POLACHECK: DISTRIBUTION OF SEARCHING EFFORT 



ter, this third event was included in the cluster 

 and the fourth event was examined. Whenever a 

 set or chase was found for which the distance be- 

 tween it and all members of the last defined clus- 

 ter exceeded the clustering parameter, a new 

 cluster was formed. This process was repeated 

 until all sets and chases within a cruise were 

 placed in a cluster. 



Using this algorithm, all the activities within a 

 cruise could be considered to occur either between 

 or within clusters. Isolated sets or chases (i.e., 

 clusters containing only a single event) were con- 

 sidered as occurring between clusters. Distances 

 travelled (i.e., distance searched and distance 

 run) within a cluster were defined as the dis- 

 tances travelled after the first set or chase until 

 the last set or chase in that cluster. Distances 

 travelled between clusters were defined from the 

 last event of the previous cluster to the first event 

 of the subsequent cluster. The distances travelled 

 until the location of the first set or chase and after 

 the last one were not included because of the large 

 distances involved in reaching the fishing 

 grounds. 



The location of a cluster was estimated by cal- 

 culating the centroid for all sets and chases 

 within it. The size of a cluster was estimated by 

 determining the radius of the smallest circle with 

 a center at the centroid that encompassed all sets 

 and chases within it. 



The sensitivity of this algorithm to the value of 

 the clustering parameter was examined for val- 

 ues of 50, 75, 100, and 150 miles. For most of the 

 results, only clusters with at least three members 

 are considered as clusters. Clusters with only two 

 members have been excluded from most of the 

 summary results describing a cluster and also in 

 the comparisons of results between and within 

 clusters. This was done because two physically 

 close events did not seem to warrant being called 

 a cluster. Yet, given the relative difficulty in lo- 

 cating potential sets, two close events might be 

 considered as areas of potentially good fishing. 

 Clusters with only two members contained 18% of 

 all sets and chases when the cluster parameter 

 equalled 50 miles and 6% of all sets when the 

 value equalled 150 miles. The overall results and 

 conclusions are robust to whether or not clusters 

 with two members are included or excluded. 



An average intercluster distance for a cruise 

 was calculated in order to get an indication of the 

 stability of the clustering algorithm to the value 

 of cluster parameters. The intercluster distance 

 was defined as the distance from the nearest 



member of a cluster or isolated set to the next set 

 and represents the minimum value that the clus- 

 ter parameter would have to be for a cluster or 

 isolated set to be combined in a single cluster with 

 the next set. 



Encounter rates for schools of spotted dolphin 

 for each cruise were calculated between and 

 within clusters as the total number of sightings 

 divided by the total distance searched. In these 

 rates, if the first chase or set within a cluster was 

 based on a sighting of spotted dolphin, this sight- 

 ing was included in the encounter rates between 

 and not within a cluster. For the analysis of these 

 encounter rates, clusters were classified accord- 

 ing to the percentage of the total number of sets 

 and chases within a cluster that involved schools 

 of dolphins. In calculating the number of events 

 that occurred within a cluster, sequential non- 

 dolphin sets in which no searching was done be- 

 tween them were counted as a single event. This 

 was done to reduce the effect of multiple sets on 

 the same floating object counting as a large clus- 

 ter. 



In order to see whether the searching behavior 

 within the defined clusters resulted in biased esti- 

 mates of encounter rates for dolphins if the clus- 

 ters were ignored in the estimates, two different 

 estimates for the overall encounter rate for a 

 cruise were calculated and compared. The first 

 estimate, which will be referred to as the unad- 

 justed rate, was simply the total number of en- 

 counters divided by the total distance searched 

 for an entire cruise. This would be an unbiased 

 estimate if search was in fact random. The second 

 estimate, which will be referred to as the adjusted 

 encounter rate, was calculated as the weighted 

 average of the encounter rate within and between 

 clusters. The weights for the encounter rate 

 within clusters were equal to the diameter of the 

 cluster. The weights between clusters equalled 

 the total distance searched between clusters. In 

 effect, this adjusted encounter rate is an estimate 

 of what the encounter rate would have been if a 

 vessel had made a straight line crossing of each 

 cluster. (In the calculation of these adjusted en- 

 counter rates, clusters with two members were 

 treated the same as other clusters to simplify the 

 calculations.) 



The analyses in this paper are based on 35 

 cruises. This represents a subset of the cruises in 

 1979 with NMFS observers, which in turn is a 

 subset of all purse seine cruises for tuna in the 

 ETP during 1979. Analyses were restricted to 

 1979 because only for this year have the data 



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