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Figure 36: Map showing the migration routes and the 95% kernel home ranges of the 99 harbour porpoises tagged in Danish Waters between 1997 and 2013 in Danish waters.
6.4 Modelling porpoise distribution from satellite positions
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Figure 37: June-August. Left: Mean prediction of the “probability of pres-ence of harbour porpoise” based on 100 bootstraps model. Right: The un-certainty of the prediction ex-pressed by the coefficient of variations (CV).
The construction area is outlined on the map as well as the three SAMBAH C-POD positions (black dots).
The so-called AUC (Area Under the receiver operating Curve) value can be used to eval-uate the model performance. The AUC is the probability that a randomly chosen present site will be ranked in relation to prediction above a randomly chosen background site (see (Philips & Dudik, 2008) for more details). A value of AUC=0.5 means that the model performance is equal to that of a random prediction. The mean AUC for 100 bootstrap models was calculated to be 0.927 (SD=0.011). According to Elith (2002) models with AUC values above 0.75 are considered potentially useful.
The importance of the variables is evaluated by the jack-knife test. First, the gain (im-provement of model performance) is measured when one variable is the only variable in the model, and then the decrease in gain, if that variable is omitted from the full model, is measured. As can be seen in Figure 38, salinity and temperature are the most im-portant variables when used in isolation. Distance to land and depth are also imim-portant, while front, slope, sediment, curvature and ship traffic appear unimportant. Salinity is also the variable that reduces the gain the most if omitted, and thus appears to have the most information that is not represented by the other variables.
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Figure 38: June-August. Results of the jack-knife test of variable importance measured by the gain of the variables. Left: The variable used in isolation.
Right: The decrease in gain when omitted from the model. Error bars repre-sent standard deviation.
Figure 38 shows response curves for the four most important variables (salinity, tem-perature, distance to land and depth. The response curve illustrates the relationship be-tween probability of presence and environmental variables. The probability of presence increase sharply when the salinity reaches ca. 7‰. The temperature response curve shows high variability between the model runs up to about 15 degrees, where the prob-ability appears to drop followed by an increase. This may be caused by the present of one or few low temperatures in the dataset and must be considered as an artefact. The distance to land curve is rather constant, but with a tendency of a parabolic shape. The probability of presence decreases more or less continuously with increasing depths.
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Figure 39: Summer (Jun-Aug). Response curves. The curves show how the probability of occurrence changes as the variable is varied, keeping all other variables at their average sample value. Response curve for all 100 boot-strap models are shown with the mean curve in red.
Results, autumn (September-November)
Figure 40 shows a map of suitable habitat areas in the Western Baltic during autumn (Sep-Nov) based on the results of 100 bootstrap models. The most important areas are in the south-western part of the study area, in the waters between Falster and Germa-ny. The eastern part of the study area appears not to include suitable areas. In the stud-ied area, there is a gradient of salinity with highest salinity in the western part and low-est in the eastern part (see Appendix 4). As most of the positions of harbour porpoise are from the western part, the MaxEnt model “catches” this and salinity comes out as the most important variable, which is also mirrored in the prediction of suitable habi-tats. The uncertainty of the model prediction is generally higher in the eastern part than in the western part of the studied area, which reflects the fewer observations here.
The Kriegers Flak area lies on the border between areas with relatively high suitability in the western part and low suitability in the eastern part.
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Figure 40: September-November. Left: Mean prediction of the “probability of presence of harbour porpoise based on 100 bootstraps model. Right: The uncertainty of the prediction expressed by the coefficient of variations (CV).
The construction area is outlined on the map as well as the three SAMBAH C-POD positions (black dots).
The mean AUC value for the 100 bootstrap models was 0.893 (SD=0.011). This was a lit-tle lower than the AUC obtained for the summer (Jun-Aug) period but still at a satisfac-tory level. In a previous study using MaxEnt and harbour porpoise satellite positions in inner Danish waters, AUCs ranged from 0.70 to 0.86 (Edrén, Wisz, Teilmann, Dietz, &
Söderkvist, 2010).
The jack-knife test of variable importance shows that salinity is by far the most im-portant variable both when evaluated by the gain when used as single variable and gain decrease when omitted from the model (Figure 41). Other variables with some im-portance are temperature, distance to land and v-velocity.
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Figure 41: September-November. Results of the jack-knife test of variable importance measured by the gain of the variables. Left: The variable used in isolation. Right: The decrease in gain when omitted from the model. Error bars represent standard deviation.
Figure 42 shows the response curves for the four most important variables. The proba-bility of presence increases from a salinity of approximately 7‰ up to the maximums at 9 and 11‰. The probability of presence appears to have a maximum just above 11 °C and decrease with higher temperatures. The distance to land curve is rather constant, except for an increase some distance from land and out to a distance of approximately 20 km. The response curve of v-Velocity shows a continuous increase from the lowest velocity to the highest.
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Figure 42: September-November. Response curves. The curves show how the probability of occurrence changes as the variable is varied, keeping all other variables at their average sample value. Response curve for all 100 bootstrap models are shown by the mean curve in red.
MaxEnt results compared to SAMBAH acoustical data
Both the MaxEnt results from summer (Jun–Aug) (Figure 37) and autumn (Sep–Nov) (Figure 40) seem to be in accordance with the SAMBAH C-POD results (Figure 31). The model predicts a higher probability of porpoise occurrence in the western part of the Kriegers Flak project area compared to the eastern part in both seasons. The C-POD re-sults show much higher detections at the stations to the west, 8005 and 8007, than at the eastern station (1001) for the same months (Figure 31). This is also illustrated in Fig-ure 43, where results from the MaxEnt model are plotted as a function of DPM per day.
When looking at each season separately (Blue: summer (Jun-Aug), Red: autumn (Sep-Nov)), the results seem very coherent, station 1001 has the lowest score on both axes, station 8007 is intermediate and 8005 shows the highest value. The two variables are significantly correlated, which adds validation to the MaxEnt model. Also, the period of high detections of the C-PODs starts in June and ends in November/December (Figure 31), with hardly any detections in January – May, corresponding well with the satellite data which only show few observations of tagged animals in the period December – May (Table 9), hence modelling was not possible for this period.
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Figure 43: The MaxEnt predicted mean of probability of presence of por-poises as a function of DPM per day (from C-PODs) with std. error bars.
Blue: Results from summer (Jun-Aug), Red: Results from autumn (Sep-Nov).
All points were included in calculation of the Pearson correlation coefficient.
6.5 Biology of the harbour seal