Stochastic formulation of ecological models and their applications

Trends in Ecology and Evolution

Volumn 27, Issue 6, 2012, Pages 337-345

  Black, Andrew J ^a   McKane, Alan J ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ECOLOGICAL MODELING; NUMERICAL MODEL; POPULATION STRUCTURE; STOCHASTICITY; THEORETICAL STUDY;

ALGORITHM; ANIMAL; COMPUTER SIMULATION; ECOLOGY; EPIDEMIC; HUMAN; REVIEW; STATISTICS; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; COMPUTER SIMULATION; ECOLOGY; EPIDEMICS; HUMANS; MODELS, THEORETICAL; STOCHASTIC PROCESSES;

EID: 84861331629     PISSN: 01695347     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tree.2012.01.014     Document Type: Review

References (90)

1. McKane A.J., Newman T.J. Predator-prey cycles from resonant amplification of demographic stochasticity. Phys. Rev. Lett. 2005, 94:218102.
2. Ross J.V. Stochastic models for mainland-island metapopulations in static and dynamic landscapes. Bull. Math. Biol. 2006, 68:417-449.
3. Black A.J., McKane A.J. Stochastic amplification in an epidemic model with seasonal forcing. J. Theor. Biol. 2010, 267:85-94.
4. Shahrezaei V., Swain P.S. Analytical distributions for stochastic gene expression. Proc. Natl. Acad. Sci. U.S.A. 2008, 105:17256-17261.
5. Butler T., Goldenfeld N. Fluctuation-driven Turing patterns. Phys. Rev. E 2011, 84:011112.
6. Higgins K., et al. Stochastic dynamics and deterministic skeletons: population behavior of Dungeness crab. Science 1997, 276:1431-1435.
7. Stenseth N.C., et al. Phase- and density-dependent population dynamics in Norwegian lemmings: interaction between deterministic and stochastic processes. Proc. R. Soc. B 1998, 265:1957-1968.
8. Bjornstad O.N., Grenfell B.T. Noisy clockwork: time series analysis of population fluctuations in animals. Science 2001, 293:638-643.
9. Rohani P., et al. The interplay between determinism and stochasticity in childhood diseases. Am. Nat. 2002, 159:469-481.
10. Reuman D.C., et al. Power spectra reveal the influence of stochasticity on nonlinear population dynamics. Proc. Nat. Acad. Sci. U.S.A. 2006, 103:18860-18865.
11. Krkosek M., et al. Cycles, stochasticity and density dependence in pink salmon population dynamics. Proc. R. Soc. B 2011, 278:2060-2068.
12. Gillespie D.T. Markov Processes: An Introduction for Physical Scientists 1992, Academic Press.
13. Assaf M., Meerson B. Extinction of metastable stochastic populations. Phys. Rev. E 2010, 81:021116.
14. Ovaskainen O., Meerson B. Stochastic models of population extinction. Trends Ecol. Evol. 2010, 25:643-652.
15. van Kampen N.G. Stochastic Processes in Physics and Chemistry 1992, Elsevier.
16. Alonso D., McKane A.J. Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model. Bull. Math. Biol. 2002, 64:913-958.
17. Newman T.J., et al. Extinction times and moment closure in the stochastic logistic process. Theor. Popul. Biol. 2004, 65:115-126.
18. Simoes M., et al. Stochastic fluctuations in epidemics on networks. J. R. Soc. Interface 2008, 5:555-566.
19. Rozhnova G., Nunes A. Cluster approximations for infection dynamics on random networks. Phys. Rev. E 2009, 80:051915.
20. Sharkey K.J. Deterministic epidemiological models at the individual level. J. Math. Biol. 2008, 57:311-331.
21. Dangerfield C.E., et al. Integrating stochasticity and network structure into an epidemic model. J. R. Soc. Interface 2009, 6:761-774.
22. Keeling M.J., Ross J.V. On methods for studying stochastic disease dynamics. J. R. Soc. Interface 2008, 5:171-181.
23. Goshal G., et al. SIS epidemics with household structure: the self-consistent field method. Math. Biosci. 2004, 190:71-85.
24. Ross J.V., et al. Calculation of disease dynamics in a population of households. PLoS ONE 2010, 5:e9666.
25. Kurtz T. Strong approximation theorems for density dependent Markov chains. Stoch. Process Appl. 1978, 6:223-240.
26. Baxendale P.H., Greenwood P.E. Sustained oscillations for density dependent Markov processes. J. Math. Biol. 2010, 63:433-457.
27. Wang Z., Goldenfeld N. Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts. Phys. Rev. E 2010, 82:011918.
28. Goutsias J. Classical versus stochastic kinetics modeling of biochemical reaction systems. Biophys. J. 2007, 92:2350-2365.
29. Grima R. Noise-induced breakdown of the Michaelis-Menten equation in steady-state conditions. Phys. Rev. Lett. 2009, 102:218103.
30. Campillo F., et al. Stochastic modeling of the chemostat. Ecol. Model. 2011, 222:2676-2689.
31. McKane A.J., Newman T.J. Stochastic models in population biology and their deterministic analogs. Phys. Rev. E 2004, 70:041902.
32. Durrett R., Levin S. The importance of being discrete (and spatial). Theor. Popul. Biol. 1994, 46:363-394.
33. McKane A.J., et al. Analytic solution of Hubbell's model of local community dynamics. Theor. Popul. Biol. 2004, 65:67-73.
34. Antonovics J., Edwards M. Spatio-temporal dynamics of bumblebee nest parasites (Bombus subgenus Psythirus ssp.) and their hosts (Bombus spp.). J. Anim. Ecol. 2011, 80:999-1011.
35. Volkov I., et al. Density dependence explains tree species abundance and diversity in tropical forests. Nature 2005, 438:658-661.
36. Muneepeerakul R., et al. Neutral metacommunity models predict fish diversity patterns in Mississippi-Missouri basin. Nature 2008, 453:220-222.
37. Rosindell J., et al. Protracted speciation revitalizes the neutral theory of biodiversity. Ecol. Lett. 2010, 13:716-727.
38. Vanpeteghem D., Haegeman B. An analytic approach to spatio-temporal dynamics of neutral community models. J. Math. Biol. 2010, 61:323-357.
39. Kuske R., et al. Sustained oscillations via coherence resonance in SIR. J. Theor. Biol. 2007, 245:459-469.
40. Brauer F., Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology 2001, Springer.
41. Priestley M.B. Spectral Analysis and Time Series 1982, Academic Press.
42. Boland R.P., et al. Limit cycles, complex Floquet multipliers and intrinsic noise. Phys. Rev. E 2009, 79:051131.
43. Pineda-Krch M., et al. A tale of two cycles - distinguishing quasi-cycles and limit cycles in finite predator-prey populations. Oikos 2007, 116:53-64.
44. Turing A.M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 1952, 237:37-72.
45. Maron J.L., Harrison S. Spatial pattern formation in an insect host-parasitoid system. Science 1997, 278:1619-1621.
46. Reitkerk M., van de Koppel J. Regular pattern formation in real ecosystems. Trends Ecol. Evol. 2008, 23:169-175.
47. Murray J.D. Mathematical Biology, II: Spatial Models and Biomedical Applications 2002, Springer-Verlag.
48. Butler T., Goldenfeld N. Robust ecological pattern formation induced by demographic noise. Phys. Rev. E 2009, 80:030902.
49. Biancalani T., et al. Stochastic Turing patterns in the Brusselator model. Phys. Rev. E 2010, 81:046215.
50. Scott M., et al. Approximating intrinsic noise in continuous multispecies models. Proc. R. Soc. A 2010, 467:718-737.
51. Woolley T.E., et al. Power spectra methods for a stochastic description of diffusion on deterministically growing domains. Phys. Rev. E 2011, 84:021915.
52. Bartlett M.S. Stochastic Population Models in Ecology and Epidemiology 1960, Methuen.
53. Nasell I. Stochastic models of some endemic infections. Math. Biosci. 2002, 179:1-19.
54. Stollenwerk N., Jansen V.A.A. Meningitis, pathogenicity near criticality: the epidemiology of meningococcal disease as a model for accidental pathogens. J. Theor. Biol. 2003, 222:347-359.
55. Bauch C.T., Earn D.J.D. Transients and attractors in epidemics. Proc. R. Soc. Lond. B 2003, 270:1573-1578.
56. Keeling M.J., Rohani P. Modelling Infectious Diseases in Humans and Animals 2007, Princeton University Press.
57. Metcalf C.J.E., et al. The epidemiology of rubella in Mexico: seasonality, stochasticity and regional variation. Epidemiol. Infect. 2011, 139:1029-1038.
58. Altizer S., et al. Seasonality and the dynamics of infectious diseases. Ecol. Lett. 2006, 9:467-484.
59. Mantilla-Beniers N.B., et al. Decreasing stochasticity through enhanced seasonality in measles epidemics. J. R. Soc. Interface 2010, 7:727-739.
60. Earn D., et al. A simple model for complex dynamical transitions in epidemics. Science 2000, 287:667-670.
61. Bauch C.T., Earn D.J.D. Interepidemic intervals in forced and unforced SEIR models. Fields Inst. Comm. 2003, 36:33-44.
62. Coulson T., et al. Skeletons, noise and population growth: the end of an old debate?. Trends Ecol. Evol. 2004, 19:359-364.
63. Nguyen H.T.H., Rohani P. Noise, nonlinearity and seasonality: the epidemics of whooping cough revisited. J. R. Soc. Interface 2008, 5:403-413.
64. Black A.J., McKane A.J. Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough. J. R. Soc. Interface 2010, 7:1219-1227.
65. Rohani P., et al. Opposite patterns of synchrony in sympatric disease metapopulations. Science 1999, 286:968-971.
66. Traulsen A., et al. Coevolutionary dynamics: from finite to infinite populations. Phys. Rev. Lett. 2005, 95:238701.
67. Reichenbach T., et al. Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 2007, 448:1046-1049.
68. Altrock P.M., et al. Stochastic slowdown in evolutionary processes. Phys. Rev. E 2010, 82:011925.
69. Thomas P., et al. Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models. J. Chem. Phys. 2010, 133:195101.
70. Assaf M., et al. Determining the stability of genetic switches: explicitly accounting for mRNA noise. Phys. Rev. Lett. 2011, 106:248102.
71. Waclaw B., et al. Dynamical phase transition in a model for evolution with migration. Phys. Rev. Lett. 2011, 105:268101.
72. Lloyd A.L. Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods. Proc. R. Soc. Lond. B 2001, 268:985-993.
73. Ross J.V., et al. On parameter estimation in population models II: multi-dimensional processes and transient dynamics. Theor. Popul. Biol. 2009, 75:123-132.
74. Powell C.R., Boland R.P. The effects of stochastic population dynamics on food web structure. J. Theor. Biol. 2009, 257:170-180.
75. Murase Y., et al. Effects of demographic stochasticity on biological community assembly on evolutionary time scales. Phys. Rev. E 2010, 81:041908.
76. Galla T. Independence and interdependence in the nest-site choice by honeybee swarms: agent-based models, analytical approaches and pattern formation. J. Theor. Biol. 2010, 262:186-196.
77. Spence L.A., et al. Disturbance affects short-term facilitation, but not long-term saturation, of exotic plant invasion in New Zealand forest. Proc. R. Soc. B 2011, 278:1457-1466.
78. Levins R. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am. 1969, 15:227-240.
79. Grimm V., et al. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 2005, 310:987-991.
80. Ferguson N.M., et al. Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 2005, 437:209-214.
81. Hubbell S.P. The Unified Neutral Theory of Biodiversity and Biogeography 2001, Princeton University Press.
82. Moran P.A.P. The Statistical Processes of Evolutionary Theory 1962, Oxford University Press.
83. Alonso D., et al. The merits of neutral theory. Trends Ecol. Evol. 2006, 21:451-457.
84. Rosindell J., et al. The unified neutral theory of biodiversity and biogeography at age ten. Trends Ecol. Evol. 2011, 26:340-348.
85. Warren P.B. Biodiversity on island chains: neutral model simulations. Phys. Rev. E 2010, 82:051922.
86. Economo E.P., Keitt T.H. Species diversity in neutral metacommunities: a network approach. Ecol. Lett. 2008, 11:52-62.
87. Hanski I. Metapopulation Ecology 1999, Oxford University Press.
88. Ross J.V., et al. Metapopulation persistence in a dynamic landscape: more habitat or better stewardship?. Ecol. Appl. 2008, 18:590-598.
89. Levin S.A., Segel L.A. Hypothesis for origin of planktonic patchiness. Nature 1976, 259:659.
90. Waddell J.N., et al. Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. Theor. Popul. Biol. 2010, 77:279-286.