Growth equations and curves for citrus trees
AuthorsF. M. Turrell
M. J. Garber
W. W. Jones
W. C. Cooper
R. H. Young
Authors AffiliationsF. M. Turrell was Professor of Biochemistry and Plant Physiologist, University of California, Riverside; M. J. Garber was Professor of Biostatistics, Biometrician and Director, Computing Center, University of California, Riverside; W. W. Jones was Professor of Horticulture and Horticulturist, University of California, Riverside; W. C. Cooper was Plant Physiologist and Leader of Citrus and Subtropical Fruit Investigations, ARS, USDA at Orlando, Florida, Weslaco, Texas, and Indio, California; R. H. Young was Plant Physiologist, ARS, USDA, Fruit, Vegetable, Soil and Water Research Laboratory, Weslaco, Texas.
Hilgardia 39(16):429-445. DOI:10.3733/hilg.v39n16p429. January 1969.
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Percival Allen, J. H. Gaddum, and S. C Pearce writing in Nature in 1945, all have emphasized the advantages of using the simple and powerful methods afforded by logarithmic transformations in analyzing nonnormal distributions, although it had been amply demonstrated in the relative growth of animal parts by (Huxley (1932)). We have undertaken to illustrate graphically the use of logarithm and power transformations for growth models of trees in orchards and tree organs. Various parameters based on literature, either age or size dependent, are described by power functions, log-log linear curves of the type y = bxk, or semi-log linear curves, exponential functions where y = aebx. Tree height or trunk diameter versus tree age, tree-leaf surface area or number on the tree versus tree age, leaf area versus length, or leaf area versus width are linear log-log functions. It is shown that the first pair of parameters are not normally distributed; latter pairs were demonstrated to be normal. Fruit yield was a nonlinear logarithmic function of tree age and their annual size-frequency distributions were not normal, except for infinitely large populations. Individual fruit size is a linear function of log fruit age, but only the log-log relations are linear for fruit dimensions (diameter, volume, and mass) versus packing number. Log branch fresh weight, leaf and fruit fresh weight are linear functions of log tree age, as are logs of branch dry weight, of branch diameter, of number of branches and surface areas and of volumes. High positive correlations between woody organ ages and dry organ densities invalidate the Rashevsky theoretical growth equation. Insertion of new density terms satisfy validity requirements. Frequency distribution of branch-diameter per tree is a linear log-log function. It is postulated that the linearity of the log-log and semi-log dimensional relationships in plant growth result from similar physical and chemical relationships underlying growth as outlined by kinetic theory.
Anonymous. Sunkist Circular 1003, Field Dept 1957. Los Angeles
Arrhenius S. Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren. Zeitschr. physik. Chem. 1889. 4:226-48.
Barnette R. M., Debusk E. F., Hester J. B., Jones H. W. The mineral analysis of nineteen-year-old Marsh seedless grapefruit tree. Citrus Industry. 1931. 12:5-6. 34
Bartholomew E. T. Internal decline of lemons II. Growth rate, water content, and acidity of lemons at different stages of maturity. Am. Jour. Bot. 1923. 10:117-26. DOI: 10.2307/2435359 [CrossRef]
Benedict H. M., Swidler R. Non-destructive method for estimating chlorophyll content of leaves. Science. 1961. 133:2015-16. DOI: 10.1126/science.133.3469.2015 [CrossRef]
Boelter L. M. K., Gordon H. S., Griffin J. R. Free evaporation into air of water from a free horizontal quiet surface. Ind. and Engin. Chem. 1946. 38:596-600. DOI: 10.1021/ie50438a018 [CrossRef]
Cahoon G. A., Morton E. S., Jones W. W., Garber M. J. Effects of various types of nitrogen fertilizers on root density and distribution as related to water infiltration and fruit yields of Washington Navel oranges in a long-term fertilizer experiment. Proc. Amer. Soc. Hort. Sci. 1959. 74:289-99.
Cameron S. H., Appleman D. The distribution of total nitrogen in the orange tree. Proc. Amer. Soc. Hort. Sci. 1934. 30:341-48.
Camp P. R. The formation of ice at water-solid interfaces. Ann. New York Acad. Sci. 1965. 125(2):317-43. DOI: 10.1111/j.1749-6632.1965.tb45400.x [CrossRef]
Chapman H. D., Parker E. R. Weekly absorption of nitrate by young bearing orange trees growing out of doors in solution cultures. Plant Physiol. 1942. 17:366-76. DOI: 10.1104/pp.17.3.366 [CrossRef]
Cooper W. C., Peynado A., Furr J. R., Hilgeman R. H., Cahoon G. A., Boswell S. B. The growth and fruit quality of Valencia oranges in relation to climate. Proc. Amer. Soc. Hort. Sci. 1963. 82:180-92.
Elsasser W. M. Synopsis of organismic theory. J. Theoretical Biology. 1964. 7:53-67. DOI: 10.1016/0022-5193(64)90040-2 [CrossRef]
Gregory F. G. Studies in the energy relations of plants. I. The increase in area of leaves and leaf surface of Cucumis sativus. Ann. Bot. 1921. 35:93-123.
Grunow August. 10-20th annual reports. Desert grapefruit marketing program. Grapefruit Administrative Committee and Grapefruit Advisory Board 1951-61. Phoenix, Ariz. 83 collective pages
Harding P. L., Fisher D. F. Seasonal changes in Florida grapefruit. U.S.D.A. Tech. Bull. 1945. 886:1-100.
Huxley J. S. Problems of relative growth. 1932. New York: The Dial Press. 276p.
Johnson F. H., Eyring H., Pollisar M. J. The kinetic basis of molecular biology. 1954. New York: John Wiley and Sons, Inc. 874p.
Longfield-Smith L. Report of the Winter Haven Chemical Laboratory, season of 1933-34. Florida Dept. Agr. Chem. Lab. Bull. 1935. p.90.
Mazur Peter. The role of cell membranes in the freezing of yeast and other single cells. Ann. New York Acad. Sci. 1965. 125:658-76. DOI: 10.1111/j.1749-6632.1965.tb45420.x [CrossRef]
Millard E. B. Physical chemistry for colleges. 1937. 3rd Ed. New York: McGraw Hill Book Co. 522p.
Monselise S. P., Turrell F. M. Tenderness, climate and citrus fruit. Science. 1959. 129:639-40. DOI: 10.1126/science.129.3349.639 [CrossRef]
Parker E. R., Turrell F. M., Bonner James. Effects of organic matter and certain growth substances on the development of young orange trees in the orchard. Proc. Amer. Soc. Hort. Sci. 1940. 38:49-58.
Pauling C., Hanawalt P. Nonconservative DNA replication in bacteria after thymine starvation. Proc. Nat’l. Acad. Sci. 1965. 54:1728-35. DOI: 10.1073/pnas.54.6.1728 [CrossRef]
Pearsall W. H. Growth studies VI. On the relative sizes of growing plant organs. Ann. Bot. 1927. 41:549-56.
Rashevsky N. Outline of a new mathematical approach to general biology: 1. Bull. Math. Biophys. 1943. 5:33-47. DOI: 10.1007/BF02478117 [CrossRef]
Salt R. W. Application of nucleation theory to the freezing of super-cooled insects. Jour. Insect Physiol. 1958. 2:178-88. DOI: 10.1016/0022-1910(58)90003-9 [CrossRef]
Savage Z. Citrus yield per tree by age. Agr. Ext. Service Econ. Ser. 1960. 60-8:Univ. of Fla. 10p. Mimeo
Showers Byron J. 2nd-9th annual reports 1943-50. Desert grapefruit marketing program. Grapefruit Administrative Committee and Grapefruit Advisory Board. Phoenix, Ariz. 99 collective pages
Ting I. P., Loomis W. E. Further studies concerning stomatal diffusion. Plant Physiol. 1965. 40:220-28. DOI: 10.1104/pp.40.2.220 [CrossRef]
Turrell F. M. The relation between chlorophyll concentration and the internal surface of mesomorphic and xeromorphic leaves grown under artificial light. Proc. Iowa Acad. Sci. 1939. 46:107-17.
Turrell F. M. Tables of surfaces and volumes of spheres and of prolate and oblate spheroids, and spheroidal coefficients. 1946. Berkeley and Los Angeles: Univ. of Calif. Press. 153p. pp + XXXI Illustrated
Turrell F. M. Rate of vaporization of sulfur. Science. 1947. 105:434 DOI: 10.1126/science.105.2730.434 [CrossRef]
Turrell F. M. Growth of the photosynthetic area of citrus. Bot. Gaz. 1961. 122:285-98. DOI: 10.1086/336117 [CrossRef]
Turrell F. M. Internal surface-intercellular space relationships and the dynamics of humidity maintenance in leaves. Humidity and Moisture. 1965. II:39-53. A. Wexler, Ed. New York: Reinhold Book Co
Turrell F. M., Austin S. W. Comparative nocturnal budgets of large and small trees. Ecology. 1965. 46:25-34. DOI: 10.2307/1935255 [CrossRef]
Turrell F. M., Austin S. W. Transpiration rates of citrus fruit in still air 1966. Unpublished. Project 1731
Turrell F. M., Austin S. W., McNee Dan, Park W. J. Thermal conductivity of functional citrus tree wood. Plant Physiol. 1967. 42:1025-34. DOI: 10.1104/pp.42.8.1025 [CrossRef]
Turrell F. M., Carlson Jane P., Klotz L. J. Surface and volume determinations of citrus fruits. Proc. Amer. Soc. Hort. Sci. 1945. 46:159-65.
Turrell F. M., Monselise S. P., Austin S. W. Effect of climatic district and of location in tree on tenderness and other physical characteristics of citrus fruit. Botan. Gaz. 1964. 125:158-70. DOI: 10.1086/336265 [CrossRef]
Turrell F. M., Slack D. L. Specific gravity of citrus fruits. Proc. Amer. Soc. Hort. Sci. 1948. 52:245-50.
Turrell F. M., Waldbauer Louis. A photoelectric colorimeter; its application in the measurement of the concentration of colored substances in solution. Proc. Iowa Acad. Sci. 1935. 42:63-66.
Turrell F. M., Weber J. R., Storherr R. W. Metabolism of P32-labeled disodium monohydrogen orthophosphate and octamethylpyro-phosphoramide in bean plants. 1955. Univ. of Calif. Riverside. AEC Project AT (11-1)-34
Turrell F. M., Wedding R. T., Cohan Marjorie S., Weber J. R., Horspool R. P. The mode of action of elemental sulfur in “sulfur-burn” Program Rep. 1955. pp.1-16. No. 5F. Univ. of Calif.-AEC Contract AT (11-1)-34, Project 6
Turrell F. M., Young R. H., Austin S. W., Garber M. J. Growth of the woody frame of the grapefruit tree (Citrus Paradisi, Macf.). Amer. Jour. Bot. 1965. 52:619
Webber H. J., Batchelor L. D. The citrus industry, Vol. I. 1943. Berkeley and Los Angeles: Univ. of Calif. Press. 1028p.
Zscheile F. P., Porter J. W. Analytical methods for carotenes of Lycopersicon species and strains. Anal. Chem. 1947. 19:47-51. DOI: 10.1021/ac60001a013 [CrossRef]