Calibrating Hall-Effect valvometers accounting for electromagnetic properties of the sensor and dynamic geometry of the bivalves shell

Abstract Hall-Effect valvometry (HES) is being used to describe bivalve valve gape variations and infer environmental perturbations in a variety of aquatic environments. Surprisingly, the published calibrations in ecological literature ignore both the electromagnetic properties of HES and that the valves rotate around their hinge when they move. The high sensitivity of HES suggests these features should be accounted for explicitly to estimate measurement accurately. To address these issues, two calibration functions were developed based on the electromagnetic properties of the HES: one assumes that the HES and magnet are maintained on the same linear axis, and the second model accounts for the geometric properties of the system (i.e. variations of the angle between HES and the magnet during shell rotation). The great scallop ( Pecten maximus ) was used as biological model because of its large range of valve openings. HES were installed on the flat valve and magnets installed on the opposing rounded valve; 12 individuals of similar size (10 ± 1(SD) cm), were equipped and placed in controlled experimental conditions. A calibration was done for each individual once time series recordings were completed. The variability of parameter estimates was calculated with a bootstrap method. The second model (with rotatation) improves valve gape distance estimates for larger openings despite the decrease of sensor sensitivity. To infer valve gape dynamics, the reciprocal calculation of the calibration function was formalized and applied to the Hall voltage time series. Our analysis suggests that under controlled laboratory conditions, scallops are partially open most of the time (inter-valve distance equal ca . 27 mm on average, or 45 % of the average maximum opening distance). Interspersed in this continuous regime, individual scallops performed closing events at a frequency of ca . 2.5 closings per hour. A closing event is a movement that is fast enough relative to the recording frequency (10 Hz) to qualify as discrete. We find that the inversed calibration model without rotation allows negative value estimates, which indicates that this calibration function is incorrect. In contrast, the inversed calibration model with valve rotation around the hinge constrains gape distance values in their domain of definition which automatically excludes sensor readings that produce negative values from estimated gape time series.

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