# Pinus patula Branch biomass from D and H (Table 4)

Branch biomass equation for Pinus patula, Mexico, from Martínez-Domínguez et al. 2020. 25 trees, DBH 3.5–25.7 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Martínez-Domínguez et al. 2020 (Section 3.1 (Model 1, Table 1)):

> y = e(−β0 + β1 ln (D × TH))

Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#equation

In this library's units, ready to compute (branch biomass in kg):

```
Branch biomass = exp(-7.8825 + 1.8028 * ln(D * H))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-7.8825 + 1.8028 * ln(D * TH)), with D in cm, TH in m; output in kg.
Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Pinus patula (species), family Pinaceae; conifer
- Where: Ixtlán de Juárez, Sierra Norte, Oaxaca (pine-oak forest). Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#where
- Biomes: temperate, montane
- Stand: natural
- Trees measured: 25. Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#n_trees
- DBH range: 3.5–25.7 cm. Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#dbh
- Height range: 4.32–20.18 m. Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#height
- R²: 0.9825. Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#r2
- Method: nonlinear regression (SAS PROC MODEL), exponential form. Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#checked_at

A missing fit statistic is one the source doesn't state, or that we haven't recorded; it is never estimated. Outside the stated DBH range or region, the equation is an extrapolation.

## Source

Martínez-Domínguez, A., Ruiz-Aquino, F., Santiago-García, W., et al. (2020). Allometric equations to estimate aboveground and belowground biomass of Pinus patula Schiede ex Schltdl. & Cham. Forest Science and Technology, 16(3), 161-170.

- DOI: https://doi.org/10.1080/21580103.2020.1801526
- Access: open access
- Copy we read: https://www.tandfonline.com/doi/full/10.1080/21580103.2020.1801526
- Every equation from this source: https://treeallometry.org/sources/martinez-dominguez-2020/
- Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#source

## The facts, in the source's words

**Equation** (Section 3.1 (Model 1, Table 1)):

> y = e(−β0 + β1 ln (D × TH))

Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#equation

**Equation** (Table 4, Branches row, p. 165):

> δ0 7.8825, δ1 1.8028, R2 0.9825

Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#quote-expression

**Trees measured** (Abstract):

> a destructive analysis was made of 25 trees distributed in five diameter classes

Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#quote-fit-n-trees

**Smallest DBH** (Section 3.1):

> diameter at breast height (D) that varied from 3.5 cm to 25.7 cm, with a total height (TH) fluctuating from 4.32 m to 20.18 m

Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#quote-fit-dbh-min-cm

**Our note:** Printed form y = e^(−β0 + β1 ln(D × TH)); the tabulated β0 is positive and enters with a minus sign, as printed. Units are D in cm, TH in m, biomass in kg dry weight (Figure 3). No correction factor stated. Parameters read from Table 4 of the journal PDF (p. 165); the HTML version offers no CSV for Table 4. The paper also fits an additive simultaneous system (Table 6) with slightly different parameters; not added. The foliage model (Table 4: ϖ0 8.1986, ϖ1 1.6628, R2 0.9762) is not added here; the printed additive formula in Section 3.3 shows the foliage intercept without the minus sign, but Figure 3(d) (p. 166) prints the fitted foliage curve as y = e^(−8.198579+(1.66277 ln(D x TH))), n=25, so the sign is a typesetting slip and the model could be added as exp(−8.1986 + 1.6628 ln(D × TH)). Authors recommend use for 5 to 25 cm DBH.

## Checks this equation passes

On every build, the library's form and the source's own form (in its units) must both give these values within 1%.

| Inputs | Expected | We get | From |
| --- | --- | --- | --- |
| D = 8, H = 7 | 0.535 | 0.535 | Computed from the printed form: computed from the published form |
| D = 13, H = 12 | 3.39 | 3.39 | Computed from the printed form: computed from the published form |
| D = 22, H = 18 | 18.2 | 18.2 | Computed from the printed form: computed from the published form |

Cite: https://treeallometry.org/equations/martinez-dominguez-2020-branch/#checks

The calculator on the page shows carbon as biomass × 0.47 (IPCC 2006 Guidelines, Vol. 4, Ch. 4, Table 4.3) and CO₂e as carbon × 44/12.

## How to cite

Cite the source for the equation: Martínez-Domínguez, A., Ruiz-Aquino, F., Santiago-García, W., et al. (2020). Allometric equations to estimate aboveground and belowground biomass of Pinus patula Schiede ex Schltdl. & Cham. Forest Science and Technology, 16(3), 161-170. https://doi.org/10.1080/21580103.2020.1801526

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Pinus patula Branch biomass from D and H (Table 4)", checked 2026-11-02, https://treeallometry.org/equations/martinez-dominguez-2020-branch/. Data CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quotes are the authors' words.

Data for this equation: https://treeallometry.org/data/equations/martinez-dominguez-2020-branch.json
Report a problem: email info@restorationscope.com with the equation id (martinez-dominguez-2020-branch) and where the right value appears.