FISHERY BULLETIN: VOL. 86, NO. 2 



tions. Included in the recorded data are informa- 

 tion on all changes in a vessel's activity; the loca- 

 tion, tjqae, and catch of all purse seine sets; and 

 the location and identity of all marine mammal 

 sightings. In these data, a vessel's activity is clas- 

 sified into one of five mutually exclusive cate- 

 gories: searching, running, setting, chasing, or 

 resting. Searching is defined to be whenever a 

 vessel is moving and the crew are actively search- 

 ing for signs of tuna; running, anytime the vessel 

 is moving but not actively searching for signs of 

 fish (e.g., moving locations at night); chasing, 

 anytime schools of dolphins are being pursued 

 before the net has begun to be set. More detailed 

 descriptions of the available data, collection pro- 

 cedures and their preparation for the analyses 

 below can be found in Polacheck (1983, 1984^). 

 The analyses in this paper were part of a larger 

 project on the use of these observer data for as- 

 sessing the relative abundances of dolphin stocks. 

 As such, the emphasis in this paper is on the 

 encounter rate for the most important dolphin 

 species for the fishery (spotted dolphin), although 

 catch rates for tuna are also considered. The re- 

 sults presented in this paper are based on two 

 different approaches for analyzing the data. The 

 first method is a set of nearest neighbor calcula- 

 tions, and the second is a cluster analysis. 



The nearest neighbor calculations were per- 

 formed in order to get an indication whether ves- 

 sels tend to search in the vicinity of a previous 

 encounter (either a sighting of marine mammals 

 or a set on tuna). In these calculations, the phys- 

 ical distance between either the next or preceding 

 encounter is compared with the distance to the 

 nearest other encounter made within the entire 

 cruise. Also, the proportion of times in which the 

 nearest encounter is not either the next or preced- 

 ing one is calculated. For a vessel that never re- 

 turned to the area of an encounter, this propor- 

 tion would equal 1. Similarly, if a vessel never 

 returned to the area of an encounter, the ratio of 

 the distance between either the next or preceding 

 encounter and the distance to the nearest other 

 encounter within an entire cruise would also 

 equal 1. Note that the expected values for these 

 proportions with random search are not necessar- 

 ily 1. The expected value will be dependent both 

 on the distribution of potential encounters and 



3Polacheck, T. 1984. Documentation of the time sequen- 

 tial files created ft-om the tuna boat observer data bases for 

 analyzing relative abundances. Natl. Mar. Fish. Serv., South- 

 west Fish. Cent., Adm. Rep. LJ-84-33, 26 p. 



the definition of random search (see Discussion). 

 These calculations were performed separately for 

 sets and chases for tuna and for the sightings of 

 spotted dolphin. In performing these nearest 

 neighbor calculations, the first and last encounter 

 during a cruise were not included. 



The other main approach used for examining 

 the data is a form of cluster analysis. When the 

 sequences of distances between sets and chases 

 within any cruise were examined, they appeared 

 to be spatially and temporally clustered in the 

 sense that sets and chases in which the distance 

 to the next set or chase was small tended to be 

 clumped sequentially. This observation led to the 

 development of an algorithm for clustering sets 

 and chases that were spatially and temporally 

 related. Standard clustering algorithms were not 

 appropriate in this situation because of the prob- 

 lem of scaling spatial and temporal distances 

 within a common metric (i.e., how much time 

 should be equal to a given distance). 



Note that the term "clustered" or "clustered 

 distribution" is used in this paper to refer to any 

 distribution in which high- and low-density areas 

 are more frequent than would be expected if the 

 distribution was generated by a Poisson process. 

 The term is not meant to refer to any particular 

 nonhomogeneous process. A cluster is considered 

 as an area of high density and should not be con- 

 strued as referring to a discrete unit. 



The primary purpose of the clustering al- 

 gorithm was to define areas which a fisherman 

 might have thought to have a high density of 

 potential fishing targets so that the searching be- 

 havior of a vessel could be compared between 

 these areas and outside them. This analysis ex- 

 ploits the fact that the physical distance between 

 events is partially independent of the distance 

 that a vessel travels to locate them. Since the 

 purpose of the algorithm was to define areas of 

 potentially good fishing, chases of dolphin, as well 

 as sets, have been included as events in the clus- 

 tering algorithm. (Sets made for the purpose of 

 washing the net were not used.) The clustering 

 algorithm began with consideration of the dis- 

 tance between the first and second set and/or 

 chase. If this distance was less than a specified 

 amount, then these two events were placed in the 

 same cluster, and the distance between these two 

 and the third event were examined. This specified 

 amount will be referred to as the clustering 

 parameter. If the distance between the third 

 event and either of the events within the cluster 

 was less than the value of the clustering parame- 



354 



