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What is a scientific model?

Updated Tuesday 29th March 2016

BBC Inside Science answers a listener question by discussing scientific models and how they are used.

climate model Copyrighted image Icon Copyright: Production team In response to a listener question, Adam Rutherford asks various scientists - what is a 'model' in science? Andrew Ponson introduces us to the concept, Carole Haswell discusses how they work in astronomy, Paul Donald explains their use in conservation science and hydrologist Nick Reynard talks about using models to simulate extreme weather events such as flooding.

Question from Jim Hay: "I wonder if you could explain what a model is? The term is used so frequently on science programmes that I just let it slide past me but the fact is I don’t know what it means exactly when a scientist says that they made a model."

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Full transcript: click to reveal

ADAM RUTHERFORD: In fact we talk about models in science pretty much every single programme. Listener Jim Hay wrote in and asked this very simple question: I wonder if you could explain what a model is? The term is used so frequently on BBC science programmes that I just let it slide past me but the fact is I don’t know what it means exactly when a scientist says that they made a model. I recently acquired a modern, very big, A-level textbook on physics and I note that neither model nor modelling appear in the index.

Well thank you Jim because it’s a worthy reminder that science can be technical, and you have to tell us when we’re talking jargon. Anyway, at the most basic level, a model is a way of taking data and measurements from the real world and simulating what happens when we fiddle around with them: how much rainfall, the flow of rivers, that type of thing. It’s a way of simplifying the chaos of the physical world, in a computer so that we can try to predict what might happen in the real world. You can run simulations thousands of times, each with very subtle changes to see what happens.

When Jim asked this question, we realised that most weeks we talk about some new science that uses models in this way. In the last fortnight we had the evolution of the DNA of ancient farmers, we had the melting of the Antarctic ice sheets, and today we’ve got Nick Reynard modelling floods in Cumbria. So we’ve asked a few of our guests to tell us what they mean when they use scientific models. Andrew Ponson and Carole Haswell told me what models are to astrophysicists.

ANDREW PONSON: I would say a model is a set of ideas we have around how some specific aspect of nature works. And normally when we call it a model, we probably mean it’s tentative at some level. So we’re not trying to make a claim that we’ve summarised everything about how that particular thing works.

ADAM RUTHERFORD: Which would be a theory or a law?

ANDREW PONSON: Exactly! We’re trying to give some impression that we haven’t yet packaged up everything about that particular aspect of nature, but we have some working set of ideas that we’re using to create tests that we can then go and compare to reality.

ADAM RUTHERFORD: And from a practical point of view, as an astronomer, Carol, how do you model things?

CAROLE HASWELL: I was actually quite old as a scientist when I read something that one of my colleagues had written in one of our physics courses, and he wrote the essence of being a physicist is knowing which approximations to make. And so whenever we’re seeking to understand something, you need to tease out what are the important things that are influencing this. Because you can’t possibly hope to create a replica of the whole universe because you’d need the whole universe to do it and you wouldn’t gain anything by doing that. So what you need to do is work out what are the really important key things that perhaps you can write down some simple mathematics, and work with and generate some insights.

So it’s this sort of stripped down mathematical description of the essence of things that you can then embody a computer code with. So you can put the system of simple equations or perhaps quite complex equations into a computer programme and you can then set the programme to go to watch the interplay of the various factors that you’ve teased out as being important. So, for example, if you were trying to understand how the planets in the solar system move, then you would need to put in a mathematical description of gravity, and then you could set your solar system going and watch things moving. And you wouldn’t need to describe all of the autonomic physics that gives you the structure of each individual planet. For your model of the solar system you could have a rather simple description of gravity, and that would be sufficient for what you’re trying to look at.

ADAM RUTHERFORD: So it’s a way of plugging in multiple observations, and then making predictions about what will happen based on what we’ve already seen?

CAROLE HASWELL: Well it’s a way of using what you’ve observed to work out what you think is the most important things that are governing the behaviour. And then setting up something that encapsulates what you think is important, to see if that actually reproduces what you’re observing.

ADAM RUTHERFORD: These types of models are used across all fields in science. Here’s RSPB conservation scientist Paul Donald on how simulations can help him understand bird behaviour.

PAUL DONALD: To me a model is a formula that helps me to explain variation in something I’m interested in. So let me give you an example. Let’s say that I’m interested in a particular species of bird, let’s say skylarks, for example, and I go out and I collect data on the numbers of skylarks in, let’s say, a hundred fields across Southern England. And what I would certainly find is that the number of skylarks varies between different fields. Some fields will have very few birds, maybe none at all; other fields may have lots of birds. So I’m interested to know why some fields have more skylarks in them than others, and I would use a model to look at that.

So what I would do, while I was out collecting my counts of skylarks, is I would also measure a whole load of other things that I think might possibly explain the variation in skylark numbers. So I would collect data on, for example, things like what crop type was in the field, because it’s entirely possible that they like certain crop types than others. I would collect data on the size of the field. I might collect data on the hedge cover, the number of trees nearby, all these sorts of things that could possibly explain it.

What the model would do is it would allow me to identify which of those predict skylark numbers and which ones don’t. So if we set it up like this. You see we’ve got this first column here. This is my column of skylark counts. For each field I’ve got a count and then for each field I’ve got a value of the size of the field. I’ve got what the crop was, what the crop was in the previous year, soil type, hedge row and so and so and so and so. So what I want to do now is I want to put this into a model, into the software, and ask that to identify which of those predictors or explanatory variables, as we call them, best explains variation in my skylark numbers.

So if we just click this button here that sends it off to the programme, and give it a couple of seconds to run - there it is. So the model has run and if I open up the model, okay, so what it’s showing me here is you can see here that it’s showing me that field size has a positive influence on skylark numbers. The bigger the field size, the more skylarks there are. And it’s also showing me that there’s in effect a crop type there. It’s showing me that spring cereals here have more skylarks in them than winter cereals here, and that that effect is additional to the effect of crop type. And there’s various other columns as well with all the other data. So what I can do is I can refine this model now, and that will give me a very good idea of why it is that the numbers of skylarks, the thing that I’m interested in, varies between different fields.

So the real skill, in a way, with these things is in the interpretation. So what this model shows is that for the variables that I’ve put into it, some of them significantly predict skylark numbers and others don’t, but it can’t predict things I haven’t put in. What if, for example, the most important thing determining skylark numbers is none of the things I’ve measured? Maybe it’s something else. Maybe it’s weather or the slope of the field or the soil type, or something like this. Something I haven’t measured at all. So the model is essentially wrong because I haven’t measured the thing that’s the most important driver of skylark population numbers. It may still be that the things I’ve measured are partially determining skylark numbers, but the real underlying thing I may not have measured at all. So there’s a kind of standard thing in ecology that says all models are wrong, but some of them are useful.

This is the only method really so, if I was only interested in one thing, the relationship between skylark numbers and field size, for example, I could simply plot them out and see, if as field size gets bigger, skylark numbers increase. But you can only do that for one thing at a time. I can’t look at all these different variables at the same time, and that’s what the model allows me to do. And it’s an absolutely fundamental tool in ecology and conservation is this kind of way of analysing data.

Modelling never really fails in the sense that. If you know what the mathematical formula is doing, it’s infallible in a way. It fails if you don’t measure the right things or if you interpret them in the wrong way. I can give you an example. Let’s say what my model here on the screen shows is that you get more skylarks in big fields. So I might go away and say OK, the answer to this problem of decline in skylarks is we need to make all our fields bigger, but what if they only choose big fields, not because they’re big but because they can see predators coming from a long way away, for example. So it’s not the size of the field that the birds are responding to? It’s how well they can see predators, and that’s the important thing that determines the numbers.

So it may well be that you could actually do more for skylarks by perhaps taking down field boundaries, making the fields appear larger for the birds. So you’ve got to be very careful how you interpret the output of these models.

ADAM RUTHERFORD: Paul Donald there. So this is important: all models are wrong. They’re simulations but some are very useful. Back to the floods in Cumbria, which hydrologist Nick Reynard has been simulating. Nick, how does modelling help us understand these extreme weather events?

NICK REYNARD: OK, so ideally of course we’d have data absolutely everywhere, so we’d understand what was going on in the river system and with the rainfall all the time everywhere. We can’t have that, it’s not practical and it’s too expensive, so we have to be able to fill the gaps. And we use models to do that. So we fill the gaps in space and in time by working out how the rainfall moves through the landscape into the rivers and then ultimately out into the seas, and the models are just computer simulations of how that water moves so that we can actually understand where high and low flows occur anywhere across the county or even across Europe or across the globe. So that’s what we use models for, and that helps us understand right now what the hydrology is doing, what the flows are like, but it also allows us to use those models to forecast and predict what the flows might be like in the future.

ADAM RUTHERFORD: Nick Reynard from the Centre of Ecology and Hydrology.

ADAM RUTHERFORD: At the most basic level, a model is a way of taking data and measurements from the real world and simulating what happens when we fiddle around with them: how much rainfall, the flow of rivers, that type of thing. It’s a way of simplifying the chaos of the physical world, in a computer so that we can try to predict what might happen in the real world. You can run simulations thousands of times, each with very subtle changes to see what happens.

ANDREW PONSON, Astrophysicist: I would say a model is a set of ideas we have around how some specific aspect of nature works. And normally when we call it a model, we probably mean it’s tentative at some level. So we’re not trying to make a claim that we’ve summarised everything about how that particular thing works. We’re trying to give some impression that we haven’t yet packaged up everything about that particular aspect of nature, but we have some working set of ideas that we’re using to create tests that we can then go and compare to reality.

climate computer model Copyrighted image Icon Copyright: Production team CAROLE HASWELL, Astrophysicist: ...One of my colleagues wrote [that] the essence of being a physicist is knowing which approximations to make. And so whenever we’re seeking to understand something, you need to tease out what are the important things that are influencing this. [...] It’s this sort of stripped down mathematical description of the essence of things that you can then embody a computer code with. So you can put the system of simple equations or perhaps quite complex equations into a computer programme and you can then set the programme to go to watch the interplay of the various factors that you’ve teased out as being important. So, for example, if you were trying to understand how the planets in the solar system move, then you would need to put in a mathematical description of gravity, and then you could set your solar system going and watch things moving. [...] It’s a way of using what you’ve observed to work out what you think is the most important things that are governing the behaviour. And then setting up something that encapsulates what you think is important, to see if that actually reproduces what you’re observing.

Flock of red knot birds Copyright free image Icon Copyright free: Public domain image PAUL DONALD, RSPB conservation scientist: To me a model is a formula that helps me to explain variation in something I’m interested in. So let me give you an example. Let’s say that I’m interested in a particular species of bird, let’s say skylarks, for example, and I go out and I collect data on the numbers of skylarks in, let’s say, a hundred fields across Southern England. And what I would certainly find is that the number of skylarks varies between different fields. Some fields will have very few birds, maybe none at all; other fields may have lots of birds. So I’m interested to know why some fields have more skylarks in them than others, and I would use a model to look at that.

So while I was out collecting my counts of skylarks, is I would also measure a whole load of other things that I think might possibly explain the variation in skylark numbers. What the model would do is it would allow me to identify which of those predict skylark numbers and which ones don’t. [...] The real skill, in a way, with these things is in the interpretation. So what this model shows is that for the variables that I’ve put into it, some of them significantly predict skylark numbers and others don’t, but it can’t predict things I haven’t put in. [...] So the model is essentially wrong because I haven’t measured the thing that’s the most important driver of skylark population numbers. It may still be that the things I’ve measured are partially determining skylark numbers, but the real underlying thing I may not have measured at all. So there’s a kind of standard thing in ecology that says all models are wrong, but some of them are useful.

This is the only method really so, if I was only interested in one thing, the relationship between skylark numbers and field size, for example, I could simply plot them out and see, if as field size gets bigger, skylark numbers increase. But you can only do that for one thing at a time. I can’t look at all these different variables at the same time, and that’s what the model allows me to do. And it’s an absolutely fundamental tool in ecology and conservation is this kind of way of analysing data.

flood Copyrighted image Icon Copyright: Used with permission NICK REYNARD, Hydrologist, extreme weather: Ideally we’d have data absolutely everywhere, so we’d understand what was going on in the river system and with the rainfall all the time everywhere. We can’t have that, it’s not practical and it’s too expensive, so we have to be able to fill the gaps. And we use models to do that. So we fill the gaps in space and in time by working out how the rainfall moves through the landscape into the rivers and then ultimately out into the seas, and the models are just computer simulations of how that water moves so that we can actually understand where high and low flows occur anywhere across the county or even across Europe or across the globe. So that’s what we use models for, and that helps us understand right now what the hydrology is doing, what the flows are like, but it also allows us to use those models to forecast and predict what the flows might be like in the future.

This is an extended feature from BBC Inside Science originally broadcast on 10th December 2015.
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