FISHERY BULLETIN: VOL. 87, NO. 4, 1989 



of peaks and valleys to slide uniformly sideways 

 from "right" to "left". 



was then estimated as the sum of the estimates 

 for each stratum. 



Stratification Schemes 



TVOD collected under each of the eight cases 

 were subjected to three types of stratifica- 

 tion: 1) none, 2) raw encounter rate, and 3) 

 smoothed encounter rate. 



In the case of no stratification, school abun- 

 dance was estimated simply as 



{TEIAS) * {TA) 



(1) 



where TE is total number encounters by all ves- 

 sels during time steps 400 to 600, AS is total area 

 searched during that time, and TA is total area 

 simulated (1,200 x 1,200 nmi). In this case, all 1° 

 squares were treated as a single gi"oup or stra- 

 tum. 



In stratifying by raw encounter rate, en- 

 counter rates (schools encountered per nautical 

 miles searched during the last 200 time steps) 

 were calculated for each 1° square. The squares 

 were subsequently ranked in ascending order of 

 encounter rate, and grouped into (n) strata. 

 Strata were demarcated on the basis of including 

 at least {m) schools (encounters) per stratum. 

 Both (n) and (m) were calculated using an algor- 

 ithm developed by the Inter-American Tropical 

 Tuna Commission for their line transect analyses 

 of dolphin abundance in the ETP (Buckland and 

 Anganuzzi 1988). School abundance was then 

 estimated for each stratum separately. Total 

 school abundance in the entire 1,200 x 1,200 nmi 

 area was then estimated simply as the sum of 

 these estimates per stratum. 



In stratifying by smoothed encounter rate, en- 

 counter rates in each 1° square were smoothed 

 according to the algorithms developed by Buck- 

 land and Anganuzzi (1988). Squares were then 

 ranked and assigned to strata based on these 

 smoothed encounter rates. This smoothing 

 algorithm generally creates strata composed of 

 contiguous areas of squares, arrayed in decreas- 

 ing order from area of apparent high density to 

 areas of lower density. It is not uncommon, how- 

 ever, for some squares in a given strata to be 

 scattered in areas isolated from the majority for 

 that stratum. 



The smoothed encounter rates generated by 

 the algorithm were used only during this stratifi- 

 cation step; school abundances were estimated 

 for each stratum using the raw (actual) en- 

 counter rate. Total abundance of dolphin schools 



Estimates Derived 



Two types of estimates were derived from 

 these simulated TVOD: total abundance of dol- 

 phin schools in the entire simulated area, and 

 change in school abundance from one sampling 

 period to another, where this change was esti- 

 mated simply as the ratio of school abundance 

 estimates derived under two different sets of 

 initial conditions in the model. Thus, school 

 abundances were estimated first, and change 

 estimates derived subsequently from these 

 abundances. These estimates of change were 

 calculated as a very simple analogy to a trend 

 estimate, e.xtending in this case over two sam- 

 pling periods instead of over series of estimates. 

 This two-sample change estimate is only a rough 

 approximation to a trend estimate derived from 

 a series of measurements (Gerodette 1987). 

 However, conclusions about the effects of incon- 

 sistent biases on this change estimate will be 

 valid for trend estimates also, except for the 

 unlikely case in which effects of various inconsis- 

 tent biases cancel each other out, so that the 

 trend estimate reflects the actual trend, but only 

 fortuitously. 



Change estimates were derived under two 

 conditions. Under the first condition the esti- 

 mate was simply the ratio of the abundance 

 estimate when true density was 1,250 schools 

 (low density) to the estimate when the true 

 density was 2,500 schools (high density). All 

 other conditions in the model remained the 

 same. This simulates the situation of consistent 

 biases. 



Under the second condition, the trend esti- 

 mate was the ratio of one low-density estimate to 

 one high-density estimate, but the ratio was con- 

 structed by selecting abundance estimates from 

 cases which differed in other factors in addition 

 to differing in dolphin abundance. This simulates 

 the situation of biases being inconsistent from 

 one sampling period to the next. Three ratios 

 were selected from the many possibilities, to 

 simulate three reasonable scenarios in the real 

 ETP and to bracket a range from mild to severe 

 inconsistencies. 



The first of the three ratios was an estimate of 

 abundance change in the simple environment, 

 where in one case the environment was static 

 during the sampling period and in the other the 

 environment was moving at 1 knot. The second 



866 



