The sources of uncertainty in ecological models outlined above lead to uncertainty in model validity, predictions and forecasts obtained, and decisions made. Consequently, there is a need to address model uncertainty explicitly, which can be achieved through sensitivity (SA) and uncertainty (UA) analyses (Figure 1). SA enables the impact of uncertainties in any of the model inputs (parameters, forcing functions, boundary conditions, etc.) on one or more model outputs to be explored. This enables model validity to be assessed, as the model responses obtained in response to changes in model inputs can be compared with any a priori knowledge of system behavior. The individual input sensitivities obtained as part of SA are also useful, as they identify which inputs are most critical and should be the focus of additional data collection efforts, for example. In addition, advanced SA methods can identify the degree and nature of the interaction between inputs.
While SA enables the effect of variation in model inputs on model output(s) to be explored, it gives no consideration to the likelihood that such an input variation will occur. UA achieves this goal by using probability distributions to describe how likely particular values of the uncertain model inputs are, which can be used to determine the likelihood of certain model outputs. In the most general sense, a UA quantifies the uncertainty of model outputs as a function of the uncertainty in the model inputs. This enables confidence limits to be obtained for forecasts and predictions, and/or risk-based performance criteria, such as reliability, vulnerability, and engineering resilience, to be calculated, depending on the UA methodology selected.
The applicability of the different outcomes of SA and UA to ecological models with different purposes is shown in Table 2. It can be seen that the information obtained in relation to model validity by conducting a SA is applicable to all ecological models, irrespective of their intended use. Information regarding input sensitivity contributes toward understanding of the relative importance of model forcing functions, model parameters, and boundary conditions on model output, as well as the nature ofthese relationships over plausible parameter ranges. Consequently, this information is most useful if the aim of the modeling exercise is to obtain a better understanding of the ecological system being modeled. However, as mentioned above, such information is also useful in relation to directing data collection efforts, and is therefore also indirectly of interest to models intended for prediction, forecasting, and decision-making. Confidence limits on predictions and forecasts obtained as part of UA is of primary interest if models are used for prediction, forecasting, and decision-making. Confidence limits provide an indication of how certain a prediction or forecast is, or what the likely worst-case scenarios might be. For models used for decision-making, they also provide an indication of whether one proposed management option is clearly better than another. Risk-based performance measures are most useful if ecological models are used as the basis for decision-making, as they provide an indication of the reliability (risk of non-failure), vulnerability (likely magnitude of failure, given failure has occurred), and engineering resilience (inverse of the likely duration of failure, given failure has occurred) of an ecological system when subjected to a particular set of system states. For example, failure might correspond to the occurrence of a toxic algal bloom under a certain flow regime. Risk-based performance measures can also be used to estimate the probability that one management option is better than another.
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