Michael Plank

Michael John Plank FRSNZ (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.

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.

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).

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".

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".

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".