pi'oblem of competing species (Kothschild, 1967) 

 as they affect albacore apparent abundance on 

 ttie longline grounds are, to a degree, obviated 

 by considering, as we have done, trends in ap- 

 parent abundance in the albacore area only 



(fig. 4). 



Thus, the spatial statistics give not only 

 measurements of the spatial attributes of the 

 albacore distribution, but, from the interrela- 

 tions among the spatial statistics for catch, 

 CPUE, and effort, they also give clues on 

 changes in efficiency (the maximum efficiency 

 occurs when catch, CPUE. and effort are coin- 

 cident) and catchability. Emphasis must again 

 be placed, when considering the relative posi- 

 tion of the spatial statistics for catch, CPUE, 

 and effort, on the "apparent" rather than 

 "absolute" nature of the spatial statistics. For 

 example, if effort covered only a small portion 

 of the albacore distribution (an unlikely situa- 

 tion) then the spatial first moment, tor example, 

 would be a biased estimate of the first moment 

 of the albacore distribution, and in such a sit- 

 uation the estimated dispersion would be less 

 than the actual dispersion. Perhaps a more 

 likely source of bias than that produced by an 

 incomplete spatial coverage of the fishable 

 population by effort may arise from a variable 

 catchability of albacore over the fishing ground. 

 Therefore, any observed spatial distribution 

 may contain components owing to (1) the actual 

 distribution of the fish, (2) the gear not actually 

 covering the fishing area, or (3) situations that 

 cause catchability to vary over the fishing 

 grounds. 



Secondly, a very striking feature of the alba- 

 core data is the year-to-year constancy in 

 catch and CPUE spatial statistics. The con- 

 stancy implies that the spatial statistics for 

 any year can be predicted with a high degree 

 of accuracy. This point is demonstrated for 

 the two-dimensional first moment in figure 15. 

 We expected that the spatial statistics would be 

 much more variable than they actually were. 

 Our expectation was based on an assumption 

 that variations in the spatial statistics would be 

 influenced to a large extent by variations in the 

 oceanic environment. Examples of environ- 

 mental variability, especially in surface waters, 

 are quite common in such things as "warm 

 years," "cold years," and vagaries in the 

 position of the Kuroshio axis, for example. We 

 conclude from the relative constancy of the 

 spatial statistics, that either the environment 

 is not as variable as we may have thought (pos- 



sibly owing to the albacore being caught at 

 depths by the longline gear where the environ- 

 ment is, in actuality, relatively more constant 

 than that at the surface), or that any changes in 

 the environment that do occur have little effect 

 upon the distribution of the albacore, or that the 

 effect of the environment on the fish is masked 

 by random or unexplained variability. Thus, 

 any deviation in spatial distribution from the 

 long-term average appears to be so small that 

 it would be difficult to associate it with a bio- 

 logical cause. From a practical point of view, 

 in terms of searching for albacore, the devia- 

 tions are so small that they are rather unim- 

 portant. 



Third, it might be expected that a decline in 

 apparent abundance of the magnitude observed 

 for the albacore would be associated with large 

 changes in spatial statistics. For example, 

 since there is some size stratification on the 

 longline grounds (Suda, 1963a), an alteration in 

 the average size of fish caught would produce a 

 modification in the two-dimensional first mo- 

 ment. As we have pointed out, however, the 

 evidence on trends in average size of albacore 

 for the study period is equivocal. Also a de- 

 cline in apparent abundance might be expected 

 to produce a contraction in the horizontal space 

 occupied by the albacore. The virtual constan- 

 cy of the spatial statistics, however, suggests 

 that there is no large change in the spatial sta- 

 tistics during the study period, and therefore 

 the decline in apparent abundance was not re- 

 lated to large changes in the spatial statistics. 



The Environment and Anomalies in 

 Catch-per-unit.of-effort and Spatial Statistics 



Despite the clear trend in declining CPUE 

 and the constancy of many aspects of the spa- 

 tial statistics certain years were anomalous 

 with respect to trends and variations in these 

 indices. In CPUE for example, 1948, 1952, 

 1953, 1954, 1958, and 1961 were above the re- 

 gressed average, but 1949, 1950, 1951, 1955, 

 1956, 1957, 1959, and 1960 were poorer than 

 the regressed average. 



With respect to anomalies in spatial statis- 

 tics, the first moments for CPUE in 1954 and 

 in 1955 were to the north of the long-term first 

 moment and in 1957, 1959, and 1961 to the south 

 of the long-term moment (fig. 15). Another 

 example of deviations, which are rather small 

 for practical purposes, may be found in the 

 significant long-term trends in the spatial sta- 

 tistics: CPUE moved in a southerly direction, 



30 



