Population cycles caused by selection by density dependent competitive interactions

  • Lars Witting


Several animal species have cyclic population dynamics with phase-related cycles in life history traits such as body mass, reproductive rate, and pre-reproductive period. Although many mechanisms have been proposed there is no agreement on the cause of these cycles, and no population equation that deduces both the abundance and the life history cycles from basic ecological constraints has been formulated. Here I deduce a population dynamic equation from the selection pressure of density dependent competitive interactions in order to explain the cyclic dynamics in abundance and life history traits. The model can explain cycles by evolutionary changes in the genotype or by plastic responses in the phenotype. It treats the population dynamic growth rate as an initial condition, and its density independent fundament is Fisher’s (1930, The Genetical Theory of Natural Selection, Oxford: Clarendon) fundamental theorem of natural selection that predicts a hyper-geometrical increase in abundance. The predicted periods coincide with the cyclic dynamics of Lepidoptera, and the Calder hypothesis, which suggests that the period of population cycles is proportional to the 1/4 power of body mass, follows from first principles of the proposed density dependent ecology.


Population Abundance Intrinsic Growth Rate Population Cycle Population Equilibrium Cyclic Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abrams, P. A., Y. Harada and H. Matsuda (1993). On the relationship between quantitative genetic and ESS models. Evolution 47, 982–985.CrossRefGoogle Scholar
  2. Adam, K. D., C. M. King and W. H. Köhler (1993). Potential ecological effects of escaped transgenic animals: lessons from past biological invasions, in Transgenic Organisms, K. Wöhrmann and J. Tomiuk (Eds), Basel: Birkhäuser Verlag, pp. 153–173.Google Scholar
  3. Akçakaya, H. R. (1992). Population cycles of mammals: evidence for a ratio-dependent predation hypothesis. Ecol. Monogr. 62, 119–142.CrossRefGoogle Scholar
  4. Axelrod, R. and W. D. Hamilton (1981). The evolution of cooperation. Science 211, 1390–1396.MathSciNetGoogle Scholar
  5. Baltensweiler, W. and A. Fischlin (1988). The larch budmoth in the alps, in Dynamics of Forest Insect Populations. Patterns, Causes, Implications, A. A. Berryman (Ed.), New York: Plenum Press, pp. 331–351.Google Scholar
  6. Barbour, D. A. (1990). Synchronous fluctuations in spatially separated populations of cyclic forest insects, in Population Dynamics of Forest Insects, A. D. Watt, S. R. Leather, M. D. Hunter and N. A. C. Kidd (Eds), Andover, Hampshire: Intercept, pp. 339–346.Google Scholar
  7. Batzli, G. O. (1996). Population cycles revisited. Trends Ecol. Evol. 11, 488–489.CrossRefGoogle Scholar
  8. Bejer, B. (1988). The nun moth in european spruce forests, in Dynamics of Forest Insect Populations. Patterns, Causes, Implications, A. A. Berryman (Ed.), New York: Plenum Press, pp. 211–231.Google Scholar
  9. Berryman, A. A. (1996). What causes population cycles of forest Lepidoptera? Trends Ecol. Evol. 11, 28–32.CrossRefGoogle Scholar
  10. Bjørnstad, O. N., W. Falck and N. C. Stenseth (1995). A geographic gradient in small rodent density fluctuations: a statistical modelling approach. Proc. R. Soc. Lond. B. 262, 127–133.Google Scholar
  11. Boonstra, R. (1994). Population cycles in microtines: the senescence hypothesis. Evol. Ecol. 8, 196–216.CrossRefGoogle Scholar
  12. Boonstra, R. and P. T. Boag (1987). A test of the Chitty hypothesis: inheritance of life-history traits in meadow voles Microtus pennsylvanicus. Evolution 41, 929–947.CrossRefGoogle Scholar
  13. Boonstra, R. and W. M. Hochachka (1997). Maternal effects and additive genetic inheritance in the collared lemming Dicrostonyx groenlandicus. Evol. Ecol. 11, 169–182.CrossRefGoogle Scholar
  14. Boonstra, R. and C. J. Krebs (1979). Viability of large-and small-sized adults in fluctuating vole populations. Ecology 60, 567–573.CrossRefGoogle Scholar
  15. Bulmer, M. (1994). Theoretical Evolutionary Ecology, Massachusetts: Sinauer Associates Publishers.Google Scholar
  16. Calder, W. A. I. (1983). An allometric approach to population cycles of mammals. J. Theor. Biol. 100, 275–282.CrossRefGoogle Scholar
  17. Calder, W. A. I. (1984). Size, Function, and Life History, Cambridge: Harvard University Press.Google Scholar
  18. Charlesworth, B. (1990). Optimizations models, quantitative genetics, and mutation. Evolution 44, 520–538.CrossRefGoogle Scholar
  19. Charlesworth, B. (1994). Evolution in Age-structured Populations, 2nd edn, Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  20. Charnov, E. L. (1993). Life History Invariants. Some Explorations of Symmetry in Evolutionary Ecology, New York: Oxford University Press.Google Scholar
  21. Charnov, E. L. and J. Finnerty (1980). Vole population cycles: a case for kin-selection? Oecologia (Berl.) 45, 1–2.CrossRefGoogle Scholar
  22. Chitty, D. (1960). Population processes in the voles and their relevance to general theory. Can. J. Zool. 38, 99–113.Google Scholar
  23. Chitty, D. (1967). The natural selection of self-regulatory behaviour in animal populations. Proc. Ecol. Soc. Aust. 2, 51–78.Google Scholar
  24. Chitty, D. (1987). Social and local environments of the vole Microtus townsendii. Can. J. Zool. 65, 2555–2566.CrossRefGoogle Scholar
  25. Chitty, D. (1996). Do Lemmings Commit Suicide? Beautiful Hypotheses and Ugly Facts, New York: Oxford University Press.Google Scholar
  26. Christian, J. (1950). The adreno-pituitary system and population cycles in mammals. J. Mamm. 31, 247–259.Google Scholar
  27. Christiansen, F. B. (1991). On conditions for evolutionary stability for a continuously varying character. Am. Nat. 138, 37–50.CrossRefGoogle Scholar
  28. Clark, J. (1971). The second derivative and population modeling. Ecology 52, 606–613.CrossRefGoogle Scholar
  29. Costantino, R. F., J. M. Cushing, B. Dennis and R. A. Desharnais (1995). Experimentally induced transitions in the dynamic behavior of insect populations. Nature 375, 227–230.CrossRefGoogle Scholar
  30. Dahlsten, D. L., D. L. Rowney, W. A. Copper, S. M. Tait and J. M. Wenz (1990). Long-term population studies of the douglas-fir tussock moth in california, in Population Dynamics of Forest Insects, A. D. Watt, S. R. Leather, M. D. Hunter and N. A. C. Kidd (Eds), Andover, Hampshire: Intercept, pp. 45–58.Google Scholar
  31. Damuth, J. (1981). Population density and body size in mammals. Nature 290, 699–700.CrossRefGoogle Scholar
  32. Damuth, J. (1987). Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy-use. Biol. J. Linnean Society 31, 193–246.Google Scholar
  33. Dekker, H. (1975). A simple mathematical model of rodent population cycles. J. Math. Biol. 2, 57–67.zbMATHCrossRefGoogle Scholar
  34. Desharnais, R. A. and L. Liu (1987). Stable demographic limit cycles in laboratory populations of Tribolium castaneum. J. Anim. Ecol. 56, 885–906.Google Scholar
  35. Dieckmann, U. (1997). Can adaptive dynamics invade? Trends Ecol. Evol. 12, 128–131.CrossRefGoogle Scholar
  36. Dugatkin, L. A. and H. K. Reeve (1998). Game Theory and Animal Behavior, Oxford: Oxford University Press.Google Scholar
  37. Elton, C. (1927). Animal Ecology, London: Sidgwick & Jackson.Google Scholar
  38. Eshel, I. (1983). Evolutionary and continuous stability. J. Theor. Biol. 103, 99–111.MathSciNetCrossRefGoogle Scholar
  39. Eshel, I., U. Motro and E. Sansone (1997). Continuous stability and evolutionary convergence. J. Theor. Biol. 185, 333–343.CrossRefGoogle Scholar
  40. Ferns, P. N. (1979). Growth, reproduction and residency in a declining population of Microtus agrestis. J. Anim. Ecol. 48, 739–758.Google Scholar
  41. Fisher, R. A. (1930). The Genetical Theory of Natural Selection, Oxford: Clarendon.zbMATHGoogle Scholar
  42. Gertiz, S. A. H., É Kisdi, G. Meszéna and J. A. J. Metz (1998). Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12, 35–57.CrossRefGoogle Scholar
  43. Gertiz, S. A. H., J. A. J. Metz, É Kisdi and G. Meszéna (1997). Dynamics of adaptation and evolutionary branching. Phys. Rev. Lett. 78, 2024–2027.CrossRefGoogle Scholar
  44. Ginzburg, L. R. (1980). Ecological implications of natural selection, in Vito Volterra Symposium on Mathematical Models in Biology, Lecture Notes in Biomathematics 39, C. Barigozzi (Ed.), Berlin: Springer-Verlag, pp. 171–183.Google Scholar
  45. Ginzburg, L. R. (1986). The theory of population dynamics: I. Back to first principles. J. Theor. Biol. 122, 385–399.MathSciNetGoogle Scholar
  46. Ginzburg, L. R. (1998). Inertial growth: population dynamics based on maternal effects, in Maternal Effects as Adaptations, T. Mousseau and C. Fox (Eds), Oxford: Oxford University Press, pp. 42–53.Google Scholar
  47. Ginzburg, L. R. and D. E. Taneyhill (1994). Population cycles of forest Lepidoptera: a maternal effect hypothesis. J. Anim. Ecol. 63, 79–92.Google Scholar
  48. Ginzburg, L. R. and D. E. Taneyhill (1995). Higher growth rate implies shorter cycle, whatever the cause: a reply to Berryman. J. Anim. Ecol. 64, 294–295.Google Scholar
  49. Grenfell, B. T., O. F. Price, S. D. Albon and T. H. Clutton-Brock (1992). Overcompensation and population cycles in an ungulate. Nature 355, 823–826.CrossRefGoogle Scholar
  50. Gurney, W. S. C., S. P. Blythe and R. M. Nisbet (1980). Nicholson’s blowflies revisited. Nature 287, 17–21.CrossRefGoogle Scholar
  51. Hanski, I., L. Hansson and H. Henttonen (1991). Specialist predators, generalist predators, and the microtine rodent cycle. J. Anim. Ecol. 60, 353–367.Google Scholar
  52. Hanski, I. and E. Korpimäki (1995). Microtine rodent dynamics in northern Europe: Parameterized models for the predator—prey interaction. Ecology 76, 840–850.CrossRefGoogle Scholar
  53. Hanski, I., P. Turchin, E. Korpimäki and H. Henttonen (1993). Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. Nature 364, 232–235.CrossRefGoogle Scholar
  54. Hansson, L. (1971). Small rodent food, feeding and population dynamics: a comparison between granivorous and herbivorous species in Scandinavia. Oikos 22, 183–198.Google Scholar
  55. Hansson, L. (1987). An interpretation of rodent dynamics as due to trophical interactions. Oikos 50, 308–318.Google Scholar
  56. Hansson, L. and H. Henttonen (1985). Gradients in density variations of small rodents: the importance of latitude and snow cover. Oecologia (Berl.) 67, 394–402.CrossRefGoogle Scholar
  57. Härdling, R. (1999). Arms races, conflict costs and evolutionary dynamics. J. Theor. Biol. 196, 163–167.CrossRefGoogle Scholar
  58. Hassell, M. P., J. H. Lawton and R. M. May (1976). Patterns of dynamical behavior in single species populations. J. Anim. Ecol. 45, 471–486.Google Scholar
  59. Hofbauer, J. and K. Sigmund (Eds) (1998). Evolutionary Games and Population Dynamics, Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  60. Howell, A. B. (1923). Periodic fluctuations in the numbers of small mammals. J. Mamm. 4, 149–155.Google Scholar
  61. Hunt, F. (1982). Regulation of population cycles by genetic feedback. Existence of period solutions of a mathematical model. J. Math. Biol. 13, 271–282.zbMATHCrossRefGoogle Scholar
  62. Inchausti, P. and L. R. Ginzburg (1998). Small mammals cycles in northern Europe: patterns and evidence for a maternal effect hypothesis. J. Anim. Ecol. 67, 180–194.CrossRefGoogle Scholar
  63. Innis, G. (1972). The second derivative and population modeling: another view. Ecology 53, 720–723.CrossRefGoogle Scholar
  64. Iwasa, Y., A. Pomiankowski and S. Nee (1991). The evolution of costly mate preferences. II. The ‘handicap’ principle. Evolution 45, 1431–1442.CrossRefGoogle Scholar
  65. Jablonka, E. and M. J. Lamb (1989). The inheritance of acquired epigenetic variations. J. Theor. Biol. 139, 69–83.Google Scholar
  66. Jablonka, E. and M. J. Lamb (1998). Epigenetic inheritance in evolution. J. Evol. Biol. 11, 159–183.CrossRefGoogle Scholar
  67. Jedrzejewski, W. and B. Jedrzejewski (1996). Rodent cycles in relation to biomass and productivity of ground vegetation and predation in the Palearctic. Acta Theriol. 41, 1–34.Google Scholar
  68. Kisdi, É (1999). Evolutionary branching under asymmetric competition. J. Theor. Biol. 197, 149–162.CrossRefGoogle Scholar
  69. Kozłowski, J. (1999). Adaptation: a life history perspective. Oikos 86, 185–194.Google Scholar
  70. Krebs, C. J. (1978). A review of the Chitty hypothesis of population regulation. Can. J. Zool. 56, 2464–2480.Google Scholar
  71. Krebs, C. J. (1996). Population cycles revisited. J. Mamm. 77, 8–24.Google Scholar
  72. Krebs, C. J., S. Boutin, R. Boonstra, A. R. E. Sinclair, J. N. M. Smith, M. R. T. Dale, K. Martin and R. Turkington (1995). Impact of food and predation on the snowshoe hare cycle. Science 269, 1112–1115.Google Scholar
  73. Krebs, C. J., M. S. Gaines, B. L. Keller, J. H. Myers and R. H. Tamarin (1973). Population cycles in small rodents. Science 179, 35–41.Google Scholar
  74. Krebs, C. J. and J. Myers (1974). Population cycles in small mammals. Adv. Ecol. Res. 8, 267–399.CrossRefGoogle Scholar
  75. Krukonis, G. and W. M. Schaffer (1991). Population cycles in mammals and birds: does periodicity scale with body size? J. Theor. Biol. 148, 469–493.Google Scholar
  76. Lachmann, M. and E. Jablonka (1996). The inheritance of phenotypes: an adaptation against fluctuating environments. J. Theor. Biol. 181, 1–9.CrossRefGoogle Scholar
  77. Lidicker, W. Z. and R. S. Ostfeld (1991). Extra-large body size in California voles: Causes and fitness consequences. Oikos 61, 108–121.Google Scholar
  78. Malthus, T. R. (1798). An Essay on the Principle of Population, London: Johnson.Google Scholar
  79. Matsuda, H. and P. A. Abrams (1994). Runaway evolution to self-extinction under asymmetrical competition. Evolution 48, 1764–1772.CrossRefGoogle Scholar
  80. May, R. M. and G. F. Oster (1976). Bifurcation and dynamic complexity in simple ecological models. Amazoniana 110, 573–599.Google Scholar
  81. Maynard Smith, J. (1982). Evolution and the Theory of Games, Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  82. Maynard Smith, J. and R. L. W. Brown (1986). Competition and body size. Theor. Pop. Biol. 30, 166–179.MathSciNetCrossRefzbMATHGoogle Scholar
  83. Maynard Smith, J. and G. R. Price (1973). The logic of animal conflict. Nature 246, 15–18.CrossRefGoogle Scholar
  84. Metz, J. A. J., S. A. H. Geritz, G. Meszéna, F. J. A. Jacobs and J. S. van Heerwaarden (1996). Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction, in Stochastic and Spatial Structures of Dynamical Systems, S. J. van Strien and S. M. Verduyn Lunel (Eds), Amsterdam, The Netherlands: North Holland, pp. 183–231.Google Scholar
  85. Metz, J. A. J., R. M. Nisbet and S. A. H. Geritz (1992). How should we define ‘fitness’ for general ecological scenarios? Trends Ecol. Evol. 7, 198–202.CrossRefGoogle Scholar
  86. Morris, R. F. (1964). The value of historical data in population research, with particular reference to Hyphantria cunea drury. Can. Entomol. 96, 356–368.Google Scholar
  87. Mueller, L. D. (1997). Theoretical and empirical examination of density-dependent selection. Ann. Rev. Ecol. Syst. 28, 269–288.CrossRefGoogle Scholar
  88. Murdoch, W. W. and E. McCauley (1985). Three distinct types of dynamic behavior shown by a single planktonic system. Nature 316, 628–630.CrossRefGoogle Scholar
  89. Myllymäki, A. (1977). Demographic mechanisms in the fluctuating populations of the field vole Macrotus agrestis. Oikos 468–493, 212–214.Google Scholar
  90. Nee, S., A. F. Read, J. J. D. Greenwood and P. H. Harvey (1991). The relationship between abundance and body size in British birds. Nature 351, 312–313.CrossRefGoogle Scholar
  91. Norrdahl, K. (1995). Population cycles in northern small mammals. Biol. Rev. 70, 621–637.Google Scholar
  92. Oksanen, L. and P. Lundberg (1995). Optimization of reproductive effort and foraging time in mammals. The influence of resource level and predation risk. Evol. Ecol. 9, 54–56.CrossRefGoogle Scholar
  93. Oli, M. K. (1999). The Chitty effect: A consequence of dynamic energy allocation in a fluctuating environment. Theor. Pop. Biol. 56, 293–300.CrossRefGoogle Scholar
  94. Peters, R. H. (1983). The Ecological Implication of Body Size, Cambridge: Cambridge University Press.Google Scholar
  95. Peterson, R. O., R. E. Page and K. M. Dodge (1984). Wolves, moose, and the allometry of population cycles. Science 224, 1350–1352.Google Scholar
  96. Price, G. R. (1972). Fisher’s ‘fundamental theorem’ made clear. Ann. Hum. Genet. 36, 129–140.zbMATHMathSciNetGoogle Scholar
  97. Robertson, A. (1968). The spectrum of genetic variation, in Population Biology and Evolution, R. C. Lewontin (Ed.), New York: Syracuse University Press, pp. 5–16.Google Scholar
  98. Roff, D. A (1992). The Evolution of Life Histories. Theory and Analysis, New York: University of Chicago Press.Google Scholar
  99. Roques, A. (1988). The larch cone fly in the french alps, in Dynamics of Forest Insect Populations. Patterns, Causes, Implications, A. A. Berryman (Ed.), New York: Plenum Press, pp. 1–28.Google Scholar
  100. Rossiter, M. C. (1991). Environmentally-based maternal effects: a hidden force in insect population dynamics. Oecologia (Berl.) 87, 288–294.CrossRefGoogle Scholar
  101. Rossiter, M. C. (1992). The impact of resource variation on population quality in herbivorous insects: a critical component of population dynamics, in Resource Distribution and Animal-plant Interactions, M. D. Hunter, T. Ohgushi and P. W. Price (Eds), New York: Academic Press, pp. 13–42.Google Scholar
  102. Rossiter, M. C. (1994). Maternal effects hypothesis of herbivore outbreak. Bioscience 44, 752–763.CrossRefGoogle Scholar
  103. Rossiter, M. C. (1996). Incidence and consequences of inherited enviromental effects. Ann. Rev. Ecol. Syst. 27, 451–476.CrossRefGoogle Scholar
  104. Royama, T. (1984). Population dynamics of the spruce budworm Choristoneura fumiferana. Ecol. Monogr. 54, 429–462.CrossRefGoogle Scholar
  105. Sandefur, J. T. (1990). Discrete Dynamic Systems: Theory and Applications, Oxford: Oxford University Press.Google Scholar
  106. Simchuk, A. P., A. V. Ivashov and V. A. Companiytsev (1999). Genetic patters as possible factors causing population cycles in oak leafroller moth, Tortrix viridana L. For. Ecol. Manage. 113, 35–49.CrossRefGoogle Scholar
  107. Southwood, T. R. E. (1967). The interpretation of population change. J. Anim. Ecol. 36, 519–529.Google Scholar
  108. Stearns, S. C. (1992). The Evolution of Life Histories, Oxford: Oxford University Press.Google Scholar
  109. Stenseth, N. C. (1978). Demographic strategies in fluctuating populations of small rodents. Oecologia (Berl.) 33, 149–172.CrossRefGoogle Scholar
  110. Stenseth, N. C. (1981). On Chitty’s theory for fluctuating population: the importance of genetic polymorphism in the generation of regular density cycles. J. Theor. Biol. 90, 9–36.MathSciNetCrossRefGoogle Scholar
  111. Stenseth, N. C. (1982). Causes and consequences of dispersal in small mammals, in The Ecology of Animal Movement, I. Swingland and P. Greenwood (Eds), Oxford: Oxford University Press, pp. 62–101.Google Scholar
  112. Stenseth, N. C. (1985). Mathematical models of microtine cycles: models and the real world. Acta Zool. Fenn. 173, 7–12.Google Scholar
  113. Stenseth, N. C. (1995). Snowshoe hare populations: Squeezed from below and above. Science 269, 1061–1062.Google Scholar
  114. Stenseth, N. C., T. O. Gustafsson, L. Hansson and K. I. Ugland (1985). On the evolution of reproductive rates in microtine rodents. Ecology 66, 1795–1808.CrossRefGoogle Scholar
  115. Stenseth, N. C. and R. Ims (Eds) (1993). The Biology of Lemmings, San Diego: Academic Press.Google Scholar
  116. Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos, Reading, MA: Addison-Wesley.Google Scholar
  117. Taper, M. L. and T. J. Case (1992). Models of character displacement and the theoretical robustness of taxon cycles. Evolution 46, 317–333.CrossRefGoogle Scholar
  118. Taylor, P. D. (1989). Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol. 36, 125–143.zbMATHCrossRefGoogle Scholar
  119. Taylor, P. D. (1996). The selection differential in quantitative genetics and ESS models. Evolution 50, 2106–2110.CrossRefGoogle Scholar
  120. Thue Poulsen, E. (1979). A model for population regulation with density-and frequency-dependent selection. J. Math. Biol. 8, 325–343.MathSciNetzbMATHGoogle Scholar
  121. Tuljapurkar, S., C. Boe and K. W. Wachter (1994). Nonlinear feedback dynamics in fisheries: Analysis of the Deriso-Schnute model. Can. J. Fish. Aquat. Sci. 51, 1462–1473.CrossRefGoogle Scholar
  122. Turchin, P. (1990). Rarity of density dependence or population regulation with lags? Nature 344, 660–663.CrossRefGoogle Scholar
  123. Turchin, P., J. P. L. Lorio, A. D. Taylor and R. F. Billings (1991). Why do populations of southern pine beetles (Coleoptera: Scolytidae) fluctuate? Environ. Entomol. 20, 401–409.Google Scholar
  124. Turchin, P., L. Oksanen, P. Ekerholm, T. Oksanen and H. Henttonen (2000). Are lemmings prey or predators? Nature 405, 562–565.CrossRefGoogle Scholar
  125. Turchin, P. and A. D. Taylor (1992). Complex dynamics in ecological time series. Ecology 73, 289–305.CrossRefGoogle Scholar
  126. Vega-Redondo, F. (1996). Evolution, Games, and Economic Behaviour, Oxford: Oxford University Press.Google Scholar
  127. Vincent, T. L. and J. S. Brown (1988). The evolution of ESS theory. Ann. Rev. Ecol. Syst. 19, 423–443.CrossRefGoogle Scholar
  128. Wellington, W. G. (1965). Some maternal influences on progeny quality in the western tent caterpillar Malacosoma pluviale. Can. Entomol. 97, 1–14.CrossRefGoogle Scholar
  129. Witteman, G. J., A. Redfearn and S. L. Pimm (1990). The extent of complex population changes in nature. Evol. Ecol. 4, 173–183.CrossRefGoogle Scholar
  130. Witting, L. (1995). The body mass allometries as evolutionarily determined by the foraging of mobile organisms. J. Theor. Biol. 177, 129–137.CrossRefGoogle Scholar
  131. Witting, L. (1997). A General Theory of Evolution. By Means of Selection by Density Dependent Competitive Interactions, Århus: Peregrine Publisher, p. 330. URL Scholar
  132. Witting, L. (1998). Body mass allometries caused by physiological or ecological constraints? Trends Ecol. Evol. 13, 25.CrossRefGoogle Scholar
  133. Witting, L. (2000). Interference competition set limits to the fundamental theorem of natural selection. Acta Biotheor. 48, 107–120.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2000

Authors and Affiliations

  • Lars Witting
    • 1
  1. 1.Greenland Institute of Natural ResourcesNuukGreenland

Personalised recommendations