Beautiful, fragile and beloved, butterflies hold a special place for many here in Britain but climate change and habitat loss has affected the near 60 species which call the UK home. Thanks in large part to the research of statisticians Professor Byron Morgan and Dr Emily Dennis from the University of Kent, their study into butterfly numbers is providing conservationists and policymakers with a better understanding of these delicate insects and an insight into the changing world around us. 

These statistical ecologists have spent years passionately developing advanced mathematical models that are now being used in the field to map and manage butterfly populations across the world. We are actually trying to, with just a little bit extra, make it easier to see what's happening, trying to change the way people think about how they present their summaries of the data. We are trying to take the global picture and by bringing in environmental covariants, spatial covariants, we're trying to understand what it is that's happening. 

You don't spend, whatever it is, five or so years doing these things if you're not interested in the target species. And they're so beautiful and so fascinating and I was just very lucky that Emily Dennis, who was my research student, came with this experience in modeling butterflies and that was the basis for what we've been doing. We had these equations for some of our models and then it became apparent that there were tricks that you could do to make it, say, ten times more efficient and that was very exciting. So as a result, we now have certain methods that have become standard. 

From the field of maths and stats, Professor Morgan developed a keen interest in butterflies when he began mentoring Emily during her PhD at Kent.  I do feel like I'm fortunate to have a rewarding job where I can  see the effects of the work that I do. I mean for butterflies and moths we're really lucky to have these great datasets and to be able to work with them every day is a privilege and it's just great also to then see the impacts of that, so the indices for various species being used both for conservation and policy.  

Burton Bradstock on Dorset's Jurassic Coast is one of a network of transect sites where data are collected. Emily has been working alongside Professor Brereton from Butterfly Conservation, an organisation which looks to monitor and protects butterflies. Dr Dennis's research has had a real impact on their efforts. 

Before Emily joined we used to outsource a lot of the analysis work for two reasons really, firstly we weren't technically capable of doing a lot of the analysis but also, prior to Emily's research, a lot of the statistical techniques needed very heavy computer power and Emily's developed these more efficient methods which means that we can now run a lot of the analyses on fairly basic computers, but we also have Emily to lead on analysis that, as I said previously, we used to farm out to other organisations. It's made a huge difference because we had a lot of very good data that was almost like gathering dust that we weren't sure of how to analyse and Emily's come along and it's really helped people to use the data they've collected to inform conservation. 

I mean a very good example was we had some data on the habitat of a rare species called the High Brown Fritillery and Emily helped to analyse the vegetation data and it sort of showed that the management we were doing was not really affective because the vegetation had changed with climate change and that we need to look at new solutions. The previous management was quite costly and used to work but doesn't anymore. So it's highlighted a conservation problem that we need to solve. With climate change continuing to grab the headlines, this research could prove central in protecting the fate of butterflies and, in doing so, maintain a crucial component of our ecosystem. The data that Emily helps analyse is like a world leader in  looking at the effects of climate change on biodiversity Ð it's one of the most important data sets in the world. 

Also Emily's involved in developing biodiversity indicators, so butterflies and moths are used to tell us about the overall health of the environment and quality of life and Emily's developing some new statistical techniques to make better biodiversity indicators. So it's vitally important for Butterfly Conservation's conservation work but also it has wider value to policy and environmental management. 

Using data collected from 3000 volunteers in nearly 2900 locations,  Emily and Byron have developed a model by which to more accurately record the status of butterflies. Combined with their seasonal patterns, the model can reveal trends in each individual species. It's really quite an intensive process, so volunteers have to visit the same transect up to 26 times a year. We get all this great data in for every species, but it, of course, then needs modelling and processing, so we need to, in particular, estimate the missing counts. 

Quite often people won't be able to go out because of the weather or holidays or whatever, so we need to estimate the seasonal pattern of the species Ð so that's the time within the year that they're flying and that could be sort of one or two broods that you're fortunate to see those butterflies. So we have sophisticated models that estimate the time within each year which can also vary for each species and fill in the missing counts effectively and then, with our models, it all gets combined together to get an overall index for that species and we can look at how that index is changing over time to get trends to work out whether a species is on the whole doing well or poorly. 

The end products really are things like estimating trends, simple things like that. Which species are on the up and which ones are declining. Prior to my work the methods that we used meant that approximately 40% of the counts that, you know, volunteers had gone out and got for us weren't necessarily feeding through into the outlets. Whereas through having better statistical methods, we can use as much of the data as possible and actually get better answers as well. All good conservation underlying it needs solid evidence and from that really comes from the answers we can gain from our great datasets. And it's through the new models that we've been developing that we can make the most out of these datasets and answer the sort of questions to find out which species are most in need of conservation so that can then feed through to directing the effort of an organisation like Butterfly Conservation Ð so where are we going to target our conservation work or our advocacy and policy work to find out which species need the most help. 

Some species are clearly Red List species and some are clearly doing very well, but there's a kind of grey area in between. We are trying to refine the Red List idea by bringing in probability theory to say Ð well you know there's a species here which is on the edge. It's probably more likely to be okay than in danger, you might then prefer to put the effort on something that it is more likely to be a Red List one, rather sort of 80% Red List rather than 20% Red List. 

Discoveries such as rural butterflies faring better than those in urban areas have been made possible by Dr Dennis and Professor Morgan's model. It's also enabled a more up-to-date analysis of the abundance of butterflies, their whereabouts and what time of year they're on the fly. When I want to go and see a butterfly, I check my field guide Ð it's probably 40 years out of date. It'll say, you know, August is a good time to see this butterfly. In fact it may now be a month or so earlier. And it's the kind of modern analyses with much more data than we had before that has made this possible. 

So what about the wider impact on conservation policy? One of the main ways in which we can influence policy is through agri-environment schemes, green farming schemes, and I think the data can play a vital role in helping to assess and understand those policies and try and refine them in the future as well.   Policy - I think the main impact is thatthe work we do feeds through to government indicators, and it's really these measures that will contribute to any wider scale changes that are policy driven, and in particular through trying to meet biodiversity targets and so on. But then also in terms of conservation, we're really trying to produce better measures of how butterflies and moths are doing, both at large scales but also small scales, right down to the site, so we can really try and know where they're doing well and badly, but also why. 

So really going forward, it's much more about drilling down into the reasons and it's complicated because there's usually multiple pressures that a species might be subject to. To be able to make people that allocate money for conservation, have the right answer, make them come to the right decisions based on the right models and so on Ð I think that's where we're really going to make a difference.