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Table 1 Independent (xk) and dependent (yk) variables in models [10]. k is the hypothesis equation number. Notation: stem cross-sectional area at crown base (Ac), foliage biomass (Wf), total cross-sectional area of live branches (Ab), branch wood density (ρb), basal-area-weighted average branch length (Hb), branch biomass (Wb), crown length (Hc), stem volume above (Vc) and below the crown base (Vs), crown ratio (r) and stem from coefficient below the crown base (φs)

From: Age effect on tree structure and biomass allocation in Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies [L.] Karst.)

k

1

2

3

4a

7

8b

xk

Ac

Ac

ρbHbAb

lnHc

HcAc

(1 + r)/2r

yk

Wf

Ab

Wb

lnHb

Vc

φs

  1. a Eq. (4) was ln-transformed
  2. b φs is a free parameter that depends on crown ratio, instead of a constant value estimated by Vs/ HsAc. Hence, we hypothesised Vs = (1 + r)/2r(HsAc) and tested the age independence on φs = (1 + r)/2r