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Impact A in the impact-effect chain, for instance caused by dredging operations, does not always lead necessarily to Effect B, for example:

- a decrease of the amount of prey, only leads to a decrease of the number of predators if the availability of food is limiting for the predators;
- a change in the timing of the availability of food, as a result of the dredging activities, may lead to a 'mismatch' between the birth of juveniles and their food. This may cause growth lags and/or a lower survival rate. However, such a mismatch can only occur due to the dredging activity, if there is a tight timing between food and juveniles in the reference situation without dredging. This will be illustrated in the second example of this paragraph.

As impact A only leads to impact B in case of specific conditions, the probability that dredging has an ecological impact via the impact-effect chain is smaller than 1. By a probabilistic approach this probability can be quantified.

### Example: non-linear relations between the amount of prey and number of predators

A decrease of the amount of prey, does not necessarily lead to a decrease of the number of predators too. Figure 1 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 year-to-year 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.

*Figure 1: Example of a non-linear 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.*

As a result of the non-linearity, 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 non-linearity 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 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 non-linear relation.

### Example: mismatch

If a so-called 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:

M = duration of the mismatch (days)

H = moment of hatching of the larvae (date)

A _{ref} = moment of the phytoplankton bloom in the reference situation (date)

D = delay of the phytoplankton bloom, caused by the dredging activity (days)

A mismatch only occurs if M>0.

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.

*Figure 2: example pdf's of H, A* * _{ref} *

*and A*

_{dredging}*(=A*

_{ref}*+D)*

In a deterministic approach the only option would have been the worst-case 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).