I’ve got a headful of ideas that are driving me insane … (Bob Dylan, Maggie’s Farm)

These are all ideas that have floated through my head at one time or another that would be interesting to work on but that I simply haven’t gotten around to. Some of them could be appropriate for thesis (undergraduate, Master’s, Ph.D …) projects. Please contact me if any of them strikes you as interesting. Any of my papers that are listed below should be available at my web site (for access to PDFs use username bbpapers, password research).

Epidemics

  • use multivariate autoregressive state-space models (MARSS, e.g. from Eli Holmes’s MARSS package to explore the dynamics either of multi-species pathogens (e.g. West Nile virus, Batrachochytrium dendrobatidis) or of multiple pathogens in a single host (e.g. data from David Earn on London Bills of Mortality).
  • explore the degree to which initial epidemic curves seem to follow power-law, rather than exponential, trajectories? (inspired by Australian AIDS data from Dobson and Barnett (see STAT 4C03 lecture notes), IIDDA (under construction), perhaps look for other infectious disease data bases?)
  • use susceptible reconstruction approaches and linearization methods to solve for temporally and/or spatial varying parameters (notes) (Fine and Clarkson 1982; de Jonge 2014)
  • review of modern nonlinear methods (see BIRS notes below)

Related: Ives et al. (2003), BIRS meeting programme, especially videos, especially Wood, Timmer, King

Functional responses

  • Review/polishing of approaches for function response modeling, incorporating depletion, multi-species, etc. etc.: see online notes (PDF, Rnw). The idea here is to review current approaches and synthesize techniques, finding out which problems can be solved via judicious use of the Lambert W function, which can be solved by one-dimensional root-finding, and which have to be solved by brute force solutions of ODEs.
  • build a general-purpose multi-predator, size-dependent-prey ODE simulator; think about measures of functional diversity. Consider an evolutionary simulator (cf. (Loeuille, Loreau, and Levin 2005; Loeuille and Loreau 2006)

Related:

  • rejected NSF grant with Mike McCoy and James Vonesh
  • Okuyama and Bolker (2013)

Variance dynamics/autocorrelated growth

  • Extend growth variance model to handle other components (size-dependent growth and mortality).
  • More general growth analysis: Peacor data?

Related: M. E. Brooks, McCoy, and Bolker (2013)

Evolution of virulence

  • better analytical handle on “simple” JRSI approach to virulence evolution
  • more realistic myxomatosis models (see above)
  • West Nile virus project (A. Wong, Kilpatrick)
  • sigmavirus/Drosophila; modeling clines of virulent diseases based on differential strength of seasonal variation
  • general-purpose Mendelian genetics simulator?
  • analyze individual-level chytridiomycosis data from Cherie Briggs
  • mosquito heterogeneity slides; do simulations with spatial and among-individual heterogeneity to determine effects of heterogeneity on effective population size/\(K\)

Related: Bolker, Nanda, and Shah (2010)

Common principal components

  • test, polish, document CPC code written by Alan Wong
  • work out the multi-group BPANOVA method
  • review of quadratic vs geometric approaches to size-correction

Related: McCoy et al. (2006)

Spatial/phylogenetic (G)LM(M)s

Related: flexLambda branch of lme4

General-purpose MLE software

  • further improvements to bbmle:
    • R2ADMB backend
    • TMB backend
    • WinBUGS/NIMBLE backend ???
    • deriv() backend

Related: Bolker et al. (2013)

Mixed models

  • further investigation of Zhang et al. (2011): comparative performance of different GLMM approaches
  • Work on flexLambda branch of lme4 to implement models with flexible variance structures, correlation, etc..
  • implement Gauss-Hermite quadrature

Related: D. Bates et al. (2014)

General spatial dynamics

  • Develop a general-purpose point-process spatial simulator (for use with emonk that implements a wide set of spatial transition rules. Transition rules should be either parsed into a C function that can be compiled with the rest of the structural code, or parsed into a fairly rapidly executable set of instructions (à la Bard Ermentrout’s xppaut and xtc). Facilities for incorporating or generating maps of environmental heterogeneity? More ambitious: parallel patch and IPS models, for comparison (alternately, extend s3 to allow more quantitative analysis and make it more of a research tool)

Related: Ovaskainen et al. (2013); B. M. Bolker and Pacala (1999); Bolker (2004)

Dispersal

  • explore power, bias, etc. of inverse fitting approaches to estimation of (biological/seed) dispersal kernels, especially with multiple sites

Misc.

(as though this whole list couldn’t be lumped under “miscellaneous” …)

  • objective Bayesian “tuning” of forest models/other large-scale models with data from multiple scales (related to ideas of synthetic likelihood, e.g. Wood (2010))

References

Bates, Douglas, Martin Maechler, Benjamin M. Bolker, and Steven Walker. 2014. “lme4: Linear Mixed-Effects Models Using Eigen and S4.” http://arxiv.org/abs/1406.5823.

Bolker, B. M., and S. W. Pacala. 1999. “Spatial Moment Equations for Plant Competition: Understanding Spatial Strategies and the Advantages of Short Dispersal.” Amnat 153: 575–602.

Bolker, Benjamin. 2004. “Continuous-Space Models for Population Dynamics.” In Ecology, Genetics, and Evolution of Metapopulations, edited by Ilkka Hanski and Oscar E. Gaggioti, 45–69. San Diego, CA: Elsevier Science.

Bolker, Benjamin M., Beth Gardner, Mark Maunder, Casper W. Berg, Mollie Brooks, Liza Comita, Elizabeth Crone, et al. 2013. “Strategies for Fitting Nonlinear Ecological Models in R, AD Model Builder, and BUGS.” Edited by Satu Ramula. Methods in Ecology and Evolution 4 (6): 501–12. doi:10.1111/2041-210X.12044.

Bolker, Benjamin M., Arjun Nanda, and Dharmini Shah. 2010. “Transient Virulence of Emerging Pathogens.” J. Roy Soc. Interface 7 (46): 811–22. doi:10.1098/rsif.2009.0384.

Brooks, Mollie E., Michael W. McCoy, and Benjamin M. Bolker. 2013. “A Method for Detecting Positive Growth Autocorrelation Without Marking Individuals.” PLoS ONE 8 (10): e76389. doi:10.1371/journal.pone.0076389.

de Jonge, Michelle. 2014. “Fast Estimation of Time-Varying Transmission Rates for Infectious Diseases.” Master’s thesis, McMaster University. http://hdl.handle.net/11375/14230.

Dormann, Carsten F., Jana M. McPherson, Miguel B. Araújo, Roger Bivand, Janine Bolliger, Gudrun Carl, Richard G. Davies, et al. 2007. “Methods to Account for Spatial Autocorrelation in the Analysis of Species Distributional Data: A Review.” Ecography 30 (5): 609–28. doi:10.1111/j.2007.0906-7590.05171.x.

Fine, Paul E. M., and Jacqueline A. Clarkson. 1982. “Measles in England and Wales: I-an Analysis of Factors Underlying Seasonal Patterns.” International Journal of Epidemiology 11 (1): 5–14. doi:10.1093/ije/11.1.5.

Ives, A. R., and H. C. J. Godfray. 2006. “Phylogenetic Analysis of Trophic Associations.” The American Naturalist 168 (1): 1–14.

Ives, A. R., B. Dennis, K. L. Cottingham, and S. R. Carpenter. 2003. “Estimating Community Stability and Ecological Interactions from Time-Series Data.” Ecological Monographs 73 (2): 301–30. doi:10.1890/0012-9615(2003)073[0301:ECSAEI]2.0.CO;2.

Keitt, Timothy H. 2002. “Accounting for Spatial Pattern When Modeling Organism-Environment Interactions.” Ecography 25 (5): 616–25. http://resolver.scholarsportal.info/resolve/09067590/v25i0005/616_afspwmoi.xml.

Loeuille, Nicolas, and Michel Loreau. 2006. “Evolution of Body Size in Food Webs: Does the Energetic Equivalence Rule Hold?” Ecology Letters 9 (2): 171–78. doi:10.1111/j.1461-0248.2005.00861.x.

Loeuille, Nicolas, Michel Loreau, and Simon A. Levin. 2005. “Evolutionary Emergence of Size-Structured Food Webs.” Proceedings of the National Academy of Sciences of the United States of America 102 (16): 5761–66. http://www.jstor.org/stable/3375381.

McCoy, Michael W., Benjamin M. Bolker, Craig W. Osenberg, Benjamin G. Miner, and James R. Vonesh. 2006. “Size Correction: Comparing Morphological Traits Among Populations and Environments.” Oecologia 148: 547–54. doi:10.1007/s00442-006-0403-6.

Okuyama, Toshinori, and Benjamin M. Bolker. 2013. “Model-Based, Response Surface Approaches to Quantifying Indirect Interactions.” In Ecology and Evolution of Trait-Mediated Indirect Interactions: Linking Evolution, Community, and Ecosystem, edited by Takayuki Ohgushi, Oswald Schmitz, and Robert Holt. Cambridge University Press.

Ovaskainen, Otso, Dmitri Finkelshtein, Oleksandr Kutoviy, Stephen Cornell, Benjamin Bolker, and Yuri Kondratiev. 2013. “A General Mathematical Framework for the Analysis of Spatiotemporal Point Processes.” Theoretical Ecology. Springer Netherlands, 1–13.

Pinheiro, José C., and Douglas M. Bates. 2000. Mixed-Effects Models in S and S-PLUS. New York: Springer.

Wood, Simon N. 2010. “Statistical Inference for Noisy Nonlinear Ecological Dynamic Systems.” Nature 466 (7310): 1102–4. doi:10.1038/nature09319.

Zhang, Hui, Naiji Lu, Chanyong Feng, Sally W. Thurston, Yinglin Xia, Liang Zhu, and Xin M Tu. 2011. “On Fitting Generalized Linear Mixed-Effects Models for Binary Responses Using Different Statistical Packages.” Statistics in Medicine. doi:10.1002/sim.4265.