Power law relationships in the branching of three tree species loblolly pine red maple sugar maple
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Power Law Relationships in the Branching of Three Tree Species (Loblolly Pine, Red Maple, Sugar Maple). Stephen Burton July 24, 2009 AAMU REU. Diversity on Earth. Great diversity in organisms and habitats Much diversity follows simple patterns

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Power law relationships in the branching of three tree species loblolly pine red maple sugar maple

Power Law Relationships in the Branching of Three Tree Species (Loblolly Pine, Red Maple, Sugar Maple)

Stephen Burton

July 24, 2009

AAMU REU


Diversity on earth
Diversity on Earth Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Great diversity in organisms and habitats

  • Much diversity follows simple patterns

  • Patterns described by simple mathematical function

  • Known as “power laws”


What are power laws
What Are Power Laws? Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Ecological patterns that repeat themselves over broad scales

  • “General features of complex systems”

  • Limits of power laws from natural and mathematical laws

  • Patterns from power laws visible in organization of natural systems


Examples of power laws
Examples of Power Laws Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Metabolism and body mass

  • Heart rate, life span, and population growth

  • River systems

  • TREE STRUCTURE


Importance of power laws
Importance of Power Laws Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Reductionistic science

  • Small scales to large scales

  • Greater understanding of biodiversity

  • Further understanding of underlying principles of math and science


Power laws in trees
Power Laws in Trees Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Trunk diameter and branch diameter

  • Coniferous trees

  • Density of branches and unknown variable

  • Independent of environment so internal factor

  • Suggests a power law is present


Tree branches
Tree Branches Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Organization of leaves and support

  • Interdependent networks that maximize the health of the whole tree

  • Growth patterns reflect best interest of entire tree

  • Result of evolutionary pressures or functional requirements

  • Branches are network, so power law


Power laws in branches
Power Laws in Branches Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Shoot growth in pine species

  • Hierarchal growth: low growth in higher order branches

  • Internal control maintains pattern

  • Likely a result of a power law


Objective
Objective Species (Loblolly Pine, Red Maple, Sugar Maple)

  • The primary goal of this study was to provide evidence that the branching patterns of trees follow a power law


Species studied
Species Studied Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Loblolly Pine (Pinus taeda)

  • Red Maple (Acer rubrum)

  • Sugar Maple (Acer saccharum)


Loblolly pine
Loblolly Pine Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Southeastern U.S., Texas, Delaware

  • Second largest range

  • Coniferous

  • 30 meters tall

  • Continuous growth in diameter

  • Most widely used timber species in U.S.


Ecological importance
Ecological Importance Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Maintain balance of ecosystems

  • Adaptable, grows and reproduces quickly

  • Restore areas harmed by fire or logging

  • Site restoration due to litter layer

  • Animal habitats


Red maple
Red Maple Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Eastern U.S. to New Mexico and Dakotas

  • Deciduous

  • 30 to 40 meters tall

  • Acidic soil and marshes, but adaptable

  • Utensils and tools

  • Tourism


Sugar maple
Sugar Maple Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Widespread, Great Lakes region

  • 40 meters tall

  • Moist, fertile soil

  • Not adaptable

  • Hard wood for construction and floors

  • Cheap sugar and syrup


Measurements
Measurements Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Healthy and accessible specimens

  • Damaged or too small

  • Too few developed branches

  • Intact canopy

  • Metric tape measure


Measurement terms
Measurement Terms Species (Loblolly Pine, Red Maple, Sugar Maple)

  • L0: trunk of tree

  • L1: first level

  • L2: second level

  • L3: third level

  • L4: fourth level


Data analysis
Data Analysis Species (Loblolly Pine, Red Maple, Sugar Maple)


Graphs
Graphs Species (Loblolly Pine, Red Maple, Sugar Maple)


Loblolly pine results
Loblolly Pine Results Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Follow similar power law

  • Very narrow range of values for R-Squared

  • Follow power law very closely


Sugar maple results
Sugar Maple Results Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Follow similar power law

  • Very narrow range of values for R-Squared

  • Follow power law very closely


Red maple results
Red Maple Results Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Weaker power law

  • Very broad range of values for R-Squared

  • Follow power law less closely


Study expectations
Study Expectations Species (Loblolly Pine, Red Maple, Sugar Maple)

  • All three species would follow power law

  • Tree branches are a network

  • Networks often governed by power laws

  • Other experiments have confirmed power laws in other species

  • Two of three species followed this pattern


Red maple explanation
Red Maple Explanation Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Did not follow power law closely, but was expected to

  • Red maples in study were not fully mature

  • Approximately 2 to 3 years old

  • Canopy heights were similar to height of surrounding community

  • Still strongly competing with surrounding species for resources


Conclusion
Conclusion Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Two of most common species in U.S. follow power law closely

  • Immature trees do not follow power laws as strongly as mature trees

  • For power laws, small scale research allows predictions for large scale patterns

  • Predictive power of science increases


References
References Species (Loblolly Pine, Red Maple, Sugar Maple)

  • Adam, J. A. (2003). Mathematics in Nature: Modeling Patterns in the Natural World. Princeton: Princeton Press.

  • Brown, J. H., V. K. Gupta, B. Li, B. T. Milne, C. Restrepo, and G. B. West. 2002. The fractal nature of nature: power laws, ecological complexity and biodiversity. The Royal Society. 357: 619-626.

  • Chen, X. and B. Li. 2003. Testing the allometric scaling relationships with seedlings of two tree species. ACTA OECOLOGICA. 24: 125-129.

  • Coomes, D. A., K. L. Jenkins, and L. E. S. Cole. 2007. Scaling of tree vascular transport systems along gradients of nutrient supply and altitude. biology letters. 3: 86-89.

  • Gelderen, D. M. van. (1994). Maples of the world. Portland: Timber Press.

  • Kaiteniemi, P. and A. Lintunen. 2008. Precision of allometric scaling equations for trees can be improved by including the effect of ecological interactions. Trees. 22: 579- 584.

  • Le Hardy de Beaulieu, Antoine. (2003). An illustrated guide to maples. Portland: Timber Press.

  • Schultz, R. P. (1997). Loblolly Pine: The Ecology and Culture of Loblolly Pine (Pinus taeda L.). Washington, D. C.: U. S. Department of Agrciculture, Forest Service.

  • Suzuki, A. A. and M. Suzuki. 2009. Why do lower order branches show greater shoot growth than higher order branches? Considering space availability as a factor affecting shoot growth. Trees. 23: 69-77.

  • Watt, M. S., J. R. Moore, and B. McKinlay. 2005. The influence of wind on branch characteristics of Pinus radiata. Trees. 19:58-65.


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