Report of a cetacean survey in the Western Approaches of the ...

Part 3. Density and abundance estimates for common dolphinEstimation of density and abundance assuming g(0)=1 and no responsive movementWinter 2005Sightings made by the primary team were pooled for stratum E. Sightings made aft of the beam wereexcluded leaving 66 sightings, a sample size which we regarded as adequate to support calculation ofabundance estimation.Several outliers were identified after examining the histograms of perpendicular sighting distances.These are difficult to model and were eliminated from the dataset. Using the program Distance (Laakeet al., 1993) we fitted detection functions to this data to estimate ESW, which is defined as 1/f(0). Aregression was performed to identify any bias caused by the potential of a positive relationship betweengroup size and perpendicular distance (x) (Buckland et al., 2002). No significant relationship was found(r = 0.0286, P=0.41). This may be partly explained by the fact that common dolphins were sighted inrelatively small groups. Therefore, the expected group size used in the calculations was the simplemean group size.Akaike’s Information Criterion (AIC) was used to select among models fitted to the data where thelowest AIC value is the preferred fit. The goodness of fit for different models was also assessed usingthe χ 2 value and the relevant degrees of freedom. Out of the models tested, the half-normal key withcosine adjustment was found to be the best fit (see Table 11). The distribution of perpendiculardistances and fitted detection function are shown in Fig. 7.Having selected a model, we reviewed the options for variance estimation. For this bootstrapping,which incorporates uncertainty in model fitting and model selection, was carried out. Adequate surveyeffort was achieved in the winter 2005 and a density estimate of individuals (D) for Stratum E wasachieved by stratification according to Buckland et al. (2002; see below and Appendix 1)). Results areshown in Table 12.Winters 2004+2005Both surveys combined (2004+2005) give a sample size of 108 sightings. For this dataset, the halfnormalkey with cosine adjustment was, again, found to be the best fit (see Table 11). The distributionof perpendicular distances and fitted detection function are shown in Fig. 7. Bootstrapping was alsocarried out for variance estimation.A regression was performed to identify any bias caused by the potential of a positive relationshipbetween group size and perpendicular distance (x) (Buckland et al., 2002). For the 2004+2005 dataset asignificant relationship was found between group size and perpendicular distance (r=0.175, P=0.035)but this was not significant for the 2004+2005 Stratum E dataset (r=0.05, P=0.33). Thus, the expectedgroup size was estimated as a simple mean group size. The estimate of the density of individuals (D)for Stratum E (2004+2005) by stratification was calculated according to Buckland et al. (2002):n·f(0) ·sD = —————2·LWe calculated the coefficient of variation of estimated density using the formula: cv (D) = se(D)/D, wherese(D)=q{var(D)} and where var(D)=D 2 {cv(n) 2 +cv[f(0)] 2 + cv(s) 2 } .Results are shown in Table 12.Survey Model n ∆AIC AIC χ 2 df p2004 Halfnormal/cosine43 0.00 143.36 1.8494 4 0.76342005 Halfnormal/cosine66 0.00 216.3 1.4815 5 0.91522004+2005 Halfnormal/cosine108 0.00 343.8 1.6048 4 0.80792004+2005 Halfnormal/cosine63 0.00 187.17 2.2766 4 0.6850Stratum ETable 11. Goodness of fit tests statistics and AIC value for models fitted to the transect data.22