Necessary and sufficient conditions for R0 to be a sum of contributions of fertility loops

Journal of Mathematical Biology

Volumn 66, Issue 4-5, 2013, Pages 1099-1122

  Rueffler, Claus ^a   Metz, Johan A J ^b,c,d  

^a UNIVERSITY OF VIENNA   (Austria)

^b LEIDEN UNIVERSITY   (Netherlands)

^c NATURALIS BIODIVERSITY CENTER   (Netherlands)

^d INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS   (Austria)

Author keywords

Basic reproduction ratio; Conservation; Invasion; Matrix models; Population persistence

Indexed keywords

EID: 84874205849     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0575-0     Document Type: Article

References (15)

1. Caswell H (2001) Matrix Population Models, 2nd edn. Sinauer, US.
2. Cushing J, Yicang Z (1994) The net reproductive value and stability in matrix population models. Nat Res Model 8: 297-333.
3. de-Camino-Beck T, Lewis MA (2007) A new method for calculating net reproductive rate from graph reduction with applications to the control of invasive species. Bull Math Biol 69: 1341-1354.
4. de-Camino-Beck T, Lewis MA (2008) On net reproductive rate and the timing of reproductive output. Am Nat 172: 128-139.
5. 0 in models for infectious diseases in heterogeneous populations. J Math Biol 28: 365-382.
6. Horn R, Johnson C (1985) Matrix Analysis. Cambridge University Press, Cambridge.
7. Hurford A, Cownden D, Day T (2010) Nex-generation tools for evolutionary analysis. J R Soc Interface 7: 561-571.
8. Li C-K, Schneider H (2002) Applications of Perron-Frobenius theory to population dynamics. J Math Biol 44: 450-462.
9. Mason S (1956) Feedback theory: further properties of signal flow graphs. In: Proceedings of IRE 44: 920-926.
10. Metz JAJ.: On the concept of individual in ecology and evolution. J Math Biol (submitted).
11. Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations, vol. 68 of Lecture Notes in Biomathematics. Springer Verlag, Berlin.
12. Metz JAJ, Klinkhamer PGL, de Jong TJ (2009) A different model to explain delayed germination. Evol Ecol Res 11: 177-190.
13. Metz JAJ, Leimar O (2011) A simple fitness proxy for ESS calculations in structured populations with continuous traits, with applications to the evolution of haplo-diploids and genetic dimorphisms. J Biol Dyn 5: 163-190.
14. Rueffler C, Metz JAJ, van Dooren TJM (2012) What life cycle graphs can tell about the evolution of life histories. J Math Biol. doi: 10. 1007/s00285-012-0509-x.
15. Weppler T, Stoll P, Stöcklin J (2006) The relative importance of sexual and clonal reproduction for population growth in the long-lived alpine plant geum reptans. J Ecol 94: 869-879.