Theoretical Ecology

, Volume 8, Issue 1, pp 53–65 | Cite as

Heterogeneity in symbiotic effects facilitates Wolbachia establishment in insect populations

  • Caetano Souto-Maior
  • Joao S. Lopes
  • Erida Gjini
  • Claudio J. Struchiner
  • Luis Teixeira
  • M. Gabriela M. Gomes


Facultative vertically transmitted bacterial symbionts often manipulate its host’s reproductive biology and thus facilitate their persistence. Wolbachia is one such symbiont where frequency-dependent reproductive benefits are opposed by frequency-independent fitness costs leading to bistable dynamics. Introduction of carriers does not assure invasion unless the initial frequency is above a threshold determined by the balance of costs and benefits. Recent laboratory experiments have uncovered that Wolbachia also protects their hosts from pathogens. The expected consequence of this phenotype in natural environments is to lower the invasion threshold by a factor that increases with the extent of pathogen exposure. Here, we introduce a series of mathematical models to address how pathogen protection affects Wolbachia invasion. First, under homogeneous symbiotic effects, we obtain an analytical expression for the invasion threshold in terms of pathogen exposure, and find a regime where symbiont releases may result in elimination of the entire host population provided that abundance of virulent pathogens is high. Second, we distribute Wolbachia effects such that some carriers are totally protected and others not at all, and explore how this interplays with different pathogen intensities, to conclude that heterogeneity further lowers the threshold for Wolbachia invasion. Third, we replicate the analysis using a realistic distribution of protective effects and confirm that heterogeneity increases system resilience by reducing the odds of population collapse.


Wolbachia Symbiont Heterogeneity Invasion threshold Bistable dynamics Mathematical model 

Supplementary material

12080_2014_235_MOESM1_ESM.pdf (132 kb)
(PDF 132 KB)
12080_2014_235_MOESM2_ESM.pdf (208 kb)
(PDF 208 KB)


  1. Barton NH, Turelli M (2011) Spatial waves of advance with bistable dynamics: cytoplasmic and genetic analogues of Allee effects. Am Nat 178:E4875. doi: 10.1086/661246 CrossRefGoogle Scholar
  2. Bellows TS (1981) The descriptive properties of some models for density dependence. J Anim Ecol 50:139–156CrossRefGoogle Scholar
  3. Bian G, Joshi D, Dong Y, et al. (2013) Wolbachia invades Anopheles stephensi populations and induces refractoriness to Plasmodium infection. Science 340:748–751. doi: 10.1126/science.1236192 CrossRefPubMedGoogle Scholar
  4. Blagrove M, Arias-Goeta C, F AB, Sinkins S (2012) Wolbachia strain wMel induces cytoplasmic incompatibility and blocks dengue transmission in Aedes albopictus. Proc Natl Acad Sci 109:255–260. doi: 10.1073/pnas.1112021108 CrossRefPubMedGoogle Scholar
  5. Calvitti M, Moretti R, Skidmore AR, Dobson SL (2012) Wolbachia strain wPip yields a pattern of cytoplasmic incompatibility enhancing a Wolbachia-based suppression strategy against the disease vector Aedes albopictus. Parasit Vectors 5:254. doi: 10.1186/1756-3305-5-254 CrossRefPubMedPubMedCentralGoogle Scholar
  6. Calzolari M, Zé-Zé L, Ružk D, et al. (2012) Detection of mosquito-only flaviviruses in Europe. J Gen Virol 93:1215–1225. doi: 10.1099/vir.0.040485-0 CrossRefPubMedGoogle Scholar
  7. Carrington LB, Lipkowitz JR, Hoffmann AA, Turelli M (2011) A re-examination of Wolbachia-induced cytoplasmic incompatibility in California Drosophila simulans. PLoS One 6:e22565. doi: 10.1371/journal.pone.0022565 CrossRefPubMedPubMedCentralGoogle Scholar
  8. Caspari E, Watson GS (1959) On the evolutionary importance of cytoplasmic sterility in mosquitoes. Evolution (N Y) 13:568–570Google Scholar
  9. Chrostek E, Marialva MS, Esteves SS, Weinert LA, Martinez J, Jiggins FM, Teixeira L (2014) Wolbachia variants induce differential protection to viruses in Drosophila melanogaster: a phenotypic and phylogenomic analysis. PLoS Genet 9 ((12)):e1003896Google Scholar
  10. Crain PR, Mains JW, Suh E et al (2011) Wolbachia infections that reduce immature insect survival: predicted impacts on population replacement. BMC Evol Biol 11:290. doi: 10.1186/1471-2148-11-290 CrossRefPubMedPubMedCentralGoogle Scholar
  11. Dobson SL, Fox CW, Jiggins FM (2002) The effect of Wolbachia-induced cytoplasmic incompatibility on host population size in natural and manipulated systems. Proc Biol Sci 269:437–445. doi: 10.1098/rspb.2001.1876 CrossRefPubMedPubMedCentralGoogle Scholar
  12. Fenton A, Johnson KN, Brownlie JC, Hurst GDD (2011) Solving the Wolbachia paradox: modeling the tripartite interaction between host, Wolbachia, and a natural enemy. Am Nat 178:333–342. doi: 10.1086/661247 CrossRefPubMedGoogle Scholar
  13. Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugen 7:355–369CrossRefGoogle Scholar
  14. Gomes MGM, Lipsitch M, Wargo AR, et al. (2014) A missing dimension in measures of vaccination impacts. PLoS Pathog 10:e1003849. doi: 10.1371/journal.ppat.1003849 CrossRefPubMedPubMedCentralGoogle Scholar
  15. Hancock PA, Godfray HCJ (2012) Modelling the spread of Wolbachia in spatially heterogeneous environments. J R Soc Interface 9:3045–3054. doi: 10.1098/rsif.2012.0253 CrossRefPubMedPubMedCentralGoogle Scholar
  16. Hancock PA, Sinkins SP, Godfray HCJ (2011) Population dynamic models of the spread of Wolbachia. Am Nat 177:323–333. doi: 10.1086/658121 CrossRefPubMedGoogle Scholar
  17. Hassell M, Lawton J, May RM (1976) Patterns of dynamical behaviour in single-species populations. J Anim Ecol 45:471–486CrossRefGoogle Scholar
  18. Hedges LM, Brownlie JC, O’Neill SL, Johnson KN (2008) Wolbachia and virus protection in insects. Science 322 ((80- )):702. doi: 10.1126/science.1162418 CrossRefPubMedGoogle Scholar
  19. Hilgenboecker K, Hammerstein P, Schlattmann P, et al. (2008) How many species are infected with Wolbachia?—a statistical analysis of current data. FEMS Microbiol Lett 281:215–220. doi: 10.1111/j.1574-6968.2008.01110.x CrossRefPubMedPubMedCentralGoogle Scholar
  20. Himler AG, Adachi-Hagimori T, Bergen JE, et al. (2011) Rapid spread of a bacterial symbiont in an invasive whitefly is driven by fitness benefits and female bias. Science 332 ((80- )):254–256. doi: 10.1126/science.1199410 CrossRefPubMedGoogle Scholar
  21. Hoffmann AA, Montgomery BL, Popovici J, et al. (2011) Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission. Nature 476:454–457. doi: 10.1038/nature10356 CrossRefPubMedGoogle Scholar
  22. Hoffmann AA, Turelli M, Harshman LG (1990) Factors affecting the distribution of cytoplasmic incompatibility in Drosophila simulans. Genetics 126:933–948PubMedPubMedCentralGoogle Scholar
  23. Hoffmann AA, Turelli M, Simmons GM (1986) Unidirectional incompatibility between populations of Drosophila simulans. Evolution (N Y) 40:692–701Google Scholar
  24. Jansen VAA, Turelli M, Godfray HCJ (2008) Stochastic spread of Wolbachia. Proc R Soc B Biol Sci 275:2769–2776. doi: 10.1098/rspb.2008.0914 CrossRefGoogle Scholar
  25. Jones EO, White A, Boots M (2007) Interference and the persistence of vertically transmitted parasites. J Theor Biol 246:10–17. doi: 10.1016/j.jtbi.2006.12.007 CrossRefPubMedGoogle Scholar
  26. Jones EO, White A, Boots M (2011) The evolution of host protection by vertically transmitted parasites. Proc R Soc B Biol Sci 278:863–870. doi: 10.1098/rspb.2010.1397 CrossRefGoogle Scholar
  27. Kendall B, Fox G, Fujiwara M, Nogeire T (2011) Demographic heterogeneity, cohort selection, and population growth. Ecology 92:1985–1993CrossRefPubMedGoogle Scholar
  28. Lively CM, Clay K, Wade MJ, Fuqua C (2005) Competitive co-existence of vertically and horizontally transmitted parasites. Evol Ecol Res 7:1183–1190Google Scholar
  29. Luo S, Koelle K (2013) Navigating the devious course of evolution : the importance of mechanistic models for identifying eco-evolutionary dynamics in nature. Am Nat 181:S58–S75. doi: 10.1086/669952 CrossRefPubMedGoogle Scholar
  30. Maciel-de-Freitas R, Aguiar R, Bruno RV, et al. (2012) Why do we need alternative tools to control mosquito-borne diseases in Latin America. Mem Inst Oswaldo Cruz 107:828–829CrossRefPubMedGoogle Scholar
  31. Maciel-de-Freitas R, Koella JC, Lourenço-de-Oliveira R (2011) Lower survival rate, longevity and fecundity of Aedes aegypti (Diptera: Culicidae) females orally challenged with dengue virus serotype 2. Trans R Soc Trop Med Hyg 105:452–458. doi: 10.1016/j.trstmh.2011.05.006 CrossRefPubMedGoogle Scholar
  32. Maynard-Smith J, Slatkin M (1973) The stability of predator-prey systems. Ecology 54:384–391. doi: 10.2307/1934346 CrossRefGoogle Scholar
  33. McGraw EA, O’Neill SL (2013) Beyond insecticides: new thinking on an ancient problem. Nat Rev Microbiol 11:181–193. doi: 10.1038/nrmicro2968 CrossRefPubMedGoogle Scholar
  34. Moreira LA, Iturbe-Ormaetxe I, Jeffery JA, et al. (2009) A Wolbachia symbiont in Aedes aegypti limits infection with Dengue, Chikungunya, and Plasmodium. Cell 139:1268–1278. doi: 10.1016/j.cell.2009.11.042 CrossRefPubMedGoogle Scholar
  35. O’Hagan JJ, Hernán MA, Walensky RP, Lipsitch M (2012) Apparent declining efficacy in randomized trials: examples of the RV144 HIV vaccine and CAPRISA 004 microbicide trials. AIDS 26:123–126. doi: doi: 10.1097/QAD.0b013e32834e1ce7.Apparent doi: 10.1097/QAD.0b013e32834e1ce7.Apparent CrossRefPubMedPubMedCentralGoogle Scholar
  36. Osborne SE, Leong YS, O’Neill SL, Johnson KN (2009) Variation in antiviral protection mediated by different Wolbachia strains in Drosophila simulans. PLoS Pathog 5:e1000656. doi: 10.1371/journal.ppat.1000656 CrossRefPubMedPubMedCentralGoogle Scholar
  37. Pessoa D, Souto-Maior C, Gjini E, et al. (2014) Unveiling time in dose-response models to infer host susceptibility to pathogens, PLOS Comput Biol 10(8):e1003773Google Scholar
  38. Rasgon JL, Styer LM, Scott TW (2003) Wolbachia-induced mortality as a mechanism to modulate pathogen transmission by vector arthropods. J Med Entomol 40:125–132CrossRefPubMedGoogle Scholar
  39. Schmid-Hempel P (1998) Parasites in social insects. Princeton University PressGoogle Scholar
  40. Smith PG, Rodrigues LC, Fine PE (1984) Assessment of the protective efficacy of vaccines against common diseases using case-control and cohort studies. Int J Epidemiol 13:87–93CrossRefPubMedGoogle Scholar
  41. Southwood T, Murdie G, Yasuno M, et al. (1972) Studies on the life budget of Aedes aegypti in Wat Samphaya, Bangkok, Thailand. Bull World Health Organ 46:211–226PubMedPubMedCentralGoogle Scholar
  42. Taylor CM, Hastings A (2005) Allee effects in biological invasions. Ecol Lett 8:895–908. doi: 10.1111/j.1461-0248.2005.00787.x CrossRefGoogle Scholar
  43. Teixeira L, Ferreira A, Ashburner M (2008) The bacterial symbiont Wolbachia induces resistance to RNA viral infections in Drosophila melanogaster. PLoS Biol 6:e1000002. doi: 10.1371/journal.pbio.1000002 CrossRefPubMedCentralGoogle Scholar
  44. Turelli M (2010) Cytoplasmic incompatibility in populations with overlapping generations. Evolution (N Y) 64:232–241. doi: 10.1111/j.1558-5646.2009.00822.x Google Scholar
  45. Turelli M, Hoffmann AA (1995) Cytoplasmic incompatibility in Drosophila simulans: dynamics and parameter estimates from natural populations. Genetics 140:1319–1338PubMedPubMedCentralGoogle Scholar
  46. Turelli M, Hoffmann AA (1991) Rapid spread of an inherited incompatibility factor in California Drosophila. Nature 353:440–442. doi: 10.1038/353440a0 CrossRefPubMedGoogle Scholar
  47. Vaupel JW, Yashin AI (1985) Heterogeneity’s ruses: some surprising effects of selection on population dynamics. Am Stat 39:176–185PubMedGoogle Scholar
  48. Vavre F, Charlat S (2012) Making (good) use of Wolbachia: what the models say. Curr Opin Microbiol 15:263–268. doi: 10.1016/j.mib.2012.03.005 CrossRefPubMedGoogle Scholar
  49. Walker T, Johnson PH, Moreira LA, et al. (2011) The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations. Nature 476:450–453. doi: 10.1038/nature10355 CrossRefPubMedGoogle Scholar
  50. Werren JH, Baldo L, Clark ME (2008) Wolbachia: master manipulators of invertebrate biology. Nat Rev Microbiol 6:741–751. doi: 10.1038/nrmicro1969 CrossRefPubMedGoogle Scholar
  51. Yeap HL, Mee P, Walker T, et al. (2011) Dynamics of the “popcorn” Wolbachia infection in outbred Aedes aegypti informs prospects for mosquito vector control. Genetics 187:583–595. doi: 10.1534/genetics.110.122390 CrossRefPubMedPubMedCentralGoogle Scholar
  52. Zabalou S, Riegler M, Theodorakopoulou M (2004) Wolbachia-induced cytoplasmic incompatibility as a means for insect pest population control. Proc Natl Acad Sci USA 101:15042–15045. doi: 10.1073/pnas.0403853101 CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Caetano Souto-Maior
    • 1
  • Joao S. Lopes
    • 1
  • Erida Gjini
    • 1
  • Claudio J. Struchiner
    • 2
  • Luis Teixeira
    • 1
  • M. Gabriela M. Gomes
    • 1
  1. 1.Instituto Gulbenkian de CiênciaOeirasPortugal
  2. 2.Programa de Computação Científica, Fundação Oswaldo CruzRio de JaneiroBrazil

Personalised recommendations