Abstract
Deterministic models dominated theory in ecology for much of its history despite recognition of the role of unpredictable environmental factors in population dynamics (Hutchinson, 1951, 1961; Andrewartha and Birch, 1954, 1984; Grubb, 1977, 1986; Sale, 1977; Wiens, 1977, 1986; Connell, 1978; Hubbell, 1979, 1980; Murdoch, 1979; Connell and Sousa, 1983; Sale and Douglas, 1984; Strong, 1984, 1986). Mathematical techniques for stochastic modeling were poorly developed and poorly understood. As a consequence, most ecological thinking about the role of stochastic factors was purely intuitive. Progress in stochastic population and community models has now allowed rigorous deduction to replace intuition. This progress has shown more complicated and intricate roles for stochastic factors than previously invisaged; but as is shown in this chapter, once elucidated, these roles can be understood intuitively.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abrams P (1984) Variability in resource consumption rates and the coexistence of competing species. Theor Pop Biol 25: 106–124
Andrewartha HG, LC Birch (1954) The Distribution and Abundance of Animals. Chicago University Press, Chicago
Andrewartha HG, Birch LC (1984) The Ecological Web: More on the Distribution and Abundance of Animals. Chicago University Press, Chicago
Armstrong RA, McGehee R (1980) Competitive exclusion. Am Nat 115: 151–170
Atkinson WD, Shorrocks B (1981) Competition on a divided and ephemeral resource: a simulation model. J Anim Ecol 50: 461–471
Bailey VA, Nicholson AJ, Williams EJ (1962) Interactions between hosts and parasites when some hosts are more difficult to find than others. J Theor Biol 3: 1–18
Bulmer MG (1985) Selection for iteroparity in a variable environment. Am Nat 126: 63–71
Caswell H (1978) Predator-mediated coexistence: a nonequilibrium model. Am Nat 112: 127–154
Chesson PL (1978) Predator-prey theory and variability. Annu Rev Ecol Syst 9: 323–347
Chesson PL (1981) Models for spatially distributed populations: the effect of
within-patch variability. Theor Pop Biol 19:288–325
Chesson PL (1982) The stabilizing effect of a random environment. J Math Biol 15: 1–36
Chesson PL (1984a) The storage effect in stochastic population models. Lect Notes in Biomath 54: 76–89
Chesson PL (1984b) Variable predators and switching behavior. Theor Pop Biol 26: 1–26
Chesson PL (1985) Coexistence of competitors in spatially and temporally varying environments: a look at the combined effects of different sorts of variability. Theor Pop Biol 28: 263–287
Chesson PL (1988) Interactions between environment and competition: how fluctuations mediate coexistence and competitive exclusion. Lect Notes Biomath 77: 51–71
Chesson, PL (1989) A general model of the role of environmental variability in communities of competing species. Lect Math in the Life Sci 20, 97–123
Chesson PL, Huntly N (1988) Community consequences of life-history traits in a variable environment. Ann Zool Fenn 25:5–16 Chesson PL, Huntly N (1989) Short-term instabilities and long-term community dynamics. Trends Ecol Evol 4: 293–298
Chesson PL, Murdoch WW (1986) Aggregation of risk: relationships among host- parasitoid models. Am Nat 127: 696–715
Chesson PL, Warner RR (1981) Environmental variability promotes coexistence in lottery competitive systems. Am Nat 117: 923–943
Colwell RK (1974) Predictability, constancy and contingency of periodic phenomena. Ecology 55: 1148–1153
Comins HN, Noble IR (1985) Dispersal, variability and transient niches: species coexistence in a uniformly variable environment. Am Nat 126: 706–723
Connell JH (1978) Diversity in tropical rainforests and coral reefs. Science 199: 1302–1310
Connell JH (1979) Tropical rainforests and coral reefs as open non-equilibrium systems. In Anderson RM, Turner BD, Taylor LR (eds) Population Dynamics. Blackwell, Oxford, pp 141–163
Connell JH, Sousa WP (1983) On the evidence needed to judge ecological stability or persistence. Am Nat 121: 789–824
Crowley PH (1981) Dispersal and the stability of predator-prey interactions. Am Nat 118: 673–701
Ellner SP (1984) Stationary distributions for some difference equation population models. J Math Biol 19: 169–200
Ellner S (1987a) Alternate plant life history strategies. Vegetatio 69: 199–208
Ellner S (1987b) Competition and dormancy: a reanalysis and review. Am Nat 130: 798–803
Feller W (1971) An Introduction to Probability Theory and Its Applications. Vol 2, 2nd ed. Wiley, New York
Gillespie JH (1978) A general model to account for enzyme variation in natural populations. V. The SAS-CCF model. Theor Pop Biol 14: 1–45
Gilpin ME (1987) Spatial structure and population vulnerability. In Soule ME (ed) Viable Populations for Conservation. Cambridge University Press, Cambridge, pp 125–139
Grubb PJ (1977) The maintenance of species richness in plant communities: the regeneration niche. Biol Rev 52: 107–145
Grubb PJ (1986) Problems posed by sparse and patchily distributed species in species-rich plant communities. In Diamond J, Case T (eds) Community Ecology. Harper & Row, New York, pp 207–225
Hassell MP (1978) The Dynamics of Arthropod Predator-Prey Systems. Princeton University Press, Princeton
Hastings A (1977) Spatial heterogeneity and the stability of predator-prey systems. Theor Pop Biol 12: 37–48
Hastings A (1978) Spatial heterogeneity and the stability of predator-prey systems: predator mediated coexistence. Theor Pop Biol 14: 380–395
Hastings A (1980) Disturbance, coexistence, history and competition for space. Theor Pop Biol 18: 361–373
Hastings A, Caswell H (1979) Role of environmental variability in the evolution of life history strategies. Proc Natl Acad Sci USA 76: 4700–4703
Hatfield J, Chesson PL (1989) Diffusion approximation and stationary distribution for the lottery competition model. Theor Pop Biol 36: 251–266
Hubbell SP (1979) Tree dispersion, abundance, and diversity in a tropical dry forest. Science 203: 1299–1309
Hubbell SP (1980) Seed predation and the coexistence of tree species in tropical forests. Oikos 35: 214–299
Hutchinson GE (1951) Copepodology for the ornithologist. Ecology 32: 571–577
Hutchinson GE (1961) The paradox of the plankton. Am Nat 95: 137–145
Ives A (1988) Covariance, coexistence and the population dynamics of two competitors using patchy resource. J Theor Biol 133: 345–361
Ives AR, May RM (1985) Competition within and between species in a patchy environment: relations between macroscopic and microscopic models. J Theor Biol 115: 65–92
Iwasa Y Roughgarden J (1986) Interspecific competition and among metapopulations with space-limited subpopulations. Theor Pop Biol 30: 194–214
Lande R, Barrowclough G (1987) Effective population size, genetic variation and their use in population management. In Soule ME (ed) Viable Populations for Conservation. Cambridge University Press, Cambridge, pp 87–123
Leigh EG Jr (1981) The average life time of a population in a varying environment. J Theor Biol 90: 213–239
Levins R (1979) Coexistence in a variable environment. Am Nat 114: 765–783
Lewontin RC, Cohen D (1969) On population growth in a randomly varying environment. Proc Natl Acad Sci USA 62: 1056–1060
Ludwig D (1976) Persistence of dynamical systems under random perturbations. Soc Ind Appl Math Am Math Soc Proc 10: 87–104
May RM (1973) Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton
May RM (1978) Host-parasitoid systems in patchy environments: a phenomenological model. J Anim Ecol 47: 833–844
May RM, Oster GF (1976) Bifurcations and dynamic complexity in simple ecological models. Am Nat 110: 573–599
Maynard Smith J (1974) Models in Ecology. Cambridge University Press, Cambridge
Milligan BG (1986) Invasion and coexistence of two phenotypically variable species. Theor Pop Biol 30: 245–270
Murdoch WW (1979) Predation and the dynamics of prey populations. Fortschr Zool 25: 245–310
Pacala SW (1987) Neighborhood models of plant population dynamics. 3. Models with spatial heterogeneity in the physical environment. Theor Pop Biol 31:359– 392
Pacala SW, Roughgarden J (1982) Spatial heterogeneity and interspecific competition. Theor Pop Biol 121: 92–113
Pimm SL, Jones HL, Diamond J (1988) On the risk of extinction. Am Nat 132: 757–785
Reeve JD (1988) Environmental variability, migration, and persistence in host- parasitoid systems. Am Nat 132: 810–836
Roughgarden J (1974) Niche width: biogeographic patterns among Anolis lizard populations. Am Nat 108: 429–442
Roughgarden J (1979) Theory of Population Genetics and Evolutionary Ecology: An Introduction. Macmillan, New York
Sale PF (1977) Maintenance of high diversity in coral reef fish communities. Am Nat 111: 337–359
Sale PF, Douglas WA (1984) Temporal variability in the community structure of fish on coral patch reefs and the relation of community structure to reef structure. Ecology 65: 409–422
Shigesada N (1984) Spatial distribution of rapidly dispersing animals in heterogeneous environments. Lect Notes Biomath 54: 478–501
Shigesada N, Roughgarden J (1982) The role of rapid dispersal in the population dynamics of competition. Theor Pop Biol 21: 253–373
St Amant J (1970) The mathematics of predator-prey interactions. MA thesis, University of California, Santa Barbara
Strong DR (1984) Density vague ecology and liberal population regulation in insects. In Price PW, Slobodchikoff CN (eds) A New Ecology: Novel Approaches to Interactive Systems. Wiley, New York, pp 313–327
Strong DR (1986) Density vagueness: abiding the variance in the demography of real populations. In Diamond J, Case TJ (eds) Community Ecology. Harper & Row, New York, pp 257–268
Tilman D (1982) Resource Competition and Community Structure. Princeton University Press, Princeton
Turelli M, Petri D (1980) Density dependent selection in a random environment. Proc Natl Acad Sei USA 77: 7501–7505
Wiens JA (1977) On competition and variable environments. Am Sei 65: 590–597
Wiens JA (1986) Spatial and temporal variation in studies of shrubsteppe birds. In Diamond J, Case T (eds) Community Ecology. Harper & Row, New York, pp 154–172
Yodzis P (1978) Competition for Space and the Structure of Ecological Communities. Lect Notes Biomath 25: 1–288
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Chesson, P. (1991). Stochastic Population Models. In: Kolasa, J., Pickett, S.T.A. (eds) Ecological Heterogeneity. Ecological Studies, vol 86. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3062-5_7
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3062-5_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7781-1
Online ISBN: 978-1-4612-3062-5
eBook Packages: Springer Book Archive