The components of the above relationship, and hence all ecological models, are subject to various types of uncertainty, which can generally be divided into data, knowledge/model, and parameter (Figure 1). Data uncertainty refers to the uncertainty in measured data used either as model inputs (X) or to obtain appropriate model parameters (0) by calibration. Knowledge/model uncertainty refers to the fact that all ecological models are only approximations to complex systems and therefore the precise form

of the correct model (f(.)) is also uncertain. Model uncertainty is generally the most difficult type of uncertainty to quantify. Parameter uncertainty refers to the uncertainty in the model parameter values (0), which can be due to uncertainties in the data, as discussed above, or the calibration process used. It should be noted that many other classification schemes of uncertainty exist. For example, uncertainty can also be classified as being either epistemic or aleatory in nature. Epistemic uncertainty results from a lack of knowledge about a particular input or process while aleatory uncertainty results from the inherent randomness or natural variability of a quantity or process.

Uncertainty in data affects all model types and can take a number of forms. First, data are subject to measurement errors, which could be due to the type of instrument used (e.g., measurement precision), how well the instrument is calibrated, how the data are read (e.g., automatic logging, manual reading), how frequently the data are measured and recorded (e.g., are all major system variations captured), and how the data are transmitted and stored. Second, the length of data records is usually limited and generally does not contain information on all possible conditions the system under consideration is likely to encounter. Third, data may not be available for all input variables that have an impact on model output. Consequently, the data may present an incomplete or skewed picture ofthe state ofa system. All of these factors can result in uncertainties in the outputs of ecological models.

As can be seen in Table 1, data are used to varying degrees during the model specification process, depending on the model type used. When specifying process-driven models, measured data are generally only used for the calibration of model parameters (0), as the functional form of the model (f(.)) and the model inputs (X) (i.e., which model inputs to include, not their actual values) are determined by the equations describing the underlying physical processes. In statistical models, data are also used for model calibration (i.e., to estimate values of 0), but additionally, they can be used to determine which potential model input variables (X) (and corresponding lags, if

Table 1 Use of data for model development | |||

Functional |
Inputs |
Parameters | |

Model type |
form (f()) |
(X) |
(6) |

Process-driven |
X |
x |
V |

Data-driven | |||

Statistical |
xa |
V |
V |

Artificial |
V |
V |
V |

intelligence |

aWhile the most appropriate form of traditional statistical models has to be determined by the modeler, data can be used to assist with this process (e.g., regression models).

aWhile the most appropriate form of traditional statistical models has to be determined by the modeler, data can be used to assist with this process (e.g., regression models).

applicable) have a significant impact on the model out-put(s), using dependence measures such as correlation or mutual information. However, the choice of an appropriate functional form of the model (f(.)) has to be made by the model developer. When developing artificial intelligence models, the available data are not only used to calibrate the model and to determine appropriate model inputs, but are generally also used to determine the most appropriate functional form of the model.

When developing process-driven and statistical data-driven models, knowledge of the functional form of the model is required (Table 1 ). This is a potential source of uncertainty, as the most appropriate model structure is difficult to determine due to the high-dimensional and highly nonlinear nature ofecological systems. In addition, the development of process-driven models requires an understanding of the underlying physical processes, introducing further sources of uncertainty. However, as mentioned previously, these problems do not arise when developing artificial intelligence models, as the functional form of the model is chosen using the data themselves. However, this does not mean that artificial intelligence models are devoid ofmodel uncertainty, as an appropriate model structure is obtained with the aid of the available data, which are themselves subject to different types of uncertainty, as discussed previously.

Model parameter uncertainty arises because ecological model parameters can vary spatially and are not precisely known in most models. Even when historical data exist to calibrate the model parameters, most models are over-parametrized and there are usually insufficient data to identify a distinct parameter set. Furthermore, identifying the best single model parameter set, given a set of calibration data, is almost always a difficult global optimization problem, which can only be solved using heuristic optimization methods that are not guaranteed to find the best solution. Consequently, ecological models will typically have a number of parameter sets that predict the calibration data equally well.

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