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 ∗𝐸𝑋𝑃( ∗ ) [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 ∗ (𝐷𝐵𝐻 ∗H ) + 0.0009 ∗ Eucryphia cordifolia 22.2 34 (𝐷𝐵𝐻 )
Nothofagus dombeyi 𝑉 = −0.001846 + 0.000037 ∗ (𝐷𝐵𝐻 ∗𝐻) Ni 50
𝑉 = −0.2129 + 0.000014 ∗ (𝐷𝐵𝐻 ∗𝐻) + 0.000459 ∗ Aextoxicon 24.8 104 punctatum (𝐷𝐵𝐻 ) Laureliopsis 𝑉 = 0.00003 ∗ (𝐷𝐵𝐻 ∗𝐻) −9.258∗10 ∗ (𝐷𝐵𝐻 ∗ 32.7 84 philippiana 𝐻)
Drimys winteri V = 0.000007357 ∗ (𝐷𝐵𝐻 ∗𝐻) + 0.000371 ∗ (𝐷𝐵𝐻 ) 26.3 117
V = 0.000025 ∗ (𝐷𝐵𝐻 ∗𝐻) + 1.40850 ∗ 10 ∗ Amomyrtus meli 23.5 99 (𝐷𝐵𝐻 ∗𝐻) − 1.28933 ∗ 10 ∗ (𝐷𝐵𝐻 ∗𝐻)
Weinmannia V = −0.1052 + 0.00004606 ∗ (𝐷𝐵𝐻 ∗𝐻) + 0.0001776 ∗ Ni Ni trichosperma 𝐷𝐵𝐻 + 0.0002609 ∗ 𝐻 Proteaceae and V = 0.000025 ∗ (𝐷𝐵𝐻 ∗𝐻) 20.1 29 others species
Luma apiculata V = 0.0381 + 0.4731 ∗ ( ) ∗ (−5.081 + 0.7704 ∗ 𝐻) Ni Ni
V = 0.000028 ∗ (𝐷𝐵𝐻 ∗𝐻) + 7.0473 ∗ 10 ∗ (𝐷𝐵𝐻 ∗ Amomyrtus luma 17.5 49 𝐻) −2.583∗10 ∗ (𝐷𝐵𝐻 ∗𝐻 )
Podocarpus sp V = 0.00004375 ∗ 𝐷𝐵𝐻 ∗ 𝐻 + 0.00009836 ∗ 𝐷𝐵𝐻 Ni Ni
Saxegothaea V = (−9.915425 + 0.939798 ∗ LN(DBH ∗H) Ni 30 conspicua Dasyphyllum V = 0.000799 + 0.000033318 ∗ (𝐷𝐵𝐻 ∗𝐻) Ni 50 diacanthoides
Persea lingue V = −0.041488 + 0.000448 ∗ (𝐷𝐵𝐻 ) + 0.003063 ∗ 𝐻 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* 𝑌 =𝛼+
Site 0.2786 𝐿𝑜𝑔( 𝑑𝑏ℎ) + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 (2013) + All trees Treatment 0.8799 𝑆𝑖𝑡𝑒 + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 ∗𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡
Diameter class * 𝑆𝑖𝑡𝑒 +𝑎 + ɛ 0.0001* Treatment * Site
𝑌 =𝛼+ Log(d) 0.0001* Log (pai in 𝑌 =𝛼+ 𝐿𝑜𝑔( 𝑑𝑏ℎ) + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 (2013) + Diameter class 0.0001* diameter) Mid- 𝑆𝑖𝑡𝑒 + 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 +𝑑𝑏ℎ𝑐𝑙𝑎𝑠𝑠∗ Site 0.0164* 𝐿𝑜𝑔( 𝑑𝑏ℎ) + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 (2013) + (cm year-1) tolerant Treatment 0.3352 𝑆𝑖𝑡𝑒 + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 ∗𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 ∗𝑠𝑖𝑡𝑒+𝑎 + ɛ
Diameter class * 𝑆𝑖𝑡𝑒 +𝑎 + ɛ 0.0001* Treatment * Site
Log(d) 0.0001*
Diameter class 0.0001* 𝑌 =𝛼+ Shade- Site 0.6215 𝐿𝑜𝑔( 𝑑𝑏ℎ) + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 (2013) + tolerant Treatment 0.5161 𝑆𝑖𝑡𝑒 + 𝑑𝑏ℎ 𝑐𝑙𝑎𝑠𝑠 ∗𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 Diameter class * 0.0001* 𝑆𝑖𝑡𝑒 +𝑎 + 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 * 𝑌 =𝛼 +
Height class 2.2e-16 * 𝑌𝑒𝑎𝑟 + 𝐻𝑒𝑖𝑔ℎ 𝑐𝑙𝑎𝑠𝑠 +
Site 0.0113* 𝑆𝑖𝑡𝑒 + 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 + Shade- Treatment 0.5267 𝑌𝑒𝑎𝑟 ∗ 𝑆𝑖𝑡𝑒∗ intolerant Year * Site * Treatment 2.2e-16 * 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 +
𝐻𝑒𝑖𝑔ℎ 𝑐𝑙𝑎𝑠𝑠 ∗𝑌𝑒𝑎𝑟+ Height class * Year 2.2e-16 *
𝑎 + ɛ 𝑌 =𝛼+ Year 7.2e-07 * 𝑌 =𝛼+𝑌𝑒𝑎𝑟+ 𝑌𝑒𝑎𝑟 + 𝐻𝑒𝑖𝑔ℎ𝑡 𝑐𝑙𝑎𝑠𝑠 + Regeneration Height class 2.2e-16 * + 𝐻𝑒𝑖𝑔ℎ 𝑐𝑙𝑎𝑠𝑠 +𝑆𝑖𝑡𝑒+ 𝑆𝑖𝑡𝑒 + 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 + density Site 0.0474* 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 +𝑌𝑒𝑎𝑟∗ Mid-tolerant 𝑌𝑒𝑎𝑟 ∗ 𝑆𝑖𝑡𝑒 ∗ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 + (n ha-1) Treatment 0.3900 𝑆𝑖𝑡𝑒 ∗ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 + 𝐻𝑒𝑖𝑔ℎ𝑡 𝑐𝑙𝑎𝑠𝑠 ∗𝑌𝑒𝑎𝑟+𝑎 + Year * Site * Treatment 2.2e-16 * 𝐻𝑒𝑖𝑔ℎ 𝑐𝑙𝑎𝑠𝑠 ∗𝑌𝑒𝑎𝑟+ ɛ Height class * Year 2.2e-16 * 𝑎 + ɛ
Year 2.2e-16 * 𝑌 =𝛼+𝑌𝑒𝑎𝑟+
Height class 2.2e-16 * + 𝐻𝑒𝑖𝑔ℎ 𝑐𝑙𝑎𝑠𝑠 +𝑆𝑖𝑡𝑒+
Shade- Site 0.0100* 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 +𝑌𝑒𝑎𝑟∗
tolerant Treatment 0.9176 𝑆𝑖𝑡𝑒 ∗ 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 +
Year * Site * Treatment 2.2e-16 * 𝐻𝑒𝑖𝑔ℎ 𝑐𝑙𝑎𝑠𝑠 ∗𝑌𝑒𝑎𝑟+
Height class * Year 2.2e-16 * 𝑎 + 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 𝑌 = 𝑆𝑖𝑡𝑒+𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 Treatment 0.039*
Site 0.5154 .1) Ingrowth density (n° ha Mid-tolerant 𝑌 = 𝑆𝑖𝑡𝑒+𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 Treatment 0.158
Site 0.3620
Shade-tolerant 𝑌 = 𝑆𝑖𝑡𝑒+𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 Treatment 0.082
Pai basal area (m2 ha-1 Site 0.0110* Stand level 𝑌 = 𝑆𝑖𝑡𝑒+𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 year-1) Treatment 0.0227*
Site 0.0428* 3 -1 -1 Pai volume (m ha year ) Stand level 𝑌 = 𝑆𝑖𝑡𝑒+𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 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).
Seedlings Saplings HRBA LRBA HRBA LRBA Species 2013 2019 2013 2019 2019 Intolerant Embothrium coccineum 0 0 0 23±23 0 0 Weinmannia trichosperma 0 23±46 0 0 0 0 Sub-total 0 23±46 0 23±23 0 0 Mid-tolerant Caldcluvia paniculata 116±89 162±205 162±139 93±131 116±139 93±185 Eucryphia cordifolia 3,125±1,735 3,588±2,075 2,500±1,559 2,963±1,872 1,319±333 1,667±293 Gevuina avellana 1,065±537 1,806±548 880±325 1,227±863 810±443 486±306 Sub-total 4,306±2,284 5,556±1,872 3,542±1,900 4283±2,837 2,245±547 2,246±746 Tolerant Aextoxicon punctatum 1,435±1,461 5,856±5731 1,134±754 3,009±2,365 301±315 162±139 Amomyrtus luma 625±761 5,046±1,919 1,551±1,355 6,088±2,679 579±531 949±583 Amomyrtus meli 2,338±2,014 4,074±4,183 1,690±1,150 3,796±1,584 532±639 301±244 Laureliopsis philippiana 463±484 880±1,213 486±333 694±773 162±89 185±200 Lomatia ferruginea 2,245±1,831 3,032±1,535 1,968±816 3,843±2,035 648±535 486±456 Myrceugenia planipes 1,644±1,239 3,009±2,756 1,296±1,074 2,685±2,291 139±220 347±450 Other species* 69±139 116±231 23±46 93±107 23±46 0 Persea lingue 1,481±2,537 509±307 1,736±1,140 671±731 46±92 69±139 Raukaua laetevirens 0 370±273 463±865 648±1,235 23±46 23±46 Rhaphithamnus spinosus 139±93 370±239 69±89 301±366 23±46 23±46 Sub-total 10,439±5,115 23,262±11,969 10,416±2,890 21,828±9,225 2,476±1,725 2,545±1,216
* Dasyphyllum diacanthoides, Lomatia dentata, Myrceugenia ovata
Figure S1. Diameter distribution after harvest and 5/6 years later, according to site and treatment: a) Low residual basal area Llancahue; b) High residual basal area Llancahue; c)
Low residual basal area Los Riscos; d) High residual basal area Los Riscos.
References
1. Drake, F.; Emanuelli, P.; Acuña, E. Compendio de Funciones Dendrométricas del Bosque Nativo; CONAF y Sociedad Alemana de Cooperación Técnica: Santiago, Chile, 2003; p. 96.