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Coexistence of temporally segregated competitors in a cyclic environment. (English) Zbl 0683.92019

Summary: Coexistence of temporally segregated competitors in a cyclic environment (e.g., univoltine insect species active in different seasons) is investigated using discrete dynamical models involving two consumers competing for the exploitation of one resource. Coexistence turns out to hinge first and foremost on the difference between the time scales of resource and consumer dynamics. When the dynamics of the resource is discrete with a time step equal to or only slightly shorter than that of the consumers, temporal segregation of consumers does not make for their coexistence. Beyond a critical frequency of resource dynamics, coexistence becomes possible between completely temporally segregated species, and gets easier as resource dynamics gets more frequent (tending to continuity) and faster, and as the consumers are more efficient and more similar. When the time scale of resource dynamics is short enough, coexistence also becomes possible between species that overlap in time. However, there is a limiting amount of temporal overlap they can tolerate, which increases as their efficiency, their similarity, and resource availability increase.

MSC:

92D40 Ecology
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[1] Armstrong, R.A.; McGehee, R., Competitive exclusion, Amer. nat, 115, 151-170, (1980)
[2] Chesson, P.L., Environmental variation and the coexistence of species, (), 240-256
[3] Cushing, J.M., Two species competition in a periodic environment, J. math. biol, 10, 385-400, (1980) · Zbl 0455.92012
[4] Cushing, J.M., Periodic two-predator, one-prey interactions and the time sharing of a resource niche, SIAM J. appl. math, 44, 392-410, (1984) · Zbl 0554.92016
[5] Cushing, J.M., Periodic Lotka-Volterra competition equations, J. math. biol, 24, 381-403, (1986) · Zbl 0608.92019
[6] Grenney, W.J.; Bella, D.A.; Curl, H.C., A theoretical approach to interspecific competition in phytoplankton communities, Amer. nat, 107, 405-425, (1973)
[7] Hsu, S.B.; Hubbel, S.P.; Waltman, P., Competing predators, SIAM J. appl. math, 35, 617-625, (1978) · Zbl 0394.92025
[8] Hsu, S.B.; Hubbel, S.P.; Waltman, P., A contribution to the theory of competing predators, Ecol. monogr, 48, 337-349, (1978)
[9] Hutchinson, G.E., The paradox of the plankton, Amer. nat, 95, 137-145, (1961)
[10] Levin, S.A.; Udovic, J.D., A mathematical model of coevolving populations, Amer. nat, 111, 657-675, (1977)
[11] Levins, R., Evolution in communities near equilibrium, (), 16-50
[12] Levins, R., Coexistence in a variable environment, Amer. nat, 114, 765-783, (1979)
[13] Loreau, M., Niche differentiation and community organization in forest carabid beetles, (), 465-487
[14] Loreau, M., Determinants of the seasonal pattern in the niche structure of a forest carabid community, Pedobiologia, 31, 75-87, (1988)
[15] MacArthur, R.H.; Levins, R., Competition, habitat selection and character displacement in a patchy environment, (), 1207-1210
[16] May, R.M., Stability and complexity in model ecosystems, (1974), Princeton Univ. Press Princeton, NJ
[17] May, R.M.; Oster, G.F., Bifurcations and dynamic complexity in simple ecological models, Amer. nat, 110, 573-599, (1976)
[18] de Mottoni, P.; Schiaffino, A., Competition systems with periodic coefficients: a geometric approach, J. math. biol, 11, 319-385, (1981) · Zbl 0474.92015
[19] Namba, T., Competitive co-existence in a seasonally fluctuating environment, J. theor. biol, 111, 369-386, (1984)
[20] Puccia, C.J.; Levins, R., Qualitative modeling of complex systems, (1985), Harvard Univ. Press Cambridge, MA
[21] Rosenblat, S., Population models in a periodically fluctuating environment, J. math. biol, 9, 23-36, (1980) · Zbl 0426.92018
[22] Schoener, T.W., Effects of density-restricted food encounter on some single-level competition models, Theor. pop. biol, 13, 365-381, (1978)
[23] Smith, H.L., Competitive coexistence in an oscillating chemostat, SIAM J. appl. math, 40, 498-522, (1981) · Zbl 0467.92018
[24] Stewart, F.M.; Levin, B.R., Partitioning of resources and the outcome of interspecific competition: A model and some general considerations, Amer. nat, 107, 171-198, (1973)
[25] Vance, R.R., The stable coexistence of two competitors for one resource, Amer. nat, 126, 72-86, (1985)
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