Scaling from trees to forests: Tractable macroscopic equations for forest dynamics

Ecological Monographs

Volumn 78, Issue 4, 2008, Pages 523-545

  Strigul, Nikolay ^a,b   Pristinski, Denis ^c   Purves, Drew ^a   Dushoff, Jonathan ^a,d   Pacala, Stephen ^a  

^a PRINCETON UNIVERSITY   (United States)

^b Stevens Institute of Technology   (United States)

^c NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

^d MCMASTER UNIVERSITY   (Canada)

Author keywords

Crown plasticity; Forest dynamics; Forest scaling; Individual based forest simulator; Light competition; Macroscopic equations

Indexed keywords

ABUNDANCE; COEXISTENCE; COMPETITION (ECOLOGY); FOREST DYNAMICS; FOREST MANAGEMENT; FORESTRY MODELING; INDIVIDUAL-BASED MODEL; LIFE CYCLE; LIGHT AVAILABILITY; SIZE STRUCTURE;

EID: 55949097851     PISSN: 00129615     EISSN: 15577015     Source Type: Journal    
DOI: 10.1890/08-0082.1     Document Type: Article

References (96)

1. Adams, T. A., D. W. Purves, and S. W. Pacala. 2007. Understanding height-structured competition in forests: is there an R* for light? Proceedings of the Royal Society B 274: 3039-3042.
2. Adler, F. R. 1996. A model of self-thinning through local competition. Proceedings of the National Academy of Sciences (USA) 93:9980-9984.
3. Anderson, R. M., and R. M. May. 1991. Infectious diseases of humans, dynamics and control. Oxford University Press, New York, New York, USA.
4. Assmann, E. 1970. The principles of forest yield study. Pergamon Press, Oxford, UK.
5. Botkin, D. B. 1993. Forest dynamics, an ecological model. Oxford University Press. New York.
6. Botkin, D. B., J. F. Janak, and J. R. Wallis. 1972. Some ecological consequences of a computer model of forest growth. Journal of Ecology 60:849-872.
7. Bragg, D. C. 2001. Potential relative increment (PRI): a new method to empirically derive optimal tree diameter growth. Ecological Modelling 137:77-92.
8. Brisson, J. 2001. Neighborhood competition and crown asymmetry in Acer saccharum, Canadian Journal of Forest Research 31:2151-2159.
9. Bugmann, H. 2001. A review of forest gap models. Climatic Change 51:259-305.
10. Busgen, M., and E. Munch. 1929. The structure and life of forest trees. [English translation by T. Thomson.] Chapman and Hall, London, UK.
11. Connell, J. H. 1971. On the role of natural enemies in preventing competitive exclusion in some marine animals and in rain forest trees. Pages 298-310 in P. J. Den Boer and G. R. Gradwell, editors. Dynamics of populations: proceedings of the advanced study institute on dynamics of numbers of populations. Center for Agricultural Publishing and Documentation, Wageningen, The Netherlands.
12. Curtin, R. A. 1970. Dynamics of tree and crown structure in Eucalyptus oblique. Forest Science 16:321-328.
13. DeAngelis, D. L., K. A. Rose, L, B, Crowder, E. A. Marschall, and D. Lika. 1993. Fish cohort dynamics: application of complementary modeling approaches. American Naturalist 142:604-622.
14. De Kroon, H., H. Huber, J. F. Stuefer, and J. M. van Groenendael. 2005. A modular concept of phenotypic plasticity in plants. New Phytologist 166:73-82.
15. Deutschman, D. H., S. A. Levin, and S. W. Pacala. 1999. Error propagation in a forest succession model: the role of fine-scale heterogeneity in light. Ecology 80:1927-1943.
16. Di Lucca, C. M. 1998. TASS/SYLVER/TIPSY: systems for predicting the impact of silvicultural practices on yield, lumber value, economic return and other benefits. Pages 7-16 in C. R. Bamsey, editor, Stand density management conference: using the planning tools. Alberta Environmental Protection, Edmonton, Alberta, Canada.
17. Durrett, R., and S. A. Levin. 1994. Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London, Series B 343:329-350.
18. Engler, A. 1924. Heliotropismus und Geotropismus der Bäume und deren waldbaumliche Bedeutung. Mitteilungen der Schweizerischen Centralanstalt für das Forstliche Versuchswesen 13:225-283.
19. Ford, E. D. 1992. The control of tree structure and productivity through the interaction of morphological development and physiological processes. International Journal of Plant Sciences 153:S147-S162.
20. Franco, M. 1986. The influences of neighbours on the growth of modular organisms with an example from trees. Philosophical Transactions of the Royal Society of London B 313:209-225.
21. Frelich, L. E., and G. L. Martin. 1988. Effects of crown expansion into gaps on evaluation of disturbance intensity in northern hardwood forests. Forest Science 34:530-536.
22. Friend, A. D., A. K. Stevens, R. G. Knox, and M. G. R. Cannell. 1997. A process-based, terrestrial biosphere model of ecosystem dynamics (Hybrid v. 3.0). Ecological Modelling 95:249-287.
23. Garcia, O. 2005. TADAM: a dynamic whole-stand approximation for the TASS growth model. Forestry Chronicle 81: 575-581.
24. Godin, C. 2000. Representing and encoding plant architecture: A review. Annals of Forest Science 57:413-438.
25. Grace, J. 1977. Plant response to wind. Academic Press New York, USA.
26. Grote, R., and H. Pretzsch. 2002. A model for individual tree development based on physiological processes. Plant Biology 4:167-180.
27. Gysel, L. W. 1951. Borders and openings of beech-maple woodlands in southern Michigan. Journal of Forestry 49:13-19.
28. Halle, F., R. A. A. Oldeman, and P. B. Tomlinson. 1978. Tropical trees and forests: an architectural analysis. Springer-Verlag, Berlin, Germany.
29. Harper, J. L. 1977. Population biology of plants, Academic Press, New York, New York, USA.
30. Hethcote, H. W. 2000. The mathematics of infectious diseases. SIAM Review 42:599-653.
31. Hibbs, D. E. 1982. Gap dynamics in a hemlock-hardwood forest. Canadian Journal of Forest Research 12:522-527.
32. Hoshino, D., N. Nishimura, and S. Yamamoto. 2001. Age, size structure and spatial pattern of major tree species in an old-growth Chamaecyparis obtusa forest, Central Japan. Forest Ecology and Management 152:31-43.
33. Hurtt, G. C, P. R. Moorcroft, S. W. Pacala, and S. A. Levin. 1998. Terrestrial models and global change: challenges for the future. Global Change Biology 4:581-590.
34. Ishizuka, M. 1984. Spatial pattern of trees and their crowns in natural mixed forests. Japanese Journal of Ecology 34:421-430.
35. Janzen, D. H. 1970. Herbivores and the number of tree species in tropical forests. American Naturalist 104:501-529.
36. King, D. A., and O. L. Loucks. 1978. The theory of tree bole and branch form. Radiation and Environmental Biophysics 15:141-165.
37. Kohyama, T. 1993. Size-structured tree populations in gapdynamic forest: the forest architecture hypothesis for the stable coexistence of species. Journal of Ecology 81:131-143.
38. Kohyama, T. 2006. The effect of patch demography on the community structure of forest trees. Ecological Research 21: 346-355.
39. Kohyama, T., E. Suzuki, T. Partomihardjo, and T. Yamada. 2001. Dynamic steady state of patch-mosaic tree size structure of a mixed dipterocarp forest regulated by local crowding. Ecological Research 16:85-98.
40. Kovats, M. 1993. A comparison of British, Swedish and British Columbian growth and yield predictions for lodgepole pine. Forestry Chronicle 69:450-457.
41. Larson, P. R. 1963. Stem form development of forest trees. Forest Science Monographs 5:1-41.
42. Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 33:183-212.
43. Leslie, P. H. 1948. Some further notes on the use of matrices in population mathematics. Biometrika 35:213-245.
44. Levin, S. A., and S. W. Pacala. 1997. Theories of simplification and scaling of spatially distributed processes. Pages 271-295 in D. Tilman and P. Kareiva, editors. Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, New Jersey, USA.
45. Levin, S. A., and R. T. Paine. 1974. Disturbance, patch formation, and community structure. Proceedings of the National Academy of Sciences (USA) 71:2744-2747.
46. Liu. J., and P. S. Ashton. 1995. Individual-based simulation models for forest succession and management. Forest Ecology and Management 73:157-175.
47. Loehle, C. 1986. Phototropism of whole trees: effects of habitat and growth form. American Midland Naturalist 116:190-196.
48. Lotka, A. J. 1907. Relation between birth rates and death rates. Science 26:21-22.
49. Lotka, A. J. 1922. The stability of the normal age distribution. Proceedings of the National Academy of Sciences (USA) 8: 339-345.
50. Lotka, A. J. 1939. On an integral equation in population analysis, Annals of Mathematical Statistics 10:144-161.
51. Mav, R. M. 2004. Uses and abuses of mathematics in biology. Science 303:790-793.
52. McKendrick, A. G. 1926. Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society 44:1-34.
53. McMahon, T. A., and R. E. Kronauer. 1976. Tree structures: deducing the principle of mechanical design. Journal of Theoretical Biology 59:443-66.
54. Medvigy, D. M. 2006. The state of the regional carbon cycle: results from a coupled constrained ecosystem-atmosphere model. Dissertation. Harvard University, Cambridge, Massachusetts, USA.
55. Metz, J. A. J., and O. Diekmann, 1986. The dynamics of physiologically structured populations. Lecture notes in biomathematics 68. Springer, New York, New York, USA.
56. Mitchell, K. J. 1969. Simulation of growth of even-aged stands of white spruce. Yale University School of Forestry Bulletin 75:1-48.
57. Mitchell, K. J. 1975. Dynamics and simulated yield of Douglas fir. Forest Science Monograph 17:1-39.
58. Mitchell, K. J. 1980. Distance dependent individual tree stand models: concepts and applications. Pages 100-137 in K. M. Brown and F. R. Clarke, editors. Forecasting forest stand dynamics: proceedings of the workshop. June 24. 25, Lakehead University. Thunder Bay, Ontario, Canada.
59. Moorcroft, P. R., G. C. Hurtt, and S. W. Pacala. 2001. A method for scaling vegetation dynamics: the ecosystem demography model (ED). Ecological Monographs 71:557-585.
60. Munro, D. D. 1974. Forest growth models: a prognosis. Pages 7-21 in J. Fries, editor. Growth models for tree and stand simulation. Royal College of Forest Research, Stockholm, Sweden.
61. Muth, C. C. and F. A. Bazzaz. 2002. Tree canopy displacement at forest gap edges. Canadian Journal of Forest Research 32: 247-254.
62. Olesen, T. 2001. Architecture of a cool-temperature rain forest canopy. Ecology 82:2719-2730.
63. Oliver. C. D.. and B. C. Larson. 1996. Forest stand dynamics. Wiley, New York, USA.
64. Oster. G., and Y. Takahashi. 1974. Models for age-specific interactions in a periodic environment. Ecological Monographs 44:483-501.
65. Pacala, S. W., C. D. Canham, J. Saponara, J. A. Silander, R. K. Kobe, and E. Ribbens. 1996. Forest models defined by field measurements: estimation, error analysis and dynamics. Ecological Monographs 66:1-43.
66. Pacala, S. W., C. D. Canham, and J. A. Silander. 1993. Forest models defined by field measurements. 1. The design of a northeastern forest simulator. Canadian Journal of Forest Research 23:1980-1988.
67. Pacala, S. W., and D. H. Deutschman. 1995. Details that matter: The spatial distribution of individual trees maintains forest ecosystem function. Oikos 74:357-365.
68. Pacala, S. W., and S. A. Levin. 1997. Biologically generated spatial pattern and the coexistence of competing species. Pages 204-232 in D. Tilman and P. Kareiva, editors. Spatial ecology: The role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, New Jersey, USA.
69. Perry, G. L. W., and N. J. Enright. 2006. Spatial modelling of vegetation change in dynamic landscapes: a review of methods and applications. Progress in Physical Geography 30:47-72.
70. Prctzsch, H. 2002. A unified law of spatial allometry for woody and herbaceous plants. Plant Biology 4:159-166.
71. Rogers. G. F. 1989. Asymmetrical growth of the crowns of neighbouring desert shrubs. Journal of Arid Environments 17:319-326.
72. Rouvinen, S., and T. Kuuluvainen. 1997. Structure and asymmetry of tree crowns in relation to local competition in a natural mature Scots pine forest. Canadian Journal of Forest Research 27:890-902.
73. Rouvinen, S., and T. Kuuluvainen. 2005. Tree diameter distributions in natural and managed old Pinus sylvestris-dominated forests. Forest Ecology and Management 208:45-61.
74. Shugart, H. H. 1984. A theory of forest dynamics. The ecological implications of forest succession models. Springer, New York, New York, USA.
75. Sinko, J. W., and W. Streifer. 1967. A new model for age-size structure of a population ecology. Ecology 48:910-918.
76. Sorrensen-Cothern, K. A., E. D. Ford, and D. G. Sprugel. 1993. A model of competition incorporating plasticity through modular foliage and crown development. Ecological Monographs 63:277-304.
77. Sterck, F. J., F. Schieving, A. Lemmens, and T. L. Pons. 2005. Performance of trees in forest canopies: explorations with a bottom-up functional-structural plant growth model. New Phytologist 166:827-843.
78. Stoll, P.. and B. Schmid. 1998. Plant foraging and dynamic competition between branches of Pinus sylvestris in contrasting light environments. Journal of Ecology 86:934-945.
79. Strigul, N. S. 2007. A new method of scaling of vegetation dynamics from individual level to forest ecosystem based on crown plasticity. Dissertation. Stevens Institute of Technology. Hoboken, New Jersey, USA.
80. Takenaka. A. 1994. A simulation-model of tree architecture development based on growth response to local light environment. Journal of Plant Research 107:321-330.
81. Tilman, D. 1994. Competition and biodiversity in spatially structured habitats. Ecology 75:2-16.
82. Trimble, R., and H. Tryon. 1966. Crown encroachment into openings cut in Appalachian hardwood stands. Journal of Forestry 64:104-108.
83. Umeki. K. 1995a. Modeling the relationship between the asymmetry in crown display and local environment. Ecological Modelling 82:11-20.
84. Umeki, K. 1995b. Importance of crown position and morphological plasticity in competitive interaction in a population of Xanthium canadense. Annals of Botany 75:259-265.
85. Umeki. K. 1995c. A comparison of crown asymmetry between Picea abies and Betula maximowicziana. Canadian Journal of Forest Research 25:1876-1880.
86. Umeki, K. 1997. Effect of crown asymmetry on size-structure dynamics of plant populations. Annals of Botany 79:631-641.
87. Van Sickle, J. 1977. Analysis of a distributed-parameter population model based on physiological age. Journal of Theoretical Biology 64:571-586.
88. von Foerster, H. 1959. Some remarks on changing populations. Pages 382-407 in F. Stohlman, Jr., editor. The kinetics of cellular proliferation. Grune and Stratton, New York, New York, USA.
89. Waller, D. M. 1986. The dynamics of growth and form. Pages 291-320 in M. J. Crawley, editor. Plant ecology. Blackwell Scientific Publications. Oxford, UK.
90. Watt, A. S. 1947. Pattern and process in the plant community. Journal of Ecology 35:1-22.
91. Webster, C. R., and C. G. Lorimer. 2005. Minimum opening sizes for canopy recruitment of midtolerant tree species: a retrospective approach. Ecological Applications 15:1245-1262.
92. Weiler, D. E. 1987a. A reevaluation of the -3/2 power rule of plant self-thinning. Ecological Monographs 57:23-43.
93. Weller, D. E. 1987b. Self-thinning exponent correlated with allometric measures of plant geometry. Ecology 68:813-821.
94. White, J., and J. L. Harper. 1970. Correlated changes in plant size and number in plant populations. Journal of Ecology 58: 467-485.
95. Woods. F. W., and R. E. Shanks. 1959. Natural replacement of chestnut by other species in the Great Smoky Mountains National Park. Ecology 40:349-361.
96. Young, T. P., and S. P. Hubbell, 1991. Crown asymmetry, treefalls, and repeat disturbance in a broad-leaved forest. Ecology 72:1464-1471.