Evaluating scaling relationships of branching structure and
biomass partitioning in managed orchard fruit species
A Weecology Production
Zachary T. Brym, Dept. of Biology and Ecology Center, Utah State University
Research Questions
Are ‘universal’ scaling relationships between diameter,
length and mass, described by the Metabolic Theory of
Ecology, conserved in managed orchard fruit species?
Where deviations occur, are they indicative of orchard
management practices (i.e., pruning)?
Mass vs. Diameter
Length vs. Diameter
Prediction:
M ~ D8/3 (Niklas & Spatz, 2004)
Tree-level:
Exponent
[95% Confidence]
Intercept
R2
2.49
2.48
4.37
[2.32, 2.68]
[2.31, 2.67]
[1.47, 12.9]
-0.93
-0.90
-5.16
0.974
0.980
0.489
Exponent
[95% Confidence]
Intercept
R2
2.48
2.57
2.46
[2.43, 2.53]
[2.48, 2.67]
[2.39, 2.53]
-1.05
-1.21
-1.01
0.905
0.869
0.907
Exponent
[95% Confidence]
Intercept
R2
2.56
2.63
2.76
2.76
2.51
2.47
[2.11, 3.12]
[2.42, 2.87]
[2.52, 3.02]
[2.47, 3.08]
[2.34, 2.69]
[2.27, 2.69]
-1.25
-1.19
-1.47
-1.54
-1.13
-1.06
0.647
0.907
0.788
0.929
0.916
0.851
All Apple Cherry -
Length vs. Mass
Prediction:
M ~ (D/2)2/3 (Price, Enquist & Savage, 2007)
Tree-level:
Exponent
[95% Confidence]
Intercept
R2
0.74
0.80
1.29
[0.63, 0.88]
[0.68, 0.95]
[0.35, 4.77]
-0.72
-0.81
-1.84
0.849
0.892
0.125
Exponent
[95% Confidence]
0.87
1.10
0.83
[0.82, 0.91]
[1.02, 1.19]
[0.78, 0.89]
1.09
0.70
1.19
0.442
0.420
0.491
Exponent
[95% Confidence]
Intercept
R2
1.50
1.14
1.39
1.13
1.13
1.07
[1.11, 2.02]
[0.96, 1.35]
[1.21, 1.60]
[0.83, 1.54]
[0.94, 1.36]
[0.90, 1.28]
0.33
0.75
0.43
0.70
0.54
0.66
0.154
0.614
0.482
0.418
0.406
0.347
All Apple Cherry -
Prediction:
L ~ M1/4 (Niklas & Enquist, 2001)
Tree-level:
Exponent
[95% Confidence]
Intercept
R2
0.30
0.32
0.29
[0.25, 0.35]
[0.27, 0.39]
[0.12, 0.74]
-0.67
-0.76
-0.71
0.849
0.876
0.673
Exponent
[95% Confidence]
Intercept
R2
0.35
0.43
0.33
[0.33, 0.36]
[0.40, 0.46]
[0.32, 0.35]
1.19
0.89
1.28
0.632
0.658
0.638
Exponent
[95% Confidence]
Intercept
R2
0.58
0.43
0.50
0.41
0.45
0.43
[0.49, 0.70]
[0.39, 0.48]
[0.46, 0.55]
[0.31, 0.55]
[0.39, 0.53]
[0.38, 0.50]
0.61
0.93
0.75
0.99
0.71
0.79
0.688
0.840
0.766
0.500
0.587
0.580
All Apple Cherry -
Experimental Systems
Kaysville Experimental Orchard, USU Ag. Experiment St.
Medium-density Apple (Malus x sylvestris var. domestica)
- 3.5 x 5.5 m spacing, Vertical Axe training system
- NC-140 2003 Golden Delicious rootstock trial
- designed to evaluate dwarfing, yield, and disease resistance
Low-density Tart Cherry (Prunus cerasus, mahaleb)
- 3.65 x 6.1 m spacing, general open vase training
- management abandoned for more than 5 yrs.
- secondary branches closer to wild-type habit
Branch-level:
Key Findings
Mass ~ Diameter is strongly conserved.
The estimated scaling exponent is just shy of 8/3,
the theoretical self-loading limit before buckling.
Length ~ Diameter is moderately conserved.
Confidence intervals include the 2/3 prediction, but
also 3/4. Vigorous shoots suggests pruning signals.
All Apple Cherry -
Rootstocks:
Bud.9 CG.3041CG.6210 M.26 JM.8 PiAu.5683 -
Branch-level:
All Apple Cherry -
Rootstocks:
Bud.9 CG.3041CG.6210 M.26 JM.8 PiAu.5683 -
Intercept
R2
Branch-level:
All Apple Cherry -
Rootstocks:
Bud.9 CG.3041CG.6210 M.26 JM.8 PiAu.5683 -
Length ~ Mass is moderately conserved.
Confidence intervals include the 1/4 prediction, but
also 2/3. Vigorous wood may have lower density.
The Diameter Ratio is moderately consistent.
The ratio is higher than predicted, indicative of area
decreasing branching. Slow taper in large supporting
branches results from pruning of smaller end shoots.
Future Directions
Explore data for spatially explicit branching architecture and develop
a model for effects of pruning on canopy shape and structure.
Explore predictive power of non-destructive tree morphology (e.g.,
canopy volume and light interception) on yield in commercial tart
cherry orchards of Utah Co.
Develop agroecological philosophy for forest-like orchard
agroecosystems.
Diameter Ratio
Branch-level
AllAppleCherry-
Prediction: Dk+1/Dk ~ 0.5
Exponent
[95% Confidence]
Intercept
R2
0.68
0.67
0.75
[0.65, 0.71]
[0.61, 0.72]
[0.71, 0.79]
-8.48
-11.4
-8.78
0.569
0.418
0.693
R2 = 0.569
Acknowledgements
Legend
Prediction Exponent 95% CI Cherry Bud.9 CG.6210 JM.8 -
Apple CG.3041M.26 PiAu.5683 -
Project funding provided by the Utah State University Graduate
Student Senate Research and Project Grant and the Ecology
Center Ph.D. Assistantship and Research Support Award. Field
support from the staff and researchers at the Kaysville
Experimental Orchard and USU undergraduates Josh Anderson
and Josh Shugart greatly influenced the project’s sample size.
Conference travel provided by the USU Office of Graduate
Studies, Ecology Center and Dept. of Biology, GRC, and ASHS.