# Determining Allometry and Carbon Sequestration Potential of Breadfruit (Artocarpus altilis) as a Climate-Smart Staple in Hawai‘i

^{*}

## Abstract

**:**

^{2}0.81), carbon density (r

^{2}0.87), and foliar biomass (r

^{2}0.91), which were combined to generate an allometric prediction of tree volume (r

^{2}0.98) based on tree diameter at breast height. Growth rates, as measured by diameter at breast height, were well predicted over time when trees were classified by habitat suitability. We extrapolate potential breadfruit growth and carbon sequestration in above-ground biomass to the landscape scale over time. This study shows that breadfruit is on the low end of broadleaf tropical trees in moist and wet environments, but in an orchard can be expected to sequester ~69.1 tons of carbon per hectare in its above-ground biomass over a 20-year period.

## 1. Introduction

^{2}values and are traditionally derived by destructive sampling of entire trees, which, although considered highly accurate, is expensive and time-consuming [14,16,17]. Other methods include obtaining the tree volume through detailed measurements or remote sensing technologies such as LiDAR or photogrammetry [18,19]. Statistical methods tend to apply scatter plots of individual trees to explore data trends, with emphasis on the correlation coefficients and associated errors [20,21].

## 2. Materials and Methods

#### 2.1. Overview of Sampling Approaches

#### 2.2. Woody Biomass Volumetric Measurements

#### 2.3. Wood Density and Carbon Content

^{3}) of the wood cookies was determined using the water displacement method, and the samples were then oven-dried until constant mass and weighed (g). Wood density (g/cm

^{3}) for each cookie was calculated by dividing dry mass by volume. To determine carbon density, holes were drilled through the cross-section of each cookie. The wood shavings were collected, pulverized, and encapsulated for total carbon concentration (C) analysis using an Elemental Analyzer. Carbon density (gC/cm

^{3}) was determined by multiplying the wood density by %C. Wood and carbon density were each regressed against the average branch diameter to describe wood density and carbon as a function of branch diameter.

#### 2.4. Foliar Biomass Estimation

#### 2.5. Mathematical Model of Tree Biomass/Carbon

^{2}) and probability values (P) used to describe the accuracy of the mathematical equations. A spreadsheet model was used to combine all factors measured and computer total biomass and carbon for each tree measured. For each row in the spreadsheet, the major (D

_{M}) and minor (D

_{m}) diameters were used to calculate the average radius (R) in cm and the cross-sectional area (A) in cm

^{2}, as shown in Equations (1) and (2).

^{3}. For each segment, the regression equations we determined to describe the relationship of wood density ($\rho $) and carbon concentration (C

_{%}) as a function of branch radius were applied, so that total carbon density was considered a continuous function of branch thickness, as in Equations (4)–(6).

_{w}is the total carbon mass of each woody component in g. For each branch, total leaf biomass was calculated by applying the regression equation we determined to describe the relationship between leaf biomass (M

_{l}) and branch base diameter (D

_{b}), with total carbon calculated as the product of leaf biomass and the average leaf carbon density. We again leveraged branch segment number to apply an IF statement, so that the model only calculates leaf biomass for the first (base) measurement of each branch as in Equation (7):

_{l}is the total dry biomass of the leaf component in g, and C

_{l}is the total carbon mass of leafy components in g.

^{2}, P, and root mean square errors were assessed.

#### 2.6. Breadfruit Growth Rates

#### 2.7. Below Ground Biomass (BGB) and Landscape-Scale Total Biomass over Time

## 3. Results

#### 3.1. Wood Density and Carbon

^{2}= 0.799). The relationship of wood density to average radius was used as the function described in Equation (5).

^{2}values. Therefore, the linear regression was applied to describe carbon concentration as a function of stem diameter, as described in Equation (6). Despite the variation in carbon concentration, a calculation of carbon density (gC/cm

^{3}) by average branch radius yields a highly significant relationship with a robust (r

^{2}= 0.865).

#### 3.2. Foliar Biomass

^{2}= 0.907) than the tip diameter (r

^{2}= 0.819). The associated regression equation was used to describe leaf biomass as a function of terminal branch base diameter in Equation (7). Carbon percentage for the foliar biomass was determined for half (n = 20) of the samples and was found to have an average of 51.4% with a standard deviation of 1.14.

#### 3.3. Woody Biomass Volume and Total Above-Ground Biomass (ABG)

^{3}to 973,860 cm

^{3}. The resulting woody biomass from our spreadsheet model ranged from 216 g to 350,608 g, and the total foliar biomass ranged from 177 g to 36,395 g. The sum of woody and foliar biomass was used to represent the total ABG (Table 1). The total ABG for each tree was regressed against the measured DBH of those trees, demonstrating a robust non-linear relationship best described by a quadratic equation (AGB = −4.586 + 0.1635 × DBH + 0.2229 × DBH

^{2}; r

^{2}0.98, p < 0.001).

#### 3.4. Growth Curves for Breadfruit

^{2}= 0.87, p < 0.001). However, this represents highly diverse habitats across Hawai‘i Island. Trees were therefore broken into suitability classes of High (n = 38), Moderate (n = 42), and Low (n = 128) [25]. Regressions by suitability classification were best explained by quadratic functions (Figure 4; Table 2).

#### 3.5. Landscape Extrapolations

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Carbon concentration in dried breadfruit wood samples as a function of average branch radius in (

**a**) percent carbon by mass and (

**b**) carbon mass by volume.

**Table 1.**Calculated dry wood biomass, leaf biomass, and total above ground biomass (ABG) of breadfruit trees measured in this study.

DBH (cm) | Wood Biomass (g) | Leaf Biomass (g) | Total AGB (kg) |
---|---|---|---|

2.6 | 216 | 177 | 0.39 |

4.7 | 1575 | 324 | 1.90 |

6.2 | 4446 | 854 | 5.30 |

7.6 | 5520 | 1287 | 6.81 |

10.9 | 11,971 | 3851 | 15.82 |

14.4 | 32,452 | 10,054 | 42.51 |

17.1 | 59,815 | 14,139 | 73.95 |

22.4 | 83,629 | 23,186 | 106.81 |

26.9 | 124,470 | 30,854 | 155.32 |

27.4 | 144,833 | 33,566 | 178.40 |

35 | 232,102 | 36,394 | 268.50 |

41.2 | 350,608 | 31,811 | 382.42 |

**Table 2.**Equations describing the growth in DBH of 208 breadfruit trees on Hawai‘i Island classified by habitat suitability.

Suitability Class | Equation | R^{2} | RMS Error |
---|---|---|---|

High | DBH = 12.57 + 1.47(Age) − 0.007(Age)^{2} | 0.98 | 3.8 |

Medium | DBH = 5.766 + 1.47(Age) − 0.010(Age)^{2} | 0.96 | 3.6 |

Low | DBH = 3.308 + 1.07(Age) − 0.0056(Age)^{2} | 0.89 | 3.3 |

**Table 3.**Extrapolation of total CO

_{2}sequestration associated wtih a breadfruit orchard based on the growth curve, allometric equation, and wood/carbon density determine in this study.

Age | DBH (cm) | AGB (kg) | BGB (kg) | AGC (kg) | BGC (kg) | C (kg/Tree) | CO_{2} (tons/ha) |
---|---|---|---|---|---|---|---|

5 | 19.7 | 85.5 | 20.5 | 39.2 | 8.2 | 47.4 | 16.7 |

10 | 26.6 | 157.1 | 37.7 | 73.3 | 15.1 | 88.3 | 31.2 |

15 | 33.0 | 244.2 | 58.6 | 115.0 | 23.4 | 138.4 | 48.8 |

20 | 39.2 | 343.8 | 82.5 | 162.9 | 33.0 | 195.9 | 69.1 |

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**MDPI and ACS Style**

Livingston, C.; Lincoln, N.K.
Determining Allometry and Carbon Sequestration Potential of Breadfruit (*Artocarpus altilis*) as a Climate-Smart Staple in Hawai‘i. *Sustainability* **2023**, *15*, 15682.
https://doi.org/10.3390/su152215682

**AMA Style**

Livingston C, Lincoln NK.
Determining Allometry and Carbon Sequestration Potential of Breadfruit (*Artocarpus altilis*) as a Climate-Smart Staple in Hawai‘i. *Sustainability*. 2023; 15(22):15682.
https://doi.org/10.3390/su152215682

**Chicago/Turabian Style**

Livingston, Chad, and Noa Kekuewa Lincoln.
2023. "Determining Allometry and Carbon Sequestration Potential of Breadfruit (*Artocarpus altilis*) as a Climate-Smart Staple in Hawai‘i" *Sustainability* 15, no. 22: 15682.
https://doi.org/10.3390/su152215682