*2.6. Diameter of the Red Pines up to the Resin Collection Year*

The diameter of the red pines during resin collection years was estimated using the increment cores extracted from the wounded side and the opposite side. The former cores were used to measure the half diameter from the pith to the wounded surface (a or a' in Figure 4B) and the latter ones were from the pith to the tree rings formed up to the resin collection year (b or b' in Figure 4). When the cores from the wounded side and/or the other side had pith, the half diameter up to the resin collection year was measured using the lengths of a and/or b. By contrast, when both or one core had no pith, the half diameter was measured as a' and/or b'. The pith location to obtain a' and b' was estimated based on the arc of the innermost tree ring (dark black arc in B of Figure 4). The current-year thickness of the bark was applied to the bark thickness at the resin collection year. Therefore, the diameter up to the resin collection year was estimated using Equation (3).

$$D\ (cm) = a \ +b \ +2c \text{ or } D\ (cm) = a' + b' + 2c \tag{3}$$

where *D* is the diameter at the resin collection year, *a* or *a* ′ is the observed or estimated length from the pith to the outermost tree ring of the wounded side, *b* or *b* ′ is the observed or estimated length from the pith to the tree ring formed at the resin collection year at the opposite side of the wound, and *c* is the bark thickness at the current year. ܦ ሺܿ݉ሻ ൌ ܽ ܾ 2ܿ ܦ ሺܿ݉ሻ ൌ ܽ<sup>ᇱ</sup> ܾ<sup>ᇱ</sup> 2ܿ ′ ′

**Figure 4.** Illustration to estimate the diameter of red pines (*Pinus densiflora*) from the wounds of resin collection. (**A**) Cross-section with directions to extract increment cores; (**B**) estimation of the diameter at resin collection year for cores with or without pith.

The estimated dimeter (D in Figure 4), which lay extremely outside the overall distribution, had been removed from further analysis since an outlier can overestimate or underestimate the result. An outlier is determined as follows.

$$Outlier < Q\_1 - 1.5 \times (Q\_3 - Q\_1) \, or > Q\_3 + 1.5 \times (Q\_3 - Q\_1) \tag{4}$$

where *Q*<sup>1</sup> is the first quartile diameter and *Q*<sup>3</sup> is the third quartile diameter.
