## Introduction

The discipline of ecology is central to responding to a range of major challenges facing the world community over the coming years. For example, how do we predict climate impacts and respond to them effectively to protect biodiversity and human amenity? How do we design efficient agricultural systems to feed a growing population while not eroding the natural resource base? All of these issues will require tactical and strategic decision-making by governments and communities who will need to trade off different interests and philosophies. One challenge in doing this is the uncertainty that exists in our ability to understand systems and predict future outcomes.

Uncertainty is pervasive in ecology. Variability, observation error, model structure uncertainty and other sources of uncertainty are to be found in virtually all applied ecological problems. Environmental systems are complex and sometimes poorly observed. As a result, environmental managers are often compelled to make decisions in situations with incomplete information. This has resulted in a significant literature around decision-making under uncertainty. The vast majority of approaches use probability to describe uncertainty, and when relevant data are extensive, and questions are essentially empirical, a wide range of statistical approaches to inference are available. When data are sparse, or the system complex, Bayesian probabilistic methods are still well defined but this process relies on expert opinions expressed through priors and can require costly or difficult elicitation processes. When data or knowledge is very sparse, as in the case of ‘complete ignorance’ (if this in fact exists), fundamental questions about the suitability of probability arise (Colyvan 2008).

Given these issues, any new method that purports to provide a mechanism for making good decisions with sparse information is likely to attract the attention of ecologists and environmental managers. In particular, a method and theory that purports to make robust decisions in the face of ‘severe uncertainty’ is a major achievement for science. Info-gap decision theory (IGDT) makes these claims. Ben-Haim (2001, p.x) describes IGDT as radically different from all current theories of decisions under uncertainty. IGDT is different because it offers a non-probabilistic approach to decision-making under uncertainty. It claims to provide a quantitative representation of Knight's concept of true uncertainty for which ‘there is no objective measure of probability’ (Ben-Haim 2004). It has been identified as a method that is suitable when the information base is so depauperate that the analyst cannot parameterise a probability distribution, decide on an appropriate distribution or even identify the lower or upper bounds on possible parameter values (Halpern *et al*. 2006).

Since the first comprehensive description of the theory in 2001, IGDT has attracted many proponents, principally in the fields of ecology, engineering and economics. Counting citations on http://info-gap.com/ suggests that there are three books and at least 140 journal articles on this subject, which are becoming increasingly well cited (Fig. 1). It has had a significant presence in ecology being applied to a wide range of important issues, including the allocation of resources to mitigate biodiversity impacts caused by global change and the design of effective marine reserves.

Info-gap decision theory, however, has also been criticised on two grounds: (i) it is not a radically new theory but rather a reformulation of minimax analysis that has been known in the operations research literature for over 60 years and (ii) its robustness functions are ‘radius of stability’ models that only measure the robustness of a decision in the local neighbourhood of an initial estimate and not over the global uncertainty space. Hence, IGDT is utterly unsuitable to situations of severe uncertainty (Sniedovich 2008, 2008, 2010a, 2012). Ben-Haim maintains that this criticism misses the point (Ben-Haim 2012). Sniedovich (2008) bases his arguments on mathematical proofs that may not be accessible to many ecologists but the impact of his analysis is profound. It states that IGDT provides no protection against severe uncertainty and that the use of the method to provide this protection is therefore invalid.

The meaning of severe uncertainty lies at the heart of Sniedovich's second criticism and the subsequent debate within the academic community that has ensued. The term ‘severe uncertainty’ is not formally defined in IGDT. By inspection of IGDT's models of uncertainty, working assumptions and assertions, however, Sniedovich (2010b, 2012) identifies three defining characteristics: (i) the uncertainty space can be unbounded (Ben-Haim 2006, p. 210), (ii) any initial estimate of the elements within this space may be substantially wrong (Ben-Haim 2006, p. 281), and no better than a wild guess (Ben-Haim 2010, p. 2), and (iii) there are no grounds for believing that the truth is more or less likely to be in the neighbourhood of the initial estimate than in the neighbourhood of any other point in the uncertainty space.

While these characteristics provide a definition of severe uncertainty, it is not universally accepted in public debates. Burgman (2008) stipulates that Sniedovich's definition of severe uncertainty is too narrow to be useful and maintains that in the applied world of environmental decision-making, identifying decisions that are robust to the uncertainty in an initial estimate is vital. In particular, Burgman (2008) argues that IGDT is useful because there comes a time when decisions have to be made, and when this occurs, it is useful to know how much deviation around an initial estimate can be accommodated before critical performance requirements are threatened, irrespective of how one arrives at the initial estimate. Furthermore, during this process, it is understood that there is no absolute guarantee that the truth lies in the local neighbourhood of the initial estimate.

There is therefore a tension among (i) the proposed method, IGDT, (ii) a set of mathematical proofs that relate it to known techniques and clarify that it cannot deal with ‘severe uncertainty’, (iii) a rhetorical argument justifying its practical use and (iv) a community of practice that is evolving around its application. To further discussion of IGDT, we review the use of this method in ecology and provide an accessible description and analysis of the method. We also present a discussion of the issues that a potential user needs to consider in applying this approach. In Section ‘'Info-gap decision theory'’, we give a concise synopsis of IGDT. While the notation is necessarily complex, this synopsis involves no abstract mathematics or proofs and concludes with a simple example to illustrate the approach. In Section ‘'Review of ecological practice'’, we examine the most important sources of uncertainty in model-based decision-support systems and the manner in which these are addressed in ecological applications of IGDT. Section ‘'Practical utility'’ identifies practical issues that can occur with IGDT under strict or more relaxed definitions of severe uncertainty, together with a synthesis of issues identified by other authors and original insights we have gained in the process of completing this review. Section ‘'Discussion'’ discusses the IGDT method from an applied ecological perspective and concludes with recommendations for ecologists who are contemplating the use of IGDT.