Dan Haydon: Doing biology with maths

Before we start on the science what’s with the skull?
It belonged to a bison that nearly killed my PhD supervisor, a man called Eric Pianka. He’s a very interesting guy and one of the world’s leading herpetologists – a lizard ecologist who asks questions like why are there 50 species of lizard in the Great Victoria Desert in Australia but only 4 in West Texas or 12 in Namibia. So he’s thought long and hard about the structure and functioning of ecosystems empirically. He wants to know if that empirical understanding is consistent with current theory – and if not why not.

Pianka lives on a 200-acre ranch fifty miles out of Austin in the Texas hill country. He doesn’t much care for the modern world and thinks cows are an ecological disaster. It distresses him that so much of the landscape is chewed up by humans. He wouldn’t think there was a natural landscape in Europe.

He is interested in bringing back some of the species that used to be on the plains, so he keeps bison. But the herd keeps on growing, so when it gets to about 40 he sells or eats some. So one day he was trying to get some of these buffalo into trucks and one of them changed his mind and stuck its prong into his femoral artery. He nearly bled to death and had to be helicoptered to hospital. Some buffalo had to be culled anyway so he decided to cull the one that nearly culled him. When he got out of hospital he shot it.

I was out there for six years doing my PhD, so he’s a good friend and I go back to see him periodically. He doesn’t have too many friends. He gave the skull to me. It’s a story that keeps the students interested. Pianka is responsible for quite a lot of the theory they learn.

A number of scientists around the University have spoken to me about how useful they find the mathematical modelling you do with them. Dave Barry said he was sceptical at first, but is totally sold on the approach now.

That scepticism is normal among people who don’t know how modelling works or what it can offer. The bottleneck is that there aren’t that many modellers prepared to listen hard enough to the complications of the biology. Or biologists willing to take the time to understand what we do. It’s a communication game.

Our group recognises that putting time and effort into understanding each other is vital. We do a lot of that so our research is very interdisciplinary. We started something called the Boyd Orr Centre for Populations and Ecosystem Health. It’s a multidisciplinary, quantitative modelling centre which includes a lot of physicists, mathematicians, statisticians and biologists, who do mathematical modelling of biological problems.

Glasgow University is ideal for setting up such a group. There’s a great tradition of parasitology here. There’s a biomathematics group, which is very mathematical. There are ecologists and environmentalists. What they didn’t have was generic mathematical modellers. So there was a space between these disciplines and lots of interfaces for us to hook onto.

Dave Barry and his colleagues [Wellcome Trust Centre for Molecular Parasitology] provided some of those hooks. I’ve been working with Darren Monckton on the genetics of myotonic dystrophy, and with Paul Garside and Jim Brewer who are studying the movement of cells around germinal centres.

How long have you been at Glasgow University?
Nearly seven years. Before that I was at Edinburgh and a number of other universities. I was born in Cambridge, did my first degree in biology and oceanography at Southampton, then got interested in theoretical community ecology. Back in 1987 they didn’t do that in Britain, so I went to the University of Texas and did a PhD with Eric Pianka.

Theoretical community ecology?
Population ecology is the study of a single population. But a single population goes up and down for various reasons, a lot of which have to do with other populations. So as you broaden the web of ecological interactions you have to scale up from the dynamics of a single population to the dynamics of a whole community of populations. The theory of those dynamics is very challenging. One of the first theoretical community ecologists to come to this country was Robert May, the government’s chief scientific adviser for a long time. He’s a physicist. A lot of the people in theoretical community ecology are, because it’s a technical, mathematical subject.

But you’re not a mathematician?
No. I’m a biologist. I am interested in mathematical questions, but I’m not a very good mathematician. In fact I was spectacularly bad at maths.

You couldn’t have been.
You’d be surprised. I got 6% in my mock O-level maths, scraped a C in the exam and didn’t do A-level.

How did you manage to get 6%?
When I was at school maths was taught by people who understood it. It comes easy to them. They can’t understand why you can’t differentiate on the spot or integrate these functions or whatever. But 80% of us find maths hard, so being taught by the 20% who find it easy doesn’t work well. I’d much rather be taught by people who struggled, with the subject because they know what I’m likely to misunderstand and how to get me over those hurdles. It’s good to have people teach subjects they don’t find straightforward because then they have to think about it in many different ways.

So how do you get from 6% in maths to being a mathematical modeller?
What helped me was the context. At O-level we were always worrying about f(x) and dy/dx. It was abstract and never meant anything to me. When I started studying ecology and thinking about dN/dt – the rate of change of a population – that immediately made sense. You don’t need calculus to do a degree in biology. So I had to teach myself calculus when I went to Austin to do my PhD.

So why would you go into a mathematical subject like theoretical community ecology with very little maths?
I was really interested in the questions. I was able to frame the questions and understand answers a long time before I knew how they got from one to the other. The whole thing about community ecology at that time was stability analysis. Now you can’t do global stability analyses on sets of nonlinear differential equations. But you can do local stability analysis. So a lot of it came down to the behaviour of eigenvalues of Jacobian matrices. My whole PhD was on the behaviour of eigenvalues of Jacobians of nonlinear systems.

In order to do that in your first year as a PhD student you had to teach yourself calculus?

And linear algebra and stability theory. I taught myself the stuff I needed to know, so my maths is very patchy. I’m still not very good – better at some bits than others. The way we work here at Glasgow is if I get stuck on a maths problem I go over to the maths building and talk to real mathematicians. So I’m a sort of go-between.

Take the project with Dave Barry. He’s a molecular biologist. Then there’s Christina Cobbold who is a serious mathematician Then there’s me, who is translating Dave’s stuff to Christina and hers to him. You sometimes worry that you’re not doing something real, but actually that bridging role is important. It comes down to being prepared to listen hard enough to what people are saying and getting through the jargon so you can communicate it to someone else.

I’m still trying to get my head round how you can go from being so bad at maths to where you are now – how you could teach yourself so much as a PhD student. Your motivation must have been strong.

There was also a lot of time. I was there for six years and there wasn’t much else to do in Austin, Texas. I’d go out at the weekends and help Pianka build fences on his ranch to contain the buffalo. I also got quite lucky. There’s a way of thinking about eigenvalues – Gershgorin disk theorems – that is quite geometric. They hadn’t been used in ecology before, but they get you over having to work out what the eigenvalues really are. The disks are defined in the complex plane and they tell you whereabouts the eigenvalues are likely to be. Because you’re thinking about it geometrically rather than algebraically you don’t have to be very good at maths. That’s why I was able to make progress with this problem. It’s a powerful geometrical representation that can be related to ecological phenomena.

How did you come across it?

I found it in the middle of a slightly old PhD thesis – by George Sugihara. It made the whole problem very obvious. We had similar biological problems and were thinking about them in similar mathematical ways. We chewed on them together for a while. I was able to publish a paper – Pivotal Assumptions Determining the Relationship Between Stability and Complexity – that moved the subject forward a bit. I used the results on the distribution of eigenvalues in the complex plane to talk about how stability varies with complexity – which is the big question. Everyone wants to know how the stability changes as a food web or an ecosystem gets more complicated.

How are you defining complexity?

Mathematically there are three parts to complexity. One is the number of species in your community. Two is the density of interactions between the species. So with N species you have N² possible interactions between them and the percentage of those that are real is a measure of the density of connections in a food web. And the third measure is the strength of those interactions. So the stability of an equilibrium of an N-species system is governed by a Jacobian matrix formulated around that equilibrium point.

The dimensions of that matrix correspond to the number of species in the community. The percentage of non-zero elements gives the connectivity – the density of interactions. And the magnitude of those derivatives in the Jacobian correspond to the strengths of the interactions. All of these, it turns out, directly relate to the positioning and size of the Gershgorin disks in which the eigenvalues of the Jacobian must fall.

So the whole problem suddenly becomes very easy to see. In fact we used to study it sitting at the bar with the condensation rings from the bottom of Budweiser bottles. Pianka would refer to “windows of lucidity” which stretched from beers one to four – after which we probably started talking rubbish!

So all that was the basis of your PhD – do you still use these methods now?

I have a PhD student who followed up on some of this recently – and did a better job than me, I have to say. The problem is that it’s all about local stability. Ecologists worry that local stability – stability to an arbitrary small perturbation – is not the property of interest. Ecologists are interested in big perturbations. They’re really interested in the global stability of the system. Also a lot of people don’t believe ecological systems are at equilibrium. It doesn’t make sense to ask if an equilibrium point is locally stable if the system is not at it. There is a huge debate about whether ecological systems are at equilibrium. Some people believe they’re chaotically driven. Others say they’re dominated by stochastic perturbations. Some people think they do limit cycles.

These very basic questions haven’t yet been answered?

It depends on the system. If you go up to the boreal forest in Alaska you’ll see tremendous 10-year cycles, driven by snowshoe hares and lynx. Go to the Serengeti and you’ll see wildebeeste migrating once a year as the crankshaft of that system, so you couldn’t look at any part of it at any point in time and say it’s in equilibrium. But if you go to the tropics, where it’s less seasonal and there’s less migration, the populations fluctuate less and are probably closer to equilibrium.

So this whole field is still new and not well understood?

It’s not new. Community ecology has been around for a while, and it’s a conceptually very attractive field, a really neat way to think about ecosystem-level problems. But then you realise there’s no real data. It’s hard to count the number in any one species. It’s hard to count the number of species. It’s hard to recognise when there are interactions between species. And it’s difficult to tell at what spatial scale the measurements should most meaningfully be made. So you start to think it’s all looking a bit intractable. The theory is all very sexy but you can’t get the data to validate the theory.

So there’s a well-worn path people follow – from community ecology to parasitology and epidemiology, because these are lower-dimensional systems where it’s easier to collect data on more of the variables. So in epidemiology you’d be interested in the populations of susceptible, infected and recovered humans. So that’s just three dimensions, and there’s often really good data on who gets sick and who gets better. People collect that data. Robert May, former chief scientific adviser to the government took this route. He went from community ecology to one of the world’s leading epidemiologists.

Community ecology, to be honest, remains conceptually attractive but intractable. The theory has got a bit better, because we can now think about global stability and not just local stability. But it’s still almost impossible to collect data on whole communities.

You can do the theory forever, but you don’t have the empirical data to tie it to reality?

Exactly. Some people can sustain themselves with that. Others want to measure the parameters of the system and validate the theory. For me it is still an elegant, beautiful subject. But it’s not very useful, and since I’m being paid by other people I want to do something useful. I do maintain an interest in community ecology and have had students work on it recently but I’ve moved on.

So how do you describe yourself now?

I like to think about ecology in places where other people don’t think it’s going on. One reason Dave Barry’s system is so interesting is that there’s a lot of ecological dynamics during the course of a trypanosome infection. It’s a population dynamics problem just like all the problems I work on, except that instead of playing out on a landscape it plays out inside a patient. The interacting populations are elements of the immune system and the trypanosome, which comes in two different stages. It’s a population ecology problem. It’s just happening at a very different scale.

When we succeed we convince people like Dave Barry that an ecological perspective on his problem is both new and valuable. Paul Garside and Jim Brewer are interested in the movement of cells around germinal centres. I’m quite interested in the movement of wildebeeste in the Serengeti. Well it turns out that the same kinds of processes can be used to describe the movement of wildebeeste and of cells in germinal centres. The same basic mathematical representations, modified often from physics, can be useful in capturing aspects of how and why they move. The same processes but very different scales.

So you’re working on both these problems?

And a whole bunch of others. I apply population ecology tools to problems people don’t normally associate with ecology. Whether it’s trypanosomes or cells around a germinal centre or the dynamics of an RNA virus inside a cell or the evolutionary ecology of a virus as it spreads across a country. They are all applications of basic ecological ideas – old ideas in new places.

Glasgow University is a great place to do that because no one else is playing this game. There are lots of people, like Barry, Brewer and Garside, with interesting data and ecological problems that they don’t necessarily know are ecological problems. So I am able to import fresh ideas from the rich history of smart people doing ecology. That’s how I make my living.

Dave Barry mentioned that some parasitologists had yet to be convinced of the value of your approach. So I’m interested in where you’re making progress with, say, applying your methods to trypanosome infections.

It’s an exciting time in Dave’s area. Trypanosomes have this very complicated genetic archive of antigenic material, which they use to change their identify often. Dave probably knows more than anybody about how this happens and how it relates to the way the information is stored genetically. Now the way the trypanosomes play the genetics game has a lot to do with their population dynamics. But if you have the set of skills that allow you to make enquiries about the architecture of a trypanosome genome you’re unlikely to have the skills needed to recognise a population ecology problem.

So the mathematical models myself, Christina Cobbold and graduate student Erida Gjini have developed have allowed us to make interesting progress in understanding how the population dynamics are the way they are, why the architecture of the trypanosome genome is the way it is and how the two are linked together. Once you have that framework of understanding you can immediately start to suggest new sorts of experiment to do and data to collect. The injection of a quantitative dynamic and an evolutionary framework into the way Dave thinks provides him with new hypotheses and ways of testing those hypotheses.

Can you give me an example of a hypothesis suggested by the modelling?

The model predicted that the trypanosome would behave differently depending on the size of its host. The volume of blood the creature is replicating in affects the dynamics. A trypanosome infection would behave very differently for example in a cow compared to a lizard or a rabbit. You have to be careful because there might be different things going on in different species. But our model predicts that a trypanosome infection would behave very differently in a small cow compared to a large one.

So the animal has a genetic system that allows it to change its coat at a certain frequency. You wear the coat until the immune system recognises it and then it’s time to change it. The genetic architecture is set up so the coat can be switched at the right rate. It has been selected for by the environment provided by the host it evolved in. So if that host has now changed, say because of something humans have done we might expect its coat-changing frequency to want to be different. Dave is now thinking about how he can explore the effect of changing only the carrying capacity on the trypanosome dynamics.

Now we’ve got the mathematical model we can ask it what will happen if we change this or that parameter, get a direct prediction and then Dave can in principle go away and do the experiment.

How complex is this trypanosome model and how is it implemented?

Fairly simple in principle because you only have three populations That’s two types of trypanosome – slenders, which replicate inside you, but can’t be transmitted, and stumpies which are picked up by the tsetse fly and transmitted to another host. Then you have the antibodies. But because the trypanosome wears a different coat for every occasion you need a differential equation for each coat. There’s almost no limit to the number of different coats, but in practice we’re looking at a model with several hundred equations. And we have implemented it in Matlab.

Any other examples of how your mathematical models have generated useful hypotheses?

Well we do the same kind of thing with RNA viruses. I’m interested in foot and mouth disease … let me just explain something first:

One thing British scientists are being pushed hard into is something called systems biology. A lot of people think systems biology has nothing new to offer. Others wonder what makes it different from just doing biology. Part of the BBSRC website describes systems biology as an iteration between modelling and empiricism. So you go round collecting data and improving your models then collecting more data. To me there’s nothing systems biology about that. It’s just how you do science. A more convincing explanation, made elsewhere on the BBSRC site is that systems biology is examining dynamics across different scales.

So think about that in the context of the 2001 foot and mouth outbreak. During that they took samples of the virus from every infected farm. These are now stored at Pirbright and we can sequence them and get a whole genome from every virus. The genotype is slightly different at every farm, because the mutation rate of the virus is so high. So we’re interested in how this genetic diversity of the virus accumulates across the UK during a single outbreak. That will help to inform us how things like flu evolve, and also other important viruses. So we’re studying population genetics of this foot and mouth virus at very large scales, national scales.

But to understand how that diversity accumulated we had to ask how it accumulated on a farm. Because the virus is changing as it’s passing from cow to cow on one farm. So we started thinking we couldn’t understand the country-wide data until we understood a bit about how the virus gets changed while it’s on a farm. So you study that for a bit. Then you realise that to understand how it changes on a farm you need to understand how it changes inside a cow. You work this process back until you’re thinking about how the virus changes within a cell. And turns out there are all sorts of interesting questions about the population ecology of viruses in a cell.

This is systems biology. I can study genetic diversity at the level of the UK, a farm, a cow, an organ and a cell. The diversity we see at national level all arose within individual cells. And nowadays there are all sorts of interesting experiments you can do to find out how the genotype of a virus coming out of a cell differs from that going in. It’s huge.

The nice thing about systems biology is that once you can identify clear levels of organisation in your system it gives you different options for studying things. Maybe I want to know what’s going on at this level but it’s too difficult or expensive and I can only really measure it at this level. But what I can do is use the mathematics to infer what’s happening at this level and then scale it up to the level I’m interested in.

It means we can attack the problem at all these different levels. Another advantage I’ve found is that you can include all kinds of scientists in the conversation who have profoundly different interests. If I’m interested in viral replication ranging from that of a single cell to an organism, a herd, a whole country, then I can include vets, molecular biologists, pathologists, population geneticists. Remember that’s how I do my job – by gluing people together.

So really the core of what you do now is systems biology?

The systems approach is very helpful with something like foot and mouth disease. It gives you a way of thinking about the science as a whole. You can bring everyone in on the same conversation. I don’t really care if I’m working with repeatable elements in a gene or blackbirds in the back garden. To me they’re things you can count. They reproduce. They go up. They go down. What’s important is whether you can create a quantitative framework that allows you to measure something.

Do you often have a selling job with the scientists you work with?

Very much so. I started off quite sceptical myself. The number one problem you have as a modeller is you show someone a model of a system they’ve spent their life studying and the first thing they say is, ‘That’s rubbish. You’ve missed out this and this and this.’ So you go through each of those processes and explain why you think the effect will be small. A good model is a caricature. It captures the main features, without being so cluttered up that you can’t see what’s going on. People have trouble believing you can leave out 80% of the processes and not get a substantially different answer.

I had a colleague who reckoned you could learn something about the dynamics of most physical systems by setting up a single degree of freedom model.

Physicists take it to the extreme. But we know so little about the dynamics of these biological systems that even simple approaches are informative. Depending on the type of question you’re asking you can enrich the model as you require. I make slightly more complicated models than physicists. An important part of my job is to listen to the biology and introduce it when I think it’s appropriate. Most biological processes are not analytically tractable. They are nonlinear and high-dimensional, so you have to set them up as computer models.

How easy do you personally find that listening and communicating part of the job?

Reasonably so – and it goes back to having suffered the same problem myself. I could never do physics A-level problems at school because I would worry about all the extra details – like the fact that the train in the question that was slowing down might go over the points. I’ve struggled with slaying complexity and understanding why it’s OK to remove it from a model. So I am sympathetic to the researchers’ concerns and happy to talk with them.

So going back to what you were saying about maths teachers, do you think that’s partly why you’re good at this job?

Probably. A lot if this didn’t come easily to me. Another reason is that I really enjoy the socialness of science. You work with dozens of smart, unusual people and you bring something to the table and work on a problem in a purposeful way. That’s what’s enjoyable about the job. I hope Dave gets to understand the trypanosome genome and the people at Pirbright understand how viruses replicate in cells. But that’s not really what drives me. Success for me is coming up with a clever way of measuring a parameter that then tells someone else something they want to know – and engaging with them as they do it.

If someone said ‘Here’s £10 million; go off to the far side of the moon and do whatever you want’, that wouldn’t interest me at all. It’s the interactions with people that make it fun and endow it with a sense of reward. Actually cracking a problem isn’t the reward. Getting there is the reward.

I do try to prioritise by the importance of the question. As scientists we often avoid important questions so we can work on tractable questions. I don’t think that kind of expediency should be encouraged. But it is the process of science that’s fun for me rather than the results.

Can I take you back for a moment to what you were saying about the trypanosome infection model. Does what you’re doing there have any possible application in fighting the disease?

It might. When we change our patterns of land use we offer the tsetse fly a very different diet choice than they are used to. That creates a very different selective landscape for the trypanosomes. If you’re a trypanosome whose genetic architecture has been adapted to provide optimal infection dynamics in lizards or chimpanzees things will look very different if suddenly 90% of what you’re offered is a cow. As we change the landscape menu of these vectors we can expect to see the system responding, because you’ve changed the evolutionary rules of the game. If we want to learn how the pathogen will respond in an evolutionary sense these are the sorts of things we should be thinking about.

I’ve just come back from Tanzania where I’m involved with a similar problem with mosquito. As you move into a pristine environment fill it up with cows then change it to an urban environment, you’re changing the mosquito’s diet choice. Mosquitoes and the parasites they contain have evolved to a particular sort of blood, and we don’t know the consequences of changing that. It might be good or bad. Maybe mosquitoes don’t live very long on cow’s blood. We might be enhancing mosquito fitness or creating problems for them. We know shamefully little about how blood choice affects mosquito fitness. But it does come down to these sort of questions.

We want to understand how the changing patterns of land use might impact on the regional epidemiology of these problems. But we’re doing so by studying the problem at a smaller scale. We’re thinking about how changing the blood map impacts the individual fitness of parasites and vectors at a lower level of organisation. If we can characterise them we can start to scale up and make predictions at landscape levels of the effects of land use change.

How might all that help parasitologists to fight malaria or sleeping sickness? Possible applications of scientific research is something journalists often focus on too closely, but they’re also an aspect that young people and their teachers are very interested in – and I’m still not seeing a possible route to an application through changing the blood diet of the insects. Maybe there isn’t one immediately and you’re still learning how these complicated biological systems work, which could at some future time lead to an application?

To some extent, that’s right. Trypanosomes can exist in lots of different hosts and we don’t understand how something as simple as the difference between a big host and a small host impacts on the replication dynamics of the parasite in the host. As you start changing the menu or the landscape that’s one of the determinants of what will happen. It’s abstract still for the trypanosomes. I can see applications more clearly in the malaria work.

What are they?

Zooprophylaxis – changing the blood diet available to the mosquito, by for example bringing a cow into your house at night. A mosquito lives for 12-14 days. But the malaria parasite inside a mosquito takes 10 days to mature. So the parasite only just fits its host’s lifespan. If it turned out that mosquitoes lived 3 days less when on a diet of cow blood you’d have solved the problem.

So you’re looking for simple solutions based on the population dynamics?

Yes, and this is not an unexplored subject. Heather Ferguson in the office next to mine is studying what happens to the fitness – the longevity and fecundity – of mosquitoes as you change the type of blood they eat. That can be hugely significant. Because the parasite only just fits into the lifespan of the vector anything that knocks it back even by a few percent could have a huge impact. It’s such a sensitive system – you just need to tweak it a little bit – that it’s remarkable that we don’t know more about it.

There’s this idea in evolutionary ecology that if you breed younger you live less long. So can we persuade them to breed a little younger? They’d like to do that to increase their fitness. If there was selection pressure to reproduce earlier – have more eggs, double the number of eggs, I don’t care – if they only live for nine days the problem is solved. You have lots of mosquitoes but no malaria.

If you can find tricks that are evolutionarily sustainable you’re working around a lot of problems. So many of the ways we try to control pathogens involve things like drugs which create enormous selection pressure on the pathogen to become resistant. If we can find ways of intervening in these systems that work with evolution rather than against it, then you’ve got something that might work for you not against you.

And in order to work with evolution you have to understand what it’s doing at all these different levels, which is what you aim to do?

Absolutely. Selection pressure is nearly always at the level of the individual, but the problems we worry about are at the regional, community, population levels.

Are there any other nice ideas for tackling diseases coming out of mathematical modelling?

There’s a $10 million dollar fund to vaccinate dogs against rabies in Southern Tanzania. We want to maximise the efficiency of this intervention, in terms of maximum reduction in rabies cases both per vaccine and per dollar. How do you get that? Should you use all the vaccines in Dar es Salaam or spread them out over the country? What is the most effective way to run the vaccination programme? It’s simple but very important. It’s all very well having sophisticated epidemiological models but if we don’t know the best way to vaccinate dogs we can’t save as many people from rabies as we’d like to.

There’s a whole bunch of us in my office area working on this landscape ecology of dogs and how they transmit rabies. How far do they move? What proportion must you vaccinate to eliminate major outbreaks? What’s the relative importance of big towns and small villages? If you vaccinate a dog how long does it live and how many pups does it have next year that won’t have been vaccinated. If you start out with 100% coverage in about three years it’ll have fallen to about 40% because of all the new dogs being born. How often should you go back and vaccinate? Again it’s a population ecology problem. Dog demography becomes an essential part of public health. There is nearly always ecology lurking behind a lot of these problems.

Any advice for young people who, like you, are keen on biology but not on maths?

I teach maths, statistics and modelling to the undergraduates – and they don’t like it. The reason they’re doing biology is to get away from all that stuff. But it’s a shame. An awful lot of young people want to go into conservation and biodiversity. That’s very difficult to get into if what you’re bringing to the table is the same as everybody else.

Lots of people want to go and bottle-feed orang-utans, and lots of people would be quite good at it. Very few are good at doing time-series analysis on orang-utan population dynamics. So if you want to work with orang-utans one of the best ways is to recognise that what’s in limited supply is good quantitative ecologists and biologists.

For me it’s fabulous. I get to go to South America, the Serengeti, Peru, the Far East and do all these exciting things because I’m a quantitative person now. I know very little about all these systems, so I have to go out and see them and meet the people who work on them. It’s a fabulous way of doing biology that’s often overlooked by young people. It’s a really good portal to the sort of exposure they want.

So if someone still at school wanted to gain the skills that would make them in demand and allow them to do exciting biology around the world, as you do, what basic tools would you advise them to acquire?

Graphs. How to look at and interpret them. Basic statistics, means and standard deviations. Very simple dynamical models, such as exponential growth.

The mathematical models we use are basically iterative models of the form N_t+1 is some simple function of N_t. They could take a look at some of those and get an idea of what they’re about.

That is part of the Higher Maths syllabus and A-level, under ‘recurrence relations’.

Right, well they could look at simple models of that type. I remember a food chain project when I was at school of foxes and rabbits. I could never get the rabbits and foxes to co-exist. Either the rabbits went to infinity or the foxes ate them all and starved to death. But just splashing around like that starts to introduce you to the ideas. You have a population that’s changing with time, modelled by an iterative equation, and it also depends on another population with its own iterative equation.

I would encourage high school students to learn how to program. I don’t think the language matters much – the grammar is pretty universal. They could program some of these simple models and play around with them.

When did you decide to become a scientist?

Just as I was finishing my first degree. I had planned to be a fish farmer. I always wanted to live in the Highlands. But a guy in the department at Southampton came and found me after the exams. I was so interested in this stability-complexity question and it came up in the finals and he thought I gave a really good answer. So he suggested I write to the people in North America and go off and do that.

I was flattered I guess. Having been very bad at maths for such a long time it never occurred to me I could become a scientist. I didn’t really think about the practical side, whether I wanted to spend six years in Texas. It was very disruptive. I lost all my friends and my father died. You also lose your sense of identity. After six years in Texas the UK is a funny place. You can end up rootless if you’re not careful.

I’m glad I did it. But it was a life-changing experience I wouldn’t recommend lightly. Young people should maybe be wary of applying for things without thinking it through, because once the offer is made it changes the way you think about it.

You went to Oxford after the PhD in Texas. It sounds like it took you a while to adapt.

I’ve moved across the Atlantic six times and every time you go from one continent to another you go through this horrible transition. You go to the States and it seems foreign and superficial. You come to Britain and everything’s small and grotty and ineffective.

Who do you admire?

I’m a fan of Lord Alanbrooke, Montgomery’s boss during the Second World War. He had an immensely complicated job, running the entire armed forces during an intense time, with a very difficult boss in Churchill. A lot of people argue he won the war, rather than Churchill. There were black times, they thought we were being invaded, there were two disastrous defeats. He’s written these amazing diaries. He was handling huge pressures. He had to deal with Patton, Marshall, Stalin – all these strong and difficult people. He was a keen birdwatcher and would get away at every opportunity and photograph the reed warblers at the end of the garden.

Churchill gave him no credit and he’s largely been written out of history. I think that happens a lot in science too. The right people don’t always get the credit. Rosalind Franklin with DNA, Alfred Russel Wallace in evolution. It’s not always through malice but in my field it happens a lot. Robert May gets a lot of credit, but I think you have to ask where the stability-complexity debate really got ecology. A lot of the earliest epidemiologists don’t get much credit for the status of modern epidemiology. All too often it’s people who market an idea that get the credit for it. There are a lot of really smart, quiet-spoken people in the background, working out the basics and getting overlooked.

Are you one of those?

No. I get too much credit for a lot of things. As a modeller you work on all these different systems and end up as the senior author on a lot of papers. But if someone has spent five years studying a system, and knows the biology inside out, it’s debatable if I should come along, model it for three months and get a lot of the scientific kudos.

But that’s what you do?

I try to fight it. Our Nature paper is a case in point. The modelling was fairly straightforward and we tried to get the last author on the paper – Karen Laurenson, an amazing woman – to go first.

The trouble is each side argues that they couldn’t have done it without the other, which is true. But when you look at the balance of effort, modellers get too much credit. It’s why in British academia – academia the world over – you find people like me in more senior positions than empiricists. I can write papers faster and get more credit for them. Modelling is cheap and easy. You’re using other people’s data. Even if you try to play it straight it gives you a natural advantage.

It’s unusual to hear a scientist talk like that. It’s such a competitive field that they often promote their own work as hard as they can.

One of the nice things about Glasgow University is that there’s a lot less of that. I’ve worked in Oxford, Edinburgh, British Columbia, Texas. These places are full of pretty pushy people. Glasgow University is quietly spoken. There’s a lot of very decent scientists here who let the science do the talking. Fights are about who doesn’t want to go first on a paper, rather than who does. They are a particularly pleasant bunch of people here. It’s one reason I don’t want to move.

Have you any idea why it’s like that?

It’s partly tradition. My division has been mostly run by enormously able women for most of the last 15 years, whose policy I think was not to recruit anyone who would upset a working tradition of modesty and understatement. They constructed a department in which they wanted to work. The trouble with that is that the people here are now modest almost to a fault. It’s hard work to find out what my colleagues do. They won’t volunteer that they’ve just published a book or a paper or got a grant. As director of the Institute of Biodiversity, Animal Health and Comparative Medicine it’s my job to extract this information and give them credit for it – and I can’t bloody well get it out of them.

Do you think that’s something to do with female culture?

In this department, yes. More generally Glasgow is a modest university, so you’re in a quietly competent research environment with no egomaniacs. But it’s part of the Russell Group so it’s in the top twenty in the country. Glasgow is a fantastic place to work and live. Wild horses wouldn’t drag me to Oxford or Cambridge – or anywhere else in the United Kingdom.

Describe yourself in one sentence – or a bunch of adjectives.

Social, interactive, curious, synthetic – in the sense of pulling lots of different ideas and people together.

What do you do in your spare time, if any?

I walk up hills a lot. I potter around on the things WH Murray used to potter around on, like the Skye Ridge. I have tropical fish but I have trouble keeping the populations stable.

You’re kidding me.

It’s a complicated subject.

You’ve convinced me of that. But you really can’t do the population dynamics of your own fish?

What I’m trying to do is difficult. I like clouds of small fish and ideally I’d have 20 different species in big clouds. But eventually little fish grow big and eat all the small ones. I’m also interested in lichens and Caledonian pine forests.

What’s interesting about lichens?

Well a lichen is a symbiotic association of a fungus and an alga. You can mix and match the algae and fungi to create different lichens. They’re not fixed pairs and they are very poorly understood. It’s even debated whether it’s really symbiosis or enslavement. A lichenologist once described lichen as fungi that have learned to do agriculture. Lichen are very hard to keep. They’re everywhere but they are very particular about their environment. I’d like to get students to study lichen, but it’s hard to justify because they’re not that important.

And the Caledonian Pine Forest?

Historically it’s the natural state of the Highlands. Beautiful though those now are they’re pretty screwed up ecologically. The closest pocket of the ancient forest is at the bottom of Ben Lui. The trees tend to be very sparse now, one or two standing on hillocks or open forest. But they are lovely.

That was great. Thank you for talking to us.