An analytical model of stand dynamics as a function of tree growth, mortality and recruitment: The shade tolerance-stand structure hypothesis revisited

Journal of Theoretical Biology

Volumn 244, Issue 3, 2007, Pages 440-450

  Zavala, Miguel A ^a   Angulo, Óscar ^b   Bravo de la Parra, Rafael ^a   López Marcos, Juan C ^b  

^a UNIVERSITY OF ALCALÁ   (Spain)

^b UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Growth; Light competition; Mortality; Recruitment; Shade tolerance

Indexed keywords

GROWTH; LIGHT EFFECT; MORTALITY; RECRUITMENT; SHADE TOLERANCE; STAND DYNAMICS;

AGE; ANALYTIC METHOD; ARTICLE; CALCULATION; COMPETITIVE BEHAVIOR; DYNAMICS; EVALUATION; FOREST DYNAMICS; FOREST STAND; FOREST STRUCTURE; HYPOTHESIS; LIGHT; MATHEMATICAL ANALYSIS; MORTALITY; PARTIAL DIFFERENTIAL EQUATION SYSTEM; PRIORITY JOURNAL; SAPLING; SHADE TOLERANCE; SHADE TOLERANCE STAND STRUCTURE HYPOTHESIS; SIMULATION; SPECIES DIFFERENCE; TREE GROWTH;

COMPUTER SIMULATION; ENVIRONMENT; LIGHT; MODELS, BIOLOGICAL; TREES;

EID: 33845864988     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.08.024     Document Type: Article

References (72)

1. Abia L.M., Angulo O., and López-Marcos J.C. Size-structured population dynamics models and their numerical solutions. Discrete Contin. Dyn. Syst. B 4 (2004) 1203-1222
2. Abia L.M., Angulo O., and López-Marcos J.C. Age-structured population models and their numerical solution. Ecol. Modelling 188 (2005) 112-136
3. Abrams M., and Downs J.A. Successional replacement of old-growth white oak by mixed mesophytic hardwoods in southwestern Pennsylvania. Can. J. For. Res. 20 (1990) 1864-1870
4. Agren J., and Zackrisson O. Age and size structure of Pinus sylvestris populations on mires in central and northern Sweden. J. Ecol. 78 (1990) 1049-1062
5. Angulo O., and López-Marcos J.C. Numerical schemes for size-structured population equations. Math. Biosci. 157 (1999) 169-188
6. Angulo O., and López-Marcos J.C. Numerical integration of nonlinear size-structured population equations. Ecol. Modelling 133 (2000) 3-14
7. Angulo O., and López-Marcos J.C. Numerical integration of autonomous and no autonomous nonlinear size-structured population models. Math. Biosci. 177-178 (2002) 39-71
8. Angulo O., and López-Marcos J.C. Numerical integration of fully nonlinear size-structured population models. Appl. Numer. Math. 50 (2004) 291-327
9. Angulo O., Durán A., and López-Marcos J.C. A numerical simulation for the dynamics of the sexual phase of monogonont rotifera. C. R. Biologies 327 (2005) 293-303
10. Assman E. The principles of forest yield study (1970), Trans. S.H. Gardiner. Pergamon, Oxford
11. Bailey R.L., and Dell T.R. Quantifying diameter distributions with the Weibull function. For. Sci. 19 (1973) 97-104
12. Bees M.A., Angulo O., López-Marcos J.C., and Schley D. Dynamics of a structured slug population model in the absence of seasonal variation. Math. Mod. Meth. Appl. Sci. 12 16 (2006)
13. Binkley D., Stape J.L., Ryan M.G., Barnard H.R., and Fownes J. Age-related decline in forest ecosystem growth: an individual tree, stand structure hypothesis. Ecosystems 5 (2002) 58-67
14. Butson R.G., Knowles P., and Farmer Jr. R.E. Age and size structure of marginal disjunct populations of Pinus resinosa. J. Ecol. 75 (1987) 685-692
15. Calsina A., and Saldaña J. Asymptotic behaviour of a model of hierarchically structured population dynamics. J. Math. Biol. 35 (1997) 967-987
16. Canham C.D. Different responses to gaps among shade-tolerant tree species. Ecology 70 (1989) 548-550
17. Casagrandi R., and Rinaldi S. A minimal model for forest fire regimes. Am. Nat. 153 (1999) 527-539
18. Chapin III F.S., Autumn K., and Pugnaire F. Evolution of suites of traits in response to environmental stress. Am. Nat. 142 (1993) S78-S92
19. Crawley, M.J., (Ed.) 1986. Plant Ecology. Blackwell Scientific Press, Oxford.
20. Cushing, J.M., 1998. An Introduction to Structured Population Dynamics. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 71. SIAM, Philadelphia.
21. De Roos A.M. A gentle introduction to physiologically structured population models. In: Tuljapurkar S., and Caswell H. (Eds). Structured-Population Models in Marine, Terrestrial, and Freshwater Systems (1997), Chapman & Hall, New York 119-204
22. Dercole F., Niklas K., and Rand R. Self-thinning and community persistence in a simple size-structured dynamical model of plant growth. J. Math. Biol. 51 (2005) 333-354
23. Espelta J.M., Riba M., and Retana J. Patterns of seedling recruitment in West Mediterranean coppiced holm-oak (Quercus ilex L.) forests as influenced by canopy development. J. Veg. Sci. 6 (1995) 645-672
24. Ford E.D., and Newbould P.J. Stand structure and dry weight production through the sweet chestnut (Castanea sativa) coppice cycle. J. Ecol. 58 (1970) 275-296
25. Glitzenstein J.S., Harcombe P.A., and Streng D.R. Disturbance, succession and maintenance of species diversity in an east Texas forest. Ecol. Monogr. 56 (1986) 243-258
26. Gurtin M.E., and MacCamy R.C. Nonlinear age-dependent population dynamics. Arch. Rat. Mech. Anal. 54 (1974) 281-300
27. Hara T. A stochastic model and the moment dynamics of the growth and size distribution in plant populations. J. Theor. Biol. 109 (1984) 173-190
28. Hara T. Dynamics of stand structure in plant monocultures. J. Theor. Biol. 110 (1984) 223-239
29. Hara T. A model for mortality in a self-thinning plant population. Ann. Botany 55 (1985) 667-675
30. Hara T. Effects of the mode of competition on stationary size distribution in plant populations. Ann. Bot. 69 (1992) 509-513
31. Hara T., and Yokozawa M. Effects of physiological and environmental variations on size-structure dynamics in plant populations. Ann. Bot. 73 (1994) 39-51
32. Harper J.L. Population Biology of Plants (1977), Academic Press, New York
33. Hubbell S.P. Seed predation and the coexistence of tree species in tropical forests. Oikos 35 (1980) 214-229
34. Hurtt G.C., and Pacala S.W. The consequences of recruitment limitation: reconciling chance, history and competitive differences between plants. J. Theor. Biol. 176 (1995) 1-12
35. Iannelli, M., 1994. Mathematical Theory of Age-Structured Populations Dynamics. Giardini Editori e Stampatori, Pisa.
36. Kermack W., and McKendrick A. Contributions to the mathematical theory of epidemics III. Further studies on the problem of endemicity. Proc. R. Soc. 141 (1933) 94-122
37. Keyfitz N. Introduction to the Mathematics of Population (1968), Addison Wesley, Reading, MA
38. Knox R.G., Peet R.K., and Christensen N.L. Population dynamics in loblolly pine stands: changes in skewness and size inequality. Ecology 70 (1989) 1153-1166
39. Kobe R.K., Pacala S.W., Silander Jr. J.A., and Canham C.D. Juvenile tree survivorship as a component of shade tolerance. Ecol. Appl. 5 (1995) 517-532
40. Kohyama T. Simulation of the structural development of warm-temperate rain forest stands. Ann. Bot. 63 (1991) 625-634
41. Kohyama T. Simulating stationary size distribution of trees in rain forests. Ann. Bot. 68 (1991) 173-180
42. Kohyama T. Size-structured multi-species model of rain forest trees. Funct. Ecol. 6 (1992) 206-212
43. Kraev E.A. Existence and uniqueness for height structured hierarchical population models. Nat. Resour. Modelling 14 (2001) 45-70
44. Lanier, L., 1986. Précis de Sylviculture. ENGREF. Nancy.
45. Levin S.A., and Pacala S.W. Theories of simplification and scaling of spatially distributed processes. In: Tilman D., and Kareiva P. (Eds). Spatial Ecology. The Role of Space in Population Dynamics and Interspecific Interactions (1997), Princeton University Press, Princeton, NJ 271-296
46. Lieffers V.J. Stand structure variability in growth and intraspecific competition in a peatland stand of black spruce Picea mariana. Holarc. Ecol. 9 (1986) 58-64
47. Liocurt F.d. De l'aménagement des sapinières. Soc. For. Franche-Comté Belfort Bull. 6 (1898) 369-405
48. Lischke H. New developments in forest modelling: convergence between applied and theoretical approaches. Nat. Resour. Modeling 14 (2001) 71-102
49. Lischke H., Löffler T.J., and Fischlin A. Aggregation of individual trees and patches in forest succession models: capturing variability with height structured, random, spatial distributions. Theor. Popul. Biol. 54 (1998) 213-226
50. Lookingbill T., and Zavala M.A. Spatial pattern of holm oak (Quercus ilex) and downy oak (Quercus pubescens) recruitment in Aleppo pine (Pinus halepensis) dominated woodlands. J. Veg. Sci. 11 (2000) 607-612
51. Lorimer C.G. Age structure and disturbance history of a southern Appalachian virgin forest. Ecology 61 (1980) 1169-1184
52. Lorimer C.G., and Krug A.G. Diameter distributions in even-aged stands of shade-tolerant and mid-tolerant and midtolerant tree species. Am. Mid. Nat. 109 (1983) 331-345
53. Metz, J.A.J., Diekmann O., 1986. The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics, vol. 68. Springer, Berlin.
54. Nagano, M., 1978. Dynamics of stand development. In: Kira, T., Ono, Y., Osokawa, T. (Eds.), Biological Production in a Warm-Temperate Evergreen Oak Forest of Japan, vol. 18. University of Tokyo Press, JIBP Synthesis Edition, pp. 21-31.
55. Oliver C.D., and Larson B.C. Forest Stand Dynamics (1990), McGraw-Hill, New York
56. Pacala S.W., and Deutschman D. Details that matter: the spatial distribution of individual trees maintains forest ecosystem function. Oikos 74 (1995) 357-365
57. Pacala S.W., Canham C.D., Saponara J., Silander J.A., Kobe R.K., and Ribbens E. Forest models defined by field measurements: estimation, error analysis and dynamics. Ecol. Monogr. 66 (1996) 1-43
58. Parker A.J. Stand structure in subalpine forests of Yosemite National Park. California. For. Sci. 34 (1984) 1047-1058
59. Retana J., Riba M., Castell C., and Espelta J.M. Regeneration by sprouting of holm-oak (Quercus ilex) stands exploited by selection thinning. Vegetation 99-100 (1992) 355-364
60. Richards F.J. A flexible growth function for empirical use. J. Exp. Bot. 10 (1959) 290-300
61. Shinko J.W., and Streifer W. A new model for age-size structure of a population. Ecology 48 (1967) 910-918
62. Shugart H.H. A Theory of Forest Dynamics: the Ecological Implications of Forest Succession Models (1984), Springer, Berlin
63. Smith D.M. The Practice of Silviculture (1962), Wiley, New York
64. Sulsky D. Numerical solution of structured population models ii: mass structure. J. Math. Biol. 32 (1994) 491-514
65. Takada T., and Iwasa Y. Size distribution dynamics of plants with interaction by shading. Ecol. Modelling 33 (1986) 173-184
66. Tilman D. Plant strategies and the dynamics and structure of plant communities (1988), Princeton University Press, Princeton, NJ
67. Tucker S., and Zimmerman S. A nonlinear model of population-dynamics containing and arbitrary number of continuous structure variables. SIAM J. Appl. Math. 48 (1988) 549-591
68. Turnbull L.A., Crawkey M., and Rees M. Are plant populations seed-limited? A review of seed sowing experiments. Oikos 88 (2000) 225-238
69. Valladares F. Light heterogeneity and plants: from ecophysiology to species coexistence and biodiversity. In: Esser K., Lüttge U., Beyschlag W., and Hellwig F. (Eds). Progress in Botany (2003), Springer, Heidelberg 439-471
70. Von Foerster H. Some remarks on changing populations. In: Stohlman F. (Ed). The Kinetics of Cellular Proliferation (1959), Grune and Stratton, New York 382-407
71. Webb G.F. Theory of Nonlinear Age-Dependent Population Dynamics (1985), Marcel Dekker, New York
72. Zavala M.A., and Bravo de la Parra R. A mechanistic model of tree competition and facilitation for Mediterranean forests: scaling from leaf physiology to stand dynamics. Ecol. Modelling 188 (2005) 76-92