Mechanistic models of seed dispersal by wind

Theoretical Ecology

Volumn 4, Issue 2, 2011, Pages 113-132

  Nathan, Ran ^a   Katul, Gabriel G ^b,c,d   Bohrer, Gil ^e   Kuparinen, Anna ^f   Soons, Merel B ^g   Thompson, Sally E ^b   Trakhtenbrot, Ana ^a   Horn, Henry S ^h  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b DUKE UNIVERSITY   (United States)

^c Duke University   (United States)

^d POLITECNICO DI TORINO   (Italy)

^e Ohio State University   (United States)

^f UNIVERSITY OF HELSINKI   (Finland)

^g UTRECHT UNIVERSITY   (Netherlands)

^h PRINCETON UNIVERSITY   (United States)

Author keywords

Advection diffusion models; Ballistic models; Canopy turbulence; Large eddy simulations; Long distance dispersal; WALD dispersal kernel

Indexed keywords

ADVECTION-DIFFUSION EQUATION; BIFURCATION; ECOLOGICAL THEORY; LARGE EDDY SIMULATION; METAPOPULATION; POPULATION DYNAMICS; SEED DISPERSAL; TURBULENCE;

EID: 79954689611     PISSN: 18741738     EISSN: 18741746     Source Type: Journal    
DOI: 10.1007/s12080-011-0115-3     Document Type: Article

References (142)

1. Amiro BD, Davis PA (1988) Statistics of atmospheric turbulence within a natural black spruce forest canopy. Bound Lay Meteor 44: 267-283.
2. Andersen M (1991) Mechanistic models for the seed shadows of wind-dispersed plants. Am Nat 137: 476-497.
3. Augspurger CK (1986) Morphology and dispersal potential of wind-dispersed diaspores of neotropical trees. Am J Bot 73: 353-363.
4. Augspurger CK, Franson SE (1987) Wind dispersal of artificial fruits varying in mass, area, and morphology. Ecology 68: 27-42.
5. Aylor DE (2004) Survival of maize (Zea mays) pollen exposed in the atmosphere. Agric For Meteorol 123: 125-133.
6. Baldocchi D, Falge E, Gu LH, Olson R, Hollinger D, Running S, Anthoni P et al (2001) FLUXNET: a new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapor, and energy flux densities. Bull Am Meteorol Soc 82: 2415-2434.
7. Bohrer G, Nathan R, Volis S (2005) Effects of long-distance dispersal for metapopulation survival and genetic structure at ecological time and spatial scales. J Ecol 93: 1029-1040.
8. Bohrer G, Wolosin M, Brady R, Avissar R (2007) A Virtual Canopy Generator (V-CaGe) for modeling complex heterogeneous forest canopies at high resolution. Tellus 59B: 566-576.
9. Bohrer G, Katul GG, Nathan R, Walko RL, Avissar R (2008) Effects of canopy heterogeneity, seed abscission, and inertia on wind-driven dispersal kernels of tree seeds. J Ecol 96: 569-580.
10. Bohrer G, Katul GG, Walko RL, Avissar R (2009) Exploring the effects of microscale structural heterogeneity of forest canopies using large-eddy simulations. Bound Lay Meteor 132: 351-382.
11. Bohrerova Z, Bohrer G, Cho KD, Bolch MA, Linden KG (2009) Determining the viability response of pine pollen to atmospheric conditions during long-distance dispersal. Ecol Appl 19: 656-667.
12. Bou-Zeid E, Meneveau C, Parlange MB (2004) Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: Blending height and effective surface roughness. Water Resour Res 40.
13. Bullock JM, Clarke RT (2000) Long distance seed dispersal by wind: measuring and modelling the tail of the curve. Oecologia 124: 506-521.
14. Burrows FM (1973) Calculation of the primary trajectories of plumed seeds in steady winds with variable convection. New Phytol 72: 647-664.
15. Burrows FM (1975a) Calculation of the primary trajectories of dust seeds, spores and pollen in unsteady winds. New Phytol 75: 389-403.
16. Burrows FM (1975b) Wind-borne seed and fruit movement. New Phytol 75: 405-418.
17. Burton T, Sharpe D, Jenkins N, Bossanyi E (2001) Wind energy handbook. Wiley, Chichester.
18. Cionco RM (1965) A mathematical model for air flow in a vegetative canopy. J Appl Meteorol 4: 517-522.
19. Cionco RM (1978) Analysis of canopy index value for various canopy densities. Bound Lay Meteor 15: 81-93.
20. Clark JS, Silman M, Kern R, Macklin E, HilleRisLambers J (1999) Seed dispersal near and far: patterns across temperate and tropical forests. Ecology 80: 1475-1494.
21. Clark JS, Lewis M, Horvath L (2001) Invasion by extremes: population spread with variation in dispersal and reproduction. Am Nat 157: 537-554.
22. Clark DB, Olivas PC, Oberbauer SF, Clark DA, Ryan MG (2008) First direct landscape-scale measurement of tropical rain forest Leaf Area Index, a key driver of global primary productivity. Ecol Lett 11: 163-172.
23. Cody ML, Overton JM (1996) Short-term evolution of reduced dispersal in island plant populations. J Ecol 84: 53-61.
24. Cousens R, Dytham C, Law R (2008) Dispersal in plants: a population perspective. Oxford University Press, Oxford.
25. Cremer KW (1971) Speeds of falling and dispersal of seed of Pinus radiata and Pinus contorta. Aust For Res 5: 29-32.
26. Cremer KW (1977) Distance of seed dispersal in eucalypts estimated from seed weights. Aust For Res 7: 225-228.
27. Damschen EI, Brudvig LA, Haddad NM, Levey DJ, Orrock JL, Tewksbury JJ (2008) The movement ecology and dynamics of plant communities in fragmented landscapes. Proc Natl Acad Sci USA 105: 19078-19083.
28. Davis MB, Shaw RG (2001) Range shifts and adaptive responses to Quaternary climate change. Science 292: 673-679.
29. Denmead OT, Bradley EF (1985) Flux-gradient relationships in a forest canopy. In: Hutchison BA, Hicks BB (eds) The forest-atmosphere interaction. Reidel, Dordrecht, pp 421-442.
30. Dingler H (1889) Die Bewegung der pflanzlichen Flugorgane. Ackermann, Munchen.
31. Dupont S, Brunet Y (2008) Edge flow and canopy structure: a large-eddy simulation study. Bound Lay Meteor 126: 51-71.
32. Ellstrand NC (1992) Gene flow by pollen: implications for plant conservation genetics. Oikos 63: 77-86.
33. Ernst WHO, Veenendaal EM, Kebakile MM (1992) Possibilities for dispersal in annual and perennial grasses in a savanna in Botswana. Vegetatio 102: 1-11.
34. Fields DE, Sharpe DM (1980) SEDFAL: a model of dispersal of tree seeds by wind. Oak Ridge National Laboratory, Report EDFB/IBP-78/2, Oak Ridge, Tennessee.
35. Finnigan JJ, Belcher SE (2004) Flow over a hill covered with a plant canopy. Q J R Meteorol Soc 130: 1-29.
36. Fischlin A, Midgley GF, Price TJ, Leemans R, Gopal B, Turley C, Rounsevell MDA et al (2007) Ecosystems, their properties, goods and services. In: Parry ML, Canziani OF, Palutikof JP, van der Linden PJ, Hanson CE (eds) Climate change 2007: impacts, adaptation and vulnerability. Contribution of working group II to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge, pp 212-272.
37. Gardiner BA (1994) Wind and wind forces in a plantation spruce forest. Bound Lay Meteor 67: 161-186.
38. Greene DF (2005) The role of abscission in long-distance seed dispersal by the wind. Ecology 86: 3105-3110.
39. Greene DF, Johnson EA (1989) A model of wind dispersal of winged or plumed seeds. Ecology 70: 339-347.
40. Greene DF, Johnson EA (1990) The aerodynamics of plumed seeds. Funct Ecol 4: 117-126.
41. Greene DF, Johnson EA (1992) Can the variation in samara mass and terminal velocity on an individual plant affect the distribution of dispersal distances? Am Nat 139: 825-838.
42. Greene DF, Johnson EA (1996) Wind dispersal of seeds from a forest into a clearing. Ecology 77: 595-609.
43. Greene DF, Johnson EA (1997) Secondary dispersal of tree seeds on snow. J Ecol 85: 329-340.
44. Gregory PH (1945) The dispersion of air-borne spores. Trans Br Mycol Soc 28: 26-70.
45. Harper JL (1977) Population biology of plants. Academic, London.
46. Higgins SI, Richardson DM (1999) Predicting plant migration rates in a changing world: the role of long-distance dispersal. Am Nat 153: 464-475.
47. Higgins SI, Clark JS, Nathan R, Hovestadt T, Schurr F, Fragoso JMV, Aguiar MR et al (2003a) Forecasting plant migration rates: managing uncertainty for risk assessment. J Ecol 91: 341-347.
48. Higgins SI, Nathan R, Cain ML (2003b) Are long-distance dispersal events in plants usually caused by nonstandard means of dispersal? Ecology 84: 1945-1956.
49. Horn HS, Nathan R, Kaplan SR (2001) Long-distance dispersal of tree seeds by wind. Ecol Res 16: 877-885.
50. Howe HF, Smallwood J (1982) Ecology of seed dispersal. Annu Rev Ecol Syst 13: 201-228.
51. Janzen DH (1970) Herbivores and the number of tree species in tropical forests. Am Nat 104: 501-528.
52. Johnson WC, Sharpe DM, DeAngelis DL, Fields DE, Olson RJ (1981) Modeling seed dispersal and forest island dynamics. In: Burgess RL, Sharpe DM (eds) Forest island dynamics in man-dominated landscapes. Springer, New York, pp 215-239.
53. Jongejans E, Pedatella NM, Shea K, Skarpaas O, Auhl R (2007) Seed release by invasive thistles: the impact of plant and environmental factors. Proc Roy Soc Lond B 274: 2457-2464.
54. Jongejans E, Shea K, Skarpaas O, Kelly D, Sheppard AW, Woodburn TL (2008) Dispersal and demography contributions to population spread of Carduus nutans in its native and invaded ranges. J Ecol 96: 687-697.
55. Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, New York.
56. Katul GG, Albertson JD (1998) An investigation of higher-order closure models for a forested canopy. Bound Lay Meteor 89: 47-74.
57. Katul G, Hsieh CI, Kuhn G, Ellsworth D, Nie DL (1997) Turbulent eddy motion at the forest-atmosphere interface. J Geophys Res Atmos 102: 13409-13421.
58. Katul G, Wiberg P, Albertson J, Hornberger G (2002) A mixing layer theory for flow resistance in shallow streams. Water Resour Res 38: 1250. doi: 1210. 1029/2001WR000817.
59. Katul GG, Mahrt L, Poggi D, Sanz C (2004) One- and two-equation models for canopy turbulence. Bound Lay Meteor 113: 81-109.
60. Katul GG, Porporato A, Nathan R, Siqueira M, Soons MB, Poggi D, Horn HS, Levin SA (2005) Mechanistic analytical models for long-distance seed dispersal by wind. Am Nat 166: 368-381.
61. Kleyer M, Bekker RM, Knevel IC, Bakker JP, Thompson K, Sonnenschein M, Poschlod P et al (2008) The LEDA Traitbase: a database of life-history traits of the Northwest European flora. J Ecol 96: 1266-1274.
62. Kolmogorov AN (1941a) Dissipation of energy in the locally isotropic turbulence. Dokl Akad Nauk SSSR 32: 16-18, English translation in Proc Roy Soc A (1991) 434: 15-17.
63. Kolmogorov AN (1941b) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl Akad Nauk SSSR 30: 301-305, English translation in Proc Roy Soc A (1991) 434: 9-13.
64. Kuparinen A, Markkanen T, Riikonen H, Vesala T (2007a) Modeling air-mediated dispersal of spores, pollen and seeds in forested areas. Ecol Model 208: 177-188.
65. Kuparinen A, Schurr F, Tackenberg O, O'Hara RB (2007b) Air-mediated pollen flow from genetically modified to conventional crops. Ecol Appl 17: 431-440.
66. Kuparinen A, Katul G, Nathan R, Schurr FM (2009) Increases in air temperature can promote wind-driven dispersal and spread of plants. Proc Roy Soc Lond B 276: 3081-3087.
67. Kuparinen A, Savolainen O, Schurr FM (2010) Increased mortality can promote evolutionary adaptation of forest trees to climate change. For Ecol Manage 259: 1003-1008.
68. 2 levels and the fecundity of forest trees. Science 292: 95-98.
69. Lefsky MA, Cohen WB, Parker GG, Harding DJ (2002) Lidar remote sensing for ecosystem studies. Bioscience 52: 19-30.
70. Levin SA, Muller-Landau HC, Nathan R, Chave J (2003) The ecology and evolution of seed dispersal: a theoretical perspective. Annu Rev Ecol Evol Syst 34: 575-604.
71. Li B, Avissar R (1994) The impact of spatial variability of land-surface characteristics on land-surface heat fluxes. J Clim 7: 527-537.
72. Marchetto KM, Williams MB, Jongejans E, Auhl R, Shea K (2010) Applications of particle image velocimetry for seed release studies. Ecology 91: 2485-2492.
73. Massman WJ, Weil JC (1999) An analytical one-dimensional second-order closure model of turbulence statistics and the Lagrangian time scale within and above plant canopies of arbitrary structure. Bound Lay Meteor 91: 81-107.
74. Matlack GR (1987) Diaspore size, shape, and fall behavior in wind-dispersed plant species. Am J Bot 74: 1150-1160.
75. Meehl GA, Stocker TF, Collins WD, Friedlingstein P, Gayen AT, Gregory JM, Kitoh A et al (2007) Global climate projections. In: Solomon S, Qin D, Manning M et al (eds) Climate change 2007: the physical science basis. Contribution of working group I to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge, pp 747-846.
76. Miller JR, White HP, Chen JM, Peddle DR, McDermid G, Fournier RA, Shepherd P et al (1997) Seasonal change in understory reflectance of boreal forests and influence on canopy vegetation indices. J Geophys Res Atmos 102: 29475-29482.
77. Myneni RB, Hoffman S, Knyazikhin Y, Privette JL, Glassy J, Tian Y, Wang Y et al (2002) Global products of vegetation leaf area and fraction absorbed PAR from year one of MODIS data. Remote Sens Environ 83: 214-231.
78. Nathan R, Katul GG (2005) Foliage shedding in deciduous forests lifts up long-distance seed dispersal by wind. Proc Natl Acad Sci USA 102: 8251-8256.
79. Nathan R, Muller-Landau HC (2000) Spatial patterns of seed dispersal, their determinants and consequences for recruitment. Trends Ecol Evol 15: 278-285.
80. Nathan R, Safriel UN, Noy-Meir I (2001) Field validation and sensitivity analysis of a mechanistic model for tree seed dispersal by wind. Ecology 82: 374-388.
81. Nathan R, Horn HS, Chave J, Levin SA (2002a) Mechanistic models for tree seed dispersal by wind in dense forests and open landscapes. In: Levey DJ, Silva WR, Galetti M (eds) Seed dispersal and frugivory: ecology, evolution and conservation. CAB International, Wallingford, pp 69-82.
82. Nathan R, Katul GG, Horn HS, Thomas SM, Oren R, Avissar R, Pacala SW, Levin SA (2002b) Mechanisms of long-distance dispersal of seeds by wind. Nature 418: 409-413.
83. Nathan R, Horvitz N, He Y, Kuparinen A, Schurr FM, Katul GG (2011) Spread of North-American wind-dispersed trees in future environments. Ecol Lett 14: 211-219.
84. Nathan R, Sapir N, Trakhtenbrot A, Katul GG, Bohrer G, Otte M, Avissar R, Soons MB, Horn HS, Wikelski M, Levin SA (2005) Long-distance biological transport processes through the air: Can nature's complexity be unfolded in-silico? Divers Distrib 11: 131-137.
85. Nuttle T, Haefner JW (2005) Seed dispersal in heterogeneous environments: Bridging the gap between mechanistic dispersal and forest dynamics models. Am Nat 165: 336-349.
86. Okubo A, Levin SA (1989) A theoretical framework for data analysis of wind dispersal of seeds and pollen. Ecology 70: 329-338.
87. Panton R (1984) Incompressible flows. Wiley, New York.
88. Patton EG, Katul GG (2009) Turbulent pressure and velocity perturbations induced by gentle hills covered with sparse and dense canopies. Bound Lay Meteor 133: 189-217.
89. Patton EG, Shaw RH, Judd MJ, Raupach MR (1998) Large-eddy simulation of windbreak flow. Bound Lay Meteor 87: 275-306.
90. Poggi D, Katul G (2007) The ejection-sweep cycle over bare and forested gentle hills: a laboratory experiment. Bound Lay Meteor 122: 493-515.
91. Poggi D, Katul GG (2008) Micro- and macro-dispersive fluxes in canopy flows. Acta Geophys 56: 778-799.
92. Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004) The effect of vegetation density on canopy sub-layer turbulence. Bound Lay Meteor 111: 565-587.
93. Poggi D, Katul GG, Cassiani M (2008a) On the anomalous behavior of the Lagrangian structure function similarity constant inside dense canopies. Atmos Environ 42: 4212-4231.
94. Poggi D, Katul GG, Finnigan JJ, Belcher SE (2008b) Analytical models for the mean flow inside dense canopies on gentle hilly terrain. Q J R Meteorol Soc 134: 1095-1112.
95. Portnoy S, Willson MF (1993) Seed dispersal curves: behavior of the tail of the distribution. Evol Ecol 7: 25-44.
96. Raupach MR (1988) Canopy transport process. In: Steffan WL, Denmead OT (eds) Flow and transport in the natural environment: advances and applications. Springer, Berlin, pp 95-127.
97. Raupach MR (1989) A practical Lagrangian method for relating scalar concentrations to source distributions in vegetative canopies. Quart J R Meteorol Soc 115: 609-632.
98. Reed DH, Frankham R (2003) Correlation between fitness and genetic diversity. Conserv Biol 17: 230-237.
99. Reynolds AM (1999) A Lagrangian stochastic model for heavy particle deposition. J Colloid Interface Sci 215: 85-91.
100. Riba M, Mayol M, Giles BE, Ronce O, Imbert E, van der Velde M, Chauvet S et al (2009) Darwin's wind hypothesis: does it work for plant dispersal in fragmented habitats? New Phytol 183: 667-677.
101. Ridley HN (1930) The dispersal of plants throughout the world. Reeve, Ashford.
102. Savolainen O, Pyhäjärvi T, Knürr T (2007) Gene flow and local adaptation in trees. Annu Rev Ecol Evol Syst 38: 595-619.
103. 2, water, and energy fluxes over a heterogeneous sparse canopy. J Hydrometeorol 4: 798-809.
104. Schmidt W (1918) Die Verbreitung von Samen und Blutenstaub durch die Luftbewegung. Osterr Bot Z 10-12: 313-328.
105. Schupp EW, Fuentes M (1995) Spatial patterns of seed dispersal and the unification of plant population ecology. Ecoscience 2: 267-275.
106. Schurr FM, Bond WJ, Midgley GF, Higgins SI (2005) A mechanistic model for secondary seed dispersal by wind and its experimental validation. J Ecol 93: 1017-1028.
107. Schurr FM, Steinitz O, Nathan R (2008) Plant fecundity and seed dispersal in spatially heterogeneous environments: models, mechanisms and estimation. J Ecol 96: 628-641.
108. Shannon HD, Young GS, Yates MA, Fuller MR, Seegar WS (2002) American White Pelican soaring flight times and altitudes relative to changes in thermal depth and intensity. Condor 104: 679-683.
109. Sharpe DM, Fields DE (1982) Integrating the effects of climate and seed fall velocities on seed dispersal by wind: a model and application. Ecol Model 17: 297-310.
110. Shaw RH (1977) Secondary wind speed maxima inside plant canopies. J Appl Meteorol 16: 514-521.
111. Shaw RH, Patton EG (2003) Canopy element influences on resolved- and subgrid-scale energy within a large-eddy simulation. Agric For Meteorol 115: 5-17.
112. Skarpaas O, Shea K (2007) Dispersal patterns, dispersal mechanisms, and invasion wave speeds for invasive thistles. Am Nat 170: 421-430.
113. Skarpaas O, Stabbetorp OE, Ronning I, Svennungsen TO (2004) How far can a hawk's beard fly? Measuring and modelling the dispersal of Crepis praemorsa. J Ecol 92: 747-757.
114. Skarpaas O, Auhl R, Shea K (2006) Environmental variability and the initiation of dispersal: turbulence strongly increases seed release. Proc Roy Soc Lond B 273: 751-756.
115. Snow AA, Andow DA, Gepts P, Hallerman EM, Power A, Tiedje JM, Wolfenbarger LL (2005) Genetically engineered organisms and the environment: current status and recommendations. Ecol Appl 15: 377-404.
116. Soons MB, Bullock JM (2008) Non-random seed abscission, long-distance wind dispersal and plant migration rates. J Ecol 96: 581-590.
117. Soons MB, Heil GW (2002) Reduced colonization capacity in fragmented populations of wind-dispersed grassland forbs. J Ecol 90: 1033-1043.
118. Soons MB, Heil GW, Nathan R, Katul GG (2004a) Determinants of long-distance seed dispersal by wind in grasslands. Ecology 85: 3056-3068.
119. Soons MB, Nathan R, Katul GG (2004b) Human effects on long-distance wind dispersal and colonization by grassland plants. Ecology 85: 3069-3079.
120. Soons MB, Messelink JH, Jongejans E, Heil GW (2005) Habitat fragmentation reduces grassland connectivity for both short-distance and long-distance wind-dispersed forbs. J Ecol 93: 1214-1225.
121. Stephenson CM, Kohn DD, Park KJ, Atkinson R, Edwards C, Travis JM (2007) Testing mechanistic models of seed dispersal for the invasive Rhododendron ponticum (L.). Perspect Plant Ecol Evol Syst 9: 15-28.
122. Stoll R, Porté-Agel F (2006) Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resour Res 42: W01409. doi: 01410. 01029/02005WR003989.
123. 2 in relation to climate: a cross-biome analysis across multiple time scales. Biogeosciences 6: 2297-2312.
124. Stull RB (1988) An introduction to boundary-layer meteorology. Kluwer, Dordrecht.
125. Tackenberg O (2003) Modeling long distance dispersal of plant diaspores by wind. Ecol Monogr 73: 173-189.
126. Thomas CD, Cameron A, Green RE, Bakkenes M, Beaumont LJ, Collingham YC, Erasmus BFN et al (2004) Extinction risk from climate change. Nature 427: 145-148.
127. Thompson S, Katul G (2008) Plant propagation fronts and wind dispersal: an analytical model to upscale from seconds to decades using superstatistics. Am Nat 171: 468-479.
128. Thompson S, Katul G (2009) Secondary seed dispersal and its role in landscape organization. Geophys Res Lett 36.
129. Thompson S, Katul G, Terborgh J, Alvarez-Loayza P (2009) Spatial organization of vegetation arising from non-local excitation with local inhibition in tropical rainforests. Phys D 238: 1061-1067.
130. Thomson DJ (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180: 529-556.
131. Thuiller W, Lavorel S, Araujo MB, Sykes MT, Prentice IC (2005) Climate change threats to plant diversity in Europe. Proc Natl Acad Sci USA 102: 8245-8250.
132. Trakhtenbrot A (2010) Dispersal of plant seeds by wind in heterogeneous environments. The Hebrew University of Jerusalem, Jerusalem. Ph. D. thesis.
133. Troen I, Petersen EL (1989) European wind atlas. Riso National Laboratory, Roskilde.
134. van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 0. 0007 to 900 cycles per hour. J Meteorol 14: 160-164.
135. van der Pijl L (1982) Principles of dispersal in higher plants, 3rd edn. Springer, Berlin.
136. Weil JC, Sullivan PP, Moeng CH (2004) The use of large-eddy simulations in Lagrangian particle dispersion models. J Atmos Sci 61: 2877-2887.
137. Willson MF (1993) Dispersal mode, seed shadows, and colonization patterns. Vegetatio 107(108): 261-280.
138. Willson MF, Rice BL, Westoby M (1990) Seed dispersal spectra: a comparison of temperate plant communities. J Veg Sci 1: 547-562.
139. Wolfenbarger DO (1946) Dispersion of small organisms, distance dispersion rates of bacteria, spores, seeds, pollen and insects: incidence rates of diseases and injuries. Am Midl Nat 35: 1-152.
140. Wright SJ, Trakhtenbrot A, Bohrer G, Detto M, Katul GG, Horvitz N, Muller-Landau HC, Jones FA, Nathan R (2008) Understanding strategies for seed dispersal by wind under contrasting atmospheric conditions. Proc Natl Acad Sci USA 105: 19084-19089.
141. Yang B, Morse AP, Shaw RH, KT PU (2006) Large-eddy simulation of turbulent flow across a forest edge. Part II: momentum and turbulent kinetic energy budgets. Bound Lay Meteor 121: 433-457.
142. Yue WS, Parlange MB, Meneveau C, Zhu WH, van Hout R, Katz J (2007) Large-eddy simulation of plant canopy flows using plant-scale representation. Bound Lay Meteor 124: 183-203.