Stochastic frontier analysis of a classic self-thinning experiment

Austral Ecology

Volumn 29, Issue 4, 2004, Pages 408-417

  Bi, Huiquan ^a  

^a Research School of Biological Sciences   (Australia)

Author keywords

Fertility gradient; Self thinning boundary line; Site carrying capacity; Time course of self thinning

Indexed keywords

BOUNDARY LINE; CARRYING CAPACITY; SELF THINNING; SOIL FERTILITY;

EID: 4143050234     PISSN: 14429985     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1442-9993.2004.01379.x     Document Type: Article

References (63)

1. Aigner D., Lovell K., Schmit P. (1977) Formulation and estimation of stochastic frontier production models. J. Econometrics 6, 21-37.
2. Augspurger C. (1996) Editor's Note - Emphasizing new ideas to stimulate research in ecology. Ecology 77, 1698.
3. Barreto L. S. (1989) The '3/2 power law': a comment on the specific constancy of K. Ecol. Model. 45, 237-42.
4. Battese G. E. & Coelli T. J. (1988) Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. J. Econometrics 38, 387-99.
5. Battese G. E. & Coelli T. J. (1992) Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India. J. Productivity Anal. 3, 149-69.
6. Battese G. E. & Coelli T. J. (1995) A model for technical effects in a stochastic frontier production function for panel data. Empir. Econ. 20, 325-32.
7. Battese G. E. & Corra G. S. (1977) Estimation of a production frontier model: with application to the pastoral zone of eastern Australia. Aust. J. Agric. Econ. 21, 169-79.
8. Bazzaz F. A. & Harper J. L. (1976) Relationship between plant weight and numbers in mixed populations of Sinapis alba (L.) Rabenh and Lepidium sativum L. J. Appl. Ecol. 13, 211-16.
9. Bégin E., Bégin J., Bélanger L., Rivest L., Tremblay S. (2001) Balsam fir self-thinning relationship and its constancy among different ecological regions. Can. J. For. Res. 31, 950-59.
10. Bi H. (2001) The self-thinning surface. For. Sci. 47, 361-70.
11. Bi H. & Turvey N. D. (1997) A method of selecting data points for fitting the maximum biomass-density line for stands undergoing self-thinning. Aust. J. Ecol. 22, 356-9.
12. Bi H., Wan G., Turvey N. D. (2000) Estimating the self-thinning boundary line as a density-dependent stochastic biomass frontier. Ecology 81, 1477-83.
13. Cade B. S. & Guo Q. (2000) Estimating effects of constraints on plant performance with regression quantiles. Oikos 91, 245-54.
14. Cade B. S., Terrell J. W., Schroeder R. L. (1999) Estimating effects of limiting factors with regression quantiles. Ecology 80, 311-23.
15. Coelli T. (1995) Estimators and hypothesis tests for a stochastic frontier function: a Monte Carlo analysis. J. Productivity Anal. 6, 247-68.
16. Coelli T. (1996) A Guide to FRONTIER Version 4.1:A Computer Program for Stochastic Frontier Production and Cost Function Estimation. Working Paper 96/07. Centre for Efficiency and Productivity Analysis, University of New England, Armidale.
17. Coelli T., Prasada Rao D. S., Battese G. E. (1998) An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, Boston.
18. DeBell D. S., Harms W. R., Whitesell C. D. (1989) Stockability: a major factor in productivity differences between Pinus taeda plantations in Hawaii and the southeastern United States. For. Sci. 35, 708-19.
19. Drew T. J. & Flewelling J. W. (1977) Some recent Japanese theories of yield-density relationships and their application to Monterey pine plantations. For. Sci. 23, 517-34.
20. Drew T. J. & Flewelling J. W. (1979) Stand density management: an alternative approach and its application to Douglas-fir plantations. For. Sci. 25, 518-32.
21. Farrell M. J. (1957) The measurement of productive efficiency. J. R. Stat. Soc. A 120, 253-81.
22. Flesher E. & Ley E. (1996) A frontier model for landscape ecology: the Tapir in Hondurus. Environ. Ecol. Stat. 3, 119-125.
23. Furnas R. E. (1981) A Resource Theory of Self-Thinning in Plant Populations. PhD Thesis, Cornell University, Ithaca, NY, USA.
24. Givnish T. J. (1986) Biomechanical constraints on self-thinning in plant populations. J. Theor. Biol. 119, 139-46.
25. Goldberg D. E. & Scheiner S. M. (1993) ANOVA and ANCOVA: Field competition experiments. In: Design and Analysis of Ecological Experiments (eds S. M. Scheiner & J. Gurevitch) pp. 69-93. Chapman & Hall, New York.
26. Greene W. (1993) Econometric Analysis, 2nd edn. Macmillan Publishing, New York.
27. Greene W. (1997) Frontier production functions. In: Handbook of Applied Econometrics: Microeconomics (eds H. Pesaran & P. Schmidt) pp. 81-166. Blackwell Publishers, Oxford.
28. Hall P., Park B. U., Stern S. E. (1998) On polynomial estimators of frontiers and boundaries. J. Multivariate Anal. 66, 71-98.
29. Hara T. (1984) Modelling the time course of self-thinning in crowded plant populations. Ann. Bot. 53, 181-8.
30. Harms W. R., DeBell D. S., Whitesell C. D. (1994) Stand and tree characteristics and stockability in Pinus taeda plantations in Hawaii and South Carolina. Can. J. For. Res. 24, 511-21.
31. Harms W. R., Whitesell C. D., DeBell D. S. (2000) Growth and development of loblolly pine in a spacing trial planted in Hawaii. For. Ecol. Manage. 126, 13-24.
32. Harper J. (1977) Population Biology of Plants. Academic Press, London.
33. Hozumi K. (1983) Ecological and mathematical considerations on self-thinning in even-aged pure stands. III. Effect of the linear growth factor on self-thinning and its model. Bot. Mag. Tokyo 96, 171-91.
34. Hutchings M. J. & Budd C. S. J. (1981) Plant competition and its course through time. Bioscience 31, 640-45.
35. Hynynen J. (1993) Self-thinning models for even-aged stands of Pinus sylvestris, Picea abies and Betula pendula. Scand. J. For. Res. 8, 326-36.
36. Kira T., Ogasawa H., Sakazaki N. (1953) Intraspecific competition among higher plants. I. Competition-yield-density interrelationship in regularly dispersed populations. J. Inst. Polytechnic, Osaka City University D4, 1-16.
37. Koyama H. & Kira T. (1956) Intraspecific competition among higher plants VIII. Frequency distribution of individual plant weight as affected by the interaction between plants. J. Inst. Polytechnic, Osaka City University D7, 73-94.
38. Kumbhakar S. C. & Lovell C. A. K. (2000) Stochastic Frontier Analysis. Cambridge University Press, Cambridge.
39. Maller R. A., de Boer E. S., Joll L. M., Anderson D. A., Hinde J. P. (1983) Determination of the maximum foregut volume of western rock lobster (Panulirus cygnus) from field data. Biometrics 39, 541-51.
40. Meeusen W. & van den Broeck J. (1977) Efficiency estimation from Cobb-Douglas production functions with composed error. Int. Econ. Rev. 18, 435-44.
41. Morris E. C. (2002) Self-thinning lines differ with fertility level. Ecol. Res. 17, 17-28.
42. Morris E. C. (2003) How does fertility of the substrate affect intraspecific competition? Evidence and synthesis from self-thinning. Ecol. Res. 18, 287-305.
43. Morris E. C. & Myerscough P. J. (1985) Nutrient level effects on thinning and non-thinning effects in even-aged populations of subterranean clover. Aust. J. Ecol. 10, 469-79.
44. Morris E. C. & Myerscough P. J. (1991) Self-thinning and competition intensity over a gradient of nutrient availability. J. Ecol. 79, 903-23.
45. Norberg R. Å. (1988) Theory of growth geometry of plants and self-thinning of plant populations: geometric similarity, elastic similarity, and different growth modes of plant parts. Am. Nat. 131, 220-56.
46. Oliver C. D. & Larson B. C. (1996) Forest Stand Dynamics. John Wiley and Sons, New York.
47. Schmidt P. & Lin T. F. (1984) Simple tests of alternative specifications in stochastic frontier models. J. Econometrics 24, 349-61.
48. Shinozaki H. & Kira T. (1956) Intraspecific competition among higher plants VII. Logistic theory of the C-D effect. J. Inst. Polytechnic, Osaka City University D7, 35-72.
49. Smith N. J. & Hann D. W. (1984) A new analytical model based on the -3/2 power rule of self-thinning. Can. J. For. Res. 14, 605-9.
50. Stevenson R. E. (1980) Likelihood functions for generalized stochastic frontier estimation. J. Econometrics 13, 57-66.
51. Strub M. R. & Bredenkamp B. V. (1985) Carrying capacity and thinning response of Pinus taeda in the CCT experiments. S. Afr. For. J. 128, 6-11.
52. Thomson J. D., Weiblen G., Thomson B. A., Alfaro S., Legendre P. (1996) Untangling multiple factors in spatial distributions: Lilies, gophers and rocks. Ecology 77, 1698-751.
53. Turnblom E. C. & Burk T. E. (2000) Modelling self-thinning of unthinned Lake States red pine stands using nonlinear simultaneous differential equations. Can. J. For. Res. 30, 1410-18.
54. Weller D. E. (1987) A reevaluation of the -3/2 power rule of plant self-thinning. Ecol. Monogr. 57, 23-43.
55. Westoby M. (1981) The place of the self-thinning rule in population dynamics. Am. Nat. 118, 581-7.
56. Westoby M. (1984) The self-thinning rule. Adv. Ecol. Res. 14, 167-225.
57. White J. (1980) Demographic factors in populations of plants. In: Demography and Evolution in Plant Populations (ed. O. T. Solbrig) pp. 21-48. University of California Press, Berkeley, CA.
58. White J. & Harper J. L. (1970) Correlated changes in plant size and number in plant populations. J. Ecol. 58, 467-85.
59. Whittington R. (1984) Laying down the -3/2 power law. Nature 311, 217.
60. Yoda K., Kira T., Hozumi K. (1957) Intraspecific competition among higher plants IX. Further analysis of the competitive interaction between adjacent individuals. J. Inst. Polytechnic, Osaka City University D8, 161-78.
61. Yoda K., Kira T., Ogawa H., Hozumi K. (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions (Intraspecific competition among higher plants XI). J. Biol., Osaka City University 14, 107-29.
62. Zeide B. (1987) Analysis of the 3/2 power law of self-thinning. For. Sci. 33, 517-37.
63. Zhang L., Moore J. A., Newberry J. D. (1993) Estimating asymptotic attributes of forest stands based on biomathematical rationales. Ecol. Applic. 3, 743-8.