Small-boat surveys for coastal dolphins: line-transect surveys for Hector's dolphins

Fishery Bulletin, July, 2004 by Stephen Dawson, Elisabeth Slooten, Sam DuFresne, Paul Wade, Deanna Clement

L = length of transect line.

A conventional estimate of density of groups, assuming no responsive movement and g(0) = 1 (all animals on the trackline seen with certainty) is calculated as

(5) [D.sub.s] = [n.sub.s]f(0)/2L.

A corrected estimate, allowing for responsive movement and including an estimate of g(0) is given by

(6) [D.sub.U] = [n.sub.s][f.sub.s](0)/2L[g.sub.s](0),

(7) where [f.sub.s](0) = [g.sub.s](0)/[[integral].sup.w.sub.0][g.sub.s](y)dy,

(8) [g.sub.s](y) = [n.sub.hs][f.sub.hs](y)/[n.sub.h][f.sub.h](y).

A correction factor for abundance estimates of Hector's dolphin groups can be estimated by

Using Distance 3.5, we fitted a half-normal model with cosine adjustments to estimate f(0). The half-normal model was fitted to helicopter data to estimate [f.sub.h](0) and the uniform model with cosine adjustments was used to estimate [f.sub.hs](0). All were selected by using AIC. Potential model choices were the following: hazard/cosine, hazard/ polynomial, half-normal/cosine, half-normal/hermite and uniform/cosine (Buckland et al., 1993). Truncation distance was 640 in for boat sightings, and 1000 m for helicopter and duplicate sightings. To ensure that only high-quality data were used to estimate effective half search widths, sightings for which range (radial distance) was estimated by eye and those made during Beaufort sea state >2 were removed before f(0) estimation.

The error for the correction factor (c) was estimated by bootstrapping on transect lines and applying the estimation procedure to each of 199 bootstrap data sets. The standard deviation of the bootstrap estimates was used as the standard error of (c).

Ideally, the correction factor would be estimated separately for each survey from separate sets of boat-and-helicopter trials conducted in areas of representative density. Financial and logistical constraints prevented this; therefore the correction factor estimated in 1998-99 was applied to each of the line-transect surveys reported in the present study. We note that this is not uncommon (e.g., Carretta et al., 2001).

Unbiased abundance estimates were calculated by

(10) [N.sub.u] = c[N.sub.s].

The CVs of the corrected abundance estimates ([N.sub.U]) were calculated with the following equation (Turnock et al., 1995):

CV(c) = [square root of (C[V.sup.2] (c) C[V.sup.2]([N.sub.s])],

where CV(c) = SE(c)/c.

Upper ([N.sub.UC]) and lower ([N.sub.LC]) 95% confidence intervals for [N.sub.U] were calculated by using the Satterthwaite degrees of freedom procedure outlined in Buckland et al. (1993). This procedure assumes a log-normal distribution of [N.sub.C], using

(13) [N.sub.LC] = [N.sub.U] / C, and

[N.sub.UC] = [N.sub.U]C,

The Satterthwaite degrees of freedom (df) for corrected abundance estimate confidence intervals were calculated by

(15) df = C[V.sup.4](N.sub.U)/ [C[V.sup.4](c)/B-1] [C[V.sup.4]([N.sub.S])/d[f.sub.s]],

where B is the number of bootstrap samples, and d[f.sub.S] is the Satterthwaite degrees of freedom for the uncorrected abundance estimate, [N.sub.S] (see Buckland et al., 1993).

The CV of combined abundance estimates ([N.sub.[U.sub.i]]) was computed by

(16) SE(total) = [square root of ({S[E.sup.2](N.sub.U1) S[E.sup.2]([N.sub.U2]) ... S[E.sup.2] ([N.sub.Ui)})]

and

(17) CV(total) = SE(total)/[N.sub.U](total).

Results

The three line-transect surveys covered 2061 km of transect, and 231 sightings were used to estimate density (Table 2). Sighting rates were highest around Banks Peninsula (Table 3).

The simultaneous boat-and-helicopter surveys indicated that boat observers missed 11.4% of the dolphins on the trackline, but that strong responsive movement towards the boat resulted in apparent densities twice as high as they normally would be (Table 3). If the observers' attention was drawn to dolphin groups by the position of the helicopter, the results of these trials would be biased. This is unlikely, however, because several groups sighted by the helicopter observer subsequently passed within 200 m of the boat and were not seen by observers. We saw no evidence that the dolphins were affected by the helicopter.