Month: September 2013

The polarisation of debate is a common characteristic of our society. My dim memories of a first year philosophy class (augmented by a dip into wikipedia) recalls the ‘Hegelian Dialectic’ as a clash of opposite concepts, a “thesis” and “anti-thesis” leading to a “synthesis” that integrates these two, and produces a higher understanding than is found in either concept on its own. I would not pretend to explain or even understand Hegel; I only point out that the underlying idea, that the confrontation of opposites lead to a synthesis, is in contrast to what seems to be the all too common outcome of debate, which polarisation; two sides, led by strong advocates, become increasingly entrenched in their own points of view with little regard or respect for their opposition. Legal advocates are not employed to present a reasoned judgement based on a balanced consideration of the arguments – instead, the advocates’ role is to defend the parties they represent to the best of their abilities. Legal advocacy is based on an important principle – that all individuals, no matter how venal they may appear in society’s eyes, are entitled to a competent defence of their point of view in a court of law. Their advocates are charged with representing them as they would do themselves had they the proper training and understanding of the legal system. However, those same principles of advocacy do not always serve us well outside the courtroom. The debates between religious fundamentalists and atheists, between the advocates of capitalism and socialism, and peace protesters and hawks, are all examples where opposing viewpoints are often led by a relatively small numbers of highly motivated individuals whose opinions lie at either end of a spectrum of ideas, with the bulk of individuals being both less committed to advocacy, and also less dogmatic in whatever their views actually are. In my view, this problem is exacerbated by the insularity that comes from the existence of relatively closed or close-knit groups of like minded individuals. This kind of community support, while in many ways a wonderful thing and central to being human, is not always conducive to openness to new ideas that contravene the current wisdom held within those groups.

The debate on badgers culling and its potential impact on bovine TB in Great Britain is an example of this kind of polarised debate – a caricature of this would point to an rural urban divide, which though overly simple (there are many farmers against badger culling, and equally many city-dwellers sympathetic to the plight of farmers), points to a differing experience of reality that inform the differing values on each side. Without pointing fingers at specific websites, I would invite the readers of this blog to do a search for arguments both for and against badger culling – at each end of the spectrum, the same types of arguments are raised as support of their particular cause.  This is not to say that all arguments regarding badger culling (either for or against) are irrational. Indeed because the facts are so unclear, the debate is made even more difficult, and there are many advocates on both sides who consider these facts in a reasoned way. The danger of course, is that the rational argument becomes lost in the polarisation of the debate.

It is in this regard that Science can play a crucial role. Scientists are human – usually but not always better educated than your typical person on the street, but with certainly no inherent moral superiority or advantages of character. As humans we are subject to the same type of prejudices and misdeeds, both petty and signficant than any other. As individuals we are fully capable of ignoring evidence and promoting our own points of view at the expense of the truth, with Sir Isaac Newton‘s altercations with Robert Hooke and Gottfried Leibniz, and the behaviour of Sir Richard Owen being notorious examples.  We as individuals are more than capable of corrupting science, sometimes  inadvertently but sometimes wilfully. What makes us different is the standard by which we are judged as scientists. The dirty tricks of political campaigns mean little after an election is won. History is continuously rewritten by the selective, interpretive memories of the individuals’ doing the writing, and because historical knowledge can be erased, recovering the truth can be impossible. In contrast science is bound by the unalterable truths of the natural world and is always ultimately judged by its relationship to it. Good scientific research will raise a hypothesis and present arguments both for and against the truth of it, providing data and/or analyses which add to these arguments, rather than simply replacing them. The science of bovine TB is as yet unclear, but it is progressing. The development of the policy of bovine TB must reference that science, so that any further decisions, be they ethical, economic, societal or political be based on the clearest understanding possible of the underlying facts.

The Goldsboro Incident really happened! Nonlinearity, mathematical and statistical models


Opening up the paper today, I was pleased to see this story on the front page of the Guardian, about the Goldsboro incident in November 1961. Why pleased? Well for years the Goldsboro incident has been my analogy of choice for explaining the difference between linearity and nonlinearity, based on an interpretation of nonlinearity inspired by George Sugihara on physical vs. biological noise. I’ve always prefaced this analogy by saying that it was unconfirmed but useful – and now it appears to be true! So what happened in Goldsboro? From the companion piece in the Guardian:

The document, obtained by the investigative journalist Eric Schlosser under the Freedom of Information Act, gives the first conclusive evidence that the US was narrowly spared a disaster of monumental proportions when two Mark 39 hydrogen bombs were accidentally dropped over Goldsboro, North Carolina on 23 January 1961. The bombs fell to earth after a B-52 bomber broke up in mid-air, and one of the devices behaved precisely as a nuclear weapon was designed to behave in warfare: its parachute opened, its trigger mechanisms engaged, and only one low-voltage switch prevented untold carnage.


The conventional interpretation of nonlinearity. Doubling the input either more than doubles (e.g. oversteer in a car) or less than doubles (e.g. understeer) the response.

Our formal understanding of nonlinearity is based on the idea that, if we consider a response to an input, doubling the input will result, if there is a linear response, in a doubling of the response. Thus if I press the accelerator on my car twice as hard, I might expect to travel (approximately) twice as fast. In a nonlinear response, the return is either more than or less than twice.   However, an alternative understanding of nonlinearity is illustrated by the Goldsboro Incident, where the difference between 5 of 6 safeties failing, and 6 of 6, is the difference between an incident quietly swept under the rug for 50 years, and a monumental disaster.

The difference between 5 switches being triggered and 6 is the difference between a hole in the ground and a nuclear explosion.

The difference between 5 switches being triggered and 6 is the difference between a hole in the ground and a nuclear explosion.

This interpretation of nonlinearity can be viewed in terms of the difference between multiplication and addition. We are quite good at predicting additive phenomena; the problem is, we are are less proficient when it comes to multiplication. The recent story of the death of four year old Daniel Pelka (and this is a type of story repeated with tragic Sisyphean regularity) is a case in point. How could this happen? How could so many safety checks fail? How could so many people miss the warning signs? The truth of the matter is likely to be that there are many, many more cases where “the system” almost fails, but with no observable consequence. Overburdened, pressurised staff, sometimes under motivated or under pressure not to raise alarms unnecessarily, may cut corners or make mistakes far more often than we are aware. It is also likely true that because there is no immediate consequence to these actions (the effect of nonlinearity) the potential for disaster is missed. The question may in fact not be, why does this happen, but why does it not happen more often?

And this leads us to the concept of extrapolation and mathematical and statistical models. Statistical models are fantastically valuable tools for rigorously describing relationships in data. However they are fundamentally ontological in nature; that is, built to classify rather than to explain mechanisms, and thus the ultimate arbiter of the quality of a statistical model is the fit to the data. Of course, in designing the statistical model and in interpreting it, a good scientist will be aware of the existence of these underlying mechanisms. This awareness will drive both experimental design and observation, and the interpretation of the statistics. However, these considerations lie outside the statistical model itself. In contrast, mathematical models should be phenomenological, i.e. built to directly describe the often nonlinear relationships between variables, and therefore they are better suited to extrapolate or predict away from the data, rather than interpolate. What is often not understood, is that even very good mathematical models may give an inferior fit to the statistical within close bounds of the data – the aim is not to develop the best fit to the data, but to better be able to predict what may occur, when moving farther away from known data.

Mathematical models can often provide a poor fit the data, but, if formulated to appropriately describe a fundamental aspect of the data, can provide insight into possible trends as we move away from the known data.

Mathematical models can often provide a poor fit the data, but, if formulated to appropriately describe a fundamental aspect of the data, can provide insight into possible trends as we move away from the known data.

Of course, this is at best a caricature of both mathematical and statistical models, with modern quantitative sciences using in various ways combinations of both of them. Nevertheless there is a fundamental difference in models that aim to describe, and models that aim to explain, a difference that must be considered when evaluating the interpretation of any model.

Nonlinearity is a critical concept in ecology, evolution and epidemiology. The emergence of new pathogens is one example of this. For example, in a paper a few years ago, Nim Pathy and Angela McLean used a theoretical model, to ask whether or not a pathogen (in this case, avian influenza) that has caused hundreds of cases but with little transmission indicates that the species barrier cannot be crossed. Another way of looking at this question is to ask which is worse, 4 introductions of avian flu into humans from birds, or a single introduction, where a chain of 4 infections in humans occurs but the disease then fails? Extrapolation from currently observed data requires an insight into the underlying mechanisms that drive the phenomenon to be understood (in this case, the emergence of a new human pathogen). What Pathy and McLean showed using nonlinear mathematical models, was that a lack of demonstrated transmission cannot rule the possibility of adaptability, regardless of how many zoonoses have occurred – thus even when we think we are safe, we are not necessarily so.

Of course, while I am (unsurprisingly) a keen proponent of the use of mathematical models, it must always be kept in mind that prophecy is difficult, and the biblical admonition against following false prophets reflects the popularity of trying to predict the future, the frequency of our failures, and the ease with which we can be led into following those predictions, especially when espoused by recognised experts.

Bovine tuberculosis – cattle, badgers and culling

The British farming community suffers considerably from the epidemic of bovine Tuberculosis (TB) in cattle, with estimated future costs to the GB economy on the order of £100m per year. While bovine tuberculosis can be an important zoonosis, in GB this is largely controlled by milk pasteurisation, and so much of this impact is due to the effect on international trade. For the farmer, requirements put in place following the identification of a cow that tests positive on a farm include movement restrictions and the slaughter of all test positive cattle. The latter in particular can make this an extremely traumatic event for the farmer, and one which, for some at least, there is little or no hope that it will get better in the forseeable future. For these reasons, bovine TB is regarded by Defra as the most pressing animal health problem in Britain today.

circulating btb

Badgers and cattle circulate bovine TB in both directions. The problem is, we don’t know how much.

How should we control it? This much we know: badgers can infect cattle with bovine tuberculosis, and this contributes to the epidemic of bovine TB in England and Wales. This much we also know: cattle can infect badgers, and likely do so on a regular enough basis so that the cessation of cattle testing during the 2001 foot-and-mouth disease epidemic resulted in a spike of badger infection. Unfortunately, beyond that the scientific evidence is sufficiently opaque that there is no clear support for any particular policy towards its control: each of EnglandWales, and Northern Ireland (NI) have adopted different strategies, reflecting a combination of epidemiological circumstance and socio-economic factors specific to each jurisdiction (Scotland is officially TB free). Meanwhile all three jurisdictions can look on with some envy at the Republic of Ireland (ROI), where badger culling combined with intensive cattle testing and controls has resulted in a dramatic decline in cattle incidence. Whether or not the current measures lead to eradication is yet to be determined.

Unfortunately, a comparison with the ROI is not a simple one. Badger densities are lower on average compared to England and Wales, and the cattle industry enormously important to the Irish economy. In contrast, in the UK both dairy and beef cattle numbers are in decline, while the 1992 Protection of Badgers Act reflects the status of the badger in GB as a well-loved national icon. This affection is not shared in the ROI to the same extent, and in ROI official culling has been conducted continuously since the 1980’s, leading to a very different badger population compared to that in GB. Thus while the ROI can provide valuable insights that can be useful to the British situation, it cannot be used as a model for control.

And that leads us to the badger cull. At the end of August, trial culls of badgers were initiated in England, using hunting rifles as the method of choice to undertake the cull. In a statement last year from Prof. Ian Boyd (Defra’s Chief Scientist) and Mr. Nigel Gibbens (Chief Veterinary Officer), “culling … will enable us to test our assumptions about the effectiveness, safety and humaneness of culling by means of controlled shooting.” The latter two of these three points represent important considerations, so long as culling by shooting is a seriously considered option. Keeping in mind that the ethical questions associated with the widespread depopulation of a wildlife species is also a critical consideration (but a matter that lies outside this blog), many are asking whether or not the science supports the cull. Keeping in mind that effectiveness in this case relates solely to whether culling of badger populations is ‘sufficient’, there remains the question of whether or not the proposed sufficiency for a cull would reduce the incidence in cattle. Most of the evidence for bovine TB in England is based on the randomised badger culling trial (RBCT), a controlled field ‘experiment’ of massive proportions. An enormous amount was learned from the analyses conducted during and after the RBCT, and this forms the basis of most of our knowledge of bovine TB epidemiology in GB today. Extensive though the areas of the trial were, they were not comprehensive, especially considering the increase in extent of areas of high bovine TB incidence compared to when the culls were started in the late 1990’s. Thus we are largely reliant on extrapolation to understand how these data relate to disease progression elsewhere. These extrapolations have thus far been largely based on statistical arguments – at their core, they do not directly consider the complex ecology underlying the spread of the disease. Even if ‘enough badgers are culled, the result could be a reduction in cattle TB, or an increase. Because it will not be possible to compare cull areas directly to a non-cull area in a controlled fashion, it will be difficult to identify in a scientific way, the cause behind any change. Thus perhaps the best that can be said (in either direction) is that, far from either supporting or opposing the cull, the science is simply is not yet sufficiently mature to properly inform it.

Science and policy make strange bedfellows. Ironically while science is responsible for some of the most radical changes we see in society today, it is inherently conservative, classically requiring ‘95% confidence’ in order to make any decision. On the other hand, policy often simply needs a decision and that decision must take into account many factors outside of science, including socio-economics, ethics and politics. Thus it would be foolish to ever think that a matter as controversial as the control of bovine TB would ever be decided solely on the science. Despite this, science can and does play an important role in developing the evidence base for making decisions; while not science based, policy decisions must nevertheless be scientifically sound. The science behind the cull is therefore important.

Over the next several weeks and months, I’ll be publishing a series of blog articles about bovine Tuberculosis in Great Britain. In these, we’ll look at various aspects of the science that can help us understand both how bovine TB is maintained in British cattle and badgers, and how it might help us understand how to control it.