EDWARDS and KLEIBER: NONRANDOMNESS ON LINE TRANSECT ESTIMATES OF DOLPHINS 



ratio was an estimate of abundance change 

 coupled with a change in the environment from 

 simple to complex (environments remaining 

 static in both cases). The third ratio was an esti- 

 mate of abundance change coupled with a change 

 from a simple and static environment to a com- 

 plex and moving environment. These three cases 

 simulated ratio estimates of abundance changes 

 from, for example, one year to the next, where 

 conditions in the environment have also changed 

 between years. 



RESULTS 



Development of Nonrandom 

 Distributions 



Relatively similar dynamics occurred within 

 the four replicated runs of each of the eight 

 cases (Fig. 3). In all cases, nonstratified esti- 

 mates of total school abundance, calculated for 

 each of the 600 time steps, developed progres- 

 sively positive biases. Early during each simula- 

 tion, estimates were relatively accurate. But as 

 schools and vessels became progressively non- 

 randomly distributed (Fig. 3a-h), estimates 

 deteriorated owing to the concentration of 

 search effort by tuna vessels in the areas where 

 dolphin school were pi'evalent and to the con- 

 comitant avoidance by vessels of areas with few 

 schools. 



Although positive bias developed in all cases, 

 the degi-ee and progi'ession of bias was strongly 

 influenced by environmental topogi'aphy, both 

 configuration and dynamics. Relatively little 

 bias developed in cases where the topogi-aphy 

 was relatively noncomplex (Fig. 3a, c) or was 

 moving at 1 knot (Fig. 3b, d, f, h). Very large 

 biases developed in cases where the topogi'aphy 

 was complex and static (Fig. 3e, g). 



School Abundance Estimates 



Nonstratified estimates of total school abun- 

 dance, calculated from TVOD collected during 

 the last 200 time steps, show the positive bias 

 indicated in the time courses shown in Figure 3. 

 The degi-ee of positive bias in unstratified esti- 

 mates was not constant, but varied with model 

 conditions (Fig. 4). Bias was least for the case of 

 a simple, moving environment, slightly higher 

 for the complex, moving environment, slightly 

 higher again for the simple, static environment, 

 and dramatically higher for the complex, static 

 environment. 



Estimates of school abundance based on strati- 

 fication by raw encounter rate were in all cases 

 relatively accurate, although estimates tended 

 to be negatively biased for the cases of a simple 

 environment (Fig. 4). 



Estimates based on stratification by smoothed 

 encounter rate also tended to be negatively 

 biased for the cases of a simple environment 

 (Fig. 4). The case of a complex, moving environ- 

 ment led to a slight positive bias in abundance 

 estimates. But the complex, static environment 

 led to pronounced overestimates of abundance 

 that rivaled results from the unstratified an- 

 alyses. 



Reducing the underlying density of schools by 

 half, from 2,500 to 1,250 schools, was mirrored 

 by decreases of approximately one half in school 

 abundance estimates (Fig. 4). Patterns of over- 

 or underestimation under various model condi- 

 tions remained consistent over both densitites. 

 For example, the most severe bias occurred in 

 both eases under conditions of a complex, static 

 environmental topography. 



Change Estimates 



When change estimates were derived by com- 

 paring cases in which only the underlying den- 

 sity of schools was changed (i.e., when biases 

 remained consistent between sampling periods) 

 the estimates based on raw or smoothed en- 

 counter rate stratification were very accurate 

 (Fig. 5). Estimates based on unstratified data 

 were strongly biased but analyses of real TVOD 

 are never conducted on unstratified data, so 

 this case is useful only as an indication of 

 improvement in estimation achieved by strati- 

 fying. 



Inconsistent biases produced a dramatically 

 different result. Even relatively small changes in 

 underlying model conditions produced moderate 

 to large biases in the change estimates. Also, 

 these biases were neither consistently positive 

 nor consistently negative, even within a single 

 set of comparisons (Fig. 5). 



DISCUSSION 



School Abundance Estimates 



Stratification 



Overestimates were derived from nonstrati- 

 fied data in all cases because vessels (and there- 

 fore observers) spent more time (expended more 

 effort) in areas where dolphin schools were abun- 



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