On February 27^th 2020 Lancaster University ran a Statistics for the Natural Environment workshop sponsored by the Royal Statistical Society (Statistical Computing Section, Environment Section and Lancashire and East Cumbria local branch) in conjunction with the Data Science of the Natural Environment project and CEEDS at Lancaster University. The event brought together speakers from across the UK who are working in statistical approaches to a range of environmental data problems. The event equally well attended by both statisticians and environmental scientists.

The first speaker, Hannah Worthington (University of St Andrews), talked about the use of Hidden Markov Models (HMM) for gathering information populations and elaborated three case studies across land, sea and air. In each case HMMs were adapted according to behaviours of the chosen species, which include Jaguars, Grey Seals, Lapwings and Grey Herons. It was demonstrated that the HMM approach works well for estimating abundance, survival and capture probabilities, and offers computationally efficient methods to obtain parameter estimates.

This was followed by Murray Lark (University of Nottingham) who gave a good example of using multivariate geostatistical models, the linear model of coregionalization (LMCR), to predict spatial variations of selenium in the teff grain across the Amahara region in Ethiopia. Drivers of the model included direct measurements of selenium content in both soil across the region as well as teff plants and several covariates such as temperature and precipitation. The direct measurement locations had the requirement to be 2km from a road, and the locations were decided upon using the cube algorithm of Deville and Tille (1998). Different formats of prediction maps were displayed to key stakeholders in the region and feedback was received on which styles were most useful for decision making. It was agreed that continuous heat maps showing the predicted concentrations of selenium were not as intuitive and understandable as discrete heat maps where the concentrations had been banded into 5 IPCC style significance groups, for example regions labelled as ‘virtually certain’ to have significant deficiencies in selenium.

Marnie Low presented an interesting talk about the use of splines for modelling spatio-temporal groundwater contamination data. She assessed the merits of introducing a spline-based spatial structure to the ordinary approach of modelling independently time-series contamination for each well. By doing this, the model complexity increases drastically and also requires the estimation of smoothing parameters. For this reason, she reduced computational cost by proposing a set of alternatives for matrix computation using spectral decompositions to update only the parts that are required. Under different scenarios she showed the improvement of the model by using a spline-based spatio-temporal structure.

Finally, Andrew Parnell’s talk was motivated by environmental challenges that arise as mixtures of primary resources. He described this piece of research as the most exciting work he has done in the last ten years. The work focuses on how mixture models can be used to predict animal diets using their tissue samples. He started with an introduction to stable isotopes as a compound of elements that do not decay and can be measured from animal tissues such as blood, hair, feathers etc. The first case study was based on a 1 isotope example and the second example focused on a more complicated 1 isotope case study. Parnell also presented another example on 2 isotopes case study He gave real data examples using Geese and wolves’ datasets in North America. Parnell described how Bayesian inference could be used to analyse Geese dietary proportion based on Dirichlet, prior information, and with possible extension to cases where the data is changing over time. He concluded with a further possible extension of the works to fatty acid tracers instead of isotopes, and how the methods can also be applied to model sea-level reconstruction. The work was carried out using simr and SIMMS packages.

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