A common feature of ecological data sets is their tendency to contain many zero values. Statistical inference based on such data are likely to be inefficient or wrong unless careful thought is given to how these zeros arose and how best to model them. In this paper, we propose a framework for understanding how zero-inflated data sets originate and deciding how best to model them. We define and classify the different kinds of zeros that occur in ecological data and describe how they arise: either from Ôtrue zeroÕ or Ôfalse zeroÕ observations. After reviewing recent developments in modelling zero-inflated data sets, we use practical examples to demonstrate how failing to account for the source of zero inflation can reduce our ability to detect relationships in ecological data and at worst lead to incorrect inference. The adoption of methods that explicitly model the sources of zero observations will sharpen insights and improve the robustness of ecological analyses.

Expert knowledge is used widely in the science and practice of conservation because of the complexity of problems, relative lack of data, and the imminent nature of many conservation decisions. Expert knowledge is substantive information on a particular topic that is not widely known by others. An expert is someone who holds this knowledge and who is often deferred to in its interpretation. We refer to predictions by experts of what may happen in a particular context as expert judgments. In general, an expert-elicitation approach consists of five steps: deciding how information will be used, determining what to elicit, designing the elicitation process, performing the elicitation, and translating the elicited information into quantitative statements that can be used in a model or directly to make decisions. This last step is known as encoding. Some of the considerations in eliciting expert knowledge include determining how to work with multiple experts and how to combine multiple judgments, minimizing bias in the elicited information, and verifying the accuracy of expert information. We highlight structured elicitation techniques that, if adopted, will improve the accuracy and information content of expert judgment and ensure uncertainty is captured accurately. We suggest four aspects of an expert elicitation exercise be examined to determine its comprehensiveness and effectiveness: study design and context, elicitation design, elicitation method, and elicitation output. Just as the reliability of empirical data depends on the rigor with which it was acquired so too does that of expert knowledge.

Expert knowledge in ecology is gaining momentum as a tool for conservation decisionmaking where data are lacking. Yet, little information is available to help a researcher decide whether expert opinion is useful for their model, how an elicitation should be conducted, what the most relevant method for elicitation is and how this can be translated into prior distributions for analysis in a Bayesian model. In this study, we provide guidance in using expert knowledge in a transparent and credible manner to inform ecological models and ultimately natural resource and conservation decisionmaking. We illustrate the decisions faced when considering the use of expert knowledge in a model with the help of two real ecological case studies. These examples are explored further to examine the impact of expert knowledge through ÔpriorsÕ in Bayesian modeling and specifically how to minimize potential bias. Finally, we make recommendations on the use of expert opinion in ecology. We believe if expert knowledge is elicited and incorporated into ecological models with the same level of rigour provided in the collection and use of empirical data, expert knowledge can increase the precision of models and facilitate informed decision-making in a cost-effective manner. KeywordsBayesian models, bias, decision-making, expert judgement, expert opinion, prior information.Ecology Letters (2010) 13: 900-914There has been a recent surge in the use of expert knowledge in ecological models (Crome et al. 1996;Martin et al. 2005;Denham & Mengersen 2007;Griffiths et al. 2007;Mac Nally 2007;OÕLeary et al. 2008;OÕNeill et al. 2008;James et al. 2010). There are two reasons for this trend. First, the types of ecological questions being proposed, particularly those pertinent to formal decision-making, are characterized by uncertainty and paucity of empirical data. Even when data are available, they are invariably subject to error due to the size and complexity of ecological systems, resulting in parameter estimates with wide confidence intervals, leading to uninformative predictions. Second, decisions based on ecological studies focussing on conservation management of species and environmental risk assessments are often required urgently. In situations such as these where hard data are lacking yet management decisions are required, the use of expert knowledge may provide a way forward. Yet for researchers wishing to use expert knowledge, questions remain regarding how to properly conduct an elicitation and use it in a model to address the ecological research question.Although frequentist techniques are evolving to accommodate expert knowledge (e.g. Lele & Allen 2006), Bayesian methods are naturally suited to the incorporation of expert knowledge through ÔpriorsÕ; probability distributions representing what is known about the variable (Gelman et al. 2003). In this study, we focus on using Bayesian models for incorporating expert opinion. Comprehensive summaries of Bayesian modeling have been described in the statistical literature and readers ...

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Abstract. One of our greatest challenges as researchers is predicting impacts of land use on biota, and predicting the impact of livestock grazing on birds is no exception. Insufficient data and poor survey design often yield results that are not statistically significant or that are difficult to interpret because researchers cannot disentangle the effects of grazing from other disturbances. This has resulted in few publications on the impact of grazing on birds alone.Ecologists with extensive experience in bird ecology in grazed landscapes could inform an analysis when time and monetary constraints limit the amount of data that can be collected. Using responses from 20 well-recognized ecologists throughout Australia, we captured this expert knowledge and incorporated it into a statistical model using Bayesian methods. Although relatively new to ecology, Bayesian methods allow straightforward probability statements to be made about specific models or scenarios and the integration of different types of information, including scientific judgment, while formally accommodating and incorporating the uncertainty in the information provided.Data on bird density were collected across three broad levels of grazing (no/low, moderate, and high) typical of subtropical Australia. These field data were used in conjunction with expert data to produce estimates of species persistence under grazing. The addition of expert data through priors in our model strengthened results under at least one grazing level for all but one bird species examined. When experts were in agreement credible intervals were tightened substantially, whereas, when experts were in disagreement, results were similar to those evaluated in the absence of expert information. In fields where there is extensive expert knowledge, yet little published data, the use of expert information as priors for ecological models is a cost-effective way of making more confident predictions about the effect of management on biodiversity.

[1] The Brune and Churchill curves have long been used to predict sediment trapping efficiencies for reservoirs in the USA which typically experience winter and springdominant runoff. Their suitability for reservoirs receiving highly variable summer-dominant inflows has not previously been evaluated. This study compares sediment trapping efficiency (TE) data with the predictions of the two established curves for the Burdekin Falls Dam, a large reservoir in northern tropical Australia which receives highly variable summer-dominant runoff. The measured TE of the reservoir ranged between 50% and 85% and was considerably less than estimates using the Brune and Churchill curves over the 5 year study period. We modified the original equations so that daily trapping can be calculated and weighted based on daily flow volumes. This modification better accounts for shorter residence times experienced by such systems characterized by relatively high intraannual flow variability. The modification to the Churchill equation reasonably predicted sediment TEs for the Burdekin Dam for four of the five monitored years and over the whole monitoring period. We identified four key sediment particle classes: (1) <0.5 mm which exclusively passes over the dam spillway ; (2) 0.5-5.0 mm which, on average, 50% is trapped in the reservoir ; (3) 5.0-30 mm most (75%) of which is trapped; and (4) >30 mm which is almost totally (95%) trapped in the dam reservoir. We show that the modification to the Churchill equation has broader application to predict reservoir TE provided that daily flow data are available.

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SUMMARYMany studies on birds focus on the collection of data through an experimental design, suitable for investigation in a classical analysis of variance (ANOVA) framework. Although many findings are confirmed by one or more experts, expert information is rarely used in conjunction with the survey data to enhance the explanatory and predictive power of the model.We explore this neglected aspect of ecological modelling through a study on Australian woodland birds, focusing on the potential impact of different intensities of commercial cattle grazing on bird density in woodland habitat.We examine a number of Bayesian hierarchical random effects models, which cater for overdispersion and a high frequency of zeros in the data using WinBUGS and explore the variation between and within different grazing regimes and species. The impact and value of expert information is investigated through the inclusion of priors that reflect the experience of 20 experts in the field of bird responses to disturbance.Results indicate that expert information moderates the survey data, especially in situations where there are little or no data. When experts agreed, credible intervals for predictions were tightened considerably. When experts failed to agree, results were similar to those evaluated in the absence of expert information. Overall, we found that without expert opinion our knowledge was quite weak. The fact that the survey data is quite consistent, in general, with expert opinion shows that we do know something about birds and grazing and we could learn a lot faster if we used this approach more in ecology, where data are scarce.