The Fellowship will trial a new mode of cross-sector research in exploring later prehistoric wildlife and its relevance to contemporary ecological debates. The current nature conservation concept of 'rewilding' will be recast in order to reveal the 'wonder and enchantment' (Monbiot 2013) of archaeological wildlife. Wildlife is a pressing topic. Growing awareness that people are very much part of natural processes and that wildlife is central to human well-being has sparked strong responses. The rewilding movement is a prominent example. Bold experiments are underway across the globe to reinstate animals and plants destroyed locally by human activity, to restore wild areas, and to reconnect people with nature. Intellectually, social scientists have sought to elicit the lively roles that 'other-than-human' beings - plants, animals and objects - play in the world, and to question what wildlife is and what it does. Within archaeology, however, nature is still viewed largely as a waning backdrop for human life. Wildness is seen as a trait of pre-farming landscapes; past ideas about wildlife are examined only for historical periods when there are written accounts of 'the wild'. Reviews of wild plants and animals focus mainly on loss - the ruin of woodland and animal extinctions. Instances of woodland renewal and finds of aurochs, whales, pelican, etc., in human settings are treated as interesting, but mostly unexplored, asides. The period from 2500 BC-AD 43, spanning the British Bronze and Iron Ages (B/IA), is recognised as a major tipping point in the transition from natural to farmed landscapes. It is also hailed as an era in which people's understandings of nature were far away from our own. Surprisingly, no holistic ecological account exists for this period. Summaries of B/IA life repeatedly focus on the human side of the story - evidence for farming revolutions and domestication. Although the B/IA could be pivotal to understandings of human-nature relations, our appreciation of the natural world and of people's place in it at this time is scant. Wildlife has been overlooked. This Fellowship will consider holistically, for the first time, wildlife in B/IA Britain. It will examine shifts in the full makeup of plants and animals for this period, to what extent it is possible to approach archaeological wildlife, and whether or not wildlife even existed as an idea in later prehistory. A substantial volume of plant and animal remain data will be collated from diverse study areas - the Upper Thames Valley, the Fen Basin and Northumberland. Placing wildlife centre stage analytically, an original multi-stranded toolkit will be developed for investigating archaeological wildlife. Cutting-edge scientific methods will be juxtaposed with landscape-scale evidence of archaeological 'blank spaces' (B/IA wild areas?) and with objects made from wild species - nettles, wolf-teeth, and so on. By giving wildlife due attention, a richer and more vibrant understanding of later prehistory will be built, offering not only a serious challenge to existing human-centred historical accounts but also a vital link to current ecological practices. Wider outcomes of the Fellowship will be threefold. The creation of a new system for logging plant and animal remain data routinely will address urgent disciplinary agendas to improve access to palaeoecological data and to embrace open science methods. Joint work with current rewilding practitioners will allow nature conservationists to inform the research, to explore the present value of deep-time wildlife perspectives, and to set an agenda, with archaeologists, for future collaboration. The Fellowship will also spark a radical shift in disciplinary research dynamics. Uniquely in archaeology, the project will be led by a non-academic body, Oxford Archaeology, in collaboration with the Universities of Exeter, Oxford, and Toulouse, Historic England, the Archaeology Data Service and Knepp rewilding hub.

Laying eggs or giving birth to live young are two fundamentally different ways for females to produce their offspring. All birds, crocodilians, turtles, monotreme mammals (such as duck-billed platypus), and many lizards and snakes are egg-laying, as were most dinosaurs. In contrast, all placental mammals (like humans), marsupials, and some lizards and snakes are live-bearing. From studying embryos we know that many molecular and developmental aspects of these reproductive modes arose deep within the tree of life. For example, ancient egg-making structures are still retained within mammalian placenta, and the genes activated by pregnancy in lizards are the same as those activated by pregnancy in mammals and seahorses. Yet, clearly, substantial reproductive differences evolved between species; though it is not known how or why because the core genetic controls of these reproductive modes remain unknown. This major and obvious gap in our biological knowledge has persisted into the genomic era - where we can now study the entire DNA sequence of an organism - because we lacked an informative experimental model. Simply put, to test the genetic basis of traits that differ, the definitive experiment is to make a cross between the two different types. In the case of reproductive mode this is usual not possible, because species are too divergent to successfully breed. For example, no one can make a genetic cross of a platypus and a snake to test if the 'egg making DNA' is the same in both species. Our proposal seeks to shed light on the genetic basis of these fundamental reproductive traits using an exceptional species: the humbly-named 'common lizard'. Native to all of Eurasia, including the British Isles, this species harbours a secret underneath its simple brown scales: some populations are egg-laying and others are live-bearing. Like all reptiles, egg-laying is the original, or ancestral, mode. This means that many millions of years ago all common lizard females laid eggs. Then, about three million years ago, some females discarded the egg-laying tactic; no longer encircling their embryos in eggshells, the females retained their babies inside their bodies until fully developed. Why and how this happened is not known, but is presumed to be an adaptation that allowed mothers to better protect their embryos from cold and challenging environments. Amazingly, evolutionary reconstructions suggest that another million years later, some common lizards abandoned the live-bearing strategy and reversed back to egg-laying. Today we have populations with the original egg-laying strategy (mostly in the Alps), the live-bearers (across most of Eurasia), and those few that reversed back to egg-laying from live-bearing (found in the Pyrenees). Importantly, because they are closely related, individuals from all of these populations can interbreed. To test long-standing ideas about the genetic basis of fundamental reproductive traits, we plan to do controlled functional studies of the different types found within these lizards and make experimental crosses between them. By comparing the two lineages of egg-laying lizards we will be able to identify the genes necessary for egg-laying. This is due to the fact that the core genes should be found in the genomes of both and, if they are shared, these genes should be expressed in similar places and times. Then, using all the information we gain about how and where genes are active, we will use computational approaches to retrace the evolution of 'egg-laying' and 'live-bearing' genes across the history of the entire species. This will reveal how changes in a species' DNA give rise to changes in reproductive mode. Because of the ancient origins and sharing of reproductive genes across species, the lessons learned from these lizards will provide new and valuable insights into the biology, reproductive health, and evolution of all vertebrates.

The asymmetric simple exclusion process (ASEP) is a fundamental mathematical construction in statistical mechanics that combines the notion of stochastic motion with a physical requirement that matter cannot coexist in the same location. As such, it has wide-ranging applications, from traffic and fluid flow to biological processes. However, recent advances, particularly the emerging parallelism between ASEP-type processes and well-known families of orthogonal polynomials, hint at a hidden probabilistic phenomenon that promises to greatly expand the applicability of the ASEP. The key is in a common computational artifact, referred to as the matrix ansatz. In this project, we explore a new perspective on the ASEP, based on the relationship between its matrix ansatz and noncommutative infinite-dimensional phenomena. In this manner, we aim to transform the interface between the 'classical' and noncommutative probability theories, arrive at a more fundamental understanding of the ASEP, and open up innovative approaches to a long-standing open question of mathematical analysis, the free group factors isomorphism problem.

When linguists are trying to determine how different languages are related or neuroscientists wish to know how one part of the brain is associated with another, how to analyse data which is both complex and massive is a fundamental question. However, an area of Statistics, namely Functional Data Analysis, where the data is described as mathematical functions rather than numbers or vectors, has recently been shown to be very powerful in these situations. This fellowship aims to take functional data analysis and advance it so that much more complex data can be investigated. This will require establishing a careful statistical framework for the analysis of such functions even in situations where the functions have strict relationships. By considering the underlying mathematical spaces which the functions lie in, it is possible to construct valid statistical procedures, which preserve these relationships, such as the functions needing to be positive definite or the functions needing to be related by a graph or network. As an example, comparison between different languages (for example, how is French quantitatively different from Italian) can be carried out in the framework of functional data but not without considering specifically how the data should be analysed to take into account its particular properties. For example in trying to find a path from one language to another, it would be sensible to try to only go via other feasible acoustic sounds. This turns out to be mathematically related to shape analysis, a simple example of which might be how to describe going from London to Sydney. The shortest path is through the centre of the Earth, but this is not sensible, so you have to go round the world. Establishing links between shape analysis and functional data is a major aim of this fellowship. In addition, most brain analysis currently splits the brain up into lots of elements know as voxels, and then analyses these voxels one by one. However, the brain is really one object (or complex 3-D object) which should be analysed together. This is another example of functional data and the methods developed in this fellowship will enable the analysis of the brain as a single object. This will be done by examining the types of dependence between observations in brain imaging data, and using these to build such an object. Of particular interest will be the analysis of brain connections resulting from particular tasks which will require a mixture of functional data analysis and graphical or network analysis. However, before this can be done and the resulting insights into the brain found, the statistical methods required to do this need to be developed.

The asymmetric simple exclusion process (ASEP) is a fundamental mathematical construction in statistical mechanics that combines the notion of stochastic motion with a physical requirement that matter cannot coexist in the same location. As such, it has wide-ranging applications, from traffic and fluid flow to biological processes. However, recent advances, particularly the emerging parallelism between ASEP-type processes and well-known families of orthogonal polynomials, hint at a hidden probabilistic phenomenon that promises to greatly expand the applicability of the ASEP. The key is in a common computational artifact, referred to as the matrix ansatz. In this project, we explore a new perspective on the ASEP, based on the relationship between its matrix ansatz and noncommutative infinite-dimensional phenomena. In this manner, we aim to transform the interface between the 'classical' and noncommutative probability theories, arrive at a more fundamental understanding of the ASEP, and open up innovative approaches to a long-standing open question of mathematical analysis, the free group factors isomorphism problem.