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Allometry Exercise

Allometry Exercise. GEO 309 Dr. Garver. Allometry. Study of the relationship between size and shape First outlined by Otto Snell in 1892 and Julian Huxley in 1932 Practical applications; differential growth rates of the parts of a living organism Insects Children Plants.

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Allometry Exercise

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  1. Allometry Exercise GEO 309 Dr. Garver

  2. Allometry • Study of the relationship between size and shape • First outlined by Otto Snell in 1892 and Julian Huxley in 1932 • Practical applications; • differential growth rates of the parts of a living organism • Insects • Children • Plants

  3. Example assignment

  4. Assignment #1 • Can we prove a relationship between tree height and trunk diameter? • Collect data using clinometers and meter tapes. • Start by standardizing our measurement techniques (First week of allometry exercise).

  5. Clinometer an optical device for measuring elevation angles above horizontal

  6. Allometry Exercise - Part 1(Week 1) • Week 1 of exercise – Print out a copy of clinometer_training.xls • Form small groups • Go to the 5 stations listed on worksheet, each group member will; • take a clinometer reading at each station. • calculate their height at eye level. • Each group member completes their own copy of clinometer_training.xls

  7. Allometry exercise – Week 1 of exercise • Each group will then create a new spreadsheet that combines the collected data and calculates the average heights for each of the 5 stations, and the average errors. • When all groups are done we will then compare the results to the actual measured heights of the 5 stations. • Each group needs to hand in their clinometer_groupweek1.xls with each member’s individual clinometer_training.xls sheet in order to get credit for today’s exercise.

  8. How tall is the Eiffel Tower? a = ? = 29° = 575 m

  9. Measuring height using tangent function • Based on the mathematics of right triangles. • Pace off a good distance from the object you want to measure. • Record that measurement • This is the baseline of the right triangle • Second measurement is the angle between your line of sight and the ground (use a clinometer to make this measurement) • Greek letter θ (pronounced thay'-ta).

  10. The tangent (tan) function. • For a given angle, the ratio of the length of those two sides is always the same. • a/b is equal to the tangent of the angle θ. In equation form, it looks like this:a/b = tan θ • Another way to write this same equation is:a = b * tan θ • So, the height we want to measure (a) is equal to the baseline of the right triangle (b) times the tangent of the sight angle (θ). 575 * tan(29) = 575 * 0.5543 = 319 m

  11. How tall is the Eiffel Tower? a = 319 m = 29° = 575 m 575 * tan(29) = 575 * 0.5543 = 319 m

  12. Graph of tangent function from 0 to 89° • Values change slowly from 0° to 60° or 70° • Then values start to change more rapidly. • Want to make sure that you are far enough away from the object so that your sight angle is in the range where the tangent function is not changing rapidly.

  13. Graph of tangent function from 0 to 89°

  14. Calculate DBH by measuring circumference • distance around a circle – circumference • The distance across a circle through the center - diameter. • Pi is the ratio of the circumference of a circle to the diameter. • divide the circumference by the diameter, you get a value close to Pi.

  15. Week 1 of allometry exercise; • Get in groups and standardize measurement techniques for improved data collection. • Next 2 weeks – we will collect and analyze campus tree data. = 5.15 m Kyle Dr. G..

  16. 5 locations outside – Bridge, Flagged railing, Balcony1, Balcony2, Balcony3 Bridge Location Kyle clinometer reading = 18.5° Dr. G. clinometer reading = 20° Kyle eye hgt. = 1.73 m G. eye hgt. = 1.65 m 5.15 m

  17. Bridge location data:

  18. Download and read:1. Paper (see below)2. Allometry Assignment

  19. Full dataset n = 88 Example of a Plot A

  20. No eucalyptus n = 78 RSQ R 47% 69% Example of a Plot B

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