Abstract
The combination of age or size structure and density-dependent recruitment has a defining influence on the dynamics of many plant and animal populations. Over the past 40 years, population biologists have combined mathematical models and field data in attempts to better understand the dynamics of such populations. Here I present a tutorial review of the interplay between mathematical and empirical biology that has shaped our understanding of populations with these characteristics.
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Literature Cited
Abbiati, M., G. Buffoni, G. Caforio, G. Di Col, and G. Santangelo. 1992. Harvesting, predation and competition effects on a red coral population. Netherlands Journal of Sea Research 30: 219–228.
Allen, R. L., and P. Basasibwaki. 1974. Properties of age structure models for fish populations. Journal of the Fisheries Research Board of Canada 31: 1119–1125.
van der Heiden, U., and M. C. Mackey. 1982. Dynamics of destruction and renewal. Journal of Mathematical Biology 16: 75–101.
Beddington, J. R. 1974. Age distribution and the stability of simple discrete time population models. Journal of Theoretical Biology 47: 65–74.
Bence, J. R., and R. M. Nisbet. 1989. Space-limited recruitment in open systems: The importance of time delays. Ecology 70: 1434–1441.
Bergh, M. O., and W. M. Getz. 1988. Stability of discrete age-structured and aggregated delay-difference population models. Journal of Mathematical Biology 26: 551–581.
Botsford, L. W. 1981. The effects of increased individual growth rates on depressed population size. American Naturalist 117: 38–63.
Botsford, L. W. 1984. Effect of individual growth rates on expected behavior of the northern California Dungeness crab (Cancer magister) fishery. Canadian Journal of Fisheries & Aquatic Science 41: 99–107.
Botsford, L. W. 1986. Effects of environmental forcing on age-structured populations: Northern California Dungeness crab (Cancer magister) as an example. Canadian Journal of Fisheries & Aquatic Science 43: 2345–2352.
Botsford, L. W. 1991. Crustacean egg production and fisheries management. Pp. 379–394 in A. M. Wenner, ed., Crustacean Egg Production. A. A. Balkema, Rotterdam.
Botsford, L. W. 1992a. Further analysis of Clark’s delayed-recruitment model. Bulletin of Mathematical Biology 54: 275–293.
Botsford, L. W. 1992b. Individual state structure in population models. Pp. 213–236 in D. L. DeAngelis and L. J. Gross, eds., Individual-Based Models and Approaches in Ecology. Chapman & Hall, New York.
Botsford, L. W., and R. C. Hobbs. 1995. Recent advances in the understanding of cyclic behavior of Dungeness crab (Cancer magister) populations. International Council for the Exploration of the Sea Marine Sciences Symposium 199: 157–196.
Botsford, L. W., and D. E. Wickham. 1978. Behavior of age-specific, density-dependent models and the northern California Dungeness crab (Cancer magister) fishery. Journal of the Fisheries Research Board of Canada 35: 833–843.
Botsford, L. W., R. D. Methot, and W. E. Johnston. 1983. Effort dynamics of the northern California Dungeness crab (Cancer magister) fishery. Canadian Journal of Fisheries & Aquatic Science 40: 337–346.
Botsford, L. W., D. A. Armstrong, and J. Shenker. 1989. Oceanographic influences on the dynamics of commercially fished populations. Pp. 511–565 in M. R. Landry and B. M. Hickey, eds., Coastal Oceanography of Washington and Oregon. Elsevier, Amsterdam.
Botsford, L. W., C. L. Moloney, A. Hastings, J. L. Largier, T. M. Powell, K. Higgins, and J. F. Quinn. 1994. The influence of spatially and temporally varying oceanographic conditions on meroplanktonic metapopulations. Deep-Sea Research II 41: 107–145.
Caswell, H., H. E. Koenig, J. A. Resh, and Q. E. Ross. 1972. An introduction to systems science for ecologists. Pp. 3–78 in B. C. Patten, ed., Systems Analysis and Simulation in Ecology. Academic Press, New York.
Caughley, G. 1970. Eruption of ungulate populations with emphasis on Himalayan Thar in New Zealand. Ecology 51: 53–72.
Clark, C. W. 1976. A delayed-recruitment model of population dynamics, with an application to baleen whale populations. Journal of Mathematical Biology 3: 381–391.
Diekmann, O., R. M. Nisbet, W. S. C. Gurney, and F. van den Bosch. 1986. Simple mathematical models for cannibalism: A critique and a new approach. Mathematical Biosciences 78: 21–46.
Dong, Q., and G. A. Polis. 1992. The dynamics of cannibalistic populations: A foraging perspective. Pp. 13–37 in. M. A. Elgar and B. Crespi, eds., Cannibalism: Ecology and Evolution among Diverse Taxa. Oxford University Press.
Fox, L. R. 1975. Cannibalism in natural populations. Annual Review of Ecology & Systematics 6: 87–106.
Frauenthal, J. C. 1975. A dynamic model for human population growth. Theoretical Population Biology 8: 64–73.
Gabriel, W. 1985. Overcoming food limitation by cannibalism: A model study on cyclopoids. Archiv fur Hydrobiologie 21: 373–381.
Gaines, S., and J. Roughgarden. 1985. Larval settlement rate: A leading determinant of structure in an ecological community of the marine intertidal zone. Proceedings of the National Academy of Sciences (USA) 82: 3707–3711.
Gilpin, M., and I. Hanski. 1991. Metapopulation Dynamics: Empirical and Theoretical Investigations. Academic Press, London.
Guckenheimer, J., G. Oster, and A. Ipaktchi. 1977. The dynamics of density-dependent population models. Journal of Mathematical Biology 4: 101–147.
Gurney, W. S. C., R. M. Nisbet, and J. H. Lawton. 1983. The systematic formulation of tractable single-species population models incorporating age structure. Journal of Animal Ecology 52: 479–495.
Hastings, A. 1987. Cycles in cannibalistic egg-larval interactions. Journal of Mathematical Biology 24: 651–666.
Hastings, A. 1992. Age-dependent dispersal is not a simple process: Density dependence, stability and chaos. Theoretical Population Biology 41: 388–400.
Hastings, A., and R. F. Costantino. 1987. Cannibalistic egg-larva interactions in Tribolium: An explanation for the oscillations in population numbers. American Naturalist 130: 36–52.
Hastings, A., and R. F. Costantino 1991. Oscillations in population numbers: Age-dependent cannibalism. Journal of Animal Ecology 60: 471–482.
Hastings, A., and K. Higgins. 1994. Persistence of transients in spatially structured ecological models. Science (Washington, D.C.) 263: 1133–1136.
Higgins, K., A. Hastings, and L. W. Botsford. In press. Adult survivorship in the delayed-recruitment model: Influence on dynamics. American Naturalist.
Hobbs, R. C., and L. W. Botsford. 1989. Dynamics of an age-structured prey with density-and predation-dependent recruitment: The Dungeness crab and a nemertean egg predator worm. Theoretical Population Biology 36: 1–22.
Horwood, J. W. 1983. A general linear theory for the variance of yield from fish stocks. Mathematical Biosciences 64: 203–225.
Horwood, J. W. 1984. The variance and response of biological systems to variability in births and survivals. (Institute of Mathematics and Its Applications) Journal of Mathematics Applied in Medicine & Biology 1: 309–323.
Horwood, J. W., and J. A. Shepherd. 1981. The sensitivity of age-structured populations to environmental variability. Mathematical Biosciences 57: 59–82.
Keyfitz, N. 1972. Population waves. Pp. 1–38 in T. N. E. Greville, ed., Population Dynamics. Academic Press, New York.
Lee, R. 1974. The formal dynamics of controlled populations and the echo, the boom and the bust. Demography 11: 563–585.
Leopold, A., L. K. Sowls, and D. L. Spencer. 1947. A survey of over-populated deer ranges in the United States. Journal of Wildlife Management 11: 162–177.
Levin, S. A. 1981. Age structure and stability in multiple-age spawning populations. Pp. 21–45 in T. L. Vincent and J. M. Skowronski, eds., Renewable Resource Management. Springer-Verlag, New York.
Levin, S. A., and C. P. Goodyear. 1980. Analysis of an age-structured fishery model. Journal of Mathematical Biology 9: 245–274.
May, R., and G. F. Oster. 1976. Bifurcations and dynamic complexity in simple ecological models. American Naturalist 110: 573–599.
McKelvey, R., D. Hankin, K. Yanosko, and C. Snygg. 1980. Stable cycles in multistage recruitment models: An application to the northern California Dungeness crab (Cancer magister) fishery. Canadian Journal of Fisheries & Aquatic Science 37: 2323–2345.
Menshutkin, V. V. 1964. Population dynamics studied by representing the population as a cybernetic system. Voprosy Ikthiologii 1: 23–33.
Murdoch, W. W., and E. McCauley. 1985. Three distinct types of dynamic behavior shown by a single planktonic system. Nature 316: 628–630.
Nisbet, R. M., and J. R. Bence. 1989. Alternative dynamic regimes for canopy-forming kelp: A variant on density-vague population regulation. American Naturalist 134: 377–408.
Pascual, M., and H. Caswell. 1991. The dynamics of a size-classified benthic population with reproductive subsidy. Theoretical Population Biology 39: 129–147.
Pennycuick, C. J., R. M. Compton, and L. Beckingham. 1968. A computer model for simulating the growth of a population of two interacting populations. Journal of Theoretical Biology 18: 316–329.
Polis, G. 1981. The evolution and dynamics of intraspecific predation. Annual Review of Ecology & Systematics 12: 125–151.
Possingham, H., S. Tuljapurkar, J. Roughgarden, and M. Wilks. 1994. Population cycling in space-limited organisms subject to density-dependent predation. American Naturalist 143: 563–582.
Reed, W. J. 1983. Recruitment variability and age structure in harvested animal populations. Mathematical Biosciences 65: 239–268.
Ricker, W. E. 1954. Stock and recruitment. Journal of the Fisheries Research Board of Canada 11: 559–623.
Rorres, C. 1976. Stability of an age-specific population with density-dependent fertility. Theoretical Population Biology 10: 26–46.
Roughgarden, J., and Y. Iwasa. 1986. Dynamics of a metapopulation with space-limited subpopulations. Theoretical Population Biology 29: 235–261.
Roughgarden, J., Y. Iwasa, and C. Baxter. 1985. Demographic theory for an open marine population with space-limited recruitment. Ecology 66: 54–67.
Strong, D. R. 1986. Density-vagueness: Abiding the variance in the demography of real populations. Pp. 257–268 in J. Diamond and T. J. Case, eds., Community Ecology. Harper & Row, New York.
Tuljapurkar, S. 1987. Cycles in nonlinear age-structured models. I. Renewal equations. Theoretical Population Biology 32: 26–41.
Tuljapurkar, S., C. Boe, and K. W. Wachter. 1994. Nonlinear feedback dynamics in fisheries: Analysis of the Deriso-Schnute model. Canadian Journal of Fisheries & Aquatic Science 51: 1462–1473.
Usher, M. B. 1972. Developments in the Leslie matrix model. Pp. 29–60 in J. N. R. Jeffers, ed., Mathematical Models in Ecology. British Ecological Society Symposium 12. Blackwell Scientific, Oxford.
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Botsford, L.W. (1997). Dynamics of Populations with Density-Dependent Recruitment and Age Structure. In: Tuljapurkar, S., Caswell, H. (eds) Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. Population and Community Biology Series, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5973-3_12
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DOI: https://doi.org/10.1007/978-1-4615-5973-3_12
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