Fatal or Harmless: Extreme Bistability Induced by Sterilizing, Sexually Transmitted Pathogens

Bulletin of Mathematical Biology

Volumn 75, Issue 2, 2013, Pages 258-273

  Berec, Luděk ^a,b   Maxin, Daniel ^c  

^a Biology Centre of the Academy of Sciences of the Czech Republic   (Czech Republic)

^b UNIVERSITY OF SOUTH BOHEMIA   (Czech Republic)

^c VALPARAISO UNIVERSITY   (United States)

Author keywords

Disease transmission; Mating; Population dynamics; Population management; Sexually transmitted disease

Indexed keywords

ANIMALIA;

EID: 84873750513     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-012-9802-5     Document Type: Article

References (36)

1. Anderson, R. M., & May, R. M. (1979). Population biology of infectious diseases. I. Nature, 280, 361-367.
2. Berec, L., Angulo, E., & Courchamp, F. (2007). Multiple Allee effects and population management. Trends Ecol. Evol., 22, 185-191.
3. Bessa-Gomes, C., Legendre, S., & Clobert, J. (2004). Allee effects, mating systems and the extinction risk in populations with two sexes. Ecol. Lett., 7, 802-812.
4. Busenberg, S., & van den Driessche, P. (1990). Analysis of a disease transmission model in a population with varying size. J. Math. Biol., 28, 257-270.
5. Castillo-Chavez, C., & Huang, W. (1995). The logistic equation revisited: the two-sex case. Math. Biosci., 128, 299-316.
6. Caswell, H., & Weeks, D. E. (1986). Two-sex models: chaos, extinction, and other dynamic consequences of sex. Am. Nat., 128, 707-735.
7. Courchamp, F., Berec, L., & Gascoigne, J. (2008). Allee effects in ecology and conservation. Oxford: Oxford Univ. Press.
8. Dieckmann, U. (2002). Adaptive dynamics of pathogen-host interactions. In U. Dieckmann, J. A. J. Metz, M. W. Sabelis, & K. Sigmund (Eds.), Adaptive dynamics of infectious diseases (pp. 39-59). Cambridge: Cambridge Univ. Press.
9. Diekmann, O., & Kretzschmar, M. (1991). Patterns in the effects of infectious diseases on population growth. J. Math. Biol., 29, 539-570.
10. Gao, L. Q., & Hethcote, H. W. (1992). Disease transmission models with density-dependent demographics. J. Math. Biol., 30, 717-731.
11. Gascoigne, J., Berec, L., Gregory, S., & Courchamp, F. (2009). Dangerously few liaisons: a review of mate-finding Allee effects. Popul. Ecol., 51, 355-372.
12. Getz, W. M., & Pickering, J. (1983). Epidemic models: thresholds and population regulation. Am. Nat., 121, 892-898.
13. Hadeler, K. P., Waldstätter, R., & Wörz-Busekros, A. (1988). Models for pair formation in bisexual populations. J. Math. Biol., 26, 635-649.
14. Hardy, C. M., Hinds, L. A., Kerr, P. J., Lloyd, M. L., Redwood, A. J., Shellam, G. R., & Strive, T. (2006). Biological control of vertebrate pests using virally vectored immunocontraception. J. Reprod. Immunol., 71, 102-111.
15. Hilker, F. M. (2010). Population collapse to extinction: the catastrophic combination of parasitism and Allee effect. Journal of Biological Dynamics, 4, 86-101.
16. Hilker, F. M., Langlais, M., & Malchow, H. (2009). The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations. Am. Nat., 173, 72-88.
17. Iannelli, M., Martcheva, M., & Milner, F. A. (2005). Gender-structured population modeling. Philadelphia: SIAM.
18. Jaenike, A. (1996). Suboptimal virulence of an insect-parasitic nematode. Evolution, 50, 2241-2247.
19. Knell, R. J., & Webberley, K. M. (2004). Sexually transmitted diseases of insects: distribution, evolution, ecology and host behaviour. Biol. Rev., 79, 557-581.
20. Kokko, H., & Morrell, L. J. (2005). Mate guarding, male attractiveness, and paternity under social monogamy. Behav. Ecol., 16, 724-731.
21. Kramer, A. M., Dennis, B., Liebhold, A. M., & Drake, J. M. (2009). The evidence for Allee effects. Popul. Ecol., 51, 341-354.
22. Lindström, J., & Kokko, H. (1998). Sexual reproduction and population dynamics: the role of polygyny and demographic sex differences. Proc. R. Soc. Lond. B, 265, 483-488.
23. Little, S. (2001). Reproduction and breeding management in cats. Vet. Med., 96, 549-555.
24. Lockhart, A. B., Thrall, P. H., & Antonovics, J. (1996). Sexually transmitted diseases in animals: ecological and evolutionary implications. Biol. Rev., 71, 415-471.
25. McCallum, H., Barlow, N., & Hone, J. (2001). How should pathogen transmission be modelled? Trends Ecol. Evol., 16, 295-300.
26. Miller, T. E. X., & Inouye, B. D. (2011). Confronting two-sex demographic models with data. Ecology, 92, 2141-2151.
27. Møller, A. P., & Birkhead, T. R. (1992). A pairwise comparative method as illustrated by copulation frequency in birds. Am. Nat., 139, 644-656.
28. O'Keefe, K. J., & Antonovics, J. (2002). Playing by different rules: the evolution of virulence in sterilizing pathogens. Am. Nat., 159, 597-605.
29. Parvinen, K. (2005). Evolutionary suicide. Acta Biotheor., 53, 241-264.
30. Pugliese, A. (1990). Population models for diseases with no recovery. J. Math. Biol., 28, 65-82.
31. Rankin, D. J., & Kokko, H. (2007). Do males matter? The role of males in population dynamics. Oikos, 116, 335-348.
32. Shuster, S. M., & Wade, M. J. (2003). Mating systems and strategies. Princeton: Princeton Univ. Press.
33. Sloan, D. B., Giraud, T., & Hood, M. E. (2008). Maximized virulence in a sterilizing pathogen: the anther-smut fungus and its co-evolved hosts. J. Evol. Biol., 21, 1544-1554.
34. Thrall, P. H., & Antonovics, J. (1997). Polymorphism in sexual versus non-sexual disease transmission. Proc. R. Soc. Lond. B, 264, 581-587.
35. Tobin, P. C., Robinet, C., Johnson, D. M., Whitmire, S. L., Bjørnstad O. N., & Liebhold, A. M. (2009). The role of Allee effects in gypsy moth, Lymantria dispar (L.), invasions. Popul. Ecol., 51, 373-384.
36. Vynnycky, E., & White, R. G. (2010). An introduction to infectious disease modelling. Oxford: Oxford Univ. Press.