The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers

Abstract

Hedger, R. D., Martin, F., Dodson, J, J., Hatin, D., Caron, F., and Whoriskey, F. G. 2008. The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers. – ICES Journal of Marine Science, 65: 1248–1259. The principal method for interpolating the positions and speeds of tagged fish within an array of fixed acoustic receivers is the weighted-mean method, which uses a box-kernel estimator, one of the simplest smoothing options available. This study aimed to determine the relative error of alternative, non-parametric regression methods for estimating these parameters. It was achieved by predicting the positions and speeds of three paths made through a dense array of fixed acoustic receivers within a coastal embayment (Gaspé Bay, Québec, Canada) by a boat with a GPS trailing an ultrasonic transmitter. Transmitter positions and speeds were estimated from the receiver data using kernel estimators, with box and normal kernels and the kernel size determined arbitrarily, and by several non-parametric methods, i.e. a kernel estimator, a smoothing spline, and local polynomial regression, with the kernel size or smoothing span determined by cross-validation. Prediction error of the kernel estimator was highly dependent upon kernel size, and a normal kernel produced less error than the box kernel. Of the methods using cross-validation, local polynomial regression produced least error, suggesting it as the optimal method for interpolation. Prediction error was also strongly dependent on array density. The local polynomial regression method was used to determine the movement patterns of a sample of tagged Atlantic salmon (Salmo salar) smolt and kelt, and American eel (Anguilla rostrata). Analysis of the estimates from local polynomial regression suggested that this was a suitable method for monitoring patterns of fish movement.

Migration and swimming depth of Atlantic salmon kelts Salmo salar in coastal zone and marine habitats

“…1c; the configuration for 2007 was almost identical. Receivers in the continuous array were moored on a near-hexagonal grid designed to ensure complete spatial coverage, with a mean distance between neighboring receivers of 570 m. The maximum range of the transmitter within the inner bay was ~650 m, giving considerable overlap in the receiver detection ranges (Hedger et al 2008a); therefore, the configuration of receivers in the continuous array in the estuary and the inner bay was suitable for the use of non-parametric regression for the interpolation of kelt positions. Receivers outside of the continuous array (in the upper estuary and in the linear arrays in the outer bay, and in the Strait of Belle Isle) were not used for interpolating kelt positions because it was found that they provided only intermittent coverage of only some of the kelts.…”

“…Then, within the continuous array (estuary and inner bay), kelt locations were interpolated using kernel smoothing; the rationale being that this could provide a fine-scale interpolation of kelt locations allowing fine-scale patterns and their causes to be identified. A normal kernel (bandwidth = 30 min) was used because this has been shown to produce less error than the box kernel (Hedger et al 2008a). For each kelt, the location was estimated at 10 min intervals (separately in easting and northing dimensions) from the coordinates of the receivers detecting the transmitter signals.…”

Environmental influence on transmitter detection probability in biotelemetry: developing a general model of acoustic transmission

“…This was based on the assumption that a likely location of a transmitter whose signal was detected by several receivers and was in the middle of the receivers (cf. Hedger et al 2008). The largest of the calculated detection ranges for each transmission was considered as a minimum estimate of the detection range for that particular transmission and termed minimum detection range D min (eqn 1).…”

Short-term residence, home range size and diel patterns of the painted comber Serranus scriba in a temperate marine reserve

“…We used the Nadaraya-Watson normal kernel estimator (sm package in R; Bowman & Azzalini 1997) to calculate position estimates, or centre of activity (COA) locations, for monitored fish every 60 min (see Simpfendorfer et al 2002, Hedger et al 2008. Processed data were used for all of the following analyses.…”