Allometric relationships between large and small scale tree spacing studies

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Allometric relationships between large and small
scale tree spacing studies

• Mike Strub and Ralph Amateis

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Topics

• Spacing studies
• Scaling isomorphic versus allometric
• Comparison of small and large scale spacing
  studies
• Conclusions

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Spacing Studies

• Full scale studies were planted at four locations
  with three replications in the spring of 1983.
• Treatments include 4X4, 6X6, 8X8, 12X12
  and various rectangular spacings.
• A single replication of a 1/16th scale study was
  planted in the spring of 1989 and a second
  replication was planted in 1998.

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Scaling

• Early work dates back to the development of
  geometry and notions about similar triangles,
  these ideas involve a single scaling factor and
  are termed isometric.
• Latter work came from using scale models of
  engineering projects and resulted in the
  development of dimensional analysis to address
  more complex allometric problems.

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Scaling

• The dimensional analysis model is Y?X?
• These ideas have been applied to biological
  organisms in the last thirty years.

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Scaling
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Buckling Limit

• A tree will buckle under its own weight when
• Which implies that to prevent buckling

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Buckling Limitfrom McMahon and Bonner (1983)
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Buckling Limitfrom McMahon and Bonner (1983)
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Buckling Limitfrom McMahon and Bonner (1983)
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Buckling Limitfrom Horn (2000)
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4X4 spacing
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6X6 spacing
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8X8 spacing
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12X12 spacing
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4X4 spacing
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6X6 spacing
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8X8 spacing
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12X12 spacing
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4X4 tree spacing
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6X6 tree spacing
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8X8 tree spacing
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12X12 tree spacing
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D?(H-4.5)?
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D?(H-4.5)?
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Results

• Both miniature and full scale studies approach
  the buckling line in a similar fashion.
• Miniature scale studies have relatively larger
  diameters than full scale studies, likely because
  they were measured at ground line rather than
  scaled breast height.
• The miniature scale studies tend to be more
  variable than the full scale studies, perhaps
  because they are the results of a few years of
  weather rather than decades.

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4X4 tree spacing
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6X6 tree spacing
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8X8 tree spacing
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12X12 tree spacing