CRD 01-06

APPENDIX A
CHOICE OF INTERVAL FOR ANALYSIS

As noted above, the choice of interval is important in defining the sighting events that underlie the definition of closure triggers. Accordingly, an analysis is given here of how results differed using the four different intervals examined (4, 7, 10 and 14 days). A comparison of these differences is given in Appendix Table 1. Details of the comparisons between the chosen 10-day interval and the other three options are given below.  

10 days vs 7 days

The largest difference (in terms of number of events identified) was between analyses using 7- and 10-day intervals. A listing of events identified using a 7-day defining interval that differ from those identified using a 10-day defining interval, and vice versa, is given in Appendix Tables 2a and 2b together with a description of nature of the difference. In all cases (11 in total), the 10-day interval captured additional sightings that were close together in time but more than 7 days apart, thus lengthening the duration of the event concerned. However, it should be noted that all of the 11 cases began with an initial sighting of only one or two right whales; thus they would not fall within the trigger criteria proposed here.  

10 days vs 4 days

Using an interval of 4 days gave 11 events that were different (in start date) from those captured by the 10-day interval. In all cases, these were part of longer events which began earlier and usually ended later under the 10-day criterion. In other words, the shorter interval broke up more protracted events and thus did not adequately reflect residency by right whales in the area. 

10 days vs 14 days

Using the 14-day interval provided only four differences with the 10-day criterion results. These were as follows:

1. An event beginning 86.05.14 was one of only two sightings of two whales separated by 12 days. It is likely that this represented two isolated sightings of transient whales, since it was not followed by a longer event picked up by the 10-day criterion.

2. A single sighting of two whales on 86.06.19 preceded by 11 days and then merged with an event beginning (under the 10-day criterion) on 86.06.30.

3. An event beginning with one whale on 87.06.09 and consisting of two sightings (the other of a pair on 87.06.20) preceded and merged with an event beginning (under the 10-day criterion) on 87.07.07.

4. An event beginning on 89.06.22 and consisting of two sightings of single whales (the other on 89.07.03) preceded and merged with a prolonged event beginning (under the 10-day criterion) on 89.07.14 and lasting 71 days.

In summary, use of the 14-day interval either artificially connects sightings that are probably unrelated, or extends the front end of events that were already established under the 10-day criterion. Although the latter instance would marginally extend protection to the one or two animals concerned, this is not a significant benefit given the infrequency with which these cases occur and the additional costs of increasing closure times.

Appendix Table 1. Comparison of different intervals used in defining events. Data from Cape Cod Bay and Stellwagen Bank combined.

Interval

Events
Days Duration (days) _
X
Whales
Min Max Mean Min Max Mean
4 days 51 2 58 6.1 2 67 8.6 3.4
7 days 47 2 76 6.9 2 95 11.6 3.3
10 days 42 2 76 8.0 2 95 15.4 3.6
14 days 41 2 76 8.3 2 95 18.5 3.4

 
Appendix Table 2a. List of events identified using a 7-day defining interval that differ from those identified using a 10-day defining interval. Comparisons in Comments are made relative to events reported in Appendix Table 2b or to other data.

Ref
Start
date

Initial sighting

Days

Duration
Mean
RW#

Comments
A 83.05.24 1 2 5 1.0 Using the 10-day interval, this event began on 83.04.17 and lasted 42 days
B 87.08.30 1 2 3 1.0 Part of event 1 below
C 87.09.10 1 5 7 1.0 Part of event 1 below
D 89.08.02 2 8 12 2.1 Part of event 2 below
E 89.08.22 2 16 24 2.0 Part of event 2 below
F 92.08.10 2 18 22 2.8 Part of event 3 below
G 92.10.20 1 2 4 1.0 Using the 10-day interval, this event began on 92.10.04 and lasted 20 days
H 93.08.15 1 2 3 1.0 Using the 10-day interval, this event began on 93.07.28 and lasted 21 days

Appendix Table 2b. List of events identified using a 10-day defining interval that differ from those identified using a 7-day defining interval. Comparisons in Comments are made relative to events reported in Appendix Table 2a.

Ref
Start
date

Initial sighting

Days

Duration
Mean
RW#

Comments
1 87.08.21 2 8 27 1.1 Began earlier and merged into events B and C above
2 89.07.14 1 27 71 2.0 Began earlier and merged into events D and E above
3 92.07.31 2 19 32 2.8 Began earlier and merged into event F above

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(Modified Jun. 13 2008)