1. The bivalve Dreissena polymorpha has invaded many freshwater ecosystems worldwide in recent decades. Because of their high fecundity and ability to settle on almost any solid substratum, zebra mussels usually outcompete the resident species and cause severe damage to waterworks. Time series of D. polymorpha densities display a variety of dynamical patterns, including very irregular behaviours. Unfortunately, there is a lack of mathematical modelling that could explain these patterns.
2. Here, we propose a very simple discrete-time population model with age structure and density dependence that can generate realistic dynamics. Most of the model parameters can be derived from existing data on D. polymorpha. Some of them are quite variable: with respect to these we perform a sensitivity analysis of the model behaviour and verify that non-equilibrial regimes (either periodic or chaotic) are the rule rather than the exception.
3. Even in circumstances where the model dynamics are aperiodic it is possible to predict total density peaks from previous peaks. This turns out to be true also in the presence of environmental stochasticity.
4. Using the stochastic model we explore the effects of age-selective predation. Quite surprisingly, larger removal rates of adults do not always result in smaller population densities and mussel biomasses. Moreover, non-selective predation can result in skewed size-frequency distributions which, therefore, are not necessarily the footprint of predators’ preference for larger or smaller zebra mussels.