Locking life-cycles onto seasons: Circle-map models of population dynamics and local adaptation

  • William S. C. Gurney
  • Philip H. Crowley
  • Roger M. Nisbet
Article

Abstract

We have formulated a model describing the timing of maturity and reproduction in briefly semelparous organisms whose development rate is primarily controlled by environmental factors. The model is expressed as a circle-map relating time of year at maturation in successive generations. The properties of this map enable us to determine the degree of synchrony to be expected between the life-cycles of members of a population exposed to a regular seasonal environment.

We have proved that organisms with a life-history composed of a contiguous series of stages, all with development driven by the same seasonal function, cannot phase-lock their life-cycles to the seasons. However if the organism exhibits facultative diapause induced by a critical time/critical development mechanism of the type proposed by Norling (1984a,b,c) then it will always succeed in phase-locking to a perfectly periodic driving function.

Within the context of this circle-map model we have examined population extinctions caused by attempting to over-winter in an inappropriate life-history stage, or by attempting to reproduce at a time of year when this is impossible. We have shown that the possibility of such extinctions limits both the shortness of the post-critical stage, and the lateness of the critical time.

We have examined the fitness of persistent cohorts as a function of critical time and development. We find that if the post-critical stage is riskier than the pre-critical then natural selection favors a short post-critical stage and a late critical time; the limitation of this process being dependent on the proportion of the growing season over which successful reproduction is possible.

We have determined the variation with life-cycle length (and hence latitude or altitude) of the maturation pattern corresponding to optimal life-history parameters. We find that for organisms which can mature only over a small part of the growing season the majority of any latitudinal gradient exhibits a unimodal maturation pattern. Organisms which can mature and reproduce over the majority of the growing season exhibit more complex patterns, but still exhibit substantial ranges of latitude over which unimodal or bimodal patterns are optimal.

Key words

Circle-maps Synchronization Phase-locking Local adaptation Dormancy 

References

  1. Andrewartha, H. G.: Diapause in relation to the ecology of insects. Biol. Rev. 27, 50–107 (1952)Google Scholar
  2. Bak, P.: The Devil's Staircase, Phys. Today Dec. 1986, 39–45 (see inset on p. 44) (1986)Google Scholar
  3. Baskin, J. M., Baskin, C. C.: The ecological life cycle of Campanula americana in northcentral Kentucky. Bull. Torrey Bot. Club 111, 329–337 (1984)CrossRefGoogle Scholar
  4. Baskin, J. M., Baskin, C. C.: Field emergence of Lamium amplexicaule L. and L. purpureum L. in relation to the annual seed dormancy cycle. Weed Res. 26, 185–190 (1987)CrossRefGoogle Scholar
  5. Beck, S. D., Apple, J. W.: Effects of temperature and photoperiod on voltinism of geographical populations of the European corn borer, Pyrausta nubilalis. J. Econ. Entomol. 54 550–558 (1961)Google Scholar
  6. Bradshaw, W. E., Lounibos, L. P.: Evolution of dormancy and its photoperiodic control in pitcher-plant mosquitoes. Evolution 31, 546–567 (1977)CrossRefGoogle Scholar
  7. Cohen, D.: Optimizing reproduction in a randomly varying environment. J. Theor. Biol. 16, 1–14 (1967)CrossRefGoogle Scholar
  8. Conover, D. O., Heins, S. W.: Adaptive variation in environmental and genetic sex determination in a fish. Nature 326, 496–498 (1987)CrossRefGoogle Scholar
  9. Corbet, P. S.: A biology of dragonflies. Chicago: Quadrangle Books 1963.Google Scholar
  10. Corbet P. S., Harvey, I. F., Abisgold, J., Morris, F.: Seasonal regulation in Pyrrhosoma nymphulla (Sulzer) (Zygoptera: Coenagrionidae) 2. Effect of photoperiod on larval development in spring and summer. Odonatologica 18, 333–348 (1989)Google Scholar
  11. Crowley, P. H., Nisbet, R. M., Gurney, W. S. C., Lawton, J. H.: Population regulation in animals with complex life-histories: formulation and analysis of a damselfly model. Adv. Ecol. Res. 17, 1–59 (1987)CrossRefGoogle Scholar
  12. Danilevsky, A. S.: Photoperiodism and seasonal development of insects. (English translation) London: Oliver & Boyd 1965Google Scholar
  13. De Stasio, B. T., Jr.: The seed bank of a freshwater crustacean: copepodology for the plantecologist. Ecology 70, 1377–1389 (1989)CrossRefGoogle Scholar
  14. Dingle, H., Alden, B. M., Blakley, N. R., Kopec, D., Miller, E. R.: Variation in photoperiodic response within and among species of milkweed bugs (Oncopeltus). Evolution 34, 356–370 (1980a)CrossRefGoogle Scholar
  15. Dingle, H., Blakley, N. R., Miller, E. R.: Variation in body size and flight performance in milkweed bugs (Oncopeltus). Evolution 34, 371–385 (1980b)CrossRefGoogle Scholar
  16. Endler, J. A.: Geographic variation, speciation, and clines. Princeton: Princeton University Press 1977Google Scholar
  17. Farquhar, I. E.: Ergodicity and related topics. In: Biel, J., Rae, J. (eds.) Irreversibility in the Many-Body Problem, pp. 37–40. New York London: Plenum Press 1972Google Scholar
  18. Flemming, I. A., Gross, M. R.: Latitudinal clines: a trade-off between egg number and size in Pacific Salmon. Ecology 71, 1–11 (1990)CrossRefGoogle Scholar
  19. Furunishi, S., Masaki, S.: Photoperiodic control of development in the ant-lion Hagenomyia micans (Neuroptera: Myrmeleontidae). Entomol. Gener. 9, 51–62 (1983)Google Scholar
  20. Gross, K. L.: Predictions of fate from rosette size in four “biennial” plant species: Verbascum thapsus, Oenothera biennis, Daucus carota, and Tragopogon dubius. Oecologia 48, 209–213 (1981)CrossRefGoogle Scholar
  21. Gurney, W. S. C., Nisbet, R. M., Lawton, J. H.: The systematic formulation of tractable single species models incorporating age-structure, J. Anim Ecol. 52, 479–495 (1983)CrossRefGoogle Scholar
  22. Hairston, N. G., Jr., Munns, W. R., Jr.: The timing of copepod diapause as an evolutionary stable strategy. Am Nat. 123, 733–751 (1984)CrossRefGoogle Scholar
  23. Harvell, C. D., Grosberg, R. K.: The timing of sexual maturity in clonal animals. Ecology 69, 1855–1864 (1988)CrossRefGoogle Scholar
  24. Istock, C. A.: Natural selection and life history variation: theory plus lessons from a mosquito. In: Denno, R. F., Dingle (eds.) Insect life history patterns, pp. 113–127. Berlin Heidelberg New York: Springer 1981Google Scholar
  25. Istock, C. A.: Some theoretical considerations concerning life history evolution: In: Dingle, H., Hegmann, J. P. (eds.) Evolution and genetics of life histories, pp. 7–20. Berlin Heidelberg New York: Springer 1982Google Scholar
  26. Istock, C. A.: The extent and consequences of heritable variation for fitness characters. In: King, C. E., Dawson P. S. (eds.) Population biology, pp. 61–96. New York: Columbia University Press 1983Google Scholar
  27. Janzen, D.: Bamboos. In: Halevy, A. H. (ed.) Handbook of Flowering II. Florida: CRC Press 1985Google Scholar
  28. Jordan, R. G.: Geographic differentiation in the development of Aedes sierrensis (Diptera: Culicidae) in nature. Can. Entomol. 112, 205–210 (1980)Google Scholar
  29. Kidokora, T., Masaki S.: Photoperiodic response in relation to variable voltinism in the ground cricket, Pteronemobius fascipes Walker (Orthoptera: Gryllidae). Japan. J. Ecol. 28, 290–298 (1978)Google Scholar
  30. Kishino, K.: Ecological studies on the local characteristics of seasonal development in the rice stem borer, Chilo suppressalis Walker. II. Local characteristics of diapause and development. Japan. J. Appl. Entomol. Zool. 14, 1–11 (1970a)Google Scholar
  31. Kishino, K.: Ecological studies on the local characteristics of seasonal development in the rice stem borer, Chilo suppressalis Walker. III. Seasonal development on the transitional zone from the univoltine to the bivoltine areas in the rice stem borer (in Japanese, English abstract). Japan. J. Appl. Entomol. Zool. 14, 182–190 (1970b)Google Scholar
  32. Klinkhamer, P. G. L., de Jong, T. J., Meelis, E.: Life-history variation and the control of flowering in short-lived monocarps. Oikos 49, 309–314 (1987)Google Scholar
  33. Lacey, E. P.: The genetic and environmental control of reproductive timing in a short lived moncapic species Daucus carota (Umbelliferacae). J. Ecol. 74, 73–86 (1986)CrossRefGoogle Scholar
  34. Lees, A. D.: In: Tauber, M. J., Tauber, C. A., Masaki, S. (eds.) Seasonal adaptations of insects, pp. vii-viii. Oxford: Oxford University Press 1986Google Scholar
  35. Lutz, P. E., Jenner, C. E.: Life-history and photoperiodic responses of nymphs of Tetragoneuria cynosura (Say). Biol. Bull, 127, 304–316 (1964)Google Scholar
  36. Lutz, P. E.: Effects of temperature and photoperiod on larval development in Lestes eurinus (Odonata: Lestidae). Ecology 49, 637–644 (1968)CrossRefGoogle Scholar
  37. Mangel, M., Clark C. W.: Dynamic modelling in behavioural ecology. Princeton, N.J.: Princeton Press 1988Google Scholar
  38. Masaki, S.: Climatic adaptation and photoperiodic response in the band-legged ground cricket. Evolution 26, 587–600 (1973)CrossRefGoogle Scholar
  39. Masaki, S.: Seasonal and latitudinal adaptations in life cycles of crickets. In: Dingle H. (ed.) Evolution of insect migration and diapause, pp. 72–100. Berlin Heidelberg New York: Springer 1978Google Scholar
  40. Norling, U.: The life-history and seasonal regulation of Aeshna viridis Eversm. in southern Sweden (Odonata). Entomol. Scand. 2, 170–190 (1971)Google Scholar
  41. Norling, U.: The life cycle and larval photoperiodic responses of Coenagrion hastulatum (Charp.) in two climatically different areas (Odonata: Zygoptera). Odonatological 13, 429–449 (1984a)Google Scholar
  42. Norling, U.: Photoperiodic control of larval development in Leucorrhinia dubia (Vander Linden): A comparison between populations from northern and southern Sweden (Anisoptera: Libellulidae). Odonatologica 13, 529–550 (1984b)Google Scholar
  43. Norling, U.: Life history patterns in the northern expansion of dragonflies. Adv. Odonatol. 2, 127–156 (1984c)Google Scholar
  44. Parr, M. J.: Comparative notes on the distribution, ecology and behaviour of some damselflies (Odonata: Coenagionidae). Entomologist 102, 151–161 (1969)Google Scholar
  45. Parr, M. J.: The life-histories of Ischnura elegans (Vander Linden) and Coenagrion puella (L.) (Odonata) in south Lancashire. Proc. R. ent. Soc., Lond. Ser. A. 45, 172–181 (1970)Google Scholar
  46. Parr, M. J.: The life-histories of Ischnura elegans (Vander Linden). II Survivorship, local movements and dispersal. Odonatologica 2, 159–174 (1973)Google Scholar
  47. Paulson, D. R., Jenner, C. E.: Population structure in overwintering larval Odonata in North Carolina in relation to adult flight season. Ecology 52, 96–103 (1971)CrossRefGoogle Scholar
  48. Pritchard, G.: Life-history strategies in dragonflies and the colonization of North America by the genus Argia (Odonata: oenagrionidae). Adv. Odonatol. 1, 227–241 (1982)Google Scholar
  49. Pulliam, H. R.: Sources, sinks, and population regulation. Am. Nat. 132, 652–661 (1988)CrossRefGoogle Scholar
  50. Reinartz, J. A.: Life-history variation of common mulein (Verbascum thapsus). I. Latitudinal differences in population dynamics and timing of reproduction. J. Ecol. 71, 897–912 (1984)Google Scholar
  51. Richardson, J. S., Clifford, H. F.: Phenology and ecology of some Trichoptera in a low-gradient boreal stream. J. North Am. Benthol. Soc. 5, 191–199 (1986)CrossRefGoogle Scholar
  52. Riedl, H., Croft, B. A.: The effects of photoperiod and effective temperatures on the seasonal phenology of the codling moth (Lepidoptera: Tortricidae). Can. Entomol. 110, 455–470 (1978)CrossRefGoogle Scholar
  53. Roff, D.: Optimizing development time in a seasonal environment: The “ups” and “downs” of clinal variation. Oecologia 45, 202–208 (1980)CrossRefGoogle Scholar
  54. Sanders, D. S.: Insect clocks, 2nd ed. Oxford: Pergamon Press 1982Google Scholar
  55. Semlitsch, R. D., Scott, D. E., Pechmann, H. K.: Time and size at metamorphosis related to adult fitness in Ambystoma talpoideum. Ecology 69, 184–192 (1988)CrossRefGoogle Scholar
  56. Tauber, C. A., Tauber, M. J.: Evolution of seasonal adaptations and life history traits in Chrysopa: Response to diverse selective pressures. In: Dingle, H., Hegmann, J. P. (eds.) Evolution and genetics of life histories, pp. 31–72. Berlin Heidelberg New York: Springer 1982Google Scholar
  57. Tauber, M. J., Tauber, C. A., Masaki, S.:, Seasonal adaptations of insects. New York: Oxford University Press 1986Google Scholar
  58. Taylor, F.: Optimal switching to diapause in relation to the onset of winter. Theor. Popul. Biol. 18, 125–133 (1980)MATHCrossRefGoogle Scholar
  59. Taylor, F., Spalding, J. B.: Fitness functions for alternative developmental pathways in the timing of diapause induction. Am. Nat. 131, 678–699 (1988)CrossRefGoogle Scholar
  60. Thompson, J. M. T., Stewart, H. B.: Non-linear dynamics and chaos: Geometrical methods for engineers and scientists. Chichester: John Wiley & Sons 1986Google Scholar
  61. Werner, E. E.: Amphibian Metamorphosis: Growth rate, predation risk, and the optimal size at transformation. Am. Nat. 128, 319–341 (1986)CrossRefGoogle Scholar
  62. Werner, P. A.: Predictions of fate from rosette size in teasel (Dipascus fullonium L.) Oecologia 20, 197–201 (1975)CrossRefGoogle Scholar
  63. Wilbur, H. M.: Complex Life cycles. Annv. Rev. Ecol. Syst. 11, 67–93 (1980)CrossRefGoogle Scholar
  64. Wilbur, H. M., Collins, P. J.: Ecological aspects of amphibian metamorphosis. Science 182, 1305–1314 (1973)Google Scholar
  65. Wolda, H.: Insect seasonality: why? Annv. Rev. Ecol. Syst. 19, 1–18 (1988)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • William S. C. Gurney
    • 1
  • Philip H. Crowley
    • 2
  • Roger M. Nisbet
    • 1
  1. 1.Department of Statistics and Modelling ScienceUniversity of StrathclydeGlasgowUK
  2. 2.Evolutionary Ecology Research Group, T. H. Morgan School of Biological SciencesUniversity of KentuckyLexingtonUSA

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