Statistical mechanics of ecological systems: Neutral theory and beyond

Reviews of Modern Physics

Volumn 88, Issue 3, 2016, Pages

  Azaele, Sandro ^a   Suweis, Samir ^b   Grilli, Jacopo ^c   Volkov, Igor ^d   Banavar, Jayanth R ^d   Maritan, Amos ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF PADOVA   (Italy)

^c UNIVERSITY OF CHICAGO   (United States)

^d Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIODIVERSITY; STATISTICAL MECHANICS;

ECOLOGICAL SYSTEMS; EMPIRICAL DATA; HUBBELL; NEUTRAL THEORIES; NON-NEUTRAL; THEORETICAL STUDY;

ECOLOGY;

EID: 84982724519     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.88.035003     Document Type: Article

References (195)

1. Adler, P. B., J. HilleRisLambers, and J. M. Levine, 2007, Ecol. Lett. 10, 95. ECLEFU 1461-023X 10.1111/j.1461-0248.2006.00996.x
2. Adorisio, M., J. Grilli, S. Suweis, S. Azaele, J. R. Banavar, and A. Maritan, 2014, arXiv:1407.2425.
3. Allen, A. P., and V. M. Savage, 2007, Ecol. Lett. 10, 637. ECLEFU 1461-023X 10.1111/j.1461-0248.2007.01057.x
4. Allesina, S., J. Grilli, G. Barabás, S. Tang, J. Aljadeff, and A. Maritan, 2015, Nat. Commun. 6, 7842. NCAOBW 2041-1723 10.1038/ncomms8842
5. Allesina, S., and S. Tang, 2012, Nature (London) 483, 205. NATUAS 0028-0836 10.1038/nature10832
6. Alonso, D., R. S. Etienne, and A. J. McKane, 2006, Trends Ecol. Evol. 21, 451. TREEEQ 0169-5347 10.1016/j.tree.2006.03.019
7. Alonso, D., and A. J. McKane, 2004, Ecol. Lett. 7, 901. ECLEFU 1461-023X 10.1111/j.1461-0248.2004.00640.x
8. Alonso, D., A. Ostling, and R. S. Etienne, 2008, Ecol. Lett. 11, 93. ECLEFU 1461-023X 10.1111/j.1461-0248.2007.01127.x
9. Arrhenius, O., 1921, J. Ecol. 9, 95. JECOAB 0022-0477 10.2307/2255763
10. Azaele, S., A. Maritan, S. J. Cornell, S. Suweis, J. R. Banavar, D. Gabriel, and W. E. Kunin, 2015, Meth. Ecol. Evol. 6, 324. 2041-210X 10.1111/2041-210X.12319
11. Azaele, S., R. Muneepeerakul, A. Maritan, A. Rinaldo, and I. Rodriguez-Iturbe, 2009, Proc. Natl. Acad. Sci. U.S.A. 106, 7058. PNASA6 0027-8424 10.1073/pnas.0805845106
12. Azaele, S., R. Muneepeerakul, A. Rinaldo, and I. Rodriguez-Iturbe, 2010, J. Theor. Biol. 262, 323. JTBIAP 0022-5193 10.1016/j.jtbi.2009.09.026
13. Azaele, S., S. Pigolotti, J. R. Banavar, and A. Maritan, 2006, Nature (London) 444, 926. NATUAS 0028-0836 10.1038/nature05320
14. Babak, P., 2006, Phys. Rev. E 74, 021902. PRESCM 1539-3755 10.1103/PhysRevE.74.021902
15. Babak, P., and F. He, 2009, Theor. Popul. Biol. 75, 76. TLPBAQ 0040-5809 10.1016/j.tpb.2008.11.002
16. Banavar, J. R., A. Maritan, and I. Volkov, 2010, J. Phys. Condens. Matter 22, 063101. JCOMEL 0953-8984 10.1088/0953-8984/22/6/063101
17. Barabás, G., R. D'Andrea, R. Rael, G. Meszéna, and A. Ostling, 2013, Oikos 122, 1565. OIKSAA 0030-1299 10.1111/j.1600-0706.2013.00298.x
18. Bastolla, U., M. a. Fortuna, A. Pascual-García, A. Ferrera, B. Luque, and J. Bascompte, 2009, Nature (London) 458, 1018. NATUAS 0028-0836 10.1038/nature07950
19. Bell, G., 2000, Am. Nat. 155, 606. AMNTA4 0003-0147 10.1086/303345
20. Bertuzzo, E., S. Suweis, L. Mari, A. Maritan, I. Rodríguez-Iturbe, and A. Rinaldo, 2011, Proc. Natl. Acad. Sci. U.S.A. 108, 4346. PNASA6 0027-8424 10.1073/pnas.1017274108
21. Black, A. J., and A. J. McKane, 2012, Trends Ecol. Evol. 27, 337. TREEEQ 0169-5347 10.1016/j.tree.2012.01.014
22. Blythe, R. A., and A. J. McKane, 2007, J. Stat. Mech. 07, P07018. JSMTC6 1742-5468 10.1088/1742-5468/2007/07/P07018
23. Bonsall, M. B., V. A. A. Jansen, and M. P. Hassell, 2004, Science 306, 111. SCIEAS 0036-8075 10.1126/science.1100680
24. Borile, C., A. Maritan, and M. A. Muñoz, 2013, J. Stat. Mech. 04, P04032. JSMTC6 1742-5468 10.1088/1742-5468/2013/04/P04032
25. Borile, C., M. A. Muñoz, S. Azaele, J. R. Banavar, and A. Maritan, 2012, Phys. Rev. Lett. 109, 038102. PRLTAO 0031-9007 10.1103/PhysRevLett.109.038102
26. Bork, P., C. Bowler, C. de Vargas, G. Gorsky, E. Karsenti, and P. Wincker, 2015, Science 348, 873. SCIEAS 0036-8075 10.1126/science.aac5605
27. Brown, J. H., 1995, Macroecology (The University of Chicago Press, Chicago).
28. Butler, T., and N. Goldenfeld, 2009, Phys. Rev. E 80, 030902. PRESCM 1539-3755 10.1103/PhysRevE.80.030902
29. Carrara, F., F. Altermatt, I. Rodriguez-Iturbe, and A. Rinaldo, 2012, Proc. Natl. Acad. Sci. U.S.A. 109, 5761. PNASA6 0027-8424 10.1073/pnas.1119651109
30. Carrara, F., A. Rinaldo, A. Giometto, and F. Altermatt, 2014, Am. Nat. 183, 13. AMNTA4 0003-0147 10.1086/674009
31. Cencini, M., S. Pigolotti, and M. A. Muñoz, 2012, PLoS One 7, e38232. POLNCL 1932-6203 10.1371/journal.pone.0038232
32. Chandrasekhar, S., 1943, Rev. Mod. Phys. 15, 1. RMPHAT 0034-6861 10.1103/RevModPhys.15.1
33. Chase, J. M., and M. A. Leibold, 2003, Ecological niches: Linking classical and contemporary approaches (University of Chicago Press, Chicago).
34. Chave, J., 2004, Ecol. Lett. 7, 241. ECLEFU 1461-023X 10.1111/j.1461-0248.2003.00566.x
35. Chave, J., D. Alonso, and R. S. Etienne, 2006, Nature (London) 441, E1. NATUAS 0028-0836 10.1038/nature04826
36. Chave, J., and E. G. Leigh, 2002, Theor. Popul. Biol. 62, 153. TLPBAQ 0040-5809 10.1006/tpbi.2002.1597
37. Chave, J., H. C. Muller-Landau, and S. A. Levin, 2002, Am. Nat. 159, 1. AMNTA4 0003-0147 10.1086/324112
38. Chayes, J. T., L. Chayes, and E. H. Lieb, 1984, Commun. Math. Phys. 93, 57. CMPHAY 0010-3616 10.1007/BF01218639
39. Chesson, P., 2000, Annu. Rev. Ecol. Syst. 31, 343. ARECBC 0066-4162 10.1146/annurev.ecolsys.31.1.343
40. Chesson, P. L., and R. R. Warner, 1981, Am. Nat. 117, 923. AMNTA4 0003-0147 10.1086/283778
41. Chisholm, R. A., 2011, Theor. Popul. Biol. 80, 71. TLPBAQ 0040-5809 10.1016/j.tpb.2011.06.002
42. Chisholm, R. A., and J. P. O'Dwyer, 2014, Theor. Popul. Biol. 93, 85. TLPBAQ 0040-5809 10.1016/j.tpb.2014.02.002
43. Chisholm, R. A., 2014, Ecol. Lett. 17, 855. ECLEFU 1461-023X 10.1111/ele.12296
44. Clark, J. S., 2009, Trends Ecol. Evol. 24, 8. TREEEQ 0169-5347 10.1016/j.tree.2008.09.004
45. Coleman, B. D., 1981, Math. Biosci. 54, 191. MABIAR 0025-5564 10.1016/0025-5564(81)90086-9
46. Coleman, B. D., M. A. Mares, and Y.-H. Hsieh, 1982, Ecology 63, 1121. ECOLAR 0012-9658 10.2307/1937249
47. Connell, J. H., 1970, Proceedings of the Advanced Study Institute on Dynamics of Numbers in Populations, edited by P. J. Den Boer and G. R. Gradwell (Centre for Agricultural Publishing and Documentation, Wageningen) pp. 298-312.
48. Darwin, C. R., 1909, The Origin of Species (The Harvard Classics, New York), Vol. 11.
49. Davies, T. J., A. P. Allen, L. Borda-de Água, J. Regetz, and C. J. Melián, 2011, Evolution 65, 1841. EVOLAO 0014-3820 10.1111/j.1558-5646.2011.01265.x
50. Diamond, J. M., 1989, Phil. Trans. R. Soc. B 325, 469. PTRBAE 0962-8436 10.1098/rstb.1989.0100
51. Du, X., S. Zhou, and R. S. Etienne, 2011, J. Theor. Biol. 278, 127. JTBIAP 0022-5193 10.1016/j.jtbi.2011.03.003
52. Durrett, R., and S. Levin, 1996, J. Theor. Biol. 179, 119. JTBIAP 0022-5193 10.1006/jtbi.1996.0053
53. Etienne, R. S., 2005, Ecol. Lett. 8, 253. ECLEFU 1461-023X 10.1111/j.1461-0248.2004.00717.x
54. Etienne, R. S., and D. Alonso, 2005, Ecol. Lett. 8, 1147. ECLEFU 1461-023X 10.1111/j.1461-0248.2005.00817.x
55. Etienne, R. S., D. Alonso, and A. J. McKane, 2007, J. Theor. Biol. 248, 522. JTBIAP 0022-5193 10.1016/j.jtbi.2007.06.010
56. Etienne, R. S., and H. Olff, 2004 a, Am. Nat. 163, 69. AMNTA4 0003-0147 10.1086/380582
57. Etienne, R. S., and H. Olff, 2004 b, Ecol. Lett. 7, 170. ECLEFU 1461-023X 10.1111/j.1461-0248.2004.00572.x
58. Etienne, R. S., and J. Rosindell, 2011, PLoS One 6, e14717. POLNCL 1932-6203 10.1371/journal.pone.0014717
59. Ewens, W., 1972, Theor. Popul. Biol. 3, 87. 10.1016/0040-5809(72)90035-4 TLPBAQ 0040-5809
60. Feller, W., 1951, Ann. Math. 54, 173. ANMAAH 0003-486X 10.2307/1969318
61. Fisher, A., R. Corbet, and C. Williams, 1943, J. Anim. Ecol. 12, 42. JAECAP 0021-8790 10.2307/1411
62. Fisher, C. K., and P. Mehta, 2014, Proc. Natl. Acad. Sci. U.S.A. 111, 13111. PNASA6 0027-8424 10.1073/pnas.1405637111
63. Gardiner, C., 2009, Stochastic Methods: A Handbook for the Natural and Social Sciences (Springer, New York).
64. Gause, G. F., 1934, The Struggle for Existence (Williams & Wilkins Company, Baltimore).
65. Goldenfeld, N., and C. Woese, 2007, Nature (London) 445, 369. NATUAS 0028-0836 10.1038/445369a
66. Goldenfeld, N., and C. Woese, 2010, arXiv:1011.4125.
67. Gould, S. J., 1979, Am. Nat. 114, 335. AMNTA4 0003-0147 10.1086/283482
68. Gravel, D., C. D. Canham, M. Beaudet, and C. Messier, 2006, Ecol. Lett. 9, 399. ECLEFU 1461-023X 10.1111/j.1461-0248.2006.00884.x
69. Grilli, J., S. Azaele, J. R. Banavar, and A. Maritan, 2012 a, Europhys. Lett. 100, 38002. EULEEJ 0295-5075 10.1209/0295-5075/100/38002
70. Grilli, J., S. Azaele, J. R. Banavar, and A. Maritan, 2012 b, J. Theor. Biol. 313, 87. 10.1016/j.jtbi.2012.07.030 JTBIAP 0022-5193
71. Haegeman, B., and R. S. Etienne, 2008, J. Theor. Biol. 252, 288. JTBIAP 0022-5193 10.1016/j.jtbi.2008.01.023
72. Haegeman, B., and R. S. Etienne, 2009, Bull. Math. Biol. 71, 1507. BMTBAP 0092-8240 10.1007/s11538-009-9411-0
73. Haegeman, B., and R. S. Etienne, 2010, Phys. Rev. E 81, 031911. PRESCM 1539-3755 10.1103/PhysRevE.81.031911
74. Haegeman, B., and M. Loreau, 2011, J. Theor. Biol. 269, 150. JTBIAP 0022-5193 10.1016/j.jtbi.2010.10.006
75. Halley, J. M., and Y. Iwasa, 2011, Proc. Natl. Acad. Sci. U.S.A. 108, 2316. PNASA6 0027-8424 10.1073/pnas.1011217108
76. Harte, J., 2003, Nature (London) 424, 1006. NATUAS 0028-0836 10.1038/4241006a
77. Harte, J., 2011, Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford University Press, New York).
78. Harte, J., T. Zillio, E. Conlisk, and A. Smith, 2008, Ecology 89, 2700. ECOLAR 0012-9658 10.1890/07-1369.1
79. Hashitsume, N., M. Toda, R. Kubo, and N. Saitō, 1991, Statistical physics II: Nonequilibrium Statistical Mechanics (Springer Science & Business Media), Vol. 30.
80. He, F., and S. P. Hubbell, 2011, Nature (London) 473, 368. NATUAS 0028-0836 10.1038/nature09985
81. Holley, R. A., and T. M. Liggett, 1975, Ann. Probab. 3, 643. APBYAE 0091-1798 10.1214/aop/1176996306
82. Holt, R. D., 2006, Trends Ecol. Evol. 21, 531. TREEEQ 0169-5347 10.1016/j.tree.2006.08.003
83. Hu, X. S., F. L. He, and S. P. Hubbell, 2006, Oikos 113, 548. OIKSAA 0030-1299 10.1111/j.2006.0030-1299.14837.x
84. Huang, K., 2001, Introduction to Statistical Physics (CRC Press, Boca Raton, FL).
85. Hubbell, S., 2001, The Unified Theory of Biodiversity and Biogeography (Princeton University Press, Princeton, NJ).
86. Hubbell, S. P., 1979, Science 203, 1299. SCIEAS 0036-8075 10.1126/science.203.4387.1299
87. Hubbell, S. P., 2005, Funct. Ecol. 19, 166. FECOE5 1365-2435 10.1111/j.0269-8463.2005.00965.x
88. Hubbell, S. P., 2006, Ecology 87, 1387. ECOLAR 0012-9658 10.1890/0012-9658(2006)87[1387:NTATEO]2.0.CO;2
89. Hutchinson, G. E., 1957, in Cold Spring Harbor Symposia on Quantitative Biology, Vol. 22 (Cold Spring Harbor Laboratory Press), pp. 415-427.
90. Hutchinson, G. E., 1959, Am. Nat. 93, 145. AMNTA4 0003-0147 10.1086/282070
91. Janzen, D. H., 1970, Am. Nat. 104, 501. AMNTA4 0003-0147 10.1086/282687
92. Jaynes, E. T., 2003, Probability Theory: The Logic of Science (Cambridge University Press, Cambridge, England).
93. Jeraldo, P., 2012, Proc. Natl. Acad. Sci. U.S.A. 109, 9692. PNASA6 0027-8424 10.1073/pnas.1206721109
94. Kalyuzhny, M., R. Kadmon, and N. M. Shnerb, 2015, Ecol. Lett. 18, 572. ECLEFU 1461-023X 10.1111/ele.12439
95. Kalyuzhny, M., E. Seri, R. Chocron, C. H. Flather, R. Kadmon, and N. M. Shnerb, 2014, Am. Nat. 184, 439. AMNTA4 0003-0147 10.1086/677930
96. Kampen, N. V., 2007, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam), 3rd ed.
97. Keil, P., T. Herben, J. Rosindell, and D. Storch, 2010, J. Theor. Biol. 265, 78. JTBIAP 0022-5193 10.1016/j.jtbi.2010.04.014
98. Keitt, T. H., and H. E. Stanley, 1998, Nature (London) 393, 257. NATUAS 0028-0836 10.1038/30478
99. Kessler, D. A., and N. M. Shnerb, 2015, Phys. Rev. E 91, 042705. PRESCM 1539-3755 10.1103/PhysRevE.91.042705
100. Kessler, D. A., S. Suweis, M. Formentin, and N. M. Shnerb, 2015, Phys. Rev. E 92, 022722. PRESCM 1539-3755 10.1103/PhysRevE.92.022722
101. Kimura, M., 1985, The Neutral Theory of Molecular Evolution (Cambridge University Press, Cambridge).
102. Kingman, J. F. C., 1982, Stoch. Proc. Appl. 13, 235. STOPB7 0304-4149 10.1016/0304-4149(82)90011-4
103. Krishna, A., P. R. Guimara, P. Jordano, and J. Bascompte, 2008, Oikos 117, 1609. OIKSAA 0030-1299 10.1111/j.1600-0706.2008.16540.x
104. Lande, R., S. Engen, and B.-E. Saether, 2003, Stochastic Population Dynamics in Ecology and Conservation (Oxford University Press, Oxford).
105. Lebedev, N. N., 1972, Special functions and their applications (Courier Dover Publications, New York).
106. Lehnigk, S. H., 1993, The generalized Feller equations and related topics (Longman, New York).
107. Leigh, E. G., 2007, J. Evol. Biol. 20, 2075. JEBIEQ 1420-9101 10.1111/j.1420-9101.2007.01410.x
108. Lynch, H. J., E. H. Campbell Grant, R. Muneepeerakul, M. Arunachalam, I. Rodriguez-Iturbe, and W. F. Fagan, 2011, Water Resour. Res. 47, W05531. WRERAQ 0043-1397 10.1029/2010WR010330
109. MacArthur, R., 1970, Theor. Popul. Biol. 1, 1. TLPBAQ 0040-5809 10.1016/0040-5809(70)90039-0
110. MacArthur, R. H., and E. O. Wilson, 1967, The Theory of Island Biogeography (Princeton University Press, Princeton, NJ).
111. Manceau, M., A. Lambert, and H. Morlon, 2015, Ecol. Lett. 18, 347. ECLEFU 1461-023X 10.1111/ele.12415
112. Mari, L., R. Casagrandi, E. Bertuzzo, A. Rinaldo, and M. Gatto, 2014, Ecol. Lett. 17, 426. ECLEFU 1461-023X 10.1111/ele.12242
113. Martín, H. G., and N. Goldenfeld, 2006, Proc. Natl. Acad. Sci. U.S.A. 103, 10310. PNASA6 0027-8424 10.1073/pnas.0510605103
114. Martin, T. E., 1981, Am. Nat. 118, 823. AMNTA4 0003-0147 10.1086/283873
115. Masoliver, J., and J. Perelló, 2012, Phys. Rev. E 86, 041116; PRESCM 1539-3755 10.1103/PhysRevE.86.041116
116. Masoliver, J. J. Perelló Phys. Rev. E 86, 049906(E) (2012); PRESCM 1539-3755 10.1103/PhysRevE.86.049906
117. Masoliver, J. J. Perelló Phys. Rev. E 89, 029902 (2014). PRESCM 1539-3755 10.1103/PhysRevE.89.029902
118. May, R. M., 2001, Stability and Complexity in Model Ecosystems (Princeton University Press, Princeton, NJ), Vol. 6.
119. May, R. M., 2010, Phil. Trans. R. Soc. B 365, 41. PTRBAE 0962-8436 10.1098/rstb.2009.0164
120. May, R. M., and R. H. Mac Arthur, 1972, Proc. Natl. Acad. Sci. U.S.A. 69, 1109. PNASA6 0027-8424 10.1073/pnas.69.5.1109
121. McGill, B., 2003, Oikos 102, 679. OIKSAA 0030-1299 10.1034/j.1600-0706.2003.12617.x
122. McGill, B., and C. Collins, 2003, Evol. Ecol. Res. 5, 469. 1522-0613
123. McGill, B. J., B. A. Maurer, and M. D. Weiser, 2006, Ecology 87, 1411. ECOLAR 0012-9658 10.1890/0012-9658(2006)87[1411:EEONT]2.0.CO;2
124. McKane, A., D. Alonso, and R. V. Solé, 2000, Phys. Rev. E 62, 8466. PLEEE8 1063-651X 10.1103/PhysRevE.62.8466
125. McKane, A. J., D. Alonso, and R. V. Solé, 2004, Theor. Popul. Biol. 65, 67. TLPBAQ 0040-5809 10.1016/j.tpb.2003.08.001
126. Melbinger, A., and M. Vergassola, 2015, Sci. Rep. 5, 15211. SRCEC3 2045-2322 10.1038/srep15211
127. Morlon, H., G. Chuyong, R. Condit, S. Hubbell, D. Kenfack, D. Thomas, R. Valencia, and J. L. Green, 2008, Ecol. Lett. 11, 904. ECLEFU 1461-023X 10.1111/j.1461-0248.2008.01202.x
128. Mouquet, N., and M. Loreau, 2003, Am. Nat. 162, 544. AMNTA4 0003-0147 10.1086/378857
129. Muneepeerakul, R., S. Azaele, S. Levin, A. Rinaldo, and I. Rodriguez-Iturbe, 2011, J. Theor. Biol. 269, 256. 10.1016/j.jtbi.2010.11.003 JTBIAP 0022-5193
130. Muneepeerakul, R., E. Bertuzzo, H. J. Lynch, W. F. Fagan, A. Rinaldo, and I. Rodriguez-Iturbe, 2008, Nature (London) 453, 220. NATUAS 0028-0836 10.1038/nature06813
131. Mutshinda, C. M., R. B. O'Hara, and I. P. Woiwod, 2008, Funct. Ecol. 22, 340. FECOE5 1365-2435 10.1111/j.1365-2435.2007.01358.x
132. Nee, S., 2005, Funct. Ecol. 19, 173. FECOE5 1365-2435 10.1111/j.0269-8463.2005.00922.x
133. Noble, A. E., and W. F. Fagan, 2015, Theoret. Ecol. 8, 149. 10.1007/s12080-014-0240-x 1874-1738
134. Noble, A. E., A. Hastings, and W. F. Fagan, 2011, Phys. Rev. Lett. 107, 228101. PRLTAO 0031-9007 10.1103/PhysRevLett.107.228101
135. Noble, A. E., N. M. Temme, W. F. Fagan, and T. H. Keitt, 2011, J. Theor. Biol. 273, 1. JTBIAP 0022-5193 10.1016/j.jtbi.2010.12.021
136. O'Dwyer, J. P., and R. Chisholm, 2014, Ecol. Lett. 17, 961. ECLEFU 1461-023X 10.1111/ele.12299
137. O'Dwyer, J. P., and J. L. Green, 2010, Ecol. Lett. 13, 87. 10.1111/j.1461-0248.2009.01404.x ECLEFU 1461-023X
138. O'Dwyer, J. P., S. W. Kembel, and T. J. Sharpton, 2015, Proc. Natl. Acad. Sci. U.S.A. 112, 8356. PNASA6 0027-8424 10.1073/pnas.1419341112
139. Paine, Robert T., 1966, Am. Nat. 100, 65. AMNTA4 0003-0147 10.1086/282400
140. Pigolotti, S., and M. Cencini, 2009, J. Theor. Biol. 260, 83. JTBIAP 0022-5193 10.1016/j.jtbi.2009.05.023
141. Pigolotti, S., A. Flammini, and A. Maritan, 2004, Phys. Rev. E 70, 011916. PRESCM 1539-3755 10.1103/PhysRevE.70.011916
142. Pigolotti, S., A. Flammini, M. Marsili, and A. Maritan, 2005, Proc. Natl. Acad. Sci. U.S.A. 102, 15747. PNASA6 0027-8424 10.1073/pnas.0502648102
143. Pimm, S. L., G. J. Russell, J. L. Gittleman, and T. M. Brooks, 1995, Science 269, 347. SCIEAS 0036-8075 10.1126/science.269.5222.347
144. Pinto, O. A., and M. A. Muñoz, 2011, PLoS One 6, e21946. POLNCL 1932-6203 10.1371/journal.pone.0021946
145. Plotkin, J. B., M. D. Potts, N. Leslie, N. Manokaran, J. LaFrankie, and P. S. Ashton, 2000, J. Theor. Biol. 207, 81. JTBIAP 0022-5193 10.1006/jtbi.2000.2158
146. Power, D. M., 1972, Evolution 26, 451. EVOLAO 0014-3820 10.2307/2407019
147. Preston, F. W., 1948, Ecology 29, 254. ECOLAR 0012-9658 10.2307/1930989
148. Preston, F. W., 1960, Ecology 41, 611. ECOLAR 0012-9658 10.2307/1931793
149. Pueyo, S., 2006, Oikos 112, 392. OIKSAA 0030-1299 10.1111/j.0030-1299.2006.14188.x
150. Purves, D. W., and L. A. Turnbull, 2010, J. Anim. Ecol. 79, 1215. JAECAP 0021-8790 10.1111/j.1365-2656.2010.01738.x
151. Purves, D. W., and S. W. Pacala, 2005, in " Biotic interactions in the tropics: Their role in the maintenance of species diversity," edited by David Burslem, Michelle Pinard, and Sue Hartley (Cambridge University Press, Cambridge, England).
152. Ricklefs, R. E., 2003, Oikos 100, 185. OIKSAA 0030-1299 10.1034/j.1600-0706.2003.12018.x
153. Ricklefs, R. E., 2006, Ecology 87, 1424. ECOLAR 0012-9658 10.1890/0012-9658(2006)87[1424:TUNTOB]2.0.CO;2
154. Ricklefs, R. E., and S. S. Renner, 2012, Science 335, 464. SCIEAS 0036-8075 10.1126/science.1215182
155. Rosindell, J., and S. J. Cornell, 2007, Ecol. Lett. 10, 586. ECLEFU 1461-023X 10.1111/j.1461-0248.2007.01050.x
156. Rosindell, J., and S. J. Cornell, 2009, Ecology 90, 1743. ECOLAR 0012-9658 10.1890/08-0661.1
157. Rosindell, J., S. J. Cornell, S. P. Hubbell, and R. S. Etienne, 2010, Ecol. Lett. 13, 716. ECLEFU 1461-023X 10.1111/j.1461-0248.2010.01463.x
158. Rosindell, J., L. J. Harmon, and R. S. Etienne, 2015, Ecol. Lett. 18, 472. ECLEFU 1461-023X 10.1111/ele.12430
159. Rosindell, J., S. P. Hubbell, and R. S. Etienne, 2011, Trends Ecol. Evol. 26, 340. TREEEQ 0169-5347 10.1016/j.tree.2011.03.024
160. Rosindell, J., S. P. Hubbell, F. L. He, L. J. Harmon, and R. S. Etienne, 2012, Trends Ecol. Evol. 27, 203. TREEEQ 0169-5347 10.1016/j.tree.2012.01.004
161. Rosindell, J., Y. Wong, and R. S. Etienne, 2008, Ecological Informatics 3, 259. 10.1016/j.ecoinf.2008.05.001 1574-9541
162. Roughgarden, J., R. M. May, and S. A. Levin, 1989, Eds., Perspectives in Ecological Theory (Princeton University Press, Princeton, NJ), Vol. 203, pp. 203-226.
163. Scheffer, M., and E. H. van Nes, 2006, Proc. Natl. Acad. Sci. U.S.A. 103, 6230. PNASA6 0027-8424 10.1073/pnas.0508024103
164. Scheffer, M., 2012, Science 338, 344. SCIEAS 0036-8075 10.1126/science.1225244
165. Schoener, T. W., 1976, in Proceedings of the XVI International Ornithological Congress, Vol. 6 (Australian Academy of Science, Canberra, ACT), pp. 629-642.
166. Simpson, E. H., 1949, Nature (London) 163, 688. NATUAS 0028-0836 10.1038/163688a0
167. Slik, J. F., 2015, Proc. Natl. Acad. Sci. U.S.A. 112, 7472. PNASA6 0027-8424 10.1073/pnas.1423147112
168. Storch, D., 2007, Scaling Biodiversity (Cambridge University Press, Cambridge, UK).
169. Suweis, S., E. Bertuzzo, L. Mari, I. Rodriguez-Iturbe, A. Maritan, and A. Rinaldo, 2012, J. Theor. Biol. 303, 15. JTBIAP 0022-5193 10.1016/j.jtbi.2012.02.022
170. Suweis, S., and P. D'Odorico, 2014, PLoS One 9, e101851. POLNCL 1932-6203 10.1371/journal.pone.0101851
171. Suweis, S., A. Rinaldo, and A. Maritan, 2012, J. Stat. Mech. 07, P07017. 10.1088/1742-5468/2012/07/P07017 JSMTC6 1742-5468
172. Suweis, S., F. Simini, J. R. Banavar, and A. Maritan, 2013, Nature (London) 500, 449. NATUAS 0028-0836 10.1038/nature12438
173. Svenning, J.-C., and R. Condit, 2008, Science 322, 206. SCIEAS 0036-8075 10.1126/science.1164542
174. ter Steege, H., 2013, Science 342, 1243092. SCIEAS 0036-8075 10.1126/science.1243092
175. ter Steege, H., 2015, Sci. Adv. 1, e1500936. SACDAF 2375-2548 10.1126/sciadv.1500936
176. Thomas, C. D., 2004, Nature (London) 427, 145. NATUAS 0028-0836 10.1038/nature02121
177. Tilman, D., 1994, Ecology 75, 2. ECOLAR 0012-9658 10.2307/1939377
178. Tilman, D., and P. M. Kareiva, 1997, Spatial ecology: The role of space in population dynamics and interspecific interactions (Princeton University Press, Princeton, NJ), Vol. 30.
179. Ulrich, W., M. Ollik, and K. I. Ugland, 2010, Oikos 119, 1149. OIKSAA 0030-1299 10.1111/j.1600-0706.2009.18236.x
180. Vallade, M., and B. Houchmandzadeh, 2003, Phys. Rev. E 68, 061902. PRESCM 1539-3755 10.1103/PhysRevE.68.061902
181. Vallade, M., and B. Houchmandzadeh, 2006, Phys. Rev. E 74, 051914. PRESCM 1539-3755 10.1103/PhysRevE.74.051914
182. Vanpeteghem, D., O. Zemb, and B. Haegeman, 2008, Math. Biosci. 212, 88. MABIAR 0025-5564 10.1016/j.mbs.2008.01.002
183. Veech, J. A., 2006, J. Biogeography 33, 2145. JBIODN 1365-2699 10.1111/j.1365-2699.2006.01571.x
184. Vergnon, R., R. Leijs, E. H. van Nes, and M. Scheffer, 2013, Am. Nat. 182, 67. AMNTA4 0003-0147 10.1086/670589
185. Vergnon, R., E. H. van Nes, and M. Scheffer, 2012, Nat. Commun. 3, 663. NCAOBW 2041-1723 10.1038/ncomms1663
186. Vergnon, R., E. H. van Nes, and M. Scheffer, 2013, Oikos 122, 1573. 10.1111/j.1600-0706.2013.00790.x OIKSAA 0030-1299
187. Volkov, I., J. Banavar, F. He, S. Hubbell, and A. Maritan, 2005, Nature (London) 438, 658. NATUAS 0028-0836 10.1038/nature04030
188. Volkov, I., J. R. Banavar, S. P. Hubbell, and A. Maritan, 2003, Nature (London) 424, 1035. NATUAS 0028-0836 10.1038/nature01883
189. Volkov, I., J. R. Banavar, S. P. Hubbell, and A. Maritan, 2007, Nature (London) 450, 45. NATUAS 0028-0836 10.1038/nature06197
190. Volkov, I., J. R. Banavar, S. P. Hubbell, and A. Maritan, 2009, Proc. Natl. Acad. Sci. U.S.A. 106, 13854. PNASA6 0027-8424 10.1073/pnas.0903244106
191. Volkov, I., J. R. Banavar, and A. Maritan, 2006, J. Stat. Phys. 123, 167. JSTPBS 0022-4715 10.1007/s10955-006-9032-z
192. Walker, S. C., 2007, Theor. Popul. Biol. 71, 318. TLPBAQ 0040-5809 10.1016/j.tpb.2006.12.008
193. Watson, H. C., 1835, Remarks on the Geographical Distribution of British Plants;: Chiefly in Connection with Latitude, Elevation, and Climate (Longman, Rees, Orme, Brown, Green, and Longman, Paternoster-Row, London).
194. Zillio, T., J. R. Banavar, J. L. Green, J. Harte, and A. Maritan, 2008, Proc. Natl. Acad. Sci. U.S.A. 105, 18714. PNASA6 0027-8424 10.1073/pnas.0807380105
195. Zillio, T., I. Volkov, J. R. Banavar, S. P. Hubbell, and A. Maritan, 2005, Phys. Rev. Lett. 95, 098101. PRLTAO 0031-9007 10.1103/PhysRevLett.95.098101