Elasticity analysis of density-dependent matrix population models: The invasion exponent and its substitutes

Theoretical Population Biology

Volumn 65, Issue 4, 2004, Pages 401-411

  Caswell, Hal ^a   Takada, Takenori ^b  

^a WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

^b TOKAI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY DEPENDENCE; ECOLOGICAL THEORY; ELASTICITY; POPULATION DYNAMICS;

ARTICLE; HUMAN; JAPAN; POPULATION DENSITY; POPULATION GROWTH; SEXUAL BEHAVIOR; STATISTICAL MODEL; SURVIVAL RATE;

HUMANS; JAPAN; MODELS, STATISTICAL; POPULATION DENSITY; POPULATION GROWTH; REPRODUCTIVE BEHAVIOR; SURVIVAL RATE;

EID: 2442630447     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tpb.2003.09.007     Document Type: Article

References (27)

1. Caswell H. A general formula for the sensitivity of population growth rate to changes in life history parameters. Theor. Popul. Biol. 14:1978;215-230
2. Caswell, H., 2001. Matrix Population models, 2nd Edition. Construction, Analysis, and Interpretation. Sinauer Associates, Inc., Sunderland, MA.
3. Caswell H., Trevisan M.C. The sensitivity analysis of periodic matrix models. Ecology. 75:1994;1299-1303
4. Caswell H., Naiman R.J., Morin R. Evaluating the consequences of reproduction in complex salmonid life cycles. Aquaculture. 43:1984;123-134
5. Caswell, H., Takada, T., Hunter, C.M., 2004. Sensitivity analysis of equilibrium in density-dependent matrix population models. Ecology Letters (in press).
6. Cohen J.E. Ergodicity of age structure in populations with Markovian vital rates, I. countable states J. Am. Stat. Assoc. 71:1976;335-339
7. Costantino R.F., Desharnais R.A., Cushing J.M., Dennis B. Chaotic dynamics in an insect population. Science. 275:1997;389-391
8. Cushing J.M., Costantino R.F., Dennis B., Desharnais R.A., Henson S.M. Chaos in Ecology: Experimental Non-linear Dynamics. 2003;Academic Press, New York, USA
9. de Kroon H., Plaisier A., van Groenendael J., Caswell H. Elasticity. the relative contribution of demographic parameters to population growth rate Ecology. 67:1986;1427-1431
10. Ferriére R., Gatto M. Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations. Theor. Popul. Biol. 48:1995;126-171
11. Furstenberg H., Kesten H. Products of random matrices. Ann. Math. Stat. 31:1960;457-469
12. Getz W.M. Population and evolutionary dynamics of consumer-resource systems. McGlade J. Advanced Ecological Theory. 1999;194-231 Blackwell Science, Oxford, England
13. Grant A. Selection pressures on vital rates in density dependent populations. Proc. Roy. Soc. B. 264:1997;303-306
14. Grant A. Population consequences of chronic toxicity. incorporating density dependence into the analysis of life table response experiments Ecol. Model. 105:1998;325-335
15. Grant A., Benton T.G. Elasticity analysis for density dependent populations in stochastic environments. Ecology. 81:2000;680-693
16. Grant A., Benton T.G. Density-dependent populations require density-dependent elasticity analysis. an illustration using the LPA model of Tribolium J. Anim. Ecol. 72:2003;94-105
17. Guckenheimer J., Oster G., Ipaktchi A. The dynamics of density dependent population models. J. Math. Biol. 4:1977;101-147
18. Levin S.A., Goodyear C.P. Analysis of an age-structured fishery model. J. Math. Biol. 9:1980;245-274
19. Metz J.A.J., Nisbet R.M., Geritz S.A.H. How should we define 'fitness' for general ecological scenarios? Trends Ecol. Evol. 7:1992;198-202
20. Neubert M., Caswell H. Density-dependent vital rates and their population dynamic consequences. J. Math. Biol. 43:2000;103-121
21. Ott E. Chaos in Dynamical Systems. 1993;Cambridge University Press, Cambridge, England
22. Rand D.A., Wilson H.B., McGlade J.M. Dynamics and evolution. evolutionarily stable attractors, invasion exponents and phenotype dynamics Philos. Trans. Roy. Soc. London B. 343:1994;261-283
23. Takada T., Nakajima H. An analysis of life history evolution in terms of the density-dependent Lefkovitch Matrix model. Math. Biosci. 112:1992;155-176
24. Takada T., Nakajima H. Theorems on the invasion process in stage-structured populations with density-dependent dynamics. J. Math. Biol. 36:1998;497-514
25. Tuljapurkar S.D. Population Dynamics in Variable Environments. 1990;Springer, New York
26. Tuljapurkar S.D., Orzack S.H. Population dynamics in variable environments. I. Long-run growth rates and extinction. Theo. Popul. Biol. 18:1980;314-342
27. Vincent T.L., Cohen Y., Brown J.S. Evolution via strategy dynamics. Theor. Popul. Biol. 44:1993;149-176