The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes

Science

Volumn 349, Issue 6252, 2015, Pages

  Hatton, Ian A ^a   McCann, Kevin S ^b   Fryxell, John M ^b   Davies, T Jonathan ^a   Smerlak, Matteo ^c   Sinclair, Anthony R E ^d,e   Loreau, Michel ^f  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF GUELPH   (Canada)

^c PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^d UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^e TANZANIA WILDLIFE RESEARCH INSTITUTE   (Tanzania)

^f Moulis   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AQUATIC ECOSYSTEM; BIOMASS; BIOME; ECOLOGICAL THEORY; FORAGING BEHAVIOR; INVERTEBRATE; MAMMAL; PLANKTON; PLANT; POWER LAW; PREDATOR-PREY INTERACTION; TERRESTRIAL ECOSYSTEM;

AFRICAN; ALLOMETRY; AQUATIC ENVIRONMENT; ARTICLE; BIOMASS; BODY MASS; CARNIVORE; COMMUNITY; ECOSYSTEM; INVERTEBRATE; LION; MORTALITY; NULL HYPOTHESIS; PLANKTON; PLANT; PREDATOR PREY INTERACTION; PREDICTION; PRIORITY JOURNAL; SAVANNA; STEADY STATE; ANIMAL; FACTUAL DATABASE; FOOD CHAIN; MAMMAL;

INVERTEBRATA; MAMMALIA;

ANIMALS; BIOMASS; DATABASES, FACTUAL; FOOD CHAIN; INVERTEBRATES; MAMMALS; PLANKTON;

EID: 84941343227     PISSN: 00368075     EISSN: 10959203     Source Type: Journal    
DOI: 10.1126/science.aac6284     Document Type: Article

References (130)

1. S. A. Frank, The common patterns of nature. J. Evol. Biol. 22, 1563-1585 (2009). doi:10.1111/j.1420-9101.2009.01775.x; pmid: 19538344.
2. P. A. Marquet et al., Scaling and power-laws in ecological systems. J. Exp. Biol. 208, 1749-1769 (2005). doi:10.1242/jeb.01588; pmid: 15855405.
3. J. H. Brown, B. A. Maurer, Macroecology: The division of food and space among species on continents. Science 243, 1145-1150 (1989). doi:10.1126/science.243.4895.1145; pmid: 17799895.
4. S. A. Levin, The problem of pattern and scale in ecology: The Robert H. MacArthur award lecture. Ecology 73, 1943-1967 (1992). doi: 10.2307/1941447.
5. J. H. Brown, J. F. Gillooly, A. P. Allen, V. M. Savage, G. B. West, Toward a metabolic theory of ecology. Ecology 85, 1771-1789 (2004). doi: 10.1890/03-9000.
6. R. M. Sibly, J. H. Brown, A. Kodric-Brown, Metabolic Ecology: A Scaling Approach (Wiley, New York, 2012).
7. J. Harte, Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Univ. Press, Oxford, 2011).
8. M. Loreau, From Populations to Ecosystems: Theoretical Foundations for a New Ecological Synthesis (MPB-46) (Princeton Univ. Press, Princeton, NJ, 2010).
9. J. O. Farlow, A consideration of the trophic dynamics of a Late Cretaceous large-dinosaur community (Oldman Formation). Ecology 57, 841-857 (1976). doi: 10.2307/1941052.
10. R. East, Rainfall, soil nutrient status and biomass of large African savanna mammals. Afr. J. Ecol. 22, 245-270 (1984). doi: 10.1111/j.1365-2028.1984.tb00700.x.
11. G. Hemson, thesis, University of Oxford, Oxford, UK (2003).
12. S. Grange, P. Duncan, Bottom-up and top-down processes in African ungulate communities: Resources and predation acting on the relative abundance of zebra and grazing bovids. Ecography 29, 899-907 (2006). doi: 10.1111/j.2006.0906- 7590.04684.x.
13. Project Tiger Directorate, Reserve Guide: Project Tiger Reserves in India, Project Tiger India, projecttiger.nic.in/map.htm.
14. K. U. Karanth, J. D. Nichols, N. S. Kumar, W. A. Link, J. E. Hines, Tigers and their prey: Predicting carnivore densities from prey abundance. Proc. Natl. Acad. Sci. U.S.A. 101, 4854-4858 (2004). doi:10.1073/pnas.0306210101; pmid: 15041746.
15. K. Kawanishi, M. E. Sunquist, Conservation status of tigers in a primary rainforest of Peninsular Malaysia. Biol. Conserv. 120, 329-344 (2004). doi: 10.1016/j.biocon.2004.03.005.
16. T. K. Fuller, Population dynamics of wolves in North-Central Minnesota. Wildl. Monogr. 105, 1-41 (1989).
17. F. Messier, Ungulate population models with predation: A case study with the North American moose. Ecology 75, 478-488 (1994). doi: 10.2307/1939551.
18. H. Cyr, R. H. Peters, Biomass-size spectra and the prediction of fish biomass in lakes. Can. J. Fish. Aquat. Sci. 53, 994-1006 (1996). doi: 10.1139/f96-033.
19. E. McCauley, J. Kalff, Empirical relationships between phytoplankton and zooplankton biomass in lakes. Can. J. Fish. Aquat. Sci. 38, 458-463 (1981). doi: 10.1139/f81-063.
20. P. A. del Giorgio, J. M. Gasol, Biomass distribution in freshwater plankton communities. Am. Nat. 146, 135-152 (1995). doi: 10.1086/285790.
21. P. A. del Giorgio, J. J. Cole, N. F. Caraco, R. H. Peters, Linking planktonic biomass and metabolism to net gas fluxes in northern temperate lakes. Ecology 80, 1422-1431 (1999). doi: 10.1890/0012-9658(1999)080[1422:LPBAMT]2.0.CO;2.
22. X. Irigoien, J. Huisman, R. P. Harris, Global biodiversity patterns of marine phytoplankton and zooplankton. Nature 429, 863-867 (2004). doi:10.1038/nature02593; pmid: 15215862.
23. R. T. Coupland, Natural Grasslands: Eastern Hemisphere and Résumé (Elsevier, Amsterdam, ed. 1, 1993), vol. 8B.
24. P. L. Sims, J. S. Singh, W. K. Lauenroth, The structure and function of ten Western North American grasslands: I. Abiotic and vegetational characteristics. J. Ecol. 66, 251-285 (1978). doi: 10.2307/2259192.
25. P. L. Sims, J. S. Singh, The structure and function of ten Western North American grasslands: III. Net primary production, turnover and efficiencies of energy capture and water use. J. Ecol. 66, 573-597 (1978). doi: 10.2307/2259152.
26. M. A. Huston, S. Wolverton, The global distribution of net primary production: Resolving the paradox. Ecol. Monogr. 79, 343-377 (2009). doi: 10.1890/08-0588.1.
27. M. G. R. Cannell, World Forest Biomass and Primary Production Data (Academic Press, London, 1982).
28. S. T. Michaletz, D. Cheng, A. J. Kerkhoff, B. J. Enquist, Convergence of terrestrial plant production across global climate gradients. Nature 512, 39-43 (2014). pmid: 25043056.
29. C. M. Duarte, C. L. Chiscano, Seagrass biomass and production: A reassessment. Aquat. Bot. 65, 159-174 (1999). doi: 10.1016/S0304-3770(99)00038-8.
30. C. Plante, J. A. Downing, Production of freshwater invertebrate populations in lakes. Can. J. Fish. Aquat. Sci. 46, 1489-1498 (1989). doi: 10.1139/f89-191.
31. J. A. Downing, C. Plante, S. Lalonde, Fish production correlated with primary productivity, not the morphoedaphic index. Can. J. Fish. Aquat. Sci. 47, 1929-1936 (1990). doi: 10.1139/f90-217.
32. R. G. Randall, C. K. Minns, J. R. M. Kelso, Fish production in freshwaters: Are rivers more productive than lakes? Can. J. Fish. Aquat. Sci. 52, 631-643 (1995). doi: 10.1139/f95-063.
33. J. A. Downing, C. Plante, Production of fish populations in lakes. Can. J. Fish. Aquat. Sci. 50, 110-120 (1993). doi: 10.1139/f93-013.
34. S. J. McNaughton, M. Oesterheld, D. A. Frank, K. J. Williams, Ecosystem-level patterns of primary productivity and herbivory in terrestrial habitats. Nature 341, 142-144 (1989). doi:10.1038/341142a0; pmid: 2779651.
35. H. Cyr, M. L. Pace, Magnitude and patterns of herbivory in aquatic and terrestrial ecosystems. Nature 361, 148-150 (1993). doi: 10.1038/361148a0.
36. J. Cebrian, Patterns in the fate of production in plant communities. Am. Nat. 154, 449-468 (1999). doi: 10.1086/303244; pmid: 10523491.
37. J. Cebrian, J. Lartigue, Patterns of herbivory and decomposition in aquatic and terrestrial ecosystems. Ecol. Monogr. 74, 237-259 (2004). doi: 10.1890/03-4019.
38. J. M. Gasol, P. A. del Giorgio, C. M. Duarte, Biomass distribution in marine planktonic communities. Limnol. Oceanogr. 42, 1353-1363 (1997). doi: 10.4319/lo.1997.42.6.1353.
39. J. Cebrian, C. M. Duarte, The dependence of herbivory on growth rate in natural plant communities. Funct. Ecol. 8, 518-525 (1994). doi: 10.2307/2390077.
40. J. Cebrian et al., Producer nutritional quality controls ecosystem trophic structure. PLOS ONE 4, e4929 (2009). pmid: 19300514.
41. M. A. Leibold, J. M. Chase, J. B. Shurin, A. L. Downing, Species turnover and the regulation of trophic structure. Annu. Rev. Ecol. Syst. 28, 467-494 (1997). doi: 10.1146/annurev.ecolsys.28.1.467.
42. J. M. Chase, M. A. Leibold, A. L. Downing, J. B. Shurin, The effects of productivity, herbivory, and plant species turnover in grassland food webs. Ecology 81, 2485-2497 (2000). doi: 10.1890/0012-9658(2000)081[2485:TEOPHA]2.0.CO;2.
43. C. S. Elton, Animal Ecology (Univ. of Chicago Press, Chicago, IL, 1927).
44. E. P. Odum, Fundamentals of Ecology (Saunders, Philadelphia, ed. 3, 1971).
45. R. Trebilco, J. K. Baum, A. K. Salomon, N. K. Dulvy, Ecosystem ecology: Size-based constraints on the pyramids of life. Trends Ecol. Evol. 28, 423-431 (2013). doi:10.1016/j.tree.2013.03.008; pmid: 23623003.
46. M. L. Rosenzweig, Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time. Science 171, 385-387 (1971). doi:10.1126/science.171.3969.385 pmid: 5538935.
47. L. Oksanen, T. Oksanen, The logic and realism of the hypothesis of exploitation ecosystems. Am. Nat. 155, 703-723 (2000). doi:10.1086/303354; pmid: 10805639.
48. K. S. McCann, Food Webs (MPB-50) (Princeton Univ. Press, Princeton, NJ, 2011).
49. R. Arditi, L. Ginzburg, How Species Interact: Altering the Standard View on Trophic Ecology (Oxford Univ. Press, Oxford, 2012).
50. A. R. E. Sinclair, S. Mduma, J. S. Brashares, Patterns of predation in a diverse predator-prey system. Nature 425, 288-290 (2003). doi:10.1038/nature01934; pmid: 13679915.
51. N. Owen-Smith, M. G. L. Mills, Predator-prey size relationships in an African large-mammal food web. J. Anim. Ecol. 77, 173-183 (2008). doi:10.1111/j.1365-2656.2007.01314.x; pmid: 18177336.
52. H. Cyr, M. L. Pace, Allometric theory: Extrapolations from individuals to communities. Ecology 74, 1234-1245 (1993). doi: 10.2307/1940493.
53. C. Carbone, J. L. Gittleman, A common rule for the scaling of carnivore density. Science 295, 2273-2276 (2002). doi:10.1126/science.1067994; pmid: 11910114.
54. A. J. Lotka, Elements of Physical Biology (Dover, New York, 1924).
55. V. Volterra, Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560 (1926). doi: 10.1038/118558a0.
56. J. P. DeLong, D. A. Vasseur, A dynamic explanation of size-density scaling in carnivores. Ecology 93, 470-476 (2012). doi:10.1890/11-1138.1; pmid: 22624202.
57. S. Pawar, A. I. Dell, V. M. Savage, Dimensionality of consumer search space drives trophic interaction strengths. Nature 486, 485-489 (2012). pmid: 22722834.
58. C. Melis et al., Predation has a greater impact in less productive environments: Variation in roe deer, Capreolus capreolus, population density across Europe. Glob. Ecol. Biogeogr. 18, 724-734 (2009). doi: 10.1111/j.1466-8238.2009.00480.x.
59. G. Wang et al., Density dependence in northern ungulates: Interactions with predation and resources. Popul. Ecol. 51, 123-132 (2009). doi: 10.1007/s10144-008-0095-3.
60. A. Treves, A. J. Plumptre, L. T. B. Hunter, J. Ziwa, Identifying a potential lion Panthera leo stronghold in Queen Elizabeth National Park, Uganda, and Parc National des Virunga, Democratic Republic of Congo. Oryx 43, 60-66 (2009). doi: 10.1017/S003060530700124X.
61. C. Carbone, N. Pettorelli, P. A. Stephens, The bigger they come, the harder they fall: Body size and prey abundance influence predator-prey ratios. Biol. Lett. 7, 312-315 (2011). doi:10.1098/rsbl.2010.0996; pmid: 21106569.
62. B. Jedrzejewska, W. Jedrzejewski, Predation in Vertebrate Communities: The Bialowieza Primeval Forest as a Case Study (Springer, Berlin, 1998), vol. 135.
63. E. Jeppesen, J. Peder Jensen, M. Søndergaard, T. Lauridsen, F. Landkildehus, Trophic structure, species richness and biodiversity in Danish lakes: Changes along a phosphorus gradient. Freshw. Biol. 45, 201-218 (2000). doi: 10.1046/j.1365-2427.2000.00675.x.
64. Q. Dortch, T. T. Packard, Differences in biomass structure between oligotrophic and eutrophic marine ecosystems. Deep-Sea Res. A, Oceanogr. Res. Pap. 36, 223-240 (1989). doi: 10.1016/0198-0149(89)90135-0.
65. P. Legendre, L. F. Legendre, Numerical Ecology (Elsevier, Amsterdam, 2012), vol. 24.
66. K. J. Niklas, B. J. Enquist, Biomass allocation and growth data of seeded plants data set, Oak Ridge National Laboratory Distributed Active Archive Center, Oak Ridge, TN (2004), www.daac.ornl.gov.
67. K. Banse, S. Mosher, Adult body mass and annual production/biomass relationships of field populations. Ecol. Monogr. 50, 355-379 (1980). doi: 10.2307/2937256.
68. R. H. Peters, The Ecological Implications of Body Size (Cambridge Studies in Ecology, Cambridge Univ. Press, Cambridge, ed. 1, 1983).
69. T. Fenchel, Intrinsic rate of natural increase: The relationship with body size. Oecologia 14, 317-326 (1974). doi: 10.1007/BF00384576.
70. T. J. Case, On the evolution and adaptive significance of postnatal growth rates in the terrestrial vertebrates. Q. Rev. Biol. 53, 243-282 (1978). doi:10.1086/410622; pmid: 362471.
71. S. K. M. Ernest et al., Thermodynamic and metabolic effects on the scaling of production and population energy use. Ecol. Lett. 6, 990-995 (2003). doi: 10.1046/j.1461-0248.2003.00526.x.
72. J. M. Grady, B. J. Enquist, E. Dettweiler-Robinson, N. A. Wright, F. A. Smith, Evidence for mesothermy in dinosaurs. Science 344, 1268-1272 (2014). pmid: 24926017.
73. L. vonBertalanffy, Quantitative laws in metabolism and growth. Q. Rev. Biol. 32, 217-231 (1957). doi:10.1086/401873; pmid: 13485376.
74. G. B. West, J. H. Brown, B. J. Enquist, A general model for ontogenetic growth. Nature 413, 628-631 (2001). doi:10.1038/35098076; pmid: 11675785.
75. A. M. Makarieva, V. G. Gorshkov, B.-L. Li, Ontogenetic growth: Models and theory. Ecol. Modell. 176, 15-26 (2004). doi: 10.1016/j.ecolmodel.2003.09.037.
76. C. Hou et al., Energy uptake and allocation during ontogeny. Science 322, 736-739 (2008). doi:10.1126/science.1162302; pmid: 18974352.
77. J. P. De Long, J. G. Okie, M. E. Moses, R. M. Sibly, J. H. Brown, Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life. Proc. Natl. Acad. Sci. U.S.A. 107, 12941-12945 (2010). doi:10.1073/pnas.1007783107; pmid: 20616006.
78. R. M. Sibly, D. Barker, M. C. Denham, J. Hone, M. Pagel, On the regulation of populations of mammals, birds, fish, and insects. Science 309, 607-610 (2005). doi:10.1126/science.1110760; pmid: 16040705.
79. B. W. Brook, C. J. Bradshaw, Strength of evidence for density dependence in abundance time series of 1198 species. Ecology 87, 1445-1451 (2006). doi:10.1890/0012-9658(2006)87[1445:SOEFDD]2.0.CO;2; pmid: 16869419.
80. N. B. Goodwin, A. Grant, A. L. Perry, N. K. Dulvy, J. D. Reynolds, Life history correlates of density-dependent recruitment in marine fishes. Can. J. Fish. Aquat. Sci. 63, 494-509 (2006). doi: 10.1139/f05-234.
81. J. P. DeLong, T. C. Hanley, D. A. Vasseur, Competition and the density dependence of metabolic rates. J. Anim. Ecol. 83, 51-58 (2014). doi:10.1111/1365-2656.12065; pmid: 23565624.
82. R. A. Duursma et al., Self-shading affects allometric scaling in trees. Funct. Ecol. 24, 723-730 (2010). doi: 10.1111/j.1365- 2435.2010.01690.x.
83. G. B. West, B. J. Enquist, J. H. Brown, A general quantitative theory of forest structure and dynamics. Proc. Natl. Acad. Sci. U.S.A. 106, 7040-7045 (2009). doi:10.1073/pnas.0812294106 pmid: 19363160.
84. N. G. Hairston Jr., N. G. Hairston Sr., Cause-effect relationships in energy flow, trophic structure, and interspecific interactions. Am. Nat. 142, 379-411 (1993). doi: 10.1086/285546.
85. A. J. Kerkhoff, B. J. Enquist, Ecosystem allometry: The scaling of nutrient stocks and primary productivity across plant communities. Ecol. Lett. 9, 419-427 (2006). doi:10.1111/j.1461-0248.2006.00888.x; pmid: 16623727.
86. S. Watson, E. McCauley, Contrasting patterns of net-and nanoplankton production and biomass among lakes. Can. J. Fish. Aquat. Sci. 45, 915-920 (1988). doi: 10.1139/f88-112.
87. C. Packer et al., Ecological change, group territoriality, and population dynamics in Serengeti lions. Science 307, 390-393 (2005). doi:10.1126/science.1105122; pmid: 15662005.
88. J. M. Fryxell, A. Mosser, A. R. E. Sinclair, C. Packer, Group formation stabilizes predator-prey dynamics. Nature 449, 1041-1043 (2007). doi:10.1038/nature06177; pmid: 17960242.
89. W. E. Ricker, Linear regressions in fishery research. J. Fish. Board Can.30, 409-434 (1973). doi: 10.1139/f73-072.
90. B. H. McArdle, The structural relationship: Regression in biology. Can. J. Zool. 66, 2329-2339 (1988). doi: 10.1139/z88-348.
91. R. R. Sokal, F. J. Rohlf, Biometry (Freeman, New York, ed. 3, 1995).
92. P. Jolicoeur, Bivariate allometry: Interval estimation of the slopes of the ordinary and standardized normal major axes and structural relationship. J. Theor. Biol. 144, 275-285 (1990). doi: 10.1016/S0022-5193(05)80326-1.
93. D. I. Warton, I. J. Wright, D. S. Falster, M. Westoby, Bivariate line-fitting methods for allometry. Biol. Rev. Camb. Philos. Soc. 81, 259-291 (2006). doi:10.1017/S1464793106007007; pmid: 16573844.
94. R. J. Smith, Use and misuse of the reduced major axis for line-fitting. Am. J. Phys. Anthropol. 140, 476-486 (2009). doi:10.1002/ajpa.21090; pmid: 19425097.
95. E. P. White, X. Xiao, N. J. Isaac, R. M. Sibly, "Methodological tools, " in Metabolic Ecology: A Scaling Approach, (2012), pp. 7-20.
96. C. R. White, Allometric estimation of metabolic rates in animals. Comp. Biochem. Physiol. A Mol. Integr. Physiol. 158, 346-357 (2011). doi:10.1016/j.cbpa.2010.10.004; pmid: 20937406.
97. K. Nowell, P. Jackson, Wild Cats: Status Survey and Conservation Action Plan (IUCN/SSC Cat Specialist Group, Gland, Switzerland, 1996).
98. P. M. Gros, M. J. Kelly, T. M. Caro, Estimating carnivore densities for conservation purposes: Indirect methods compared to baseline demographic data. Oikos 77, 197 (1996). doi: 10.2307/3546058.
99. J. Kalff, Limnology: Inland Water Ecosystems (Prentice Hall, Upper Saddle River, NJ, 2002), vol. 592.
100. E. McCauley, in A Manual on Methods for the Assessment of Secondary Productivity in Fresh Waters (Blackwell Scientific, Oxford, 1984), pp. 228-265.
101. G. Harris, Phytoplankton Ecology-Structure, Function and Fluctuation (Chapman and Hall, New York, 1986).
102. N. Billington, A comparison of three methods of measuring phytoplankton biomass on a daily and seasonal basis. Hydrobiologia 226, 1-15 (1991). doi: 10.1007/BF00007775.
103. J. S. Singh, W. K. Lauenroth, R. K. Steinhorst, Review and assessment of various techniques for estimating net aerial primary production in grasslands from harvest data. Bot. Rev. 41, 181-232 (1975). doi: 10.1007/BF02860829.
104. D. A. Clark et al., Measuring net primary production in forests: Concepts and field methods. Ecol. Appl. 11, 356-370 (2001). doi: 10.1890/1051-0761(2001)011[0356: MNPPIF]2.0.CO;2.
105. S. P. Long, P. R. Hutchin, Primary production in grasslands and coniferous forests with climate change: An overview. Ecol. Appl. 1, 139-156 (1991). doi: 10.2307/1941807.
106. C. Plante, J. A. Downing, Empirical evidence for differences among methods for calculating secondary production. J. N. Am. Benthol. Soc. 9, 9-16 (1990). doi: 10.2307/1467929.
107. E. P. White, B. J. Enquist, J. L. Green, On estimating the exponent of power-law frequency distributions. Ecology 89, 905-912 (2008). doi:10.1890/07-1288.1; pmid: 18481513.
108. A. Clauset, C. R. Shalizi, M. E. Newman, Power-law distributions in empirical data. SIAM Rev. 51, 661-703 (2009). doi: 10.1137/070710111.
109. S. Nee, N. Colegrave, S. A. West, A. Grafen, The illusion of invariant quantities in life histories. Science 309, 1236-1239 (2005). doi:10.1126/science.1114488; pmid: 16109879.
110. M. J. Coe, D. H. Cumming, J. Phillipson, Biomass and production of large African herbivores in relation to rainfall and primary production. Oecologia 22, 341-354 (1976). doi: 10.1007/BF00345312.
111. H. Fritz, P. Duncan, On the carrying capacity for large ungulates of African savanna ecosystems. Proc. R. Soc. London Ser. B 256, 77-82 (1994). doi:10.1098/rspb.1994.0052; pmid: 8008761.
112. MAPA Project, MAPA Project, (2011), www.mapaproject.org/.
113. ALERT, African Lion and Environmental Research Trust (2011), www.lionalert.org.
114. J. Damuth, Interspecific allometry of population density in mammals and other animals: The independence of body mass and population energy-use. Biol. J. Linn. Soc. Lond. 31, 193-246 (1987). doi: 10.1111/j.1095-8312.1987.tb01990.x.
115. R. East, IUCN/SSC Antelope Specialist Group, African Antelope Database 1998 (IUCN, Gland, Switzerland, and Cambridge, UK, 1999).
116. R. J. Power, R. X. Shem Compion, Lion predation on elephants in the Savuti, Chobe National Park, Botswana. Afr. Zool. 44, 36-44 (2009). doi: 10.3377/004.044.0104.
117. J. M. Fryxell, J. Greever, A. R. E. Sinclair, Why are migratory ungulates so abundant? Am. Nat. 131, 781-798 (1988). doi: 10.1086/284822.
118. C. Kiffner, B. Meyer, M. Muhlenberg, M. Waltert, Plenty of prey, few predators: What limits lions Panthera Leo in Katavi National Park, Western Tanzania? Oryx 43, 52-59 (2009). doi: 10.1017/S0030605307002335.
119. V. J. Wilson, Mammals of the Wankie National Park, Rhodesia (Trustees of the National Museums and Monuments of Rhodesia, Salisbury, Rhodesia, 1975).
120. L. D. Harris, "An ecological description of a semi-arid East African ecosystem, " Range Science Department Science Series (11, Colorado State University, Fort Collins, CO, 1972).
121. H. F. Lamprey, The Tarangire game reserve. Tanganyika Not. Record. 60, 10-22 (1963).
122. M. G. L. Mills, Kalahari Hyenas: Comparative Behavioral Ecology of Two Species (Blackburn, Caldwell, NJ, 1990).
123. D. I. Warton, R. A. Duursma, D. S. Falster, S. Taskinen, smatr 3-an R package for estimation and inference about allometric lines. Methods Ecol. Evol. 3, 257-259 (2012). doi: 10.1111/j.2041-210X.2011.00153.x.
124. T. X. Luo, thesis, Chinese Academy of Sciences, Beijing, China (1996).
125. J. Ni, X.-S. Zhang, J. M. Scurlock, Synthesis and analysis of biomass and net primary productivity in Chinese forests. Ann. For. Sci. 58, 351-384 (2001). doi: 10.1051/forest:2001131.
126. A. M. Makarieva et al., Mean mass-specific metabolic rates are strikingly similar across life's major domains: Evidence for life's metabolic optimum. Proc. Natl. Acad. Sci. U.S.A. 105, 16994-16999 (2008). doi:10.1073/pnas.0802148105; pmid: 18952839.
127. V. M. Savage, J. F. Gillooly, J. H. Brown, G. B. West, E. L. Charnov, Effects of body size and temperature on population growth. Am. Nat. 163, 429-441 (2004). doi:10.1086/381872; pmid: 15026978.
128. R. P. Duncan, D. M. Forsyth, J. Hone, Testing the metabolic theory of ecology: Allometric scaling exponents in mammals. Ecology 88, 324-333 (2007). doi:10.1890/0012-9658(2007)88[324:TTMTOE]2.0.CO;2; pmid: 17479751.
129. W. F. Fagan, H. J. Lynch, B. R. Noon, Pitfalls and challenges of estimating population growth rate from empirical data: Consequences for allometric scaling relations. Oikos 119, 455-464 (2010). doi: 10.1111/j.1600-0706.2009.18002.x.
130. H. M. Pereira, G. C. Daily, Modeling biodiversity dynamics in countryside landscapes. Ecology 87, 1877-1885 (2006). doi:10.1890/0012-9658(2006)87[1877:MBDICL]2.0.CO;2; pmid: 16937624.