1. A Scaling Approach to Improve Variety Selection in Orchard Fruit Zack Brym Dept of Biology, Ecology Center Utah State University z.t.brym@gmail.com zackbrym.weecology.org @ZackBrym

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3. Code: github.com/weecology/branch-arch Presentations: figshare.com

4. I like open science! Code: github.com/weecology/branch-arch Presentations: figshare.com [Brym]

5. I like open science! Code: github.com/weecology/branch-arch Presentations: figshare.com You are free to:

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7. What is Scaling?

8. Scaling is the description of universal patterns

9. What is Scaling? Scaling is the description of universal patterns between: - morphological characteristics like branch diameter, length, surface area - biomass

10. What is Scaling? Scaling is the description of universal patterns between: - morphological characteristics like branch diameter, length, surface area - biomass across size, age, species.

11. What is Scaling? Scaling relationships consistent within and among ALL plants. (Niklas 2004, Price et al 2010)

12. What is Scaling? Scaling relationships consistent within and among ALL plants. (Niklas 2004, Price et al 2010) Emergent patterns illustrate similarities in physiology among plants.

13. What is Scaling? Scaling is a close relative to Allometry

14. What is Scaling? Scaling is a close relative to Allometry - long history in forestry and agriculture

15. What is Scaling? Scaling is a close relative to Allometry - long history in forestry and agriculture - usually, species-specific for individual or stand

16. What is Scaling? Applications of Scaling in Horticulture - Tree architecture  ‘Training System’

17. What is Scaling? Applications of scaling in Horticulture - Resource partitioning  ‘Yield Efficiency’

18. What is Scaling? Applications of scaling in Horticulture - Resource partitioning  ‘Yield Efficiency’ Cumulative Yield Trunk cross-sectional area

19. What is Scaling? Applications of scaling in Horticulture - Resource partitioning  ‘Yield Efficiency’ (Grossman & DeJong, 1998) B

20. Why a Scaling Approach?

22. Orchard fruit scale like natural trees! - Theoretical Prediction (Niklas and Spatz, 2004) Mass = Diameter 8/3

23. Why a Scaling Approach? Orchard fruit scale like natural trees! - Theoretical Prediction (Niklas and Spatz, 2004) Mass = Diameter 8/3 … 8/3 = 2.67

24. Why a Scaling Approach? Orchard fruit scale like natural trees! - Theoretical Prediction (Niklas and Spatz, 2004) Mass = Diameter 8/3 … 8/3 = 2.67 - Empirical Prediction (Brown 1997) Mass = Diameter 2.53

25. Why a Scaling Approach? Orchard fruit scale like natural trees! R 2 = 0.914 8/3 ?

26. Why a Scaling Approach? Orchard fruit scale like natural trees! Slope [95% CI] ; R 2 Cherry 2.46 [ 2.39, 2.53 ]; 0.909 Apple2.57 [ 2.49, 2.66 ]; 0.892 Both2.48 [ 2.43, 2.53 ]; 0.914 R 2 = 0.914 ?

27. Why a Scaling Approach? Orchard fruit scale like natural trees! Slope [95% CI] ; R 2 Cherry 2.46 [ 2.39, 2.53 ]; 0.909 Apple2.57 [ 2.49, 2.66 ]; 0.892 Both2.48 [ 2.43, 2.53 ]; 0.914 R 2 = 0.914 2.53

28. Why a Scaling Approach? Small differences in scaling distinguish varieties.

29. Why a Scaling Approach? Small differences in scaling distinguish varieties. - Appropriate architecture for Training - Optimum Yield Efficiency

30. Why a Scaling Approach? Small differences in scaling distinguish varieties. - Appropriate architecture for Training - Optimum Yield Efficiency Consistent differences can reveal important levers for developing and evaluating new varieties and orchard systems.

31. What is a Scaling Approach?

32. NC-140 2003 ‘Golden Delicious’ Dwarf Rootstocks Kaysville, Utah Bud.9Geneva 41 (CG.3041) Geneva 210 (CG.6210) M.26 JM.8 PiAu.5683 Trunk cross-sectional area

33. What is a Scaling Approach?

34. Segment – Level Diameter Length Surface Area Volume Mass Twig count Scar count

35. What is a Scaling Approach? Segment – Level Diameter Length Surface Area Volume Mass Twig count Scar count “Estimated Exponents”

36. What is a Scaling Approach? Segment – Level Diameter Length Surface Area Volume Mass Twig count Scar count Grouped pairwise and Regressed for Scaling Relationships

37. What is a Scaling Approach? Segment – Level Diameter Length Surface Area Volume Mass Twig count Scar count “Branch Metrics” “Estimated Exponents”

38. What is a Scaling Approach? Tree - Level Trunk cross-sectional area Height Spread Segment totals

39. What is a Scaling Approach? Tree – Level Trunk cross sectional area Height Segment totals Spread Segment totals “Branch Metrics” “Estimated Exponents”

40. What is a Scaling Approach? Step 1: Locate differences among rootstocks

41. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents

42. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels

43. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Segment = ‘Internode’

44. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Segment = ‘Internode’

45. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Path = Maximum branch path length

46. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Subtree = Totals from node

47. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Subtree = Totals from node

48. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Subtree = Totals from node

49. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Estimated Exponents - Scaling Levels Segment = ‘Internode’ Path = Maximum branch path length Subtree = Totals from node - Regression Parameters Exponent Intercept

51. Variance in Confidence Intervals of Estimated Exponents

52. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Branch Metrics

53. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Branch Metrics - ANOVA - Post-hoc: Duncan’s Multiple Range

54. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Branch Metrics *** Letters denote groups with significant differences in means.

55. What is a Scaling Approach? Step 1: Locate differences among rootstocks - Cumulative Yield *** Letters denote groups with significant differences in means.

56. What is a Scaling Approach? Step 2: Correlate Significant Differences

61. So, …

62. Orchard fruit scale like natural trees!

63. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield.

64. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield. Maximum Branch Path Length R 2 = 0.868 Total Number of Pruning Scars R 2 = 0.862

65. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield. Variation in estimated allometric exponents also relate strongly to cumulative yield.

66. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield. Variation in estimated allometric exponents also relate strongly to cumulative yield. Mass ~ Diameter at Segment-level R 2 = 0.782 Mass ~ Volume at Path-level R 2 = 0.782

67. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield. Variation in estimated allometric exponents also relate strongly to cumulative yield. Geneva ® 210 (aka, CG.6210) consistently produces higher yield than would be expected by body size.

68. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield. Variation in estimated allometric exponents also relate strongly to cumulative yield. Geneva ® 210 (aka, CG.6210) consistently produces higher yield than would be expected by body size. Be sure to standardize by size!!!

69. So, … Orchard fruit scale like natural trees! Branch metrics strongly relate to cumulative yield. Variation in estimated allometric exponents also relate strongly to cumulative yield. Geneva ® 210 (aka, CG.6210) consistently produces higher yield than would be expected by body size. Be sure to standardize by size!!! Use TCSA, Canopy Spread, Path Length

70. Thank You… Research Mentors: Morgan Ernest & Brent Black Research Techs & Volunteers: Josh Anderson, Josh Shugart, Morey Burnham, Ken Locey, Matt Schroer, Xiao Xiao Grower Cooperators: Appenzell Farms, Hyde Park, Utah Bishops Orchards, Guilford, Connecticut Cherry Hill Orchards, Santaquin, Utah Kaysville Research Farm, Utah State University Paradise Valley Orchards, Paradise, Utah Zollinger Fruit Farm, River Heights, Utah