Detection data were available almost continuously for four sites in the Moray Firth, starting in summer 2005 (Sutors and Lossiemouth) or 2006 (Chanonry Point and Spey Bay) until the beginning of spring 2012 (see Table S1 in Supporting information). The remaining sites were sampled discontinuously (see Table S1, Supporting information). Overall, out of more than 480 000 h of observation, the data set included 31 948 positive hourly records in which at least one bottlenose dolphin ICI was detected. Of these, more than 23 000 were recorded in the four main sites.
In seven of the twelve C-POD files, Gaussian mixture models with three components led to the identification of the expected distributions, with peaks at values corresponding to the natural logarithm of the buzz ICI, regular ICI and long ICI values in minutes (e.g. Fig. 2). In the remaining five files, two overlapping component distributions were found for the regular ICI peak, because of the low proportion of buzz ICIs present in the files. Nevertheless, the models with four components correctly discriminated this additional distribution (see Fig. S1, Supporting information) and had lower AICs when compared with the corresponding models with three components. The estimated component distributions (see Table S2, Supporting information) were then used to determine which ICIs were buzzes. As a result, buzz ICIs were identified in 14 222 of 31 948 hourly records. The average buzz ICI was 2 ms (from T-PODs) and 4 ms (from C-PODs). The discrepancy between the two instruments was accounted for in the modelling procedure by including POD type as a covariate.
Hourly Data-Full Data Set
We ran a full model with all the available explanatory variables to investigate multicollinearity, but GVIF values generally remained below 2. The GVIF was > 3 for tide speed and the tidal mixing parameter, as the calculation of mixing was based upon tide speed. Therefore, the two variables were evaluated in separate models. The model residuals were temporally autocorrelated, although less than expected (see Fig. S2, Supporting information).
For each of the five submodels (including temporal, bathymetric, tidal, oceanographic and front covariates), we compared the QIC value when it was fitted with an autocorrelation structure of order 1 (AR1) to the QIC of a working independence model. In all cases, the difference in QIC was < 2, indicating that the two versions of each submodel were substantially equivalent. This was confirmed by a qualitative comparison of the estimated model coefficients, which were virtually unaffected by the correlation structure chosen. For parsimony, we used a working independence model, as recommended when unsure about the true nature of autocorrelation (Pan 2001).
The QICu model selection procedure retained hour, year and the Julian date in the temporal submodel, depth and slope in the bathymetric submodel, tide level, tide speed and tide direction in the tidal model, SST in the oceanographic model, and front density and frontal distance in the front model. In all submodels, POD type was also identified as a relevant predictor. The five submodels were then combined into an overall model (running on a reduced data set) that also included latitude and longitude. Model selection with QICu was carried out on the overall model and, as a result, longitude, hour, year, depth, SST, tide level, tide speed and tide direction were excluded. As tide speed was removed by this second round of model selection, the tidal mixing parameter was also included, but this did not reduce the QICu. Finally, despite being retained by the QICu selection, frontal distance (P = 0·14) was not significant under the Wald's test. Conversely, POD type, latitude, Julian date, slope and front density were all significantly associated with the occurrence of buzzes (Fig. 3). The probability of buzz occurrence was lower in winter (January–April), but increased in spring and throughout summer and autumn (Fig. 3c). The use of a B-spline (instead of a cyclic spline) meant that the two extremes of the estimated relationship did not smoothly join, but we still obtained an approximate circular pattern (Fig. 3c). Greater seabed slope was associated with a higher occurrence of buzz ICIs (Fig. 3d), and there was a positive relationship between buzzes and front density (Fig. 3e).
Figure 3. Results of the model for the presence/absence of buzzing activity in each POD hourly record. The model was a binary generalized additive model with generalized estimating equations. (a) Estimated relationship between the response variable and the POD type. (b) Estimated relationship with the latitude. (c) Estimated relationship with the Julian date. (d) Estimated relationship with the slope gradient. (e) Estimated relationship with the front density. The shaded areas represent the 95% confidence intervals. The rug plot shows the actual data values.
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On average, the final model correctly classified 57·1% of observations, and the value of the area under the ROC curve was 0·59. Horton et al. (1999) goodness-of-fit test provided no evidence of lack of fit (Wald's test statistic = 4·35; d.f. = 9; P = 0·88), and the cross-validation confirmed that the model was robust. The shape of the estimated relationships (averaged across the 100 models) was consistent (see Fig. S3, Supporting information), and the model's average performance at classifying the validation sets was 56·6%, similar to the model fitted to the full data set. Moreover, the model successfully classified 77% of the 33 observed predation events as ‘presences’. The final model was then compared with a model in which the spatial covariates (slope and latitude) were replaced by POD location, to investigate the possibility that large-scale spatial mechanisms explaining the distribution of buzzing activity had been missed. The QICu suggested that the model with POD location was slightly better than the model with the spatial covariates, but its performance only increased to 58% of correct classifications.
Finally, to visualize the results, the final model was used to predict the probability of detecting buzz ICIs in each POD location. A randomly selected Julian date was used (250), together with the corresponding front maps in the average year (2009). To represent the relative importance of different areas for buzzing activity, predictions were weighted by the differential usage of those locations by dolphins. This was computed as the proportion of positive hours (hours during which at least one bottlenose dolphin ICI was detected) over the total number of hours covered by POD deployments in each location (Fig. 4; see also Fig. S4, Supporting information).
Figure 4. Map of the final model predictions in each POD location, weighted by the site usage. The probability of occurrence of buzzing activity is predicted as a function of the model covariates in that location. A randomly selected Julian date was used (250), together with the corresponding front maps in the average year (2009). Site usage was estimated as the proportion of positive hours over the total number of hours covered by POD deployments in each location.
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Hourly Data – Four Main Sites
The QIC suggested that a working independence model was preferable over the specification of an AR1 autocorrelation structure. The QICu model selection procedure retained year and Julian date, hour and tide direction, tide speed and level, and the interactions between these variables and POD location. POD type was also found to be relevant. Estimated relationships were all significant under the robust Wald's tests, but the goodness-of-fit of the final models remained virtually unchanged (57·5% of correct classifications; AUC = 0·61). Because of its collinearity with tide speed, the tidal mixing parameter was evaluated in a separate model, and it was retained by model selection as a significant linear term with an interaction with POD location.
Plots for the estimated relationships show two different patterns: (i) some variables showed a markedly different relationship with the response for each location. For example, the seasonal patterns of buzzing activity (see Fig. S5, Supporting information) or the role of the tidal flow direction (Fig. 5). (ii) other variables appeared to have an effect on the occurrence of buzz ICIs only in some locations. Tidal speed and the tidal mixing parameter, for example, were found to have an effect only at Chanonry Point and, to a much lesser extent, at the Sutors. In these locations, faster tidal flows corresponded to increased occurrence of buzzes, and well-mixed waters were preferred over stratified ones (Fig. 6).
Figure 5. Estimated relationship between buz-zing activity and tide direction in each of the four main sites. The binary generalized additive model with generalized estimating equations included the interactions between the covariates and the POD location. The shaded areas represent the 95% confidence intervals. The rug plot shows the actual data values.
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Figure 6. Estimated relationship between buz-zing activity and the tidal mixing parameter in each of the four main sites. The binary generalized additive model with generalized estimating equations included the interactions between the covariates and the POD location. The shaded areas represent the 95% confidence intervals. The rug plot shows the actual data values.
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