Sensitivity and elasticity of density-dependent population models

Journal of Difference Equations and Applications

Volumn 15, Issue 4, 2009, Pages 349-369

  Caswell, Hal ^a  

^a WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

Density dependence; Matrix calculus; Matrix population models; Perturbation analysis

Indexed keywords

EID: 68849102094     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236190802282669     Document Type: Article

References (40)

1. K.M. Abadir and J.R. Magnus, Matrix Algebra. Econometric Exercises 1. Cambridge University Press, Cambridge, UK, 2005.
2. L.Y. Adrianova, Introduction to Linear Systems of Differential Equations, American Mathematical Society, Translations of Mathematical Monographs 146, Providence Rhode Island USA, 1995.
3. A. Baudisch, Hamilton's indicators of the force of selection, Proc. Natl. Acad. Sci. USA 102 (2005), pp. 8263-8268.
4. H. Caswell, A general formula for the sensitivity of population growth rate to changes in life history parameters, Theor. Popul. Biol. 14 (1978), pp. 215-230.
5. H. Caswell, Matrix Population Models: Construction, Analysis, and Interpretation, 2nd ed., Sinauer Associates, Sinauer Associates, Sunderland, MA, 2001.
6. H. Caswell, Applications of Markov chains in demography, in MAM2006: Markov Anniversary Meeting, A. N. Langville and W. J. Stewart, eds., Boson Books, Raleigh, NC, 2006, pp. 319-334.
7. H. Caswell, Sensitivity analysis of transient population dynamics, Ecol. Lett. 10 (2007a), pp. 1-15.
8. H. Caswell, Evolutionary demography: The invasion exponent and the effective population density in nonlinear matrix models, in From Energetics to Ecosystems: the Dynamics and Structure of Ecological Systems, N. Rooney, K.S. McCann, and D.L.G. Noakes, eds., Springer, Dortrecht, Netherlands, 2007b.
9. H. Caswell, Perturbation analysis of nonlinear matrix population models, Demogr. Res. 18 (2008), pp. 59-116.
10. H. Caswell and D.E. Weeks, Two-sex models: chaos, extinction and other dynamic consequences of sex, Am. Nat. 128 (1986), pp. 707-735.
11. H. Caswell and M.G. Neubert, Reactivity and transient dynamics of discrete-time ecological systems, J. Differ. Equ. Appl. 2 (2005), pp. 295-310.
12. H. Caswell, T. Takada, and C.M. Hunter, Sensitivity analysis of equilibrium in densitydependent matrix population models, Ecol. Lett. 7 (2004), pp. 380-387.
13. J.H. Clutton-Brock, A.W. Illius, K. Wilson, B.T. Grenfell, A.D.C. MacColl, and S.D. Albon, Stability and instability in ungulate populations: An empirical analysis, Am. Nat. 149 (1997), pp. 195-219.
14. R.F. Costantino, R.A. Desharnais, J.M. Cushing, and B. Dennis, Chaotic dynamics in an insect population, Science, 275 (1997), pp. 389-391.
15. J.M. Cushing, An Introduction to Structured Population Dynamics, SIAM, Philadelphia, Pennsylvania, 1998.
16. J.M. Cushing, R.F. Costantino, B. Dennis, R.A. Desharnais, and S.M. Henson, Chaos in Ecology: Experimental Nonlinear Dynamics, Academic Press, San Diego, CA, 2003.
17. B. Dennis, B.A. Desharnais, J.M. Cushing, and R.F. Costantino, Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments, Ecol. Monogr. 65 (1995), pp. 261-281.
18. M. Emecki, S. Navarro, J.E. Donahaye, M. Rindner, and A. Azrieli, Respiration of stored product pests in hermetic conditions, in Proceedings of the International Conference on Controlled Atmosphere and Fumigation in Stored Products, E.J. Donahaye, S. Navarro, and J. G. Leesch, eds., Executive Printing Services, Clovis, CA, 2001, pp. 26-35.
19. R. Ferríre and M. Gatto, Chaotic population dynamics can result from natural selection, Proc. R. Soc. Lond. B251 (1993), pp. 33-38.
20. A. Grant and G. Benton, Elasticity analysis for density dependent populations in stochastic environments, Ecology 81 (2000), pp. 680-693.
21. 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.
22. W.D. Hamilton, The moulding of senescence by natural selection, J. Theor. Biol 12 (1966), pp. 12-45.
23. M. Iannelli, M. Martcheva, and F.A. Milner, Gender-structured Population Modeling: Mathematical Methods, Numerics, and Simulations, SIAM, Philadelphia, Pennsylvania, 2005.
24. N. Keyfitz, Linkages of intrinsic to age-specific rates, J. Am. Stat. Assoc. 66 (1971), pp. 275-281.
25. N. Keyfitz, The mathematics of sex and marriage. Proceedings of the Sixth Berkeley Symposium Mathematical Statistical Probability, 4 (1972b), pp. 89-108.
26. J.R. Magnus and H. Neudecker, Matrix differential calculus with applications to simple, Hadamard, and Kronecker products, J. Math. Psychol. 29 (1985), pp. 474-492.
27. J.R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons, New York, NY, 1988.
28. J.A.J. Metz, R.M. Nisbet, and S.A.H. Geritz, How should we define 'fitness' for general ecological scenarios?, Trends Ecol. Evol. 7 (1992), pp. 198-202.
29. D.G. Nel, On matrix differentiation in statistics, S. Afr. Stat. J. 14 (1980), pp. 137-193.
30. H. Neudecker, Some theorems on matrix differentiation with special reference to Kronecker matrix products, J. Am. Stat. Assoc. 64 (1969), pp. 953-963.
31. R.A. Pollak, Two-sex demographic models, J. Polit. Econ. 98 (1990), pp. 399-420.
32. J.H. Pollard, The continuing attempt to incorporate both sexes into marriage analysis, Int. Popul. Conf. Int. Union Sci. Study Popul. (1977), pp. 291-308.
33. D.A. Rand, H.B. Wilson, and J.M. McGlade, Dynamics and evolution: Evolutionarily stable attractors, invasion exponents and phenotype dynamics, Philos. Trans. R Soc. Lond. B343 (1994), pp. 261-283.
34. W.E. Roth, On direct product matrices, Bull. Am. Math. Soc. 40 (1934), pp. 461-468.
35. J.R. Skalski, K.E. Ryding, and J. Millspaugh, Wildlife Demography: Analysis of Sex, Age, and Count Data, Academic Press, San Diego, CA, 2005.
36. T. Takada and H. Nakajima, An analysis of life history evolution in terms of the densitydependent Lefkovitch Matrix model, Math. Biosci. 112 (1992), pp. 155-176.
37. T. Takada and H. Nakajima, Theorems on the invasion process in stage-structured populations with densitydependent dynamics, J. Math. Biol. 36 (1998), pp. 497-514.
38. S. Tuljapurkar, Stochastic matrix models, Pages 59-87 in Structured-population Models in Marine, Terrestrial, and Freshwater Systems, S. Tuljapurkar and H. Caswell, eds., Chapman and Hall, New York, USA, 2008.
39. A. Verdy and H. Caswell, Sensitivity analysis of reactive ecological dynamics, Bull. Math. Biol. (2008), in press, DOI: 10.1007/S11538-008-9312-7.
40. J.M. Yearsley, D. Fletcher, and C.M. Hunter, Sensitivity analysis of equilibrium population size in a density-dependent model for short-tailed shearwaters, Ecol. Model. 163 (2003), pp. 119-129.