### Abstract

Summary: The West, Brown, Enquist (WBE) model derives symmetrically self-similar branching to predict metabolic scaling from hydraulic conductance, K, (a metabolism proxy) and tree mass (or volume, V). The original prediction was K∝V^{0.75}. We ask whether trees differ from WBE symmetry and if it matters for plant function and scaling. We measure tree branching and model how architecture influences K, V, mechanical stability, light interception and metabolic scaling. We quantified branching architecture by measuring the path fraction, P_{f}: mean/maximum trunk-to-twig pathlength. WBE symmetry produces the maximum, P_{f} = 1.0. We explored tree morphospace using a probability-based numerical model constrained only by biomechanical principles. Real tree P_{f} ranged from 0.930 (nearly symmetric) to 0.357 (very asymmetric). At each modeled tree size, a reduction in P_{f} led to: increased K; decreased V; increased mechanical stability; and decreased light absorption. When P_{f} was ontogenetically constant, strong asymmetry only slightly steepened metabolic scaling. The P_{f} ontogeny of real trees, however, was 'U' shaped, resulting in size-dependent metabolic scaling that exceeded 0.75 in small trees before falling below 0.65. Architectural diversity appears to matter considerably for whole-tree hydraulics, mechanics, photosynthesis and potentially metabolic scaling. Optimal architectures likely exist that maximize carbon gain per structural investment.

Original language | English (US) |
---|---|

Pages (from-to) | 217-229 |

Number of pages | 13 |

Journal | New Phytologist |

Volume | 201 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

### Fingerprint

### Keywords

- Branching symmetry
- Euler buckling
- Hydraulic architecture
- Light interception
- Metabolic scaling theory
- Plant allometry
- West Brown and Enquist

### ASJC Scopus subject areas

- Plant Science
- Physiology

### Cite this

*New Phytologist*,

*201*(1), 217-229. https://doi.org/10.1111/nph.12487

**Deviation from symmetrically self-similar branching in trees predicts altered hydraulics, mechanics, light interception and metabolic scaling.** / Smith, Duncan D.; Sperry, John S.; Enquist, Brian; Savage, Van M.; Mcculloh, Katherine A.; Bentley, Lisa P.

Research output: Contribution to journal › Article

*New Phytologist*, vol. 201, no. 1, pp. 217-229. https://doi.org/10.1111/nph.12487

}

TY - JOUR

T1 - Deviation from symmetrically self-similar branching in trees predicts altered hydraulics, mechanics, light interception and metabolic scaling

AU - Smith, Duncan D.

AU - Sperry, John S.

AU - Enquist, Brian

AU - Savage, Van M.

AU - Mcculloh, Katherine A.

AU - Bentley, Lisa P.

PY - 2014/1

Y1 - 2014/1

N2 - Summary: The West, Brown, Enquist (WBE) model derives symmetrically self-similar branching to predict metabolic scaling from hydraulic conductance, K, (a metabolism proxy) and tree mass (or volume, V). The original prediction was K∝V0.75. We ask whether trees differ from WBE symmetry and if it matters for plant function and scaling. We measure tree branching and model how architecture influences K, V, mechanical stability, light interception and metabolic scaling. We quantified branching architecture by measuring the path fraction, Pf: mean/maximum trunk-to-twig pathlength. WBE symmetry produces the maximum, Pf = 1.0. We explored tree morphospace using a probability-based numerical model constrained only by biomechanical principles. Real tree Pf ranged from 0.930 (nearly symmetric) to 0.357 (very asymmetric). At each modeled tree size, a reduction in Pf led to: increased K; decreased V; increased mechanical stability; and decreased light absorption. When Pf was ontogenetically constant, strong asymmetry only slightly steepened metabolic scaling. The Pf ontogeny of real trees, however, was 'U' shaped, resulting in size-dependent metabolic scaling that exceeded 0.75 in small trees before falling below 0.65. Architectural diversity appears to matter considerably for whole-tree hydraulics, mechanics, photosynthesis and potentially metabolic scaling. Optimal architectures likely exist that maximize carbon gain per structural investment.

AB - Summary: The West, Brown, Enquist (WBE) model derives symmetrically self-similar branching to predict metabolic scaling from hydraulic conductance, K, (a metabolism proxy) and tree mass (or volume, V). The original prediction was K∝V0.75. We ask whether trees differ from WBE symmetry and if it matters for plant function and scaling. We measure tree branching and model how architecture influences K, V, mechanical stability, light interception and metabolic scaling. We quantified branching architecture by measuring the path fraction, Pf: mean/maximum trunk-to-twig pathlength. WBE symmetry produces the maximum, Pf = 1.0. We explored tree morphospace using a probability-based numerical model constrained only by biomechanical principles. Real tree Pf ranged from 0.930 (nearly symmetric) to 0.357 (very asymmetric). At each modeled tree size, a reduction in Pf led to: increased K; decreased V; increased mechanical stability; and decreased light absorption. When Pf was ontogenetically constant, strong asymmetry only slightly steepened metabolic scaling. The Pf ontogeny of real trees, however, was 'U' shaped, resulting in size-dependent metabolic scaling that exceeded 0.75 in small trees before falling below 0.65. Architectural diversity appears to matter considerably for whole-tree hydraulics, mechanics, photosynthesis and potentially metabolic scaling. Optimal architectures likely exist that maximize carbon gain per structural investment.

KW - Branching symmetry

KW - Euler buckling

KW - Hydraulic architecture

KW - Light interception

KW - Metabolic scaling theory

KW - Plant allometry

KW - West Brown and Enquist

UR - http://www.scopus.com/inward/record.url?scp=84888286817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888286817&partnerID=8YFLogxK

U2 - 10.1111/nph.12487

DO - 10.1111/nph.12487

M3 - Article

C2 - 24102299

AN - SCOPUS:84888286817

VL - 201

SP - 217

EP - 229

JO - New Phytologist

JF - New Phytologist

SN - 0028-646X

IS - 1

ER -