Scale‐dependence of movement rates in stream invertebrates

Abstract

We used analytical models and random walk simulations in a one‐dimensional habitat to study the scale‐dependence of migration rates in stream invertebrates. Our models predict that per capita migration rate is inversely proportional to patch length when patches are large compared to the scale of movements. When patches are small the scale‐dependence is weaker and primarily determined by the length of individual movements (steps) relative to patch size. Laboratory experiments using isopods (Asellus aquaticus L.) and mayfly nymphs (Baetis sp.) confirmed that the strength of the scale‐dependence decreased with increasing step length.For the case when step length distributions follow an exponential probability distribution, which is often the case for stream organisms, we provide a simple model that allows the scale‐dependence to be predicted from the mean step length. We fitted this model to published field data on drift densities at different downstream distances from a net that blocks the drift from upstream areas. Agreement between model and data was excellent in most cases. We then used already published data on the length of induced drift movements to predict the scale‐dependence that was observed in block experiments performed in the same system. Predicted and observed scale‐dependence showed very close agreement.We conclude that our models and published data on drift distances can be used to calculate the expected scale‐dependence of per capita emigration rates for a large number of taxa under a wide range of environmental conditions.