Mathematical evaluation of behavioral deterrent systems to disrupt fish movement

Abstract

Although behavioral deterrent systems, directed at exploiting fish sensory systems, are the common place in fisheries management, little is understood about the link between imposed sensory signals (e.g., sound intensity) and the resulting fish movements. Here, an advection–diffusion equation, incorporating a stimuli specific repulsive flux, is coupled with calculation of the generated stimulus field in order to model fish movement near a behavioral deterrent system. A stability analysis of this model is then used to determine the effectiveness of a deterrent stimulus to disrupt the natural movement of fish. Results of laboratory experiments of a bubble curtain to inhibit common carp, Cyprinus carpio, movement are used to develop the model and verify stability analysis predictions. This experimental data demonstrate that the acoustic stimulus (sound pressure levels) produced by bubble curtain systems can be sufficient to disrupt the natural movement of carp, i.e. inhibit fish passage. In addition, a sensitivity analysis is used to investigate how model stability is impacted by changes in movement behaviors (i.e. diffusion and advection rates). This coupling of a movement model and stability analysis could find general application in the assessment of behavioral deterrent systems, in particular at field sites where long term physical testing may be impractical.