×

Complexity does not affect stability in feasible model communities. (English) Zbl 1398.92271

Summary: The complexity-stability relation is a central issue in ecology. In this paper, we show how the sampling method most often used to parameterize an ecological community, can affect the conclusions about whether or not complexity promotes stability and we suggest a sampling algorithm that overcomes the problem. We also illustrate the importance of treating feasibility separately from stability when constructing model communities. Using model Lotka-Volterra competition communities we found that probability of feasibility decreases with increasing interaction strength and number of species in the community. However, for feasible systems we found that local stability probability and resilience do not significantly differ between communities with few or many species, in contrast with earlier studies that, did not account for feasibility and concluded that species-poor communities had higher probability of being locally stable than species-rich communities.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
60F05 Central limit and other weak theorems
Full Text: DOI

References:

[1] Anderson, H.M.; Hutson, V.; Law, R., On the conditions for permanence of species in ecological communities, Am. nat., 139, 3, 663-668, (1992)
[2] Bastolla, U.; Lässig, M.; Manrubia, S.C.; Valleriani, A., Biodiversity in model ecosystems, I: coexistence conditions for competing species, J. theor. biol., 235, 4, 521-530, (2005) · Zbl 1440.92068
[3] Berlow, E.L.; Neutel, A.-M.; Cohen, J.E.; de Ruiter, P.C.; Ebenman, B.; Emmerson, M.; Fox, J.W.; Jansen, V.A.A.; Iwan Jones, J.; Kokkoris, G.D.; Logofet, D.O.; McKane, A.J.; Montoya, J.M.; Petchey, O., Interaction strengths in food webs: issues and opportunities, J. anim. ecol., 73, 585-598, (2004)
[4] Borrvall, C.; Ebenman, B.; Jonsson, T., Biodiversity lessens the risk of cascading extinction in model food webs, Ecol. lett., 3, 2, 131-136, (2000)
[5] 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)
[6] Chen, X.; Cohen, J.E., Global stability, local stability and permanence in model food webs, J. theor. biol., 212, 2, 223-235, (2001)
[7] Christianou, M.; Ebenman, B., Keystone species and vulnerable species in ecological communities: strong or weak interactors?, J. theor. biol., 235, 95-103, (2005) · Zbl 1445.92293
[8] Cohen, J.E.; Briand, F.; Newman, C.M., Community food webs: data and theory, (1990), Springer New York · Zbl 0719.92022
[9] De Angelis, D.L., Stability and connectance in food web models, Ecology, 56, 1, 238-243, (1975)
[10] de Ruiter, P.C.; Neutel, A.M.; Moore, J.C., Energetics, patterns of interaction strengths, and stability in real ecosystems, Science, 269, 5228, 1257-1260, (1995)
[11] Drossel, B.; Higgs, P.G.; McKane, A.J., The influence of predator – prey population dynamics on the long-term evolution of food web structure, J. theor. biol., 208, 1, 91-107, (2001)
[12] Elton, C.S., The ecology of invasions by plants and animals, (1958), Chapman & Hall London
[13] Emmerson, M.C.; Raffaelli, D., Predator – prey body size, interaction strength and the stability of a real food web, J. anim. ecology, 73, 3, 399-409, (2004)
[14] Emmerson, M.C.; Yearsley, J.M., Weak interactions, omnivory and emergent food-web properties, Proc. R. soc. London ser. B, 271, 1537, 397-405, (2004)
[15] Frank, D.A.; McNaughton, S.J., Stability increases with diversity in plant communities: empirical evidence from the 1988 yellowstone drought, Oikos, 62, 360-362, (1991)
[16] Gardner, M.R.; Ashby, W.R., Connectance of large dynamical (cybernetic) systems: critical values of stability, Nature, 228, 784, (1970)
[17] Gilpin, M., Stability of feasible predator – prey systems, Nature, 254, 137-139, (1975)
[18] Givnish, T.J., Does diversity beget stability?, Nature, 371, 113-114, (1994)
[19] Goodman, D., The theory of diversity – stability relationships in ecology, Quart. rev. biol., 50, 3, 237-266, (1975)
[20] Hall, S.; Raffaelli, D., Food webs: theory and reality, (), 187-239
[21] Hastings, A., Food web theory and stability, Ecology, 69, 6, 1665-1668, (1988)
[22] Hastings, A., What equilibrium behavior of lotka – volterra models does not tell us about food webs, (), 211-217
[23] Haydon, D., Pivotal assumptions determining the relationship between stability and complexity: an analytical synthesis of the stability – complexity debate, Am. nat., 144, 1, 14-29, (1994)
[24] Haydon, D.T., Maximally stable model ecosystems can be highly connected, Ecology, 81, 9, 2631-2636, (2000)
[25] Hutson, V.; Law, R., Permanent coexistence in general models of three interacting species, J. math. biol., 21, 285-298, (1985) · Zbl 0579.92023
[26] Jansen, V.A.A.; Kokkoris, G.D., Complexity and stability revisited, Ecol. lett., 6, 6, 498-502, (2003)
[27] Jonsson, T.; Ebenman, B., Effects of predator – prey body size ratios on the stability of food chains, J. theor. biol., 193, 3, 407-417, (1998)
[28] King, A.W.; Pimm, S.L., Complexity, diversity, and stability: a reconciliation of theoretical and empirical results, Am. nat., 122, 2, 229-239, (1983)
[29] Kokkoris, G.D.; Troumbis, A.Y.; Lawton, J.H., Patterns of species interaction strength in assembled theoretical competition communities, Ecol. lett., 2, 2, 70-74, (1999)
[30] Kokkoris, G.D.; Jansen, V.A.A.; Loreau, M.; Troumbis, A.Y., Variability in interaction strength and implications for biodiversity, J. anim. ecol., 71, 362-371, (2002)
[31] Kondoh, M., Foraging adaptation and the relationship between food-web complexity and stability, Science, 299, 1388-1391, (2003)
[32] Krause, A.E.; Frank, K.A.; Mason, D.M.; Ulanowicz, R.E., Compartments revealed in food-web structure, Nature, 426, 6964, 282-285, (2003)
[33] 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)
[34] Law, R.; Morton, R.D., Alternative permanent states of ecological communities, Ecology, 74, 5, 1347-1361, (1993)
[35] Law, R.; Morton, R.D., Permanence and the assembly of ecological communities, Ecology, 77, 3, 762-775, (1996)
[36] Lawlor, L.R., A comment on randomly constructed ecosystem models, Am. nat., 112, 445-447, (1978)
[37] Lewontin, R.C., The meaning of stability, (), 13-24
[38] MacArthur, R.H., Fluctuation of animal populations and a measure of community stability, Ecology, 36, 533-536, (1955)
[39] May, R., Will a large complex system be stable?, Nature, 238, 413-414, (1972)
[40] May, R., Stability and complexity in model ecosystems, (1973), Princeton University Press Princeton, NJ, USA
[41] McCann, K.; Hastings, A., Re-evaluating the omnivory – stability relationship in food webs, Proc. R. soc. London B, 264, 1385, 1249-1254, (1997)
[42] McCann, K.; Yodzis, P., Nonlinear dynamics and population disappearances, Am. nat., 144, 5, 873-879, (1994)
[43] McCann, K.S.; Hastings, A.; Huxel, G.R., Weak trophic interactions and the balance of nature, Nature, 395, 6704, 794-798, (1998)
[44] McNaughton, S.J., Diversity and stability of ecological communities: a comment on the role of empiricism in ecology, Am. nat., 111, 515-525, (1977)
[45] Mills, L.S.; Soule, M.E.; Doak, D.F., The keystone-species concept in ecology and conservation, Bioscience, 43, 4, 219-224, (1993)
[46] Montoya, J.M.; Solé, R.V., Topological properties of food webs: from real data to community assembly models, Oikos, 102, 614-622, (2003)
[47] Moore, J.C.; Hunt, H.W., Resource compartmentation and the stability of real ecosystems, Nature, 333, 261-263, (1988)
[48] Neutel, A.; Heesterbeek, J.A.P.; de Ruiter, P.C., Stability in real food webs: weak links in long loops, Science, 296, 1120-1123, (2002)
[49] Odum, E., Fundamentals of ecology, (1953), Saunders Philadelphia
[50] Paine, R.T., Food-web analysis through field measurement of per capita interaction strength, Nature, 355, 6355, 73-75, (1992)
[51] Pimentel, D., Species diversity and insect population outbreaks, Ann. entomol. soc. am., 54, 76-86, (1961)
[52] Pimm, S.L., Complexity and stability: another look at Macarthour’s original hypothesis, Oikos, 33, 351-357, (1979)
[53] Pimm, S.L., Food webs, (1982), Chapman & Hall London, UK
[54] Pimm, S.L.; Lawton, J.H., Number of trophic levels in ecological communities, Nature, 268, 329-331, (1977)
[55] Power, M.E.; Tilman, D.; Estes, J.A.; Menge, B.A.; Bond, W.J.; Mills, L.S.; Daily, G.; Castilla, J.C.; Lubchenco, J.; Paine, R.T., Challenges in the quest for keystones, Bioscience, 46, 8, 609-620, (1996)
[56] Roberts, A., The stability of a feasible random ecosystem, Nature, 251, 607-608, (1974)
[57] Rozdilsky, I.D.; Stone, L.; Solow, A., The effects of interaction compartments on stability for competitive systems, J. theor. biol., 227, 2, 277-282, (2004) · Zbl 1439.92200
[58] Tilman, D., Biodiversity: population versus ecosystem stability, Ecology, 77, 350-363, (1996)
[59] Tilman, D.; Downing, J.A., Biodiversity and stability in grasslands, Nature, 367, 363-365, (1994)
[60] Williams, R.J.; Berlow, E.L.; Dunne, J.A.; Barabasi, A.-L.; Martinez, N.D., Two degrees of separation in complex food webs, Proc. natl. acad. sci. USA, 99, 20, 12913-12916, (2002)
[61] Woodward, G.; Ebenman, B.; Emmerson, M.; Montoya, J.M.; Olesen, J.M.; Valido, E.; Warren, P.H., Body size in ecological networks, Trends ecol. evol., 20, 7, 402-409, (2005)
[62] Yodzis, P., The stability of real ecosystems, Nature, 289, 674-676, (1981)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.