Volume 23 - Article 19 | Pages 531–548

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

By Hal Caswell

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References

Abadir, K.M. and Magnus, J.R. (2005). Matrix algebra. Econometric exercises 1. Cambridge, United Kingdom: Cambridge University Press.

Download reference in RIS | BibTeX

Arthur, B.W. (1984). The analysis of linkages in demographic theory. Demography 21(1): 109-128.

Weblink doi:10.2307/2061031
Download reference in RIS | BibTeX

Baudisch, A. (2005). Hamilton's indicators of the force of selection. Proceedings of the National Academy of Sciences 102(23): 8263-8268.

Weblink doi:10.1073/pnas.0502155102
Download reference in RIS | BibTeX

Baudisch, A. (2008). Inevitable aging? Contributions to evolutionary-demographic theory. Berlin, Germany: Springer-Verlag.

Download reference in RIS | BibTeX

Carey, J.R. and Tuljapurkar, S. (2003). Life span: evolutionary, ecological, and demographic perspectives. Population and Development Review Supplement 29: New York, NY: Population Council.

Download reference in RIS | BibTeX

Caswell, H. (1978). A general formula for the sensitivity of population growth rate to changes in life history parameters. Theoretical Population Biology 14(2): 215-230.

Weblink doi:10.1016/0040-5809(78)90025-4
Download reference in RIS | BibTeX

Caswell, H. (2001). Matrix population models: Construction, analysis, and interpretation. Second edition. Sunderland, Massachusetts, USA: Sinauer Associates.

Download reference in RIS | BibTeX

Caswell, H. (2006). Applications of Markov chains in demography. Raleigh, North Carolina, USA: Boson Books, MAM2006: Markov Anniversary Meeting.

Download reference in RIS | BibTeX

Caswell, H. (2007). Sensitivity analysis of transient population dynamics. Ecology Letters 10(1): 1-15.

Weblink doi:10.1111/j.1461-0248.2006.01001.x
Download reference in RIS | BibTeX

Caswell, H. (2008). Perturbation analysis of nonlinear matrix population models. Demographic Research 18(3): 59-116.

Weblink doi:10.4054/DemRes.2008.18.3
Download reference in RIS | BibTeX

Caswell, H. (2009a). Sensitivity and elasticity of density-dependent population models. Journal of Difference Equations and Applications 15(4): 349-369.

Weblink doi:10.1080/10236190802282669
Download reference in RIS | BibTeX

Caswell, H. (2009b). Stage, age, and individual stochasticity in demography. Oikos 118(12): 1763-1782.

Weblink doi:10.1111/j.1600-0706.2009.17620.x
Download reference in RIS | BibTeX

Charlesworth, B. (1994). Evolution in age-structured populations. Second edition. Cambridge, United Kingdom: Cambridge University Press.

Download reference in RIS | BibTeX

Demetrius, L. (1969). The sensitivity of population growth rate to perturbations in the life cycle components. Mathematical Biosciences 4: 129-136.

Weblink doi:10.1016/0025-5564(69)90009-1
Download reference in RIS | BibTeX

Desoer, C. A. (1967). Perturbations of eigenvalues and eigenvectors of a network. Paper presented at the Fifth Annual Allerton Conference on Circuit and System Theory, Urbana, Illinois, USA.

Download reference in RIS | BibTeX

Dwyer, P.S. and MacPhail, M.S. (1948). Symbolic matrix derivatives. Annals of Mathematical Statistics 19: 517-534.

Weblink doi:10.1214/aoms/1177730148
Download reference in RIS | BibTeX

Emlen, J.M. (1970). Age specificity and ecological theory. Ecology 51(4): 588-601.

Weblink doi:10.2307/1934039
Download reference in RIS | BibTeX

Euler, L. (1970). A general investigation into the mortality and multiplication of the human species. Theoretical Population Biology 1(3): 307-314 (Originally published 1760).

Weblink doi:10.1016/0040-5809(70)90048-1
Download reference in RIS | BibTeX

Faddeev, D. K. (1959). The conditionality of matrices (``Ob obuslovlennosti matrits''). Matematicheskii institut Steklov (Trudy No. 53).

Download reference in RIS | BibTeX

Faddeev, D.K. and Faddeeva, V.N. (1963). Computational methods of linear algebra. San Francisco, California, USA: W. H. Freeman.

Download reference in RIS | BibTeX

Franklin, J.N. (1968). Matrix theory. Englewood Cliffs, New Jersey, USA: Prentice-Hall.

Download reference in RIS | BibTeX

Goodman, L.A. (1971). On the sensitivity of the intrinsic growth rate to changes in the age-specific birth and death rates. Theoretical Population Biology 2(3): 339-354.

Weblink doi:10.1016/0040-5809(71)90025-6
Download reference in RIS | BibTeX

Hamilton, W.D. (1966). The moulding of senescence by natural selection. Journal of Theoretical Biology 12(1): 12-45.

Weblink doi:10.1016/0022-5193(66)90184-6
Download reference in RIS | BibTeX

Jacobi, C.J.G. (1846). Über ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen. Journal für reine und angewandte Mathematik 30: 51-95.

Download reference in RIS | BibTeX

Jenouvrier, S., Caswell, H., Barbraud, C., and Weimerskirch, H. (2010). Mating behavior, population growth and the operational sex ratio: a periodic two-sex model approach. American Naturalist 175(6): 739-752.

Weblink doi:10.1086/652436
Download reference in RIS | BibTeX

Kamen, E.W. and Heck, B.S. (1997). Fundamentals of signals and systems. Upper Saddle River, New Jersey, USA: Prentice Hall.

Download reference in RIS | BibTeX

Keyfitz, N. (1968). Introduction to the mathematics of population. Reading, Massachusetts, USA: Addison-Wesley.

Download reference in RIS | BibTeX

Keyfitz, N. (1971). Linkages of intrinsic to age-specific rates. Journal of the American Statistical Association 66(334): 275-281.

Weblink doi:10.2307/2283921
Download reference in RIS | BibTeX

Klepac, P. and Caswell, H. (2010). The stage-structured epidemic: linking disease and demography with a multi-state matrix model approach. Theoretical Ecology .

Weblink doi:10.1007/s12080-010-0079-8
Download reference in RIS | BibTeX

Leslie, P.H. (1945). On the use of matrices in certain population mathematics. Biometrika 33(3): 183-212.

Weblink doi:10.1093/biomet/33.3.183
Download reference in RIS | BibTeX

Magnus, J.R. and Neudecker, H. (1985). Matrix differential calculus with applications to simple, Hadamard, and Kronecker products. Journal of Mathematical Psychology 29(4): 474-492.

Weblink doi:10.1016/0022-2496(85)90006-9
Download reference in RIS | BibTeX

Magnus, J.R. and Neudecker, H. (1988). Matrix differential calculus with applications in statistics and econometrics. New York, NY, USA: John Wiley & Sons.

Download reference in RIS | BibTeX

Nel, D.G. (1980). On matrix differentiation in statistics. South African Statistical Journal 14: 137-193.

Download reference in RIS | BibTeX

Papoulis, A. (1966). Perturbations of the natural frequencies and eigenvectors of a network. IEEE Transactions on Circuit Theory CT-13(2): 188-195.

Download reference in RIS | BibTeX

Roff, D. A. (1992). The evolution of life histories. New York, NY, USA: Chapman and Hall.

Download reference in RIS | BibTeX

Rose, M.R. (1991). Evolutionary biology of aging. Oxford, United Kingdom: Oxford University Press.

Download reference in RIS | BibTeX

Sharpe, F.R. and Lotka, A.J. (1911). A problem in age-distribution. Philosophical Magazine 21: 435-438.

Weblink doi:10.1080/14786440408637050
Download reference in RIS | BibTeX

Stearns, S.C. (1992). The evolution of life histories. Oxford, United Kingdom: Oxford University Press.

Download reference in RIS | BibTeX

Vaupel, J.W. (2010). Biodemography of human ageing. Nature 464: 536-542.

Weblink doi:10.1038/nature08984
Download reference in RIS | BibTeX

Verdy, A. and Caswell, H. (2008). Sensitivity analysis of reactive ecological dynamics. Bulletin of Mathematical Biology 70(6): 1634-1659.

Weblink doi:10.1007/s11538-008-9312-7
Download reference in RIS | BibTeX

Wachter, K.W. and Finch, C.E. (1997). Between Zeus and the salmon: the biodemography of longevity. Washington, D.C.: National Academy Press.

Download reference in RIS | BibTeX

Williams, G.C. (1957). Pleiotropy, natural selection, and the evolution of senescence. Evolution 11: 398-411.

Download reference in RIS | BibTeX

Zadeh, L.A. and Desoer, C.A. (1963). Linear system theory. New York, NY, USA: McGraw-Hill.

Download reference in RIS | BibTeX