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**Often 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.

### Example: population dynamics

Populations 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 Figure 1. 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.

*Figure 1: example total fresh weight of a bivalve population and its distribution over different year classes*

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.

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 Leslie-matrix 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.

*Figure 2: Possible variation of the population size and population composition of bivalves, as simulated by a probabilistic population dynamical model*

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 examples

- In Case - Probabilistic effect analysis - Cause-effect chain modelling - Sandwich terns the probabilistic approach has been worked out for the variation of population composition of Sandwich Terns;
- In Van Kruchten (MSc-thesis, 2008) the probabilistic approach has been worked out for:
- the variation of population composition of bivalves;
- the influence of weather conditions on the impact of dredging on the timing of phytoplankton blooms.