site 0.0428* 3 -1 -1 Pai volume (m ha year ) Stand level = + Treatment 0.0195* Notes: Site: LL or LR; treatment: HRBA or LRBA; P: p-values of the significant tests. Table S7 Mean and standard deviation of regeneration density (per ha values) of seedlings and saplings according to species and treatment (HRBA and LRBA) in Llancahue (LL). Seedlings Saplings HRBA LRBA HRBA LRBA Species 2013 2018 2013 2018 2018 Intolerant Nothofagus dombeyi 1,505±2,827 1,019±2,037 69±139 116±231 0 0 Weinmannia trichosperma 46±53 23±46 0 0 0 0 Other species* 69±89 185±130 209±324 139±224 0 0 Subtotal 1,620±2,874 1,227±2,207 278±227 255±450 0 0 Mid-tolerant Caldcluvia paniculata 0 0 23±46 69±139 0 0 Drimys winteri 2,361±1,413 2,477±2,683 4,745±5,708 8,426±13,736 116±75 347± 66 Eucryphia cordifolia 4,352±3,272 4,931±3,748 3,171±2,523 3,032±1,332 46±93 208±208 Gevuina avellana 1,250±924 1,111±983 880±53 1,181±746 278±227 324±220 Podocarpus salignus 1,528±1,364 1,944±1,729 1,042±205 648±227 46±93 69±69 Subtotal 9491±3,339 10,463±7,085 9,861±5,540 13,356±14,456 486±456 948±734 Tolerant Aextoxicon punctatum 7,662±4,387 9,676±4,130 22,014±12,286 16,713±5,160 232±120 370±273 Amomyrtus luma 12,083±4,387 17,083±11,345 16,088±11,546 13,611±4,066 717±423 1,019±460 Amomyrtus meli 278±496 0 995±1,065 4,005±7,886 0 0 Dasyphyllum diacanthoides 486±972 787±1,092 0 417±487 0 0 Laureliopsis philippiana 1,574±1,249 1,319±669 2,269±809 2,454±1,624 486±306 348±175 Lomatia dentata 1,389±2,594 1,574±2,664 394±324 486±381 116±117 0 Lomatia ferruginea 3,218±2,572 4,931±1,711 8,380±6,101 7,060±3,539 0 185±131 Myrceugenia planipes 1,898±3,378 2,662±4,532 486±791 833±737 116±231 23±46 Persea lingue 0 255±89 0 46±53 0 0 Raukaua laetevirens 394±388 486±410 347±381 509±404 0 0 Rhaphithamnus spinosus 1,042±731 1,157±1,949 2,731±1,010 2,546±2,120 116±89 93±76 Saxegothaea conspicua 23±46 46±53 0 69±139 0 0 Other species** 23±46 139±223 0 115±232 0 0 Subtotal 30,069±14,260 40,116±13,123 53,704±19,702 48,866±18,904 1,783±306 2,038±518 * Aristotelia chilensis, Embothrium coccineum, Ovidia pillopillo. ** Luma apiculata, Myrceugenia ovata Table S8 Mean and standard deviation of regeneration density (per ha values) of seedlings and saplings according to species and treatment (HRBA and LRBA) in Los Riscos (LR).
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