Applications of percolation theory to fungal spread with synergy

Journal of the Royal Society Interface

Volumn 9, Issue 70, 2012, Pages 949-956

  Ludlam, Jonathan J ^a   Gibson, Gavin J ^b   Otten, Wilfred ^c   Gilligan, Christopher A ^d  

^a CHURCHILL COLLEGE   (United Kingdom)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF ABERTAY DUNDEE   (United Kingdom)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Bayesian inference; Markov chain methods; Microcosm experiments; Percolation; Saprotrophic invasion; Synergistic interactions

Indexed keywords

ANIMALS; BAYESIAN NETWORKS; DYNAMICS; EXPERIMENTS; INFERENCE ENGINES; MARKOV PROCESSES; PERCOLATION (SOLID STATE); POPULATION STATISTICS; SOLVENTS;

BAYESIAN INFERENCE; MARKOV CHAIN METHOD; MICROCOSM EXPERIMENTS; SAPROTROPHIC INVASION; SYNERGISTIC INTERACTION;

DISEASE CONTROL;

ARTICLE; BAYESIAN LEARNING; DISEASE CONTROL; FUNGUS; HOST SUSCEPTIBILITY; NONHUMAN; PARASITE; SAPROTROPH;

ANIMALIA; FUNGI;

EID: 84860729696     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2011.0506     Document Type: Article

References (20)

1. Frisch, H. L. & Hammersley, J. M. 1963 Percolation processes and related topics J. SIAM 11, 894-918.
2. Cardy, J. L. & Grassberger, P. 1985 Epidemic models and percolation. J. Phys. A Math. Gen. 18, L267-L271. (doi:10.1088/0305-4470/18/6/001)
3. Grassberger, P. 1983 On the critical behaviour of the general epidemic process and dynamical percolation. Math. Biosci. 63, 157-172. (doi:10.1016/0025-5564(82)90036-0)
4. Gibson, G. J., Otten, W., Filipe, J. A. N., Cook, A., Marion, G. & Gilligan, C. A. 2006 Bayesian estimation for percolation models of disease spread in plant populations. Stat. Comput. 16, 391-402. (doi:10.1007/s11222-006- 0019-z)
5. Bailey, D. J., Otten, W. & Gilligan, C. A. 2000 Percolation, heterogeneity and the saprotrophic invasion of soil by the fungal plant pathogen Rhizoctonia solani. New Phytol. 146, 535-544. (doi:10.1046/j.1469-8137.2000. 00660.x)
6. Otten, W., Bailey, D. J. & Gilligan, C. A. 2004 Empirical evidence of spatial thresholds to control invasion of fungal parasites and saprotrophs. New Phytol. 163, 125-132. (doi:10.1111/j.1469-8137.2004.01086.x)
7. Davis, S., Trapman, P., Leirs, H., Begon, M. & Heesterbeek, J. A. P. 2008 The abundance threshold for plague as a critical percolation phenomenon. Nature 454, 634-637. (doi:10. 1038/nature07053)
8. Perez-Reche, F. J., Ludlam, J. J., Taraskin, S. N. & Gilligan, C. A. 2011 Synergy in spreading processes: from exploitative to explorative foraging strategies. Phys. Rev. Lett. 106, 218701. (doi:10.1103/PhysRevLett.106.218701)
9. Lockwood, J. L. 1988 Evolution of concepts associated with soilborne plant pathogens. Annu. Rev. Phytopathol. 26, 732-746. (doi:10.1146/annurev.py. 26.090188.000521)
10. Olsson, S. 1995 Mycelial density profiles of fungi on heterogeneous media and their interpretation in terms of nutrient reallocation patterns. Mycol. Res. 99, 143-153. (doi:10.1016/S0953-7562(09)80878-2)
11. Wells, J. M., Boddy, L. & Donnelly, D. P. 1998 Wood decay and phosphorus translocation by the cord-forming basidiomycete Phanerochaete velutina: the significance of local nutrient supply. New Phytol. 138, 607-617. (doi:10.1046/j.1469-8137.1998.00144.x)
12. Davidson, F. A. 1998 Modelling the qualitative response of fungal mycelia to heterogeneous environments. J. Theor. Biol. 195, 281-292. (doi:10.1006/jtbi.1998.0739)
13. Zakaria, A. J. & Boddy, L. 2002 Mycelial foraging by Resinicium bicolor: interactive effects of resource quantity, quality and soil composition. FEMS Microbiol. Ecol. 40, 135-142. (doi:10.1111/j.1574-6941.2002.tb00945.x)
14. Gilligan, C. A. 2002 An epidemiological framework for disease management. Adv. Botanical Res. 38, 1-64. (doi:10.1016/S0065-2296(02)38027-3)
15. Sneh, B., Jabaji-Hare, S., Neate, S. & Dijst, G. (eds) 1996 Rhizoctonia species, taxonomy, molecular biology, ecology, pathology and disease control. Dordrecht, The Netherlands: Kluwer.
16. Green, P. J. 1995 Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732. (doi:10.1093/biomet/ 82.4.711)
17. Gibson, G. J. 1997 Markov chain Monte Carlo methods for fitting and testing spatio-temporal stochastic models in plant epidemiology. Appl. Stat. 46, 215-233. (doi:10. 1111/1467-9876.00061)
18. Cox, J. T. & Durrett, R. 1988 Limit-theorems for the spread of epidemics and forest fires. Stoch. Process. Appl. 30, 171-191. (doi:10.1016/0304-4149(88)90083-X)
19. O'Neill, P. D. & Becker, N. G. 2001 Inference for an epidemic when susceptibility varies. Biostatistics 2, 99-108. (doi:10.1093/biostatistics/2.1. 99)
20. Streftaris, G. & Gibson, G. J. 2004 Bayesian analysis of experimental epidemics of foot-and-mouth disease. Proc. R. Soc. Lond. B 271, 1111-1117. (doi:10.1098/rspb.2004.2715)