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Probabilistic analysis of ecological effects  Causeeffect chain modeling
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About
The quantification of ecological effects in Environmental Impact Assessments is mostly done by deterministic modelling of causeeffect chains. However, these causeeffect chains are subject to a large number of uncertainties. Part of them are inherent to natural dynamics, others are caused by a lack of knowledge on the relevant processes. In a deterministic approach these uncertainties cannot be taken into account and worstcase assumptions have to be made. The accumulation of worstcase assumptions will yield highly conservative estimates of the ultimate effect with an unknown uncertainty margin. A probabilistic approach treats uncertainties in a different way, which enables incorporating the most relevant ones in the modelling of the ecological effects. A probabilistic approach leads to insight into the probability of occurrence of the possible effects, which can be of use in discussions about the design of the project or the necessity of mitigating and compensating measures.
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Next to insight into the probability of occurrence of possible effects, a probabilistic analysis also leads to insight into the relevance of different uncertainty factors on the expected ecological effect. This indicates which factors further research should focus on, in order to reduce uncertainty in the predictions (if the nature of the uncertainty allows for such a reduction). Moreover, it is valuable information for the development of a monitoring plan in the Construction or Operation and Maintenance phase. Building with Nature interestA probabilistic approach gives more insight in the functioning of the ecological system, its internal dynamics and its response to human interventions. It shows, for instance, which factors have a relevant influence on the possibly affected species, with what intensity and what probability of occurrence. This information can be used in the design process, during construction works and for the development of an effective monitoring plan.
Sometimes significant effects (in the sense of the Birds and Habitats Directives) cannot be excluded on the basis of a deterministic approach. In that case, probabilistic analysis may be useful in order to decide whether or not mitigating or compensating measures should be taken. Deciding on the basis of a deterministic approach, without information on the probability of occurrence of the adverse effects, may lead to the implementation of unnecessary measures. Probabilistic analyses can provide a better foundation to the environmental regulations applicable to hydraulic engineering works.

How to Use
This tool focuses on the application of probabilistic analysis in causeeffect chain modelling. A general probabilistic approach for ecological risk assessment, originating from ecotoxicology, is also available: Probabilistic effect analysis  The Species Sensitivity Distribution. Essential for the probabilistic modelling of causeeffect chains is stateoftheart knowledge on these causeeffect chains, together with knowledge on probabilistic computation methods. This section provides more information on the following:
 General Approach
 Probabilistic modelling
 Probabilistic modelling and the precautionary principle
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Example of a causeeffect chain: how the changes of inorganic factors due to sand extraction activities may affect sea ducks.
Model setup for a part of the causeeffect chain above.
Modelling ecological effects, stepwise approach.
General ApproachTo be able to predict the ecological impact of a specific human intervention, the pathways by which this activity can interact with flora, fauna or ecosystems have to be known. For a deterministic as well as a probabilistic approach, the assessment of this interaction starts with insight into the causeeffect chains or networks. For a quantitative prediction of the effects of the above interaction, it is necessary to find out which quantitative relations exist between the actions and responses. For an example of a model setup that can be used in a deterministic as well as a probabilistic approach, refer to the figure in the middle. The deterministic approach will yield a single value for each effect, the probabilistic approach an approximation of the probability distribution function.
Especially in the case of long impacteffect chains, the number of uncertainties will be very large, and they may grow throughout the process. Feedback loops may even lead to their unbounded amplification. A proper elaboration of the probabilistic analysis requires an overview of the uncertainties and their influence on the probability distribution function of the effect to be considered. Depending on its influence on the final result (compared to the effect of other uncertainties), it may be necessary to incorporate a specific uncertainty in the model. The relative influence of an uncertainty can sometimes be estimated analytically, otherwise model testruns must give insight into the sensitivity of the result to a specific uncertainty variable.
Probabilistic modellingWithin causeeffect chains several types of relations and uncertainties can be distinguished. Each type of uncertainty will require a specific method of incorporation in the probabilistic model. Although different data will be necessary for each hydraulic engineering project and each impacteffect chain, the same types of uncertainties will be encountered. Therefore, the method is formulated in such a way that it can be applied to different projects and different impacteffect chains.
h3 Uncertainties on quantitative relationsEven if it is known, on a physical or ecological base, which type of quantitative relation (e.g. linear, sigmoid or exponential) holds between two factors in the causeeffect chain, the exact value of the relevant parameters might be uncertain. These parameters may be uncertain when no measurements are available or when measurements show some scatter. right Example of linear relation F(x)=a*x with uncertain parameter a Estimate of probability density function of a ExampleThe figure depicts a relation between impact y and cause x, from which measurement data are available. On the basis of these data as well as physical / ecological knowledge the relation is expected to be linear; y=f(x)=a*x. The value of parameter a can be derived from the measurement data. However, the measurements show a large scatter. In case of a deterministic approach it would be necessary to do a conservative assumption on the value of a. A conservative assumption of f(x) could for example be the red line in the adjacent figure.
In a probabilistic approach it is possible to take into account the variation of a. The measurement data can be used to estimate a probability density function (pdf) of a. Parameter a is calculated for the line from the origin to each measurement point individually. From the resulting set of different values of a the pdf is estimated. Within the Monte Carlo analysis, each simulation a different value of a will be used, randomly sampled from the pdf.
NB: In this example the cause of the variation of factor a is not known. Before taking into account uncertainties in this way, it has to be excluded that the variation of the uncertain factor is caused by another variable, from which the variation is already taken into account separately. It should be avoided that some uncertainties are incorporated more than once in the probabilistic analysis.
Uncertainties caused by natural variationsOften the magnitude of ecological effects depends largely on variables with a large natural variation, for example weather conditions or population dynamics. Due to the large, unpredictable variation of such factors, ecological impacts usually cannot be predicted accurately. The uncertainty margin of the predicted impact by a deterministic approach will be large but unknown. This uncertainty margin can be made explicit with a probabilistic approach. Within a Monte Carlo analysis the possible conditions (weather conditions, development of population composition) can be simulated randomly, a large number of times, by using probability density functions of all relevant, uncertain variables (based on known variation in these conditions). For each generated set of input variables, the ecological impact will be modeled. right
Example total fresh weight of a bivalve population and its distribution over different year classes
Example: population dynamicsPopulations can be affected if dredging influences survival rates, growth or reproduction. A population consists of several year classes and a year class exists of all individuals that are born in the same year. If dredging for example only affects reproduction in one specific year, the number of individuals of one specific year class will be lower than it would have been without the dredging activities. As a consequence, the total population size will also decrease. However, when the affected year class forms a large part of the total population, the relative decrease of the total population size will be larger than in case that the specific year class forms a small part of the total population. This is illustrated in the top figure. A 10%decrease of the number of individuals of year class A will have a larger impact on the total weight/mass of the population than a 10%decrease of the number of individuals of year class B.
So, if dredging affects only one year class (by affecting reproduction, survival of juveniles or growth of juveniles) the total impact does not depend on the magnitude of the impact on this year class only, but is also influenced by the population composition. Due to this, natural variations of the population composition can have a relevant influence on the magnitude of the impact of dredging. right Possible variation of the population size and population composition of bivalves, as simulated by a probabilistic population dynamical model
To quantify the impact on the population size when the effect on a specific year class is known, a population dynamical model (for example a Lesliematrix or a comparable approach) will be necessary in a deterministic as well as in a probabilistic approach. Relevant input variables for population dynamical models are survival rates, reproduction rates (and eventually growth rates). Instead of using constant survival and reproduction rates (deterministic approach), the variation of these variables can be taken into account in a probabilistic approach.
If measurement data are available on survival and reproduction rates, probability density functions (pdf's) of these stochastic variables can be estimated. By randomly varying these rates in the population dynamical model, the possible natural variations of the population size and composition can be simulated. It is recommended to compare the simulated variation with measurements of the population development and composition. If the simulated variation does not correspond with the variation of the population size that is observed in the field, the pdf's of the stochastic variables have to be adjusted.
If no measurements are available on the variation of survival and reproduction rates, estimating pdf's on the basis of expert judgment might be an option. In each case has to be checked whether or not the simulated variation of population size and composition is reasonable.
Other examplesIn the probabilistic approach has been worked out for the variation of population composition of Sandwich Terns;
Uncertainties caused by a lack of knowledgeProbably the most difficult type of uncertainties to deal with, are the uncertainties that are caused by a lack of knowledge. It is possible that a causeeffect chain includes some steps on which no (or hardly any) quantitative information is available. In accordance with the precautionary principle, the modeling of such parts of the causeeffect chain has to be based on a worstcase assumption. Preferably this assumption is based on expert judgment. Unless experts are able to estimate the uncertainty margin of the assumed relation too, the probabilistic modeling approach will be similar to the deterministic approach (for this part of the causeeffect chain). In case of a lack of knowledge, analyzing the sensitivity of the final results on the possible shapes of the unknown relation will be useful. If the finally predicted impact turns out to be very sensitive to the unknown factor, further research to this topic should be recommended. Also see for strategies on how to deal with uncertainties due to a lack of knowledge.
Uncertainties if impacts only occur under certain conditionsImpact A in the impacteffect chain, for instance caused by dredging operations, does not always lead necessarily to Effect B, for example:
As impact A only leads to impact B in case of specific conditions, the probability that dredging has an ecological impact via the impacteffect chain is smaller than 1. By a probabilistic approach this probability can be quantified. right Example of a nonlinear relation between the amount of prey (total weight of bivalves) and the number of predators (eiders), figure from Van Kruchten (2008). One bird day is equivalent to one bird that spends one day in a specific area.
Example: nonlinear relations between the amount of prey and number of predatorsA decrease of the amount of prey, does not necessarily lead to a decrease of the number of predators too. The figure shows the relation between the total amount of bivalves (prey) and the number of wintering sea ducks (eiders) for a specific foraging area. The total amount of bivalves is subject to a large yeartoyear variation. During some years the number of sea ducks that can survive in the foraging area is limited by the amount of bivalves. During other years the amount of bivalves is more than sufficient for all sea ducks (that potentially forage in the specific area) to survive.
As a result of the nonlinearity, the size of the bivalve population in the reference scenario has a large influence on the possible impact of dredging. During years with a large amount of bivalves, a certain decrease of this large amount of food will hardly affect the number of wintering sea ducks, while such impact will be much larger during years with a small bivalve population. For example: suppose that the dredging activity causes a 10%decrease of the bivalve population. If this occurs during a good year with a bivalve population of 16000 kg (which decreases to 14600 kg due to the dredging), the relative impact on the number of eiders is only 1% (a decrease from 2.23 to 2.20*10^5 bird days). If the 10%decrease occurs during a years with a small bivalve population (decrease from 3000 to 2700 kg) the impact on the number of eiders is 7% (a decrease from 1.11 to 1.03*10^5 bird days).
In this way the natural population dynamics of bivalves can have a large influence on the magnitude of the impact of dredging on the number of wintering sea ducks. In a probabilistic approach the natural variation of the amount of prey can be simulated. In this way the nonlinearity of the relation between the number of sea ducks and the amount of bivalves can be taken into account. With this, also the probability that the decrease of the amount of prey does not lead to a decrease of the number of predators is estimated (equal to the probability that the weight of the bivalve population is larger than circa 20.000 kg).
NB: in fact also a second type of uncertainty plays a role in Figure 1: the scatter of the measurement data around the estimated relation. It is possible to take into account this uncertainty too (see above for Uncertainties on quantitative relations). However, the influence on the final result of this uncertainty might be negligible compared to the influence of the natural population dynamics combined with the nonlinear relation.
Example: mismatchIf a socalled mismatch occurs between the availability of food (phytoplankton) and the presence of bivalve larvae, the bivalve larvae will probably catch a growth lag. At a certain moment in spring the 'phytoplankton bloom' takes place. From this moment on, sufficient food is available for an optimal growth of bivalve larvae. If the bivalve larvae hatch after the bloom started off a match occurs. Otherwise a mismatch occurs; the larvae are born before the food concentration is sufficient, resulting in a growth lag.
An increase of water turbidity (due to dredging) may delay the phytoplankton bloom. If this results in a mismatch, the bivalve population will be affected by the dredging activity. The occurrence of a mismatch can be schematized by the following simple equation:
M = A _{ref} + D  H With: A mismatch only occurs if M>0. right Example pdf's of H, A _{ref} and A _{dredging} (=A _{ref} +D)
The timing of the phytoplankton bloom as well as the timing of the hatching shows a large yearly variation. However, on average the bloom takes place during the first half of April and the hatching at the end of May. Suppose that the dredging project causes a delay D of the phytoplankton bloom of 7 days. It is unlikely, however not impossible, that such a delay leads to a mismatch. On the basis of the probabability density functions (pdf's) of the timing of the bloom (A _{ref}) and the timing of the hatching (H), the probability of occurrence of a mismatch can be estimated. This probability is visualized by the small overlap of the probability density functions of H and A _{dredging} in Figure 2. Only in case of coincidence of a late bloom with a relatively early timing of the hatching a mismatch can occur.
In a deterministic approach the only option would have been the worstcase assumption that any delay always leads to a mismatch (assumption A _{ref} =H, leading to M=D). In a probabilistic approach can be taken into account that the probability of the occurrence of a mismatch is smaller than 1.
For a further elaboration of this example is referred to Van Kruchten (2008).
Probabilistic modelling and the precautionary principleThe result of probabilistic modelling is a probability distribution function, in this case of an ecological effect. The inputs and the model used should be as realistic as possible. In view of the precautionary principle, however, the resulting probability distribution function should not give a too optimistic picture of reality. So, the probabilistic analysis should aim for 'as realistic as possible, and certainly not too optimistic'. In the following, examples are elaborated on how one can deal with the precautionary principle in a probabilistic approach.
Precautionary principle: ‘if a reasonable suspicion exists that activities can have negative consequences for the environment, measures should be taken in order to prevent these consequences or, if the prevention of these consequences is not possible, to offer protection against these consequences'. This also means that a conservative assumption will be necessary in the quantitative effect analysis, if no scientific evidence indicates that the real situation might be worse.
Example 1: Estimating probability density functions
Example 2: Lack of knowledge

Practical Applications
In the Netherlands, the probabilistic analysis of causeeffect chains was applied for the first time in ‘A probabilistic analysis of the ecological effects of sand mining for Maasvlakte 2’ (Van Kruchten, Y.J.G. , 2008). This study showed that it is possible to give insight into the probability of occurrence of ecological effects by using a probabilistic analysis.
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The study focused on the possible impact of the sand extraction activities for Maasvlakte 2, the Netherlands, on protected seaducks in the nature reserve Voordelta. The results showed that the probability of occurrence of significant effects (in the sense of the Birds Directive) was very small, which was valuable information in the discussion about the necessity of implementing mitigating or compensating measures. In '
Lessons learnedApplying a probabilistic analysis in causeeffect chain modelling is particularly useful, if the deterministic modelling requires very conservative or even worstcase assumptions. In such cases, the probabilistic approach can make the difference between a very conservative and a realistic estimate of effects. If the deterministic approach is based on realistic assumptions, a probabilistic analysis will still provide extra information, viz. the probability density function of the effect. Using a probabilistic approach for the simulation of the impact of dredging on mussels by a Dynamic Energy Budget model (see

References
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Van Kruchten, Y.J.G. (2008) A probabilistic analysis of the ecological effects of sand mining for Maasvlakte 2, MSc Thesis Faculty of Civil Engineering and Geosciences, Delft University of Technology, Port Research Centre Rotterdam  Delft, ISBN/EAN: 9789056381974 
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