UC SPARK - University of Canterbury - New Zealand

Associate Professor Michael Plank

Mathematics and Statistics

Fields of Research

  • Ecology and exploitation of fish communities
  • Complex ecological networks
  • Collective cell behaviour
  • Stochastic models in biology

Researcher Summary

My research is in mathematical modelling, particularly in ecology and physiology. The motivation for this research comes from real-world problems and the emphasis is on qualitative mathematical models that capture the essential behaviour of a particular phenomenon. I have research interests in a variety of applications: ecology and exploitation of fish communities; collective cell behaviour; complex ecological networks; invasive species; epidemiology; animal movement; neurovascular coupling. My research uses methods from a range of areas in mathematics including: dynamical systems; partial differential equations; perturbation theory; stochastic processes; and data science.

Subject Area: Disciplines

Research Projects

Research Groups

Affiliations

Research/Scholarly/Creative Works

Journal Articles
  • Mohd MH., Murray R., Plank MJ. and Godsoe W. (2018) Effects of different dispersal patterns on the presence-absence of multiple species. Communications in Nonlinear Science and Numerical Simulation 56: 115-130. http://dx.doi.org/10.1016/j.cnsns.2017.07.029.
  • Edwards AM., Robinson JPW., Plank MJ., Baum JK. and Blanchard JL. (2017) Testing and recommending methods for fitting size spectra to data. Methods in Ecology and Evolution 8(1): 57-67. http://dx.doi.org/10.1111/2041-210X.12641.
  • Kenny A., Zakkaroff C., Plank M. and David T. (2017) Massively parallel simulations of neurovascular coupling with extracellular diffusion. Journal of Computational Science Early access online http://dx.doi.org/10.1016/j.jocs.2017.07.001.
  • Mohd MH., Murray R., Plank MJ. and Godsoe W. (2017) Effects of biotic interactions and dispersal on the presence-absence of multiple species. Chaos, Solitons and Fractals 99: 185-194. http://dx.doi.org/10.1016/j.chaos.2017.04.012.
  • Plank MJ. (2017) Balanced harvesting is the bioeconomic equilibrium of a size-structured Beverton-Holt model. ICES Journal of Marine Science 74(1): 112-120. http://dx.doi.org/10.1093/icesjms/fsw161.
  • Plank MJ., Kolding J., Law R., Gerritsen HD. and Reid D. (2017) Balanced harvesting can emerge from fishing decisions by individual fishers in a small-scale fishery. Fish and Fisheries 18(2): 212-225. http://dx.doi.org/10.1111/faf.12172.
  • Auger-Méthé M., Derocher AE., DeMars CA., Plank MJ., Codling EA. and Lewis MA. (2016) Evaluating random search strategies in three mammals from distinct feeding guilds. Journal of Animal Ecology 85(5): 1411-1421. http://dx.doi.org/10.1111/1365-2656.12562.
  • Binny RN., Haridas P., James A., Law R., Simpson MJ. and Plank MJ. (2016) Spatial structure arising from neighbour-dependent bias in collective cell movement. PeerJ 4(16) e1689: 24pp. http://dx.doi.org/10.7717/peerj.1689.
  • Binny RN., James A. and Plank MJ. (2016) Collective Cell Behaviour with Neighbour-Dependent Proliferation, Death and Directional Bias. Bulletin of Mathematical Biology 78(11): 2277-2301. http://dx.doi.org/10.1007/s11538-016-0222-9.
  • Law R., Plank MJ. and Kolding J. (2016) Balanced exploitation and coexistence of interacting, size-structured, fish species. Fish and Fisheries (early access online) http://dx.doi.org/10.1111/faf.12098.
  • Plank MJ., Pitchford JW. and James A. (2016) Evolutionarily Stable Strategies for Fecundity and Swimming Speed of Fish. Bulletin of Mathematical Biology 78(2): 280-292. http://dx.doi.org/10.1007/s11538-016-0143-7.
  • van Zwieten PAM., Kolding J., Plank MJ., Hecky RE., Bridgeman TB., MacIntyre S., Seehausen O. and Silsbe GM. (2016) The Nile perch invasion in Lake Victoria: cause or consequence of the haplochromine decline? Canadian Journal of Fisheries and Aquatic Sciences 73: 1-22. http://dx.doi.org/10.1139/cjfas-2015-0130.
  • Auger-Méthé M., Derocher AE., Plank MJ., Codling EA. and Lewis MA. (2015) Differentiating the Lévy walk from a composite correlated random walk. Methods in Ecology and Evolution 6: 1179-1189. http://dx.doi.org/10.1111/2041-210X.12412.
  • Binny RN., Plank MJ. and James A. (2015) Spatial moment dynamics for collective cell movement incorporating a neighbour-dependent directional bias. Interface 12(106) 20150228: 14pp. http://dx.doi.org/10.1098/rsif.2015.0228.
  • Godsoe W., Murray R. and Plank MJ. (2015) Information on biotic interactions improves transferability of distribution models. American Naturalist 185(2): 281-290. http://dx.doi.org/10.1086/679440.
  • Godsoe W., Murray R. and Plank MJ. (2015) The effect of competition on species' distributions depends on coexistence, rather than scale alone. Ecography 38(11): 1071-1079. http://dx.doi.org/10.1111/ecog.01134.
  • James A., Molloy SM., Ponder-Sutton A., Plank MJ., Lamoureaux SL., Bourdot GW. and Kelly D. (2015) Modelling Tradescantia fluminensis to assess long term survival. Peer Journal 3 e1013 https://dx.doi.org/10.7717/peerj.1013.
  • James A., Plank MJ., Rossberg AG., Beecham J., Emmerson M. and Pitchford JW. (2015) Constructing random matrices to represent real ecosystems. American Naturalist 185(5): 680-692. http://dx.doi.org/10.1086/680496.
  • Law R., Kolding J. and Plank MJ. (2015) Squaring the circle: reconciling fishing and conservation of aquatic ecosystems. Fish and Fisheries 16(1): 160-174. http://dx.doi.org/10.1111/faf.12056.
  • Plank MJ. and Law R. (2015) Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions. Bulletin of Mathematical Biology 77(4): 586-613. http://dx.doi.org/10.1007/s11538-014-0018-8.
  • Auger-Méthé M., Plank MJ. and Codling EA. (2014) Distinguishing between Lévy walks and strong alternative models: Comment. Ecology 95: 1104-1109. http://dx.doi.org/10.1890/13-1484.1.
  • Godsoe W., Murray R. and Plank M. (2014) Information on biotic interactions improves transferability of distribution models.
  • Adams TP., Holland EP., Law R., Plank MJ. and Raghib M. (2013) On the growth of locally interacting plants: differential equations for the dynamics of spatial momentsOn the growth of locally interacting plants: differential equations for the dynamics of spatial moments. Ecology 94(12): 2732-2743. http://dx.doi.org/10.1890/13-0147.1.
  • Johnston ST., Simpson MJ. and Plank MJ. (2013) Lattice-free descriptions of collective motion with crowding and adhesion. Physics Review E: Statistical, Nonlinear, and Soft Matter Physics 88(6): 62720. http://dx.doi.org/10.1103/PhysRevE.88.062720.
  • Kelly D., Geldenhuis A., James A., Holland EP., Plank MJ., Brockie RE., Cowan PE., Harper GA., Lee WG. and Maitland MJ. (2013) Of mast and mean: differential-temperature cue makes mast seeding insensitive to climate change. Ecology Letters 16(1): 90-98. http://dx.doi.org/10.1111/ele.12020.
  • Brown RG., James A., Pitchford JW. and Plank MJ. (2012) Habitat fragmentation: Simple models for local persistence and the spread of invasive species. Journal of Theoretical Biology 310: 231-238. http://dx.doi.org/10.1016/j.jtbi.2012.06.033.
  • Cohen JE., Plank MJ. and Law R. (2012) Taylor's law and body size in exploited marine ecosystems. Ecology and Evolution 2(12): 3168-3178. http://dx.doi.org/10.1002/ece3.418.
  • Law R., Plank MJ. and Kolding J. (2012) On balanced exploitation of marine ecosystems: results from dynamic size spectra. ICES Journal of Marine Science 69(4): 602-614. http://dx.doi.org/10.1093/icesjms/fss031.
  • Plank MJ. and Simpson MJ. (2012) Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. Interface 9(76): 2983-2996. http://dx.doi.org/10.1098/rsif.2012.0319.
  • Plank MJ. and Codling EA. (2011) Sampling rate and misidentification of Lévy and non-Lévy movement paths: reply. Ecology 92(8): 1701-1702. http://dx.doi.org/10.1890/11-0249.1.
  • Plank MJ., James A. and Hannah J. (2011) Group by subject or by ability? Tertiary mathematics for engineering students. International Journal of Mathematics Education in Science and Technology 42(7): 857-865. http://dx.doi.org/10.1080/0020739X.2011.609284.
  • Sellier D., Plank MJ. and Harrington JJ. (2011) A mathematical framework for modelling cambial surface evolution using a level set method. Annals of Botany 108(6): 1001-1011. http://dx.doi.org/10.1093/aob/mcr067.
  • Codling EA. and Plank MJ. (2010) Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates. Theoretical Ecology 4(3): 397-406. http://dx.doi.org/10.1007/s12080-010-0086-9.
  • Datta S., Delius GW., Law R. and Plank MJ. (2010) A stability analysis of the power-law steady state of marine size spectra. Journal of Mathematical Biology 63(4): 779-799. http://dx.doi.org/10.1007/s00285-010-0387-z.
  • James A., Pitchford JW. and Plank MJ. (2010) Efficient or inaccurate? Analytical and numerical modelling of random search strategies. Bulletin of Mathematical Biology 72(4): 896-913. http://dx.doi.org/10.1007/s11538-009-9473-z.
  • James A., Green S. and Plank MJ. (2009) Modelling the dynamic response of oxygen uptake to exercise. Discrete and Continuous Dynamical Systems - Series B 12(2): 361-370. http://dx.doi.org/10.3934/dcdsb.2009.12.361.
  • Law R., Plank MJ., James A. and Blanchard JL. (2009) Size-spectra dynamics from stochastic predation and growth of individuals. Ecology 90(3): 802-811. http://dx.doi.org/10.1890/07-1900.1.
  • Comerford A., Plank MJ. and David T. (2008) Endothelial Nitric Oxide Synthase and Calcium Production in Arterial Geometries: An Integrated Fluid Mechanics/Cell Model. Journal of Biomechanical Engineering 130(1): 11010. http://dx.doi.org/10.1115/1.2838026.
  • James A., Plank MJ. and Brown R. (2008) Optimizing the encounter rate in biological interactions: Ballistic versus Lévy versus Brownian strategies. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 78(5): 51128. http://dx.doi.org/10.1103/PhysRevE.78.051128.
  • Kleinstreuer N., David T., Plank MJ. and Endre Z. (2008) Dynamic myogenic autoregulation in the rat kidney: a whole organ model. American Journal of Physiology: Renal Physiology 294(6): F1453-F1464. http://dx.doi.org/10.1152/ajprenal.00426.2007.
  • Chapman SJ., Plank MJ., James A. and Basse B. (2007) A nonlinear model of age and size-structured populations with applications to cell cycles. ANZIAM Journal 49(2): 151-169. http://dx.doi.org/10.1017/S144618110001275X.
  • James A., Dungan R., Plank MJ. and Ito R. (2007) A dynamical model of honeydew droplet production by sooty-beech scale insects (Ultracoelostoma spp.) in New Zealand Nothofagus forest. Ecological Modelling 209(2-4): 323-332. http://dx.doi.org/10.1016/j.ecolmodel.2007.06.024.
  • James A., Pitchford JW. and Plank MJ. (2007) An event-based model of superspreading in epidemics. Proceedings of the Royal Society B: Biological Sciences 274(1610): 741-747. http://dx.doi.org/10.1098/rspb.2006.0219.
  • Kleinstreuer N., David T., Plank MJ. and Endre Z. (2007) Myogenic autoregulation in the rat kidney: a whole-organ mathematical model. Journal of Biomechanical Science and Engineering 2 S59 http://dx.doi.org/10.1299/jbse.2.S57.
  • Plank MJ., Wall DJN. and David T. (2007) The role of endothelial calcium and nitric oxide in the localisation of atherosclerosis. Mathematical Biosciences 207(1): 26-39. http://dx.doi.org/10.1016/j.mbs.2006.08.017.
  • Comerford A., David T. and Plank MJ. (2006) Effects of arterial bifurcation geometry on nucleotide concentration at the endothelium. Annals of Biomedical Engineering 34(4): 605-617. http://dx.doi.org/10.1007/s10439-005-9046-8.
  • Plank MJ., Comerford A., David T. and Wall DJN. (2006) Concentration of blood-borne agonists at the endothelium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462(2066): 671-688. http://dx.doi.org/10.1098/rspa.2005.1591.
  • Plank MJ., Sleeman BD. and Jones PF. (2004) A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins. Journal of Theoretical Biology 229(4): 435-454.
  • Plank MJ. and Sleeman BD. (2003) A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. Mathematical Medicine and Biology 20(2): 135-181. http://dx.doi.org/10.1093/imammb/20.2.135.
  • Plank MJ., Sleeman BD. and Jones PF. (2003) A Mathematical Model of an In Vitro Experiment to Investigate Endothelial Cell Migration. Journal of Theoretical Medicine 4(4): 251-270. http://dx.doi.org/10.1080/10273660310001594200.
Authored Books
  • Jones DS., Plank MJ. and Sleeman BD. (2010) Differential Equations and Mathematical Biology. (2nd ed.). Boca Raton: Chapman and Hall. 444pp.
Chapters
  • Plank MJ., Auger-Méthé M. and Codling EA. (2013) Lévy or not? Analysing positional data from animal movement paths. In Lewis MA; Maini PK; Petrovskii SV (Ed.), Lecture Notes in Mathematics 2071: Dispersal, individual movement and spatial ecology: a mathematical perspective: 33-52. New York: Springer. http://dx.doi.org/10.1007/978-3-642-35497-7_2.
  • Plank MJ., Comerford A., Wall DJN. and David T. (2007) Modelling the Early Stages of Atherosclerosis. In Deutsch A; Brusch L; Byrne H; de Vries G; Herzel H (Ed.), Mathematical Modeling of Biological Systems, Volume I: Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis: 263-274. Boston: Birkhauser.
Conference Contributions - Other
  • Plank M., James A., Kelly D., Lamoureaux S. and Bourdôt G. (2017) Light and shade: modelling the growth of Tradescantia fluminensis. Valencia, Spain: International Workshop on Industrial Mathematics, 18 May 2017
Other
  • James A., Pitchford JW. and Plank MJ. (2013) James et al. reply (to Saavedra, S., Stouffer, D.B. "Disentangling nestedness" disentangled). Nature(500): E2-E3. http://dx.doi.org/10.1038/nature12381. [Brief Communication].
Additional Publications
  • Plank M. and Binny R. (2016) Modelling collective cell behaviour with spatial moment dynamics. Banff International Research Station for Mathematical Innovation and Discovery: Ion Transport: Electrodiffusion, Electrohydrodynamics and Homogenization, 30 May-3 Jun 2016.
  • Kolding J., Bundy A., Christensen V., Steenbeek J., Law R., Plank MJ. and van Zwieten PAM. (2015) Exploitation patterns in fisheries, a global meta-analysis from 151 Ecopath models. Rome, Italy: 2014 International Scientific Workshop of the IUCN Fisheries Expert Group, 29 Sep-2 Oct 2014. In Balanced harvest in the real world. Scientific, policy and operational issues in an ecosystem approach to fisheries: 27-32. http://archimer.ifremer.fr/doc/00255/36575/.
  • Law R., Plank MJ. and Kolding J. (2015) Balanced harvesting promotes coexistence of interacting species. Rome, Italy: 2014 International Scientific Workshop of the IUCN Fisheries Expert Group, 29 Sep-2 Oct 2014. In Balanced harvest in the real world. Scientific, policy and operational issues in an ecosystem approach to fisheries: 15-17. http://archimer.ifremer.fr/doc/00255/36575/.
  • Plank MJ., Law R. and Kolding J. (2015) Do unregulated, artisanal fisheries tend towards balanced harvesting? Rome, Italy: 2014 International Scientific Workshop of the IUCN Fisheries Expert Group, 29 Sep-2 Oct 2014. In Balanced harvest in the real world. Scientific, policy and operational issues in an ecosystem approach to fisheries: 19-21. http://archimer.ifremer.fr/doc/00255/36575/.
  • Law R., Plank M., Delius GW. and Blanchard JL. (2011) Ecological drivers of stability and instability in marine ecosystems. Nagoya, Japan: Selective Fishing and Balanced Harvest in Relation to Fisheries and Ecosystem Sustainability, 14-16 Oct 2010. : 4-5.
  • Sellier D., Plank MJ. and Harrington JJ. (2010) An extensible mathematical framework to model cambial growth and wood formation. University of California Davis, CA, USA: 6th International Workshop on Functional-Structural Plant Models, 12-17 Sep 2010. In Proceedings: 202-204.
  • Mann J., Plank M. and Wilkins A. (2007) Tree growth and wood formation - applications of anisotropic surface growth. Auckland, New Zealand: Mathematics in Industry Study Group Annual Meeting 2006 (MISG 2006), 30 Jan-3 Feb 2006. In Proceedings of the Mathematics in Industry Study Group 2006: 153-191.
  • Plank MJ., Comerford A., David T. and Wall DJN. (2005) Modelling the localisation of cardiovascular disease. Singapore: 12th International Conference on Biomedical Engineering (ICBME 2005), 7 Dec 2005. In Proceedings of the 12th International Conference on Biomedical Engineering (ICBME 2005): 1B1-1B1. http://www.icbme.org/.
  • Plank MJ. (2003) Cell-based models of tumour angiogenesis. Leeds, UK. University of Leeds.