On the availability bias in narwhal abundance estimates

Abundance estimation of narwhals is usually done with either visual or photographic aerial surveys. The basic estimation for both methods is detection of whales at the surface, and to obtain fully corrected abundance estimates, the at-surface detections need to be corrected for the proportion of whales that, at any given time, is available to be detected at the surface. The surfacing time or ‘availability correction factor’ is obtained from whales instrumented with dive recorders, that either relay concatenated information on the proportion of time spent at different depth intervals to satellites, or from recovered instruments that collect complete dive profiles, measured at high frequency. Concatenated data binned in depth histograms from Satellite-Linked-Time-Depth-Recorders (SLTDR) falls in two categories, where those that correct the zero depth values with information from the saltwater switch provide larger and apparently more accurate surfacing times, than those collected from instruments that does not correct the zero depth readings. The erroneous detection of near-surface pressure values is likely due to slow response of pressure transducers made from temperature sensitive materials. The high frequency sampling from AcousondeTM recorders documents erroneous surface detections, and adjustments of the dive profiles are needed to obtain realistic near-surface values. Any reconstruction of dive profiles and near-surface values apparently involves some level of corrections and it is recommended, for development of availability correction factors for aerial surveys, that data from zero-adjusted SLTDRs or TDR instruments are used. The mean estimate of surface time from 7 SLTDRs was 29% (CV=0.05). One SLTDR, with steel pressure transducer and zero-adjustments, that was retrieved from the whale, provided a particular long-record (83 days) of reliable high-resolution data. The surface time for this sample was 31%, when calculated as the sum of all depth readings at or above 2 m. The mean of 144 hourly depth readings during 06:00-18:00, and including dives above 3m, was 27.36% (CV=0.8) for 12 days overlapping with the usual timing of aerial surveys. Accurate estimation of smaller depth bins (e.g. 0-1 m) should, even with high resolution instruments, be used with caution when estimating availability bias.