This is a first cut at a list of topics of interest in stochastic modeling of biological dynamics. The
emphases are on (1) a broad (but hopefully not too shallow) survey of the ways in which
stochasticity can affect the dynamics of biological systems, and (2) developing a toolbox of
methods that are useful for tackling stochastic models, with emphasis on practical approximate
and/or computational methods rather than rigorous proof.
Alonso, D., A. J. McKane, and M. Pascual (2007, June). Stochastic amplification in
epidemics. Journal of The Royal Society Interface 4(14), 575 –582.
Bobashev, G. V., M. D. Goedecke, F. Yu, and J. M. Epstein (2007, December).
A hybrid epidemic model: Combining the advantages of Agent-Based and
Equation-Based approaches. In Simulation Conference, 2007 Winter, pp. 1532–1537. IEEE.
Boerlijst, M. C., M. E. Lamers, and P. Hogeweg (1993, July). Evolutionary
consequences of spiral waves in a Host–Parasitoid system. Proceedings: Biological
Sciences 253(1336), 15–18.
Boerlijst, M. C. and W. M. van Ballegooijen (2010, December). Spatial pattern
switching enables cyclic evolution in spatial epidemics. PLoS Computational Biology 6,
Bolker, B. M. and S. W. Pacala (1999). Spatial moment equations for plant
competition: understanding spatial strategies and the advantages of short dispersal.
American Naturalist 153, 575–602.
Brown, S. P., S. J. Cornell, M. Sheppard, A. J. Grant, D. J. Maskell, B. T. Grenfell,
and P. Mastroeni (2006, October). Intracellular demography and the dynamics of
salmonella enterica infections. PLoS Biol 4(11), e349.
Denny, M. and S. Gaines (2002, September). Chance in Biology: Using Probability to
Explore Nature. Princeton University Press.
Doak, D. F., D. Bigger, E. K. Harding, M. A. Marvier, R. E. O’Malley, and
D. Thomson (1998, March). The statistical inevitability of StabilityDiversity
relationships in community ecology. The American Naturalist 151(3), 264–276.
Durrett, R. and S. Levin (1994). The importance of being discrete (and spatial).
Theoretical Population Biology 46(3), 363–394.
Gaines, S. D. and M. W. Denny (1993). The largest, smallest, highest, lowest, longest,
and shortest: extremes in ecology. Ecology 74, 1677–1692.
Gillespie, D. T. (2007). Stochastic simulation of chemical kinetics. Annual Review of
Physical Chemistry 58, 35–55. PMID: 17037977.
King, A. A., S. Shrestha, E. T. Harvill, and O. N. Bjrnstad (2009, April). Evolution of
acute infections and the InvasionPersistence TradeOff. The American Naturalist 173(4),
Levin, R. D. S. A. (1994). Stochastic spatial models: A user’s guide to ecological
applications. Philosophical Transactions: Biological Sciences 343, No. 1305, 329–350.
Lloyd, A. L. (2004, February). Estimating variability in models for recurrent
epidemics: assessing the use of moment closure techniques. Theoretical Population
Biology 65(1), 49–65.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (1994). Numerical
Recipes in C: the Art of Scientific Computing. Cambridge University Press.
Rand, D. A. and H. B. Wilson (1991, nov 22). Chaotic stochasticity: a ubiquitous
source of unpredictability in epidemics. Proceedings of the Royal Society B 246(1316), 6.
Ruel, J. J. and M. P. Ayres (1999, September). Jensen’s inequality predicts effects of
environmental variation. Trends in Ecology & Evolution 14(9), 361–366.