Distribution based on spatial modelling approach

Two separate Random Forest Models were fitted for the winter and summer seasons.

The winter model was fitted using data collected during the months of January, March and April and the summer model was fitted using data collected during the months of May, July, August and September. Although data were collected during the months of February and June, these data sets were not included in the models due to very few sightings and too little effort undertaken under valid conditions because of high sea state.

Current was the most important predictor in the presence-absence part of the summer model, followed by Mean depth, Temperature and Distance to land. Conversely to the presence-absence part, for the positive part of the model the most important variable was Distance to land. The other variables, in order of importance, were Mean depth, Temper-ature and Month (Table 3.3).

Table 3.3: Relative importance of the environmental predictors for the presence/absence and the posi-tive parts of the summer model for the harbour porpoise. The importance of a particular pre-dictor is expressed as the decline in the predictive performance when that particular variable was not included in the model. Evaluation results are presented as area under receiver oper-ator curve (AUC) and Pearson's correlation coefficient respectively. Values for both stages (presence/absence and positive part) of the model are presented on separate panels.

Variable Presence / absence Positive part

Month 0.096 0.023

Mean depth 0.120 0.035

Current 0.119 0.016

Temperature 0.158 0.044

Distance to land 0.110 0.055

Model performance

AUC 0.661

Pearson's correlation coefficient 0.465

The winter model yielded somewhat different results from the summer one. The ranking of the variables for presence/absence part was as follows: Distance to land, Tempera-ture, Month, Mean depth and Current. The positive part of the model highlighted as par-ticularly important Temperature and Month, followed by Mean depth, Current and Dis-tance to land (Table 3.4).

Table 3.4: Relative importance of the environmental predictors for the presence/absence and the posi-tive parts of the winter model for the harbour porpoise. The importance of a particular predic-tor is expressed as the decline in the predictive performance when that particular variable was not included in the model. Evaluation results are presented as area under receiver oper-ator curve (AUC) and Pearson's correlation coefficient respectively. Values for both stages (presence/absence and positive part) of the model are presented on separate panels.

Variable Presence / absence Positive part

Month 0.025 0.018

Mean depth 0.021 0.007

Current 0.020 0.002

Temperature 0.039 0.019

Distance to land 0.042 0.000

Model performance

AUC 0.56

Pearson's correlation coefficient 0.01

The direction of the effects of the environmental variables were broadly concordant across seasons (Figure 3.2 and Figure 3.3). The effect of the variables Current and Tem-perature were positive, although this varied between the positive and the

pres-ence/absence part of the models. The effect of variables seems to show a larger propor-tion of nonlinearity in the presence/absence part of the model. The variable Mean Depth showed a negative effect on the positive part of the models with the species avoiding areas with mean water depth of less than 25 m.

a)

b)

Figure 3.2: Fitted functions for the two-part random forest model representing the relationship between the predictor variables, the positive (a) and presence/absence (b) parts for the harbour por-poise summer model. The values of the environmental predictor are shown on the X-axis and the density (for the positive part) and the probability of occurrence (for the presence/absence part) respectively on the Y-axis.

a)

b)

Figure 3.3: Fitted functions for the two-part random forest model representing the relationship between the predictor variables, the positive (a) and presence/absence (b) parts for the harbour por-poise winter model. The values of the environmental predictor are shown on the X-axis and the density (for the positive part) and the probability of occurrence (for the presence/absence part) respectively on the Y-axis.

For the presence/absence part of the model Mean Depth showed a negative effect throughout although this was highly nonlinear. Distance to land had a variable effect across the positive and presence/absence parts of the models and across seasons. For the positive part of the summer model it showed a peak at around 30 km distance to land, followed by a decrease at higher distances. For the presence/absence part of the model it showed a negative effect throughout.

This pattern was slightly different for the winter model which showed a positive relation-ship between Distance to land and density for the positive part of the model and a nega-tive one for the presence / absence part. The model validation showed a moderate pre-dictive ability for the summer model according to the Pearson correlation coefficient. AUC (Table 3.3). Conversely the winter model showed a poor predictive ability for both the presence/absence and positive parts. The poor predictive ability for the winter model can at least partly be explained by the little number of harbour porpoise observations during the winter months. According to Moran’s I no significant spatial autocorrelation was found in the residuals of the presence/absence part of harbour porpoise models. Results for the positive part were similar, with exception of the residuals for the month of August, which showed a significant amount of spatial autocorrelation (see Appendix).

The results of the model point at a consistent spot of high densities to the southwest of the planning area (Figure 3.4 and Figure 3.5. The area is at the south-western edge of the Horns Rev and thus characterized by a steep gradient in the bathymetry. As can be seen from the underlying bathymetric map similar characteristics are found for the other parts with high porpoise densities where similar changes from deeper to more shallow waters are found. Such structures of decreasing water depth lead to locally higher cur-rents which were found to be an important variable in the model.

Figure 3.4: Modelled spatial distribution of harbour porpoise in the study area based on aerial surveys undertaken in May, July and August 2013 (summer distribution model).

Figure 3.5: Modelled spatial distribution of harbour porpoise in the study area based on aerial surveys undertaken in January, March and April 2013 (winter distribution model).

3.1.2.2. Results of the passive acoustic monitoring (PAM)