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Group formation stabilizes predator–prey dynamics


Theoretical ecology is largely founded on the principle of mass action, in which uncoordinated populations of predators and prey move in a random and well-mixed fashion across a featureless landscape. The conceptual core of this body of theory is the functional response, predicting the rate of prey consumption by individual predators as a function of predator and/or prey densities1,2,3,4,5. This assumption is seriously violated in many ecosystems in which predators and/or prey form social groups. Here we develop a new set of group-dependent functional responses to consider the ecological implications of sociality and apply the model to the Serengeti ecosystem. All of the prey species typically captured by Serengeti lions (Panthera leo) are gregarious, exhibiting nonlinear relationships between prey-group density and population density. The observed patterns of group formation profoundly reduce food intake rates below the levels expected under random mixing, having as strong an impact on intake rates as the seasonal migratory behaviour of the herbivores. A dynamical system model parameterized for the Serengeti ecosystem (using wildebeest (Connochaetes taurinus) as a well-studied example) shows that grouping strongly stabilizes interactions between lions and wildebeest. Our results suggest that social groups rather than individuals are the basic building blocks around which predator–prey interactions should be modelled and that group formation may provide the underlying stability of many ecosystems.

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Figure 1: Group density in relation to population density for Serengeti lions and their predominant eight prey species.
Figure 2: Predicted effects of group formation by Serengeti lions and/or their prey on the functional response of individual lions.
Figure 3: Locally stable parameter combinations ( ε versus d ) for lion–wildebeest models.
Figure 4: Time-series data for Serengeti wildebeest and lions.


  1. 1

    Holling, C. S. The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can. Entomol. 91, 293–320 (1959)

    Article  Google Scholar 

  2. 2

    Arditi, R. & Ginzburg, L. R. Coupling in predator–prey dynamics: ratio-dependence. J. Theor. Biol. 139, 311–326 (1989)

    Article  Google Scholar 

  3. 3

    Cosner, C., DeAngelis, D. L., Ault, J. S. & Olson, D. B. Effects of spatial grouping on the functional response of predators. Theor. Popul. Biol. 56, 65–75 (1999)

    CAS  Article  Google Scholar 

  4. 4

    Jeschke, J. M., Kopp, M. & Tollrian, R. Predator functional responses: discriminating between handling and digesting prey. Ecol. Monogr. 72, 95–112 (2002)

    Article  Google Scholar 

  5. 5

    Abrams, P. A. & Ginzburg, L. R. The nature of predation: prey dependent, ratio dependent, or neither? Trends Ecol. Evol. 15, 337–341 (2000)

    CAS  Article  Google Scholar 

  6. 6

    Packer, C. et al. Ecological change, group territoriality, and population dynamics in Serengeti lions. Science 307, 390–393 (2005)

    ADS  CAS  Article  Google Scholar 

  7. 7

    McCauley, E., Wilson, W. & de Roos, A. M. Dynamics of age-structured and spatially-structured predator–prey interactions: individual-based models and population-level formulations. Am. Nat. 142, 412–442 (1993)

    CAS  Article  Google Scholar 

  8. 8

    Nisbet, R. M., de Roos, A. M., Wilson, W. G. & Snyder, R. E. Discrete consumers, small scale resource heterogeneity, and population stability. Ecol. Lett. 1, 34–37 (1998)

    Article  Google Scholar 

  9. 9

    Donalson, D. D. & Nisbet, R. M. Population dynamics and spatial scale: effects of system size on population persistence. Ecology 80, 2492–2507 (1999)

    Article  Google Scholar 

  10. 10

    Keeling, M. J., Wilson, H. B. & Pacala, S. W. Reinterpreting space, time lags, and functional responses in ecological models. Science 290, 1758–1761 (2000)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Pascual, M., Mazzega, P. & Levin, S. A. Oscillatory dynamics and spatial scale: the role of noise and unresolved pattern. Ecology 82, 2357–2369 (2001)

    Article  Google Scholar 

  12. 12

    Hosseini, P. R. How localized consumption stabilizes predator–prey systems with finite frequency of mixing. Am. Nat. 161, 567–585 (2003)

    Article  Google Scholar 

  13. 13

    Nachman, G. A functional response model of a predator population foraging in a patchy habitat. J. Anim. Ecol. 75, 948–958 (2006)

    Article  Google Scholar 

  14. 14

    Cantrell, R. S. & Cosner, C. The effect of spatial heterogeneity on population dynamics. J. Math. Biol. 29, 315–338 (2001)

    MathSciNet  Article  Google Scholar 

  15. 15

    Packer, C. & Ruttan, L. M. The evolution of cooperative hunting. Am. Nat. 132, 159–198 (1988)

    Article  Google Scholar 

  16. 16

    Scheel, D. & Packer, C. Group hunting behaviour of lions: a search for cooperation. Anim. Behav. 41, 697–709 (1991)

    Article  Google Scholar 

  17. 17

    Packer, C., Scheel, D. & Pusey, A. E. Why lions form groups: food is not enough. Am. Nat. 136, 1–19 (1990)

    Article  Google Scholar 

  18. 18

    McComb, K. E., Packer, C. & Pusey, A. E. Roaring and numerical assessment in contests between groups of female lions Panthera leo . Anim. Behav. 47, 379–387 (1994)

    Article  Google Scholar 

  19. 19

    Grinnell, J., Packer, C. & Pusey, A. E. Cooperation in male lions: kinship, reciprocity or mutualism? Anim. Behav. 49, 95–105 (1995)

    Article  Google Scholar 

  20. 20

    Fryxell, J. M., Greever, J. & Sinclair, A. R. E. Why are migratory ungulates so abundant? Am. Nat. 131, 781–798 (1988)

    Article  Google Scholar 

  21. 21

    Mduma, S. A. R., Sinclair, A. R. E. & Hilborn, R. Food regulates the Serengeti wildebeest population: a 40-year record. J. Anim. Ecol. 68, 1101–1122 (1999)

    Article  Google Scholar 

  22. 22

    Turchin, P. Complex Population Dynamics (Princeton Univ. Press, Princeton, NJ, 2003)

    MATH  Google Scholar 

  23. 23

    Scheel, D. Profitability, encounter rates, and prey choice of African lions. Behav. Ecol. 4, 90–97 (1993)

    Article  Google Scholar 

  24. 24

    Elliott, J. P., Cowan, I., McT & Holling, C. S. Prey capture by the African lion. Can. J. Zool. 55, 1811–1828 (1977)

    Article  Google Scholar 

  25. 25

    Rosenzweig, M. L. Paradox of enrichment—destabilization of exploitation ecosystems in ecological time. Science 171, 385–387 (1971)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Rosenzweig, M. L. & MacArthur, R. H. Graphical representation and stability conditions of predator–prey interactions. Am. Nat. 97, 209–223 (1963)

    Article  Google Scholar 

  27. 27

    Sinclair, A. R. E., Fryxell, J. M. & Caughley, G. Wildlife Ecology, Conservation, and Management (Blackwell, Oxford, 2006)

    Google Scholar 

  28. 28

    Yodzis, P. Introduction to Theoretical Ecology (Harper & Row, New York, 1989)

    MATH  Google Scholar 

  29. 29

    Hastings, A. Population Biology: Concepts and Models (Springer, New York, 1997)

    Book  Google Scholar 

  30. 30

    Mols, C. M. M. et al. Central assumptions of predator–prey models fail in a semi-natural experimental system. Proc. R. Soc. Lond. B 271 (Supplement). S85–S87 (2004)

    Article  Google Scholar 

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We thank the many individuals who have assisted with Serengeti population monitoring over the decades. J.M.F. thanks the Visitor’s Programme of the Centre for Population Biology, Imperial College London, for logistic support during the preparation of this work. This work was supported by Discovery Grants to J.M.F. and A.R.E.S. from the Natural Sciences and Engineering Research Council of Canada, and by NSF Grants for Long-Term Research in Environmental Biology and Biocomplexity to C.P.

Author Contributions Field data used for this paper came from long-term collaborative studies by J.M.F., C.P. and A.R.E.S., with statistical analysis of the data by J.M.F. and A.M. Models were developed and analysed by J.M.F. All four authors participated in discussion of the results at a workshop and contributed to manuscript preparation.

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Correspondence to John M. Fryxell.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Table 1 (listing the parameters for curves shown in Fig. 1), Supplementary Figure 1 (showing seasonal variation in wildebeest group density and number of wildebeest groups encountered during censuses), and Supplementary Equations (listing equations for population equilibria and community matrix coefficients used for local stability analysis). (PDF 216 kb)

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Fryxell, J., Mosser, A., Sinclair, A. et al. Group formation stabilizes predator–prey dynamics. Nature 449, 1041–1043 (2007).

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