ESSAI
Volume 11
Article 18
Spring 2013
Testing for Relationships between Size Variables of
Select Organisms
Ruth Groza
College of DuPage
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Recommended Citation
Groza, Ruth (2013) "Testing for Relationships between Size Variables of Select Organisms," ESSAI: Vol. 11, Article 18.
Available at: http://dc.cod.edu/essai/vol11/iss1/18
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Groza: Testing for Relationships between Size Variables
Testing for Relationships between Size Variables of Select Organisms
by Ruth Groza
(Honors Biology 1151)
ABSTRACT
his study used mathematical scaling to determine if universal allometric relationships exist
among organisms. Size variables in various species of hardwood trees, an individual Bur Oak
tree (Quercus macrocarpa), North American pine trees, diurnal North American raptors, and
the domestic dog (Canis familiaris) were investigated for allometric significance. Statistically
significant findings indicated the presence of universal scaling principles. Biomechanical constraints
may serve to regulate those universal principles.
T
INTRODUCTION
Knowledge of the relationships between size variables in organisms is significant to
biologists for it can provide a greater understanding of underlying laws governing the diversification
of life (Agrawal 2004). An organism‘s size is a primary factor in determining how its biological
structures and processes covary with each other (Price et al. 2007). Scaling relationships are of
particular relevance within an evolutionary framework, as they may aid in the prediction of
evolutionary trends and in determining how selection influences specific traits (Agrawal 2004, Price
et al. 2007). Unless they scale isometrically, an allometric relationship will occur between an
organism‘s morphological and physiological traits (Marroig 2007). Thus, revealing mechanisms that
influence allometric variation is integral to the study of biological scaling (Shingleton 2010).
In order to identify underlying mechanisms of allometric scaling, relationships between size
variables in relevant organisms must first be established. Mathematical scaling may be utilized in
determining if an allometric relationship exists between a given trait and an organism‘s mass or
height (Price et al. 2007). In this study the relationship between size variables of varying species of
hardwood tree, an individual Bur Oak, North American pine trees, diurnal North American raptors,
and the domestic dog are examined for allometric significance. The objective is to investigate the
universal nature of allometric relationships among life forms.
METHODS
Stem basal diameter and weight were measured for comparison in selected species of
hardwood trees and in an individual Bur Oak. All trees were located on the College of DuPage
campus in Illinois. Stems from fourteen species of hardwood trees were oven dried at 70° C and
measured for basal diameter and weight. Fourteen stems of varying sizes from a single Bur Oak tree
were measured similarly. Morphological data comparing the maximum heights and basal diameters
of North American trees in the genus Pinus were obtained from Little (1980).
Morphological data comparing the wingspans and weights of diurnal North American raptors
were obtained from Sibley (2000). Shoulder height and weight were measured from a random sample
of fourteen domestic dogs. Only adult dogs were selected for comparison.
Linear regression was used to test for significant relationships between the pairs of
morphological characteristics selected for analysis.
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ESSAI, Vol. 11 [2013], Art. 18
RESULTS AND DISCUSSION
In the combined comparisons of selected morphological characteristics all regression
coefficients were significant (p<0.05) (Table 1). Thus, there is evidence that biological scaling is
occurring in diverse species of animals and plants. Although further study is needed, this finding is
important because it indicates that universal underlying allometric scaling principals are governing
life forms.
Several constraining factors play a fundamental role in regulating these allometric
relationships. Maintenance of biomechanical integrity is one such factor. If an organism is to survive,
increases in body mass must correspond to viable changes in underlying skeletal structure (Sorkin
2008). The allometric scaling of trees is limited by the hydrodynamic demands of their vascular
systems and by factors associated with maintenance of vertical growth (Enquist 2003). In the case of
raptors, skeletal structure, wingspan and body mass must scale in a way that does not inhibit flight
(Sato et al. 2009). Canine weight and limb length must scale in a way that does not inhibit
locomotion or produce undue stress upon limb bones (Doube et al. 2009). Thus, animal and plant
morphology is functionally dependent upon allometric scaling principles. Further study could
determine how scaling principles influence the evolution of morphological characteristics.
LITERATURE CITED
Agrawal, A.A. 2004. The metabolic theory of ecology. Ecology 85: 1790-1791.
Coomes, D.A. and R. B. Allen. 2009. Testing the metabolic scaling theory of tree growth. Journal of
Ecology 97:1369-1373.
Doube, M., C.A.Wiktorowicz, P. Christiansen, J.R. Hutchinson, and S. Shefelbine. 2009. Threedimensional geometric analysis of felid limb bone allometry. PLoS ONE 4:4742-4752.
Enquist, B.J. 2003. Cope‘s Rule and the evolution of long-distance transport in vascular plants:
allometric scaling, biomass partitioning, and optimization. Plant, Cell and Environment 26:
151-161.
Little, E. L. 1980. The Audubon Society Field Guide to North American Trees. Alfred A. Knopf Inc,
New York, NY, USA.
Marroig, G. 2007. When size makes a difference: allometry, life-history and morphological evolution
of caphuchins (Cebus) and squirrels (Saimiri) monkeys (Cebinae, Platyrrhini).
Evolutionary Biology 7:20-46.
Price, C. A., B.J. Enquist, and V.M. Savage. 2007. A general model in botanical form for allometric
covariation and function. Proceedings of the National Academy of Sciences of the United
States of America 104: 13204-13209.
Sato, K., K.Q. Sakamoto, Y. Watanuki, A. Takahashi, N. Katsumata, C. Bost, and H. Weimerskirch.
2009. Scaling of soaring seabirds and implications for flight abilities of giant pterosaurs.
PLoS ONE 4:5400-5406.
Shingleton, A. 2010. Allometry: The study of biological scaling. Nature Education Knowledge 3:2.
Sibley, D. A. 2000. The Sibley Guide to Birds. Chantileer Press, Inc, New York, NY, USA.
Sorkin, B. 2008. A biomechanical constraint on body mass in terrestrial mammalian predators.
Lethaia 41:333-347.
Stegen, J.C., B.J. Enquist, and Regis Ferriere. 2009. Advancing the metabolic theory of biodiversity.
Ecology Letters 12:1001-1015.
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Groza: Testing for Relationships between Size Variables
Table 1. Regression equations, coefficients of regression statistics, and significance between selected morphological parameters among
plants and animals.
______________________________________________________________________________________________________
Description of organism(s)
Regression equation
Regression
Significance
coefficient
______________________________________________________________________________________________________
Bur oak
Stem weight (g) = -0.8676 + 0.8188(Basal diameter(mm))
0.52
P < 0.05
Varying species of hardwood trees
Stem weight (g) = -0.9144 + 0.8376(Basal diameter(mm))
0.55
P < 0.05
Height (m) = 11.725 + 16.626(Basal diameter(m)
0.41
P < 0.05
Shoulder height (cm) = 19.956 + 1.212(Weight (kg))
0.86
P < 0.05
0.79
P < 0.05
Pine trees
Domestic dog
Diurnal North American raptors
Wingspan (cm) = 92.731 + 0.0208(Weight(g))
_____________________________________________________________________________________________________
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