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Articles

Capturing chaos: a multidisciplinary approach to nonlinear population dynamics

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References

  • R. Abraham and C. Shaw, Dynamics: The Geometry of Behavior: Part 1: Periodic Behavior, 5th ed., Aerial Press, sine loco,  2016.
  • R. Anderson, D.M. Gordon, M. Crawley, and M.P. Hassell, Variability in the abundance of animal and plant species. Nature 296 (1982), pp. 245–248.
  • M.S. Bartlett, Stochastic Population Models, Methuen, London, 1960.
  • H.P. Benoît, E. McCauley, and J.R. Post, Testing the demographic consequences of cannibalism in Tribolium confusum. Ecology 79 (1998), pp. 2839–2851.
  • E. Braverman, and D. Franco, Stabilization of structured populations via vector target-oriented control. Bull. Math. Biol. 79 (2017), pp. 1759–1777.
  • H. Caswell, Matrix Population Models: Construction, Analysis, and Interpretation, Sinauer Associates, Sunderland, MA, 2006.
  • H. Caswell, Perturbation analysis of nonlinear matrix population models. Demogr. Res. 18 (2008), pp. 59–116.
  • H. Caswell, Sensitivity and elasticity of density-dependent population models. J. Diff. Equ. Appl. 15 (2009), pp. 349–369.
  • R.N. Chapman, The quantitative analysis of environmental factors. Ecology 9 (1928), pp. 111–122.
  • B. Charlesworth, Evolution in Age-Structured Populations, Cambridge University Press, Cambridge, England, 1994.
  • W. Cheung, The effects of natural selection on nonlinear population dynamics, MS thesis, California State University, Los Angeles, 2002.
  • R.F. Costantino, and R.A. Desharnais, Population Dynamics and the Tribolium Model: Genetics and Demography, Monographs on Theoretical and Applied Genetics 13, Springer-Verlag, New York, 1991.
  • R.F. Costantino, J.M. Cushing, B. Dennis, and R.A. Desharnais, Experimentally induced transitions in the dynamic behaviour of insect populations. Nature 375 (1995), pp. 227–230.
  • R.F. Costantino, R.A. Desharnais, J.M. Cushing, and B. Dennis, Chaotic dynamics in an insect population. Science 275 (1997), pp. 389–391.
  • R.F. Costantino, J.M. Cushing, B. Dennis, R.A. Desharnais, and S.M. Henson, Resonant population cycles in temporally fluctuating habitats. Bull. Math. Biol. 60 (1998), pp. 247–273.
  • R.F. Costantino, R.A. Desharnais, J.M. Cushing, B. Dennis, S.M. Henson, and A.A. King, Nonlinear stochastic population dynamics: The flour beetle Tribolium as an effective tool of discovery, in Advances in Ecological Research, R.A. Desharnais, ed., Academic Press, New York, 2005. pp. 101–141.
  • J.M. Cushing, B. Dennis, R.A. Desharnais, and R.F. Costantino, Moving toward an unstable equilibrium: Saddle nodes in population systems. J. Anim. Ecol. 67 (1998), pp. 298–306.
  • J.M. Cushing, R.F. Costantino, B. Dennis, R.A. Desharnais, and S.M. Henson, Nonlinear population dynamics: Models, experiments and data. J. Theor. Biol. 194 (1998), pp. 1–9.
  • J.M. Cushing, S.M. Henson, R.A. Desharnais, B. Dennis, R.F. Costantino, and A. King, A chaotic attractor in ecology: Theory and experimental data. Chaos Solitons Fract. 12 (2001), pp. 219–234.
  • J.M. Cushing, R.F. Costantino, B. Dennis, R. Desharnais, and S.M. Henson, Chaos in Ecology: Experimental Nonlinear Dynamics, Academic Press, San Diego, 2002.
  • C. de Vries, and H. Caswell, Stage-structured evolutionary demography: Linking life histories, population genetics, and ecological dynamics. Am. Nat. 193 (2019), pp. 545–559.
  • C. de Vries, R.A. Desharnais, and H. Caswell, A matrix model for density-dependent selection in stage-classified populations, with application to pesticide resistance in Tribolium. Ecol. Model. 416 [108875] (2020).
  • B. Dennis, Allee effects: Population growth, critical density, and the chance of extinction. Nat. Resour. Model 3 (1989), pp. 481–538.
  • B. Dennis, R.A. Desharnais, J.M. Cushing, and R.F. Costantino, Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments. Ecol. Monographs 65 (1995), pp. 261–282.
  • B. Dennis, R.A. Desharnais, J.M. Cushing, and R.F. Costantino, Transitions in population dynamics: Equilibria to periodic cycles to aperiodic cycles. J. Anim. Ecol. 66 (1997), pp. 704–729.
  • B. Dennis, R.A. Desharnais, J.M. Cushing, S.M. Henson, and R.F. Costantino, Estimating chaos and complex dynamics in an insect population. Ecol. Monographs 71 (2001), pp. 277–303.
  • R.A. Desharnais, and R.F. Costantino, Genetic analysis of a population of Tribolium: VII. stability: Response to genetic and demographic perturbations. Can. J. Genet. Cytol. 22 (1980), pp. 577–589.
  • R.A. Desharnais, and R.F. Costantino, The approach to equilibrium and the steady-state probability distribution of adult numbers in Tribolium brevicornis. Am. Nat. 119 (1982), pp. 102–111.
  • R.A. Desharnais, and L. Liu, Stable demographic limit cycles in laboratory populations of Tribolium castaneum. J. Anim. Ecol. 56 (1987), pp. 885–906.
  • R.A. Desharnais, R.F. Costantino, J.M. Cushing, S.M. Henson, and B. Dennis, Chaos and population control of insect outbreaks. Ecol. Lett. 4 (2001), pp. 229–235.
  • R.A. Desharnais, J. Edmunds, R.F. Costantino, and S.M. Henson, Species competition: Uncertainty on a double invariant loop. J. Diff. Equ. Appl. 11 (2005), pp. 311–325.
  • R.A. Desharnais, R.F. Costantino, J.M. Cushing, S.M. Henson, B. Dennis, and A.A. King, Experimental support of the scaling rule for demographic stochasticity. Ecol. Lett. 9 (2006), pp. 537–547.
  • R.A. Desharnais, D.C. Reuman, R.F. Costantino, and J.E. Cohen, Temporal scale of environmental correlations affects ecological synchrony. Ecol. Lett. 21 (2018), pp. 1800–1811.
  • M. Doebeli, The evolutionary advantage of controlled chaos. Proc. Royal Soc. Lond. Ser. B: Biol. Sci. 254 (1993), pp. 281–285.
  • J. Edmunds, J.M. Cushing, R.F. Costantino, S.M. Henson, B. Dennis, and R.A. Desharnais, Park’s Tribolium competition experiments: A non-equilibrium species coexistence hypothesis. J. Anim. Ecol. 72 (2003), pp. 703–712.
  • S.P. Ellner, and P. Turchin, When can noise induce chaos and why does it matter: A critique. Oikos 111 (2005), pp. 620–631.
  • S.P. Ellner, and J. Guckenheimer, Dynamic Models in Biology, 1st ed., Princeton University Press, Princeton, NJ, 2006.
  • I. Fuwape, and S. Ogunjo, Bifurcation and mixed tracking of the discrete fractional LPA model. Int. J. Dyn. Control 7 (2019), pp. 308–312.
  • G. Gause, The Struggle for Existence, Williams and Wilkins, Baltimore, MD, 1964.
  • C. Godfray, and M. Hassell, Chaotic beetles. Science 275 (1997), pp. 323–324.
  • A. Grant, and T.G. Benton, Density-dependent populations require density-dependent elasticity analysis: An illustration using the LPA model of Tribolium. J. Anim. Ecol. 72 (2003), pp. 94–105.
  • J.V. Greenman, and T.G. Benton, The amplification of environmental noise in population models: Causes and consequences. Am. Nat. 161 (2003), pp. 225–239.
  • V. Hajnová, and L. Přibylová, Two-parameter bifurcations in LPA model. J. Math. Biol. 75 (2017), pp. 1235–1251.
  • G. Hardin, The competitive exclusion principle. Science 131 (1960), pp. 1292–1297.
  • S.M. Henson, J.M. Cushing, R.F. Costantino, B. Dennis, and R.A. Desharnais, Phase switching in population cycles. Proc. Royal Soc. Lond. Ser. B: Biol. Sci. 265 (1998), pp. 2229–2234.
  • S.M. Henson, R.F. Costantino, J.M. Cushing, B. Dennis, and R.A. Desharnais, Multiple attractors, saddles, and population dynamics in periodic habitats. Bull. Math. Biol. 61 (1999), pp. 1121–1149.
  • S.M. Henson, Multiple attractors and resonance in periodically forced population models. Phys. D: Nonlinear Phenom. 140 (2000), pp. 33–49.
  • S.M. Henson, R.F. Costantino, J.M. Cushing, R.A. Desharnais, B. Dennis, and A.A. King, Lattice effects observed in chaotic dynamics of experimental populations. Science 294 (2001), pp. 602–605.
  • S.M. Henson, R.F. Costantino, R.A. Desharnais, J.M. Cushing, and B. Dennis, Basins of attraction: Population dynamics with two stable 4-cycles. Oikos 98 (2002), pp. 17–24.
  • F.M. Hilker and F.H. Westerhoff, Preventing extinction and outbreaks in chaotic populations. Am. Nat. 170 (2007), pp. 232–241.
  • W.T. Jamieson and O. Merino, On the LPA model with μa = 1. Sarajevo J. Math. 18 (2022), pp. 7–23.
  • D.A. Jillson and R.F. Costantino, Growth, distribution, and competition of Tribolium castaneum and Tribolium brevicornis in fine-grained habitats. Am. Nat. 116 (1980), pp. 206–219.
  • D.A. Jillson, Insect populations respond to fluctuating environments. Nature 288 (1980), pp. 699–700.
  • P. Kareiva, Predicting and producing chaos. Nature 375 (1995), pp. 189–190.
  • A.A. King, R.F. Costantino, J.M. Cushing, S.M. Henson, R.A. Desharnais, and B. Dennis, Anatomy of a chaotic attractor: Subtle model-predicted patterns revealed in population data. Proc. Natl. Acad. Sci. 101 (2004), pp. 408–413.
  • L.A. Klimko, and P.I. Nelson, On conditional least squares estimation for stochastic processes. Ann. Stat. 6 (1978), pp. 629–642.
  • P.H. Leslie, A stochastic model for studying the properties of certain biological systems by numerical methods. Biometrika 45 (1958), pp. 16–31.
  • P.H. Leslie, T. Park, and D.B. Mertz, The effect of varying the initial numbers on the outcome of competition between two Tribolium species. J. Anim. Ecol. 37 (1968), pp. 9–23.
  • E. Liz, and A. Ruiz-Herrera, Chaos in discrete structured population models. SIAM J. Appl. Dyn. Syst. 11 (2012), pp. 1200–1214.
  • M. Lloyd, Self regulation of adult numbers by cannibalism in two laboratory strains of flour beetles (Tribolium castaneum). Ecology 49 (1968), pp. 245–259.
  • E.N. Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci. 20 (1963), pp. 130–141.
  • R.M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, 1973.
  • R.M. May, Biological populations with nonoverlapping generations: Stable points, stable cycles, and chaos. Science 186 (1974), pp. 645–647.
  • R.M. May, Theoretical Ecology: Principles and Applications, Saunders, 1976.
  • D.B. Mertz, Age-distribution and abundance in populations of flour beetles. I. Experimental studies. Ecol. Monographs 39 (1969), pp. 1–31.
  • C. Moon, and N.A. Lazar, Hypothesis testing for shapes using vectorized persistence diagrams. J. R. Stat. Soc. Ser. C Appl. Stat. 22 (2023), pp. 628–648.
  • L.D. Mueller, and A. Joshi, Stability in Model Populations, Princeton University Press, Princeton, NJ, 2020.
  • A.J. Nicholson, The self-adjustment of populations to change. Cold Spring Harbor Sympos. Quant. Biol. 22 (1957), pp. 153–173.
  • R.M. Nisbet, and W.S.C. Gurney, Population dynamics in a periodically varying environment. J. Theor. Biol. 56 (1976), pp. 459–475.
  • R.M. Nisbet, and W.S.C. Gurney, Modelling Fluctuating Populations, Wiley, Chichester, 1982.
  • T. Park, Experimental studies of interspecies competition. III relation of initial species proportion to competitive outcome in populations of Tribolium. Physiol. Zool. 30 (1957), pp. 22–40.
  • T. Park, P.H. Leslie, and D.B. Mertz, Genetic strains and competition in populations of Tribolium. Physiol. Zool. 37 (1964), pp. 97–162.
  • T. Park, D.B. Mertz, W. Grodzinski, and T. Prus, Cannibalistic predation in populations of flour beetles. Physiol. Zool. 38 (1965), pp. 289–321.
  • C.T. Perretti, S.B. Munch, and G. Sugihara, Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data. Proc. Natl. Acad. Sci. 110 (2013), pp. 5253–5257.
  • E. Ranta, P. Lundberg, and V. Kaitala, Ecology of Populations, Cambridge University Press, Cambridge, England, 2005.
  • T.R.C. Read, and N.A.C. Cressie, Goodness-of-Fit Statistics for Discrete Multivariate Data, Springer Science & Business Media, New York, 2012.
  • D.C. Reuman, R.A. Desharnais, R.F. Costantino, O.S. Ahmad, and J.E. Cohen, Power spectra reveal the influence of stochasticity on nonlinear population dynamics. Proc. Natl. Acad. Sci. 103 (2006), pp. 18860–18865.
  • D.C. Reuman, R.F. Costantino, R.A. Desharnais, and J.E. Cohen, Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations. Ecol. Lett. 11 (2008), pp. 820–830.
  • T.L. Rogers, B.J. Johnson, and S.B. Munch, Chaos is not rare in natural ecosystems. Nat. Ecol. Evol. 6 (2022), pp. 1105–1111.
  • J. Roughgarden, Density-dependent natural selection. Ecology 52 (1971), pp. 453–468.
  • W.M. Schaffer, B.E. Kendall, C.W. Tidd, and L.F. Olsen, Transient periodicity and episodic predictability in biological dynamics. Math. Med. Biol. 10 (1993), pp. 227–247.
  • I. Scheuring, and G. Domokos, Sturdy cycles in the chaotic Tribolium castaneum data series. Theor. Popul. Biol. 67 (2005), pp. 127–139.
  • J.F. Selgrade, and J.H. Roberds, On the structure of attractors for discrete, periodically forced systems with applications to population models. Phys. D: Nonlinear Phenom. 158 (2001), pp. 69–82.
  • T.A. Severini, Likelihood Methods in Statistics, Oxford University Press, Oxford, 2001.
  • L. Shulenburger, Y.-C. Lai, T. Yalçınkaya, and R.D. Holt, Controlling transient chaos to prevent species extinction. Phys. Lett. A 260 (1999), pp. 156–161.
  • H.L. Smith, The discrete dynamics of monotonically decomposable maps. J. Math. Biol. 53 (2006), pp. 747–758.
  • H.L. Smith, and H.R. Thieme, Dynamical Systems and Population Persistence, American Mathematical Society, Providence, R.I., 2010.
  • R.V. Solé, J.G. Gamarra, M. Ginovart, and D. López, Controlling chaos in ecology: From deterministic to individual-based models. Bull. Math. Biol. 61 (1999), pp. 1187–1207.
  • Y. Takeuchi, Y. Iwasa, and K. Sato, eds. Mathematics for Ecology and Environmental Sciences, Springer, Berlin, 2007.
  • S. Utida, Cyclic fluctuations of population density intrinsic to the host-parasite system. Ecology 38 (1957), pp. 442–449.
  • K.E.F. Watt, Ecology & Resource Management, McGraw Hill Publishing Company, New York, 1968.

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