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Dr Stephen Woodcock


Stephen joined UTS in 2010 as a Lecturer in the School of Mathematical Sciences. Prior to this, he was a Research Associate at the University of Glasgow and also worked in private sector consultancy/analysis in London. In addition, he is now an Associate Member of theClimate Change Cluster (C3) at UTS.

His primary research interests lie in the application of mathematical models to describe biological and ecological systems. The main motivation behind his work is a drive to develop readily implemented solutions and models for pressing real-world problems in the biological and environmental sciences. As such, he works primarily in multidisciplinary teams alongside marine biologists, microbial ecologists and environmental engineers.

His research projects have covered a vast range of applications from improving the design and efficiency of wastewater treatment systems to understanding and modelling the growth of biofilms on riverbeds. Current research topics include modelling the biogeography around the Great Barrier Reef, calibrating and interpreting data from marine fluorescence meters and examining the effect of habitat loss upon fish behaviour in marine parks.

Stephen is a keen and committed teacher and has co-ordinated and taught subjects from the first year undergraduate level through to Honours. He has supervised research students at both the Honours and PhD level. Additional to his main duties at UTS, he is a frequent and enthusiastic contributor to High School outreach programs and widening participation schemes.

Stephen holds a PhD in Civil Engineering from the University of Glasgow (2007) and a MMath in Mathematics from the University of Oxford (2003).



Australian Mathematical Society (AustMS)

Australian and New Zealand Industrial and Applied Mathematics (ANZIAM)

Committee Roles:

ANZIAM (Australian and New Zealand Industrial and Applied Mathematics) Engineering Mathematics Group Committee member (2011-2013)

Senior Lecturer, School of Mathematical and Physical Sciences
Associate Member, Climate Change Cluster
MMath(Oxon), Ph D
+61 2 9514 7602
Can supervise: Yes

Lecturing and Co-Ordination:

37161: Probability and Random Variables

37262: Simulation Modelling

35101/37313: Introduction to Linear Dynamical Systems

35363: Stochastic Models

Mathematical Ecology and Biology (Honours reading subject)

Numerical Solutions of Stochastic Differential Equations (Honours reading subject)

Teaching and Learning Roles:

Program Director for School of Mathematical Sciences Honours students (BMathFin(Hons) and BSc(Hons)

Chair of School of Mathematical Sciences Honours Subcommittee

Program Director for BSc undergraduate students (Mathematical Sciences Foundation Stream)

Member of School of Mathematical Sciences Teaching and Learning Committee

Teaching and Learning Grants:

Slipping Between the Cracks? Maximising the Effectiveness of Prerequisite Paths (Vice-Chancellor's Learning and Teaching Small Grant 2013, in conjunction with Stephen Bush)

Journal articles

Woodcock, S. & Sloan, W.T. 2017, 'Biofilm community succession: a neutral perspective.', Microbiology, vol. 163, no. 5, pp. 664-668.
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Although biofilms represent one of the dominant forms of life in aqueous environments, our understanding of the assembly and development of their microbial communities remains relatively poor. In recent years, several studies have addressed this and have extended the concepts of succession theory in classical ecology into microbial systems. From these datasets, niche-based conceptual models have been developed explaining observed biodiversity patterns and their dynamics. These models have not, however, been formulated mathematically and so remain untested. Here, we further develop spatially resolved neutral community models and demonstrate that these can also explain these patterns and offer alternative explanations of microbial succession. The success of neutral models suggests that stochastic effects alone may have a much greater influence on microbial community succession than previously acknowledged. Furthermore, such models are much more readily parameterised and can be used as the foundation of more complex and realistic models of microbial community succession.
Fransen, J., Bush, S., Woodcock, S., Novak, A., Deprez, D., Baxter-Jones, A.D.G., Vaeyens, R. & Lenoir, M. 2017, 'Improving the Prediction of Maturity From Anthropometric Variables Using a Maturity Ratio', Pediatric Exercise Science.
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Woodcock, S. 2016, 'Development of enquiry-oriented learning in the mathematical sciences', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, vol. 57, pp. C1-C13.
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Camp, E.F., Smith, D.J., Evenhuis, C., Enochs, I., Manzello, D., Woodcock, S. & Suggett, D.J. 2016, 'Acclimatization to high-variance habitats does not enhance physiological tolerance of two key Caribbean corals to future temperature and pH.', Proceedings. Biological sciences / The Royal Society, vol. 283, no. 1831.
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Corals are acclimatized to populate dynamic habitats that neighbour coral reefs. Habitats such as seagrass beds exhibit broad diel changes in temperature and pH that routinely expose corals to conditions predicted for reefs over the next 50-100 years. However, whether such acclimatization effectively enhances physiological tolerance to, and hence provides refuge against, future climate scenarios remains unknown. Also, whether corals living in low-variance habitats can tolerate present-day high-variance conditions remains untested. We experimentally examined how pH and temperature predicted for the year 2100 affects the growth and physiology of two dominant Caribbean corals (Acropora palmata and Porites astreoides) native to habitats with intrinsically low (outer-reef terrace, LV) and/or high (neighbouring seagrass, HV) environmental variance. Under present-day temperature and pH, growth and metabolic rates (calcification, respiration and photosynthesis) were unchanged for HV versus LV populations. Superimposing future climate scenarios onto the HV and LV conditions did not result in any enhanced tolerance to colonies native to HV. Calcification rates were always lower for elevated temperature and/or reduced pH. Together, these results suggest that seagrass habitats may not serve as refugia against climate change if the magnitude of future temperature and pH changes is equivalent to neighbouring reef habitats.
Heidrich, E.S., Curtis, T.P., Woodcock, S. & Dolfing, J. 2016, 'Quantification of effective exoelectrogens by most probable number (MPN) in a microbial fuel cell', Bioresource Technology, vol. 218, pp. 27-30.
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The objective of this work was to quantify the number of exoelectrogens in wastewater capable of producing current in a microbial fuel cell by adapting the classical most probable number (MPN) methodology using current production as end point. Inoculating a series of microbial fuel cells with various dilutions of domestic wastewater and with acetate as test substrate yielded an apparent number of exoelectrogens of 17 per ml. Using current as a proxy for activity the apparent exoelectrogen growth rate was 0.03 h1. With starch or wastewater as more complex test substrates similar apparent growth rates were obtained, but the apparent MPN based numbers of exoelectrogens in wastewater were significantly lower, probably because in contrast to acetate, complex substrates require complex food chains to deliver the electrons to the electrodes. Consequently, the apparent MPN is a function of the combined probabilities of members of the food chain being present.
Woodcock, S., Manojlovic, B., Baird, M.E. & Ralph, P.J. 2015, 'A Poisson-Pareto Model of chlorophyll-A Fluorescence Signals in Marine Environments', ANZIAM J, vol. 56, no. 4, pp. 373-370.
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Woodcock, S. 2015, 'Development of enquiry-oriented learning in the mathematical sciences', ANZIAM Journal, vol. 57, pp. 1-1.
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Woodcock, S. & Bush, S. 2014, 'Slipping between the cracks? Maximising the effectiveness of prerequisite paths in UTS Maths degrees', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, vol. 55, pp. C297-C314.
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Woodcock, S., Besemer, K., Battin, T.J., Curtis, T.P. & Sloan, W.T. 2013, 'Modelling the effects of dispersal mechanisms and hydrodynamic regimes upon the structure of microbial communities within fluvial biofilms', Environmental Microbiology, vol. 15, no. 4, pp. 1216-1225.
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The spatial distribution of microbial taxa is determined primarily by physical and chemical environments and by dispersal. In a homogeneous landscape with limited dispersal, the similarity in abundance of taxa in samples declines with separation distance. We present a one-dimensional model for the spatial autocorrelation in abundances arising from immigration from some remote community and dispersal between environmentally similar landscape patches. Spatial correlation in taxa abundances were calculated from biofilms from the beds of two flumes which differed only in their bedform profiles; one flat and the other a periodic sawtooth shape. The hydraulic regime is approximately uniform over the flat bed, whereas the sawtooth induces fast flow over the peaks and recirculation in the troughs. On the flat bed, the correlation decline between samples was reproduced by a model using one biologically reasonable parameter. A decline was apparent in the other flume; however, a better fit was achieved when dispersal was not assumed constant everywhere. However, analysis of finer-resolution data for the heterogeneous flume suggested even this model did not adequately capture the community's complexity. We conclude that hydrodynamics are a strong driver of taxa-abundance patterns in stream biofilms. However, local adaptability must also be considered to build up a complete mechanistic model.
Woodcock, S., Van der Gast, C.J., Bell, T., Lunn, M., Curtis, T.P., Head, I. & Sloan, W.T. 2007, 'Neutral assembly of bacterial communities', FEMS Microbiology Letters, vol. 62, no. 2, pp. 171-180.
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Two recent, independent advances in ecology have generated interest and controversy: the development of neutral community models (NCMs) and the extension of biogeographical relationships into the microbial world. Here these two advances are linked by predicting an observed microbial taxavolume relationship using an NCM and provide the strongest evidence so far for neutral community assembly in any group of organisms, macro or micro. Previously, NCMs have only ever been fitted using species-abundance distributions of macroorganisms at a single site or at one scale and parameter values have been calibrated on a case-by-case basis. Because NCMs predict a malleable two-parameter taxa-abundance distribution, this is a weak test of neutral community assembly and, hence, of the predictive power of NCMs. Here the two parameters of an NCM are calibrated using the taxa-abundance distribution observed in a small waterborne bacterial community housed in a bark-lined tree-hole in a beech tree. Using these parameters, unchanged, the taxa-abundance distributions and taxavolume relationship observed in 26 other beech tree communities whose sizes span three orders of magnitude could be predicted. In doing so, a simple quantitative ecological mechanism to explain observations in microbial ecology is simultaneously offered and the predictive power of NCMs is demonstrated.
Sloan, W.T., Woodcock, S., Lunn, M., Head, I. & Curtis, T.P. 2007, 'Modeling taxa-abundance distributions in microbial communities using environmental sequence data', Microbial Ecology, vol. 53, no. 3, pp. 443-455.
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We show that inferring the taxa-abundance distribution of a microbial community from small environmental samples alone is difficult. The difficulty stems from the disparity in scale between the number of genetic sequences that can be characterized and the number of individuals in communities that microbial ecologists aspire to describe. One solution is to calibrate and validate a mathematical model of microbial community assembly using the small samples and use the model to extrapolate to the taxa-abundance distribution for the population that is deemed to constitute a community. We demonstrate this approach by using a simple neutral community assembly model in which random immigrations, births, and deaths determine the relative abundance of taxa in a community. In doing so, we further develop a neutral theory to produce a taxa-abundance distribution for large communities that are typical of microbial communities. In addition, we highlight that the sampling uncertainties conspire to make the immigration rate calibrated on the basis of small samples very much higher than the true immigration rate. This scale dependence of model parameters is not unique to neutral theories; it is a generic problem in ecology that is particularly acute in microbial ecology. We argue that to overcome this, so that microbial ecologists can characterize large microbial communities from small samples, mathematical models that encapsulate sampling effects are required
Sloan, W.T., Lunn, M., Woodcock, S., Head, I., Nee, S. & Curtis, T.P. 2006, 'Quantifying the roles of immigration and chance in shaping prokaryote community structure', Environmental Microbiology, vol. 8, no. 4, pp. 732-740.
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Naturally occurring populations of bacteria and archaea are vital to life on the earth and are of enormous practical significance in medicine, engineering and agriculture. However, the rules governing the formation of such communities are still poorly understood, and there is a need for a usable mathematical description of this process. Typically, microbial community structure is thought to be shaped mainly by deterministic factors such as competition and niche differentiation. Here we show, for a wide range of prokaryotic communities, that the relative abundance and frequency with which different taxa are observed in samples can be explained by a neutral community model (NCM). The NCM, which is a stochastic, birthdeath immigration process, does not explicitly represent the deterministic factors and therefore cannot be a complete or literal description of community assembly. However, its success suggests that chance and immigration are important forces in shaping the patterns seen in prokaryotic communities.
Woodcock, S., Curtis, T.P., Head, I., Lunn, M. & Sloan, W.T. 2006, 'Taxa-area relationships for microbes: the unsampled and the unseen', Ecology Letters, vol. 9, no. 7, pp. 805-812.
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The recent observation of a powerlaw relationship, S ? Az, between number of taxa, S, and area, A, for microbial eukaryotes and bacteria suggests that this is one of the few generic relationships in ecology, applicable to plants, animals and microbes. However, the rate of increase in the number of species with area varies from approximately the fourth (z = 0.26) to as little as the 50th root (z = 0.0019) in microbes. This is an enormous range for which no quantitative explanation has been proffered. We show by sampling from synthetic populations that the disparity between sample and community sizes in microbial community surveys means z can be considerably underestimated and accrual of rare taxa with increasing area will not be detectable. Significant microbial taxaarea relationships will only be observed when changes in community structure within samples correlate with area. Thus, the very low z values observed recently cannot be used as the sole evidence in support of any particular community theory of community assembly. More generally, this suggests that our search for patterns and laws in the microbial world will be profoundly influenced and, potentially distorted by the sample sizes that are typical of microbial community surveys.
Curtis, T.P., Head, I., Lunn, M., Woodcock, S., Schloss, P.D. & Sloan, W.T. 2006, 'What is the extent of prokaryotic diversity?', Proceedings Of The Royal Society Of London Series..., vol. 361, no. 1475, pp. 2023-2037.
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The extent of microbial diversity is an intrinsically fascinating subject of profound practical importance. The term `diversity may allude to the number of taxa or species richness as well as their relative abundance. There is uncertainty about both, primarily because sample sizes are too small. Non-parametric diversity estimators make gross underestimates if used with small sample sizes on unevenly distributed communities. One can make richness estimates over many scales using small samples by assuming a species/taxa-abundance distribution. However, no one knows what the underlying taxa-abundance distributions are for bacterial communities. Latterly, diversity has been estimated by fitting data from gene clone libraries and extrapolating from this to taxa-abundance curves to estimate richness. However, since sample sizes are small, we cannot be sure that such samples are representative of the community from which they were drawn. It is however possible to formulate, and calibrate, models that predict the diversity of local communities and of samples drawn from that local community. The calibration of such models suggests that migration rates are small and decrease as the community gets larger. The preliminary predictions of the model are qualitatively consistent with the patterns seen in clone libraries in `real life. The validation of this model is also confounded by small sample sizes. However, if such models were properly validated, they could form invaluable tools for the prediction of microbial diversity and a basis for the systematic exploration of microbial diversity on the planet.


Woodcock, S. 2017, 'How predictable are the Oscars? More than you might think', The Conversation.
Woodcock, S. 2017, 'Paradoxes of probability and other statistical strangeness', The Conversation.
Woodcock, S. 2016, 'We need a fairer system for deciding rain-affected games in Twenty20 cricket', The Conversation.
Woodcock, S. 2016, 'A tip to win your office footy tipping? Don't listen to the experts', The Conversation.
Palmer, C., Hall, G., Westerman, H., Henderson, J. & Mountain, W. 2016, 'The curious incentives and consequences of negative gearing', The Conversation.
Woodcock, S. 2016, 'The Melbourne Cup: why you didn't win', Money Magazine.
Woodcock, S. 2015, 'Socceroos have a host-nation advantage in the Asian Cup'.
Woodcock, S. 2015, 'The maths of congestion: springs, strings and traffic jams'.
Woodcock, S. 2015, 'The legacy of John Nash and his equilibrium theory'.
Woodcock, S. 2015, 'NRL grand final: Who has the edge as Broncos face Cowboys?', The Conversation.
Woodcock, S. 2014, 'Number crunching the odds on the NRL Grand Final', The Conversation.
Woodcock, S. 2014, 'Jarryd Hayne's code-shift and the 'unscrupulous diner' in NRL'.
Woodcock, S. 2014, 'Do historical trends in Melbourne Cup champions point to a winner?'.


Woodcock, S.M. & Cheung, B. Decision Technology Ltd 2010, Consumer decisions, information and understanding - A behavioural economics perspective, pp. 1-63, London.
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