×

zbMATH — the first resource for mathematics

Positive complexity-stability relations in food web models without foraging adaptation. (English) Zbl 1402.92424
Summary: R. M. May’s [“Will a large complex system be stable?”, Nature 238, 413–414 (1972; doi:10.1038/238413a0)] local stability analysis of random food web models showed that increasing network complexity leads to decreasing stability, a result that is contradictory to earlier empirical findings. Since this seminal work, research of complexity-stability relations became one of the most challenging issues in theoretical ecology. We investigate conditions for positive complexity-stability relations in the niche, cascade, nested hierarchy, and random models by evaluating the network robustness, i.e., the fraction of surviving species after population dynamics. We find that positive relations between robustness and complexity can be obtained when resources are large, Holling II functional response is used and interaction strengths are weighted with the number of prey species, in order to take foraging efforts into account. In order to obtain these results, no foraging dynamics needs to be included. However, the niche model does not show positive complexity-stability relations under these conditions. By comparing to empirical food web data, we show that the niche model has unrealistic distributions of predator numbers. When this distribution is randomized, positive complexity-stability relations can be found also in the niche model.

MSC:
92D40 Ecology
PDF BibTeX Cite
Full Text: DOI
References:
[1] Brose, U.; Williams, R.J.; Martinez, N.D., Comment on “foraging adaptation and the relationship between food-web complexity and stability”, Science, 301, 918b, (2003)
[2] Brose, U.; Williams, R.J.; Martinez, N.D., Allometric scaling enhances stability in complex food webs, Ecol. lett., 9, 1228-1236, (2006)
[3] Brown, J.H.; Gillooly, J.F.; Allen, A.P.; Savage, V.M.; West, G.B., Toward a metabolic theory of ecology, Ecology, 85, 1771-1789, (2004)
[4] Cattin, M.F.; Bersier, L.F.; Banašek-Richter, C.; Baltensperger, R.; Gabriel, J.P., Phylogenetic constraints and adaptation explain food-web structure, Nature, 427, 835-839, (2004)
[5] Cohen, J.E.; Newman, C.M., A stochastic theory of community food webs: models and aggregated data, Proc. R. soc. lond. B, 224, 421-448, (1985)
[6] Dunne, J.A.; Williams, R.J.; Martinez, N.D., Food web structure and network theory: the role of connectance and size, Proc. nat. acad. sci., 99, 12917-12922, (2002)
[7] Elton, C.S., Ecology of invasions by animals and plants, (1958), Chapman & Hall London
[8] Garcia-Domingo, J.L.; Saldaña, J., Food-web complexity emerging from ecological dynamics on adaptive networks, J. theor. biol., 247, 819-826, (2007)
[9] Gentleman, W.; Leising, A.; Frost, B.; Strom, S.; Murray, J., Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics, Deep sea res. II, 50, 2847-2875, (2003)
[10] Holling, C.S., Some characteristics of simple types of predation and parasitism, Can. entom., 91, 385-398, (1959)
[11] Kondoh, M., Foraging adaptation and the relationship between food-web complexity and stability, Science, 299, 1388-1391, (2003)
[12] Kondoh, M., Response to comment on “foraging adaptation and the relationship between food-web complexity and stability”, Science, 301, 5635, 918, (2003)
[13] Kondoh, M., Does foraging adaptation create the positive complexity – stability relationship in realistic food-web structure?, J. theor. biol., 238, 646-651, (2005)
[14] Law, R.; Blackford, J.C., Self-assembling food webs: a global viewpoint of coexistence of species in lotka – volterra communities, Ecology, 73, 2, 567-578, (1992)
[15] MacArthur, R.H., Fluctuations of animal populations and a measure of community stability, Ecology, 36, 533-536, (1955)
[16] May, R.M., Will a large complex system be stable?, Nature, 238, 413-414, (1972)
[17] McCann, K.S., The diversity – stability debate, Nature, 405, 228-233, (2000)
[18] Morton, D.R.; Law, R., Regional species pools and the assembly of local ecological communities, J. theor. biol., 187, 321-331, (1997)
[19] Odum, E., Fundamentals of ecology, (1953), Saunders Philadelphia
[20] Rossberg, A.G.; Matsuda, H.; Amemiya, T.; Itoh, K., An explanatory model for food-web structure and evolution, Ecol. comp., 2, 312-321, (2005)
[21] Rossberg, A.G.; Matsuda, H.; Amemiya, T.; Itoh, K., Food webs: experts consuming families of experts, J. theor. biol., 241, 552-563, (2006)
[22] Stouffer, D.B.; Camacho, J., Quantitative patterns in the structure of model and empirical food webs, Ecology, 86, 1301-1311, (2005)
[23] Uchida, S.; Drossel, B., Relation between complexity and stability in food webs with adaptive behavior, J. theor. biol., 247, 713-722, (2007)
[24] Williams, R.J.; Martinez, N.D., Simple rules yield complex food webs, Nature, 404, 180-183, (2000)
[25] Williams, R.J.; Martinez, N.D., Stabilization of chaotic and non-permanent food web dynamics, Eur. phys. J. B, 38, 297-303, (2004)
[26] Williams, R.J.; Martinez, N.D., Success and its limits among structural models of complex food webs, J. animal ecol., 77, 512-519, (2008)
[27] Yodzis, P., The stability of real ecosystems, Nature, 289, 674-676, (1981)
[28] Yodzis, P.; Innes, S., Body size and consumer – resource dynamics, Amer. naturalist, 139, 6, 1151-1175, (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.