Michael John Plank (born 1979) is a New Zealand mathematician. Born and educated in England, he is a professor in mathematics and statistics at the University of Canterbury, and a principal investigator at Te Pūnaha Matatini. Plank's research has focused on mechanistic mathematical and stochastic models and areas of expertise include ecological and social networks, population dynamics, epidemiological models and marine ecosystems. His work has included developing and applying models to the balanced managing of fishing sites, revitalisation of endangered languages and invasive plant and weed impact. As a co-Lead for Covid-19 Modelling Aotearoa, a research programme established initially under Te Pūnaha Matatini but independent since 2021, he came to prominence as a COVID-19 modeller and frequent commentator in the media during the COVID-19 pandemic in New Zealand. Plank has received several awards in recognition of contributions to the field of applied mathematics, particularly for his explanations of how mathematical modelling can benefit social and ecological environments and concerns.
Early life and education Plank grew up in Hathersage, an English village in the Peak District. His interest for mathematics developed when he was at primary school. Plank received a Bachelor of Science with honours from the University of Bristol in 2000, and, three years later, a PhD in applied mathematics from the University of Leeds. The title of his thesis was Cell-based models of tumour angiogenesis, with Brian Sleeman as his supervisor.
Career Plank took a post-doctoral fellowship at the University of Canterbury at the beginning of 2004, attracted to New Zealand by his love of mountains and tramping. He liked the country's lifestyle and secured a position as a lecturer at the same university beginning in the 2006 academic year, rising to the rank of full professor. He is also a principal investigator at Te Pūnaha Matatini, and since 2021, a Co-Lead for Covid-19 Modelling Aotearoa, an independent research programmed funded by the Ministry of Health (New Zealand).
Commentary on modelling theories Movement models Plank has contributed to the debate about the limitations and possibilities for two different movement models: the composite correlated random walk; and the Lévy walk. In 2008, Plank co-authored a review paper that explored the mathematics behind the random walks model used to understand the biological processes of the movement of animals, micro-organisms and cells. The paper noted that some of these basic models had limitations due to confusion in the literature between patterns that were observed and the underlying processes that may have generated them. The paper concluded random walk models allowed the systematic identification of these underlying mechanisms. A further study in the same year presented a composite search model for non-destructive foraging behaviour based on Brownian motion compared to the Lévy walk. While it was shown that distinguishing between the two models might be difficult based on data in practice, the paper concluded that a "mathematical expression" had shown the "composite search model provides higher foraging efficiency than the Lévy model". The conclusion from the paper was that the composite search model provided higher foraging efficiency than the Lévy model, a finding also confirmed in a 2011 paper co-authored by Plank. By 2015, a research project in which Plank participated, presented a method that could differentiate between the two models using a simulation study and possible likelihood functions including for a possible hidden Markov chain. In the Summary, the study concluded [that] "by providing the means to differentiate between the two most prominent search models in the literature, and a framework that could be extended to include other models, we facilitate further research into the strategies animals use to find resource".
Nestedness Plank was part of a team that challenged the view nestedness increased the accuracy of a model to predict the survival of a specific species, and proposed that a "simpler metric—the number of mutualistic partners a species has—is a much better predictor of individual species survival and hence, community persistence". The research team examined previous data and applied "computational and statistical methods to 59 empirical datasets representing mutualistic plant-pollinator networks..[which they said could]...disprove the accepted theory of nestedness". Plank stated:Real-life networks, whether they are from ecology, economics, or Facebook, can be large and complex. This makes it difficult to tease apart causal relationships from confounding factors. This is where mathematical models come into their own. They allow us to systematically change one network attribute, such as nestedness, whilst controlling for other variables.
Two biological scientists disputed this conclusion publishing data that showed a positive relationship between nestedness and persistence, and James et al. cited data in a response that concluded "[while]...nestedness is an interesting abstract network property that undoubtedly influences the statistical behaviour of large systems of differential equations...general conclusions allowing nestedness to be used as a predictor of empirical biodiversity cannot currently be justified".
Selected research Balanced harvesting of commercial fishing In 2013, Plank suggested there needed to be a change in the way fish were caught commercially. He proposed a mathematically- based model to introduce "balanced harvesting...[with]...less emphasis on catching big fish...[and more on]...catching a balanced cross-section". This supported the findings in an earlier research paper, co-authored by Plank, which explained that while the reasoning to protect small fish was to reduce the risk of damaging the life cycle, because the small fish had higher productivity, they might be more resilient than large fish in sustaining possible exploitation and it could be better to "distribute fishing more widely across species and body sizes, balancing it more closely to the natural productivity of different organisms". The research, based on population dynamics underpinning the mathematical modelling, laid the groundwork for constructive discussion on fisheries management and how practices could potentially change in future. In a paper, he published jointly in the journal Fish and Fisheries in June 2018 Plank noted: You are tracking biomass around an ecosystem in which there are predators and prey, big fish and small fish. You can then study the consequences of both predation and fishing and track the loss of biomass out of the ecosystem using different variables,...[and by comparing]...balanced harvesting with current fishing strategies [find] that balanced harvesting can mitigate that impact by reducing the number of large fish being caught.
While the idea did receive support, there was also some criticism and Plank co-authored a paper that examined the theory, evidence and legality of balanced harvest and the degree that it could limit potential jeopardizing of marine resources. It noted that the debate was ongoing but concluded balanced harvest met legal frameworks, including those for conservation, was likely to support trophic of populations and increase the yield, and if successful would lead to a "moderate reduction of biomass of all ecological groups". A further paper noted also that maximising yields and economic profits, and minimising environmental impact and biodiversity loss [was] "more of a sociopolitical question than a scientific one, and [would] clearly involve compromises".
Models for language transmission Plank has collaborated to research strategies used to revitalise endangered languages and based on data from Wales, developed a model regarding language transmission by "dividing the population into defined proficiency categories and dynamically quantifying transition rates between categories...[to]...predict changes in proficiency levels over time and, ultimately, whether a given endangered language is on a long-term trajectory towards extinction or recovery". Te reo Māori, the indigenous language of New Zealand, was a case study and using census data, the findings suggested that te reo Māori was on a "pathway towards extinction", but there were strategies that could restore the language "to an upward trajectory", with the research paper concluding: Possible government measures [included] the provision of language-medium early childhood education; integration of the language into the primary and secondary school curriculum; development of the quantity and quality of teachers; investment in language-immersion education as a crucial avenue for the development of proficiency.
Modelling invasive species and weed impact Plank was an Associate Investigator for the NZ Institute of Mathematics and its Applications (NZIMA)-funded Canterbury Research programme on Modelling Invasive Species and Weed Impact, which recognised that "invasive, non-native plants are a major component of global environmental change...[and aimed to]... "determine the optimal use of resources between the competing demands of controlling existing weeds and stopping new weeds, thus minimising the negative impacts on indigenous biodiversity and ecosystem processes". The project began with a workshop in 2007 that was attended by 51 international mathematicians, statisticians and ecologists.
COVID-19 response in New Zealand Modelling During the COVID-19 pandemic, Plank applied his expertise to modelling the disease in New Zealand, and was a frequent media commentator. As a mathematical modelling expert in infectious diseases, Plank worked with Te Pūnaha Matatini, a research centre hosted at the University of Auckland, leading to work with Covid-19 Modelling Aotearoa, to aid the New Zealand response to COVID-19. This involved application of mathematical models to explore a series of scenarios specific to New Zealand's situation during the pandemic and to directly inform the New Zealand Government policymakers. On 25 March 2020 a state of emergency was declared in New Zealand after rising numbers of COVID cases and the country went into full lockdown. At that time, Plank, as one of the team at Te Pūnaha Matatini, co-authored a document based on simulations that had been used for a possible spread of COVID-19 in New Zealand and the model results allowed for a cautious conclusion that strategies to suppress the spread of the virus had two key benefits: "(1) it may be possible to delay the epidemic for long enough that a vaccine and/or effective treatment become widely available in NZ; and (2) it allows NZ to learn from rapidly unfolding events in other countries. This could include learning which mitigation strategies are most successful, and how to ensure timing of control interventions is robust to uncertainty".