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Professor Michael Plank

Contact

Department: Mathematics and Statistics

Email: michael.plank@canterbury.ac.nz

Direct Dial: +64 3 3692462

Office:

Language: English

About
Research / Creative works
Supervision
Networks
Projects

Fields of Research

  • Mathematical modelling of complex biological and social systems
  • Mathematical epidemiology
  • Ecology and exploitation of marine ecosystems
  • Stochastic models

Researcher Summary

Michael Plank is a Professor in the School of Mathematics and Statistics at the University of Canterbury in New Zealand, a Fellow of the New Zealand Mathematical Society, and a Principal Investigator at Te Pūnaha Matatini, New Zealand's Centre of Research Excellence in Complex Systems. He obtained his BSc(Hons) in Mathematics from the University of Bristol in 2000 and his PhD in Applied Mathematics from the University of Leeds in 2003. He started at the University of Canterbury as a postdoctoral research fellow in 2004 and as a permanent academic staff member in 2006.

Professor Plank is an expert in mathematical modelling of complex biological and social systems at multiple scales, from intracellular signalling and collective cell behaviour, through to large ecosystem dynamics. His research is application-driven and focuses on mechanistic mathematical and stochastic models that capture emergent behaviour and offer qualitative insight into underlying mechanisms. His areas of expertise include ecological and social networks, population dynamics, epidemiological models, size-structured marine ecosystems, collective cell behaviour, and intracellular dynamics. His research draws on numerous fields in applied mathematics including stochastic processes, integro and partial differential equations, dynamical systems, spatial moment dynamics, statistical modelling, and parameter inference.

Subject Area: Disciplines

  • Mathematics: Applied Mathematics; Biomathematics

Research/Scholarly/Creative Works

Journal Articles
  • Law R. and Plank MJ. (2023) Fishing for biodiversity by balanced harvesting. Fish and Fisheries 24(1): 21-39. http://dx.doi.org/10.1111/faf.12705.
  • Lustig A., Vattiato G., Maclaren O., Watson LM., Datta S. and Plank MJ. (2023) Modelling the impact of the Omicron BA.5 subvariant in New Zealand. Journal of The Royal Society Interface 20(199) http://dx.doi.org/10.1098/rsif.2022.0698.
  • Vattiato G., Lustig A., Maclaren O., Binny RN., Hendy SC., Harvey E., O'Neale D. and Plank MJ. (2023) Modelling Aotearoa New Zealand's COVID-19 protection framework and the transition away from the elimination strategy. Royal Society Open Science 10(2) http://dx.doi.org/10.1098/rsos.220766.
  • Binny RN., Lustig A., Hendy SC., Maclaren OJ., Ridings KM., Vattiato G. and Plank MJ. (2022) Real-time estimation of the effective reproduction number of SARS-CoV-2 in Aotearoa New Zealand. PeerJ 10 http://dx.doi.org/10.7717/peerj.14119.
  • Binny RN., Priest P., French NP., Parry M., Lustig A., Hendy SC., Maclaren OJ., Ridings KM., Steyn N. and Vattiato G. (2022) Sensitivity of Reverse Transcription Polymerase Chain Reaction Tests for Severe Acute Respiratory Syndrome Coronavirus 2 Through Time. The Journal of infectious diseases 227(1): 9-17. http://dx.doi.org/10.1093/infdis/jiac317.
  • Hendy SC., Wiles S., Binny R. and Plank MJ. (2022) Comment on ‘Government mandated lockdowns do not reduce COVID-19 deaths: implications for evaluating the stringent New Zealand response’. New Zealand Economic Papers 56(1): 29-35. http://dx.doi.org/10.1080/00779954.2022.2034176.
  • Klowss JJ., Browning AP., Murphy RJ., Carr EJ., Plank MJ., Gunasingh G., Haass NK. and Simpson MJ. (2022) A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling. Journal of the Royal Society Interface 19(189) http://dx.doi.org/10.1098/rsif.2021.0903.
  • Plank MJ. (2022) Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model. Mathematical Biosciences 351 http://dx.doi.org/10.1016/j.mbs.2022.108885.
  • Plank MJ., Hendy SC., Binny RN., Vattiato G., Lustig A. and Maclaren OJ. (2022) Using mechanistic model-based inference to understand and project epidemic dynamics with time-varying contact and vaccination rates. Scientific Reports 12(1) http://dx.doi.org/10.1038/s41598-022-25018-3.
  • Plank MJ., James A., Lustig A., Steyn N., Binny RN. and Hendy SC. (2022) Potential reduction in transmission of COVID-19 by digital contact tracing systems: a modelling study. Mathematical Medicine and Biology 39(2): 156-168. http://dx.doi.org/10.1093/imammb/dqac002.
  • Steyn N., Lustig A., Hendy SC., Binny RN. and Plank MJ. (2022) Effect of vaccination, border testing, and quarantine requirements on the risk of COVID-19 in New Zealand: A modelling study. Infectious Disease Modelling 7(1): 184-198. http://dx.doi.org/10.1016/j.idm.2021.12.006.
  • Steyn N., Plank MJ., Binny RN., Hendy SC., Lustig A. and Ridings K. (2022) A COVID-19 vaccination model for Aotearoa New Zealand. Scientific Reports 12(1) http://dx.doi.org/10.1038/s41598-022-06707-5.
  • Takashina N., Plank MJ., Jenkins CN. and Economo EP. (2022) Species-range-size distributions: Integrating the effects of speciation, transformation, and extinction. Ecology and Evolution 12(1) http://dx.doi.org/10.1002/ece3.8341.
  • Vattiatio G., Lustig A., Maclaren OJ. and Plank MJ. (2022) Modelling the dynamics of infection, waning of immunity and re-infection with the Omicron variant of SARS-CoV-2 in Aotearoa New Zealand. Epidemics 41 http://dx.doi.org/10.1016/j.epidem.2022.100657.
  • Vattiato G., Maclaren O., Lustig A., Binny RN., Hendy SC. and Plank MJ. (2022) An assessment of the potential impact of the Omicron variant of SARS-CoV-2 in Aotearoa New Zealand. Infectious Disease Modelling 7(2): 94-105. http://dx.doi.org/10.1016/j.idm.2022.04.002.
  • Binny RN., Baker MG., Hendy SC., James A., Lustig A., Plank MJ., Ridings KM. and Steyn N. (2021) Early intervention is the key to success in COVID-19 control. Royal Society Open Science 8(11) http://dx.doi.org/10.1098/rsos.210488.
  • Hackney M., James A. and Plank MJ. (2021) Cooperative and non-cooperative behaviour in the exploitation of a common renewable resource with environmental stochasticity. Applied Mathematical Modelling 89: 1041-1054. http://dx.doi.org/10.1016/j.apm.2020.06.079.
  • Hendy S., Steyn N., James A., Plank MJ., Hannah K., Binny RN. and Lustig A. (2021) Mathematical modelling to inform New Zealand’s COVID-19 response. Journal of the Royal Society of New Zealand 51(S1): S86-S106. http://dx.doi.org/10.1080/03036758.2021.1876111.
  • James A., Plank MJ., Binny RN., Lustig A., Hannah K., Hendy SC. and Steyn N. (2021) A structured model for COVID-19 spread: Modelling age and healthcare inequities. Mathematical Medicine and Biology 38(3): 299-313. http://dx.doi.org/10.1093/imammb/dqab006.
  • James A., Plank MJ., Hendy S., Binny R., Lustig A., Steyn N., Nesdale A. and Verrall A. (2021) Successful contact tracing systems for COVID-19 rely on effective quarantine and isolation. PLoS ONE 16(6 June) http://dx.doi.org/10.1371/journal.pone.0252499.
  • James A., Plank MJ., Hendy S., Binny RN., Lustig A. and Steyn N. (2021) Model-free estimation of COVID-19 transmission dynamics from a complete outbreak. PLoS ONE 16(3 March) http://dx.doi.org/10.1371/journal.pone.0238800.
  • Mugford J., Moltchanova E., Plank M., Sullivan J., Byrom A. and James A. (2021) Citizen science decisions: A Bayesian approach optimises effort. Ecological Informatics 63 http://dx.doi.org/10.1016/j.ecoinf.2021.101313.
  • Novaglio C., Blanchard JL., Plank M., van Putten EI., Audzijonyte A., Porobic J. and Fulton EA. (2021) Exploring trade-offs in mixed fisheries by integrating fleet dynamics into multispecies size-spectrum models. Journal of Applied Ecology http://dx.doi.org/10.1111/1365-2664.14086.
  • Plank MJ., Binny RN., Hendy SC., Lustig A. and Ridings K. (2021) Vaccination and testing of the border workforce for COVID-19 and risk of community outbreaks: A modelling study. Royal Society Open Science 8(9) http://dx.doi.org/10.1098/rsos.210686.
  • Plank MJ., James A. and Steyn N. (2021) Comment: Weekly COVID-19 testing with household quarantine and contact tracing is feasible and would probably end the epidemic. Royal Society Open Science 8(6) http://dx.doi.org/10.1098/rsos.201546.
  • Steyn N., Binny R., Hannah K., Hendy S., James A., Lustig A., Ridings K., Plank M. and Sporle A. (2021) Māori and Pacific people in New Zealand have a higher risk of hospitalisation for COVID-19. New Zealand Medical Journal 134(1538): 29-43. http://dx.doi.org/10.1101/2020.12.25.20248427.
  • Steyn N., Plank MJ., James A., Binny RN., Hendy SC. and Lustig A. (2021) Managing the risk of a COVID-19 outbreak from border arrivals. Journal of the Royal Society Interface 18(177) http://dx.doi.org/10.1098/rsif.2021.0063.
  • Turner RM., Brockerhoff EG., Bertelsmeier C., Blake RE., Caton B., James A., MacLeod A., Nahrung HF., Pawson SM. and Plank MJ. (2021) Worldwide border interceptions provide a window into human-mediated global insect movement. Ecological Applications 31(7) http://dx.doi.org/10.1002/eap.2412.
  • Vattiato G., Plank MJ., James A. and Binny RN. (2021) Individual heterogeneity affects the outcome of small mammal pest eradication. Theoretical Ecology 14(2): 219-231. http://dx.doi.org/10.1007/s12080-020-00491-6.
  • Zhou S., Garcia SM., Kolding J. and Plank MJ. (2021) Commentary: Fishing Without a Trace? Assessing the Balanced Harvest Approach Using EcoTroph. Frontiers in Marine Science 7 http://dx.doi.org/10.3389/fmars.2020.610216.
  • Barrett-Walker T., Plank MJ., Ka'ai-Mahuta R., Hikuroa D. and James A. (2020) Kia kaua te reo e rite ki te moa, ka ngaro: Do not let the language suffer the same fate as the Moa. Journal of the Royal Society Interface 17(162) http://dx.doi.org/10.1098/rsif.2019.0526.
  • Binny RN., Law R. and Plank MJ. (2020) Living in groups: Spatial-moment dynamics with neighbour-biased movements. Ecological Modelling 415 http://dx.doi.org/10.1016/j.ecolmodel.2019.108825.
  • Browning AP., Jin W., Plank MJ. and Simpson MJ. (2020) Identifying density-dependent interactions in collective cell behaviour. Journal of the Royal Society Interface 17(165) http://dx.doi.org/10.1098/rsif.2020.0143.
  • Burgess MG. and Plank MJ. (2020) What unmanaged fishing patterns reveal about optimal management: Applied to the balanced harvesting debate. ICES Journal of Marine Science 77(3): 901-910. http://dx.doi.org/10.1093/icesjms/fsaa012.
  • Edwards AM., Robinson JPW., Blanchard JL., Baum JK. and Plank MJ. (2020) Accounting for the bin structure of data removes bias when fitting size spectra. Marine Ecology Progress Series 636: 19-33. http://dx.doi.org/10.3354/meps13230.
  • Plank MJ. (2020) Asymptotic expansion approximation for spatial structure arising from directionally biased movement. Physica A: Statistical Mechanics and its Applications 541 http://dx.doi.org/10.1016/j.physa.2019.123290.
  • Plank MJ., Simpson MJ. and Binny RN. (2020) Small-scale spatial structure influences large-scale invasion rates. Theoretical Ecology 13(3): 277-288. http://dx.doi.org/10.1007/s12080-020-00450-1.
  • Steyn N., Binny R., Hannah K., Hendy S., James A., Kukutai T., Lustig A., McLeod M., Plank MJ. and Ridings K. (2020) Estimated inequities in COVID-19 infection fatality rates by ethnicity for Aotearoa New Zealand. New Zealand Medical Journal 133: 28-39.
  • Surendran A., Plank MJ. and Simpson MJ. (2020) Population dynamics with spatial structure and an Allee effect: Population dynamics with an Allee effect. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476(2242) http://dx.doi.org/10.1098/rspa.2020.0501.
  • Surendran A., Plank MJ. and Simpson MJ. (2020) Small-scale spatial structure affects predator-prey dynamics and coexistence. Theoretical Ecology 13(4): 537-550. http://dx.doi.org/10.1007/s12080-020-00467-6.
  • Turner RM., Plank MJ., Brockerhoff EG., Pawson S., Liebhold A. and James A. (2020) Considering unseen arrivals in predictions of establishment risk based on border biosecurity interceptions. Ecological Applications 30(8) http://dx.doi.org/10.1002/eap.2194.
  • Hackney M., James A. and Plank MJ. (2019) Emergence of balanced harvesting in an agent-based model of an open-access small-scale fishery. Mathematical Biosciences 316 http://dx.doi.org/10.1016/j.mbs.2019.108245.
  • James A., Chisnall R. and Plank MJ. (2019) Gender and societies: A grassroots approach to women in science. Royal Society Open Science 6(9) http://dx.doi.org/10.1098/rsos.190633.
  • James A., McLeod J., Hendy S., Marks K., Rusu D., Nik S. and Plank MJ. (2019) Using family network data in child protection services. PLoS ONE 14(10) http://dx.doi.org/10.1371/journal.pone.0224554.
  • Kenny A., Plank MJ. and David T. (2019) Minimal model of calcium dynamics in two heterogeneous coupled cells. Neurocomputing 323: 128-138. http://dx.doi.org/10.1016/j.neucom.2018.09.074.
  • Kenny A., Plank MJ. and David T. (2019) The effects of cerebral curvature on cortical spreading depression. Journal of Theoretical Biology 472: 11-26. http://dx.doi.org/10.1016/j.jtbi.2019.04.006.
  • Lustig A., James A., Anderson D. and Plank M. (2019) Pest control at a regional scale: Identifying key criteria using a spatially explicit, agent‐based model. Journal of Applied Ecology 56(7): 1515-1527. http://dx.doi.org/10.1111/1365-2664.13387.
  • Plank MJ., Stringer N., Lamoureaux SL., Bourdôt GW. and James A. (2019) Limiting Effect of Self-Shading on the Height of Tradescantia fluminensis Mats. Bulletin of Mathematical Biology 81(10): 3918-3932. http://dx.doi.org/10.1007/s11538-019-00631-y.
  • Surendran A., Plank MJ. and Simpson MJ. (2019) Spatial structure arising from chase-escape interactions with crowding. Scientific Reports 9(1) http://dx.doi.org/10.1038/s41598-019-51565-3.
  • Zhou S., Kolding J., Garcia SM., Plank MJ., Bundy A., Charles A., Hansen C., Heino M., Howell D. and Jacobsen NS. (2019) Balanced harvest: concept, policies, evidence, and management implications. Reviews in Fish Biology and Fisheries 29(3): 711-733. http://dx.doi.org/10.1007/s11160-019-09568-w.
  • Browning AP., McCue SW., Binny RN., Plank MJ., Shah ET. and Simpson MJ. (2018) Inferring parameters for a lattice-free model of cell migration and proliferation using experimental data. Journal of Theoretical Biology 437: 251-260. http://dx.doi.org/10.1016/j.jtbi.2017.10.032.
  • Kenny A., Plank MJ. and David T. (2018) Macro scale modelling of cortical spreading depression and the role of astrocytic gap junctions. Journal of Theoretical Biology 458: 78-91. http://dx.doi.org/10.1016/j.jtbi.2018.09.006.
  • Kenny A., Plank MJ. and David T. (2018) The role of astrocytic calcium and TRPV4 channels in neurovascular coupling. Journal of Computational Neuroscience 44(1): 97-114. http://dx.doi.org/10.1007/s10827-017-0671-7.
  • Kenny A., Zakkaroff C., Plank M. and David T. (2018) Massively parallel simulations of neurovascular coupling with extracellular diffusion. Journal of Computational Science 24: 116-124. http://dx.doi.org/10.1016/j.jocs.2017.07.001.
  • Law R. and Plank MJ. (2018) Balanced harvesting could reduce fisheries-induced evolution. Fish and Fisheries 19(6): 1078-1091. http://dx.doi.org/10.1111/faf.12313.
  • Mathias EJ., Kenny A., Plank MJ. and David T. (2018) Integrated models of neurovascular coupling and BOLD signals: Responses for varying neural activations. NeuroImage 174: 69-86. http://dx.doi.org/10.1016/j.neuroimage.2018.03.010.
  • McIntosh A., McHugh PA., Plank MJ., Jellyman PG., Warburton H. and Greig HS. (2018) Capacity to support predators scales with habitat size. Science Advances 4(7) eaap7523 http://dx.doi.org/10.1126/sciadv.aap7523.
  • 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.
  • Plank MJ. (2018) How should fishing mortality be distributed under balanced harvesting? Fisheries Research 207: 171-174. http://dx.doi.org/10.1016/j.fishres.2018.06.003.
  • Plank MJ., Allen MS., Nims R. and Ladefoged TN. (2018) Inferring fishing intensity from contemporary and archaeological size-frequency data. Journal of Archaeological Science 93: 42-53. http://dx.doi.org/10.1016/j.jas.2018.01.011.
  • Surendran A., Plank MJ. and Simpson MJ. (2018) Spatial Moment Description of Birth–Death–Movement Processes Incorporating the Effects of Crowding and Obstacles. Bulletin of Mathematical Biology 80(11): 2828-2855. http://dx.doi.org/10.1007/s11538-018-0488-1.
  • 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.
  • Johny JP., Plank MJ. and David T. (2017) Importance of Altered Levels of SERCA, IP3R, and RyR in Vascular Smooth Muscle Cell. Biophysical Journal 112(2): 265-287. http://dx.doi.org/10.1016/j.bpj.2016.11.3206.
  • Mathias EJ., Plank MJ. and David T. (2017) A model of neurovascular coupling and the BOLD response PART II. Computer Methods in Biomechanics and Biomedical Engineering 20(5): 519-529. http://dx.doi.org/10.1080/10255842.2016.1255733.
  • Mathias EJ., Plank MJ. and David T. (2017) A model of neurovascular coupling and the BOLD response: PART I. Computer Methods in Biomechanics and Biomedical Engineering 20(5): 508-518. http://dx.doi.org/10.1080/10255842.2016.1255732.
  • 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. and Pitchford JW. (2017) Unfinished synchrony. Proceedings of the National Academy of Sciences of the United States of America 114(26): 6658-6660. http://dx.doi.org/10.1073/pnas.1707731114.
  • 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.
  • Simpson MJ. and Plank MJ. (2017) Simplified calculation of diffusivity for a lattice-based random walk with a single obstacle. Results in Physics 7: 3346-3348. http://dx.doi.org/10.1016/j.rinp.2017.08.063.
  • 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.
  • Irons C., Plank MJ. and Simpson MJ. (2016) Lattice-free models of directed cell motility. Physica A: Statistical Mechanics and its Applications 442: 110-121. http://dx.doi.org/10.1016/j.physa.2015.08.049.
  • Kolding J., Bundy A., van Zwieten PAM. and Plank MJ. (2016) Fisheries, the inverted food pyramid. ICES Journal of Marine Science (early access online) http://dx.doi.org/10.1093/icesjms/fsv225.
  • Law R., Plank MJ. and Kolding J. (2016) Balanced exploitation and coexistence of interacting, size-structured, fish species. Fish and Fisheries 17(2): 281-302. http://dx.doi.org/10.1111/faf.12098.
  • Mohd MH., Murray R., Plank MJ. and Godsoe W. (2016) Effects of dispersal and stochasticity on the presence–absence of multiple species. Ecological Modelling 342: 49-59. http://dx.doi.org/10.1016/j.ecolmodel.2016.09.026.
  • 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.
  • 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.
  • 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.
  • Hadfield J., Plank MJ. and David T. (2013) Modeling secondary messenger pathways in neurovascular coupling. Bulletin of Mathematical Biology 75(3): 428-443. http://dx.doi.org/10.1007/s11538-013-9813-x.
  • 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.
  • 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.
  • Plank MJ. and Simpson MJ. (2013) Lattice-free models of cell invasion: discrete simulations and travelling waves. Bulletin of Mathematical Biology 75(11): 2150-2166. http://dx.doi.org/10.1007/s11538-013-9885-7.
  • Bartlett J. and Plank MJ. (2012) Epidemic dynamics on random and scale-free networks. ANZIAM Journal 54: 3-22. http://dx.doi.org/10.1017/S1446181112000302.
  • 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.
  • James A., Pitchford JW. and Plank MJ. (2012) Disentangling nestedness from models of ecological complexity. Nature 487(7406): 227-230. http://dx.doi.org/10.1038/nature11214.
  • 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 Law R. (2012) Ecological drivers of stability and instability in marine ecosystems. Theoretical Ecology 5(4): 465-480. http://dx.doi.org/10.1007/s12080-011-0137-x.
  • Plank MJ. and Simpson MJ. (2012) Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. Journal of the Royal Society Interface 9(76): 2983-2996. http://dx.doi.org/10.1098/rsif.2012.0319.
  • James A., Plank MJ. and Edwards AM. (2011) Assessing Lévy walks as models of animal foraging. Journal of the Royal Society Interface 8(62): 1233-1247. http://dx.doi.org/10.1098/rsif.2011.0200.
  • Plank MJ. (2011) Effects of diet breadth on the stability of size spectra. ANZIAM Journal 53(1): 38-47. http://dx.doi.org/10.1017/S1446181112000041.
  • 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.
  • Plank MJ. and Codling EA. (2009) Sampling rate and misidentification of Lévy and non-Lévy movement paths. Ecology 90(12): 3546-3553.
  • Basse B. and Plank M. (2008) Modelling biological invasions over homogeneous and inhomogeneous landscapes using level set methods. Biological Invasions 10(2): 157-167. http://dx.doi.org/10.1007/s10530-007-9119-8.
  • Codling EA., Plank MJ. and Benhamou S. (2008) Random walk models in biology. Journal of the Royal Society Interface 5(25): 813-834. http://dx.doi.org/10.1098/rsif.2008.0014.
  • 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.
  • Plank MJ. and James A. (2008) Optimal foraging: Lévy pattern or process? Interface: Journal of the Royal Society 5(26): 1077-1086. http://dx.doi.org/10.1098/rsif.2008.0006.
  • 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., Wall DJN. and David T. (2006) Atherosclerosis and calcium signalling in endothelial cells. Progress in Biophysics and Molecular Biology 91(3): 287-313. http://dx.doi.org/10.1016/j.pbiomolbio.2005.07.005.
  • Plank MJ. and Sleeman BD. (2004) Lattice and non-lattice models of tumour angiogenesis. Bulletin of Mathematical Biology 66(6): 1785-1819. http://dx.doi.org/10.1016/j.bulm.2004.04.001.
  • 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., Sleeman BD. and Jones PF. (2004) The role of the angiopoietins in tumour angiogenesis. Growth Factors 22(1): 1-11. http://dx.doi.org/10.1080/08977190310001643218.
  • 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. and Sleeman BD. (2003) Tumour-induced Angiogenesis: A Review. Journal of Theoretical Medicine 5(3-4): 137-153.
  • 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. (2009) Differential equations and mathematical biology, second edition. 1-444.
Chapters
  • Kolding J., Law R., Plank MJ. and van Zwieten PAM. (2016) The optimal fishing pattern. In Craig JF (Ed.), Freshwater Fisheries Ecology: 524-540. New York: Wiley-Blackwell. http://dx.doi.org/10.1002/9781118394380.ch41.
  • 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 - Published
  • 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. In Balanced harvest in the real world. Scientific, policy and operational issues in an ecosystem approach to fisheries: 27-32. IUCN/EBCD/FAO.
  • Law R., Plank MJ. and Kolding J. (2015) Balanced harvesting promotes coexistence of interacting species. In Balanced harvest in the real world. Scientific, policy and operational issues in an ecosystem approach to fisheries: 15-17.
  • Plank MJ., Law R. and Kolding J. (2015) Do unregulated, artisanal fisheries tend towards balanced harvesting? In Balanced harvest in the real world. Scientific, policy and operational issues in an ecosystem approach to fisheries: 19-21.
  • Law R., Plank M., Delius GW. and Blanchard JL. (2011) Ecological drivers of stability and instability in marine ecosystems. In Garcia SM (Eds). : 4-5. Brussels: IUCN.
  • Sellier D., Plank MJ. and Harrington JJ. (2010) An extensible mathematical framework to model cambial growth and wood formation. In Proceedings: 202-204.
  • Timmins SM., James A., Stover J. and Plank M. (2010) Is garden waste dumping really a problem? In Zydenbos SM (Eds). : 455-458. New Zealand Plant Protection Society.
  • Mann J., Plank M. and Wilkins A. (2007) Tree growth and wood formation - applications of anisotropic surface growth. 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. In Proceedings of the 12th International Conference on Biomedical Engineering (ICBME 2005): 1B1-1B1.
  • Plank MJ. and Sleeman BD. (2003) A lattice-free model of tumour angiogenesis. In : 75-78.
Conference Contributions - Other
  • Lustig A., Vattiato G., Maclaren O., Watson L., Datta S. and Plank MJ. (2022) Covid-19 Modelling Aotearoa: mathematical modelling of Covid-19 in New Zealand. Queenstown: Queenstown Research Week Infectious Diseases Satellite Meeting, 29 Aug 2022.

Student Supervision

Displaying all items.
    Completed
  • PhD - Binny R: Spatial moment models of collective cell behaviour (2015)
  • PhD - Comerford A: An integrated fluid mechanics/cell model for atherosclerosis (2007)
  • PhD - Graybill S: Modelling nephron dynamics and tubuloglomerular feedback (2010)
  • PhD - Hackney M: Modelling cooperative and competitive behaviour in the exploitation of marine resources (2019)
  • PhD - Halafihi T: Ecology and biology of Etelis coruscans and Pristipomoides filamentosus at seamounts: Case Study at Tonga Deepwater Drop-line Fishery (2015)
  • PhD - Kenny A: Parallel neurovascular coupling models and associated spreading depression (2019)
  • PhD - Kleinstreuer N: Mathematical modelling of renal autoregulation (2009)
  • PhD - Mathias E: Computational modelling of neurovascular coupling and the BOLD signal (2017)
  • PhD - Mohd H: Modelling the presence-absence of multiple species (2016)
  • PhD - Mugford J: Developing methods to reduce uncertainty with citizen science data (2021)
  • PhD - Pallippadan Johny J: Modulating factors of intracellular calcium dynamics in vascular smooth muscle cell (2016)
  • PhD - Vattiato G: Modelling individual heterogeneity in behaviour for wildlife management and conservation (2022)
  • PhD - Warburton H: Body size, interaction strength, and food web stability (2015)
  • Masters - Kenny A: Calcium dynamics and wave propagation in coupled cells (2016)
  • Masters - Merry S: Quantifying the effect of individual heterogeneity in epidemic spread on a network. (2021)

Editorial Work

Displaying all items.
  • ANZIAM Journal Associate Editor ( 2010 - 2023)
  • Applied Mathematical Modelling Editorial Board Member ( 2021 - 2023)

Affiliations

  • Te Pūnaha Matatini (Teaching/Research Organisation): Principal Investigator
  • Society for Mathematical Biology (Professional Organisation): Member
  • Association for Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) (Professional Organisation): Member
  • New Zealand Mathematical Society (Inc.) (Professional Organisation): Member

Research Groups

  • Biomathematics Research Centre

Research Projects

  • NZIMA programme on Modelling Invasive Species and Weed Impact
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