Fishery Bulletin 104(1) 



and fish movements was estimated from the measure- 

 ments of the artificial objects, for which the true size 

 was known. Because the measurement variance was 

 expected to be larger for the mobile artificial fish than 

 for the rigid objects, an extended linear mixed-effects 

 model (Pinheiro and Bates, 2000) was used to account 

 for this expected heteroscedasticity. The model included 

 true length as a fixed effect and observer as a random 

 effect. Fixed objects and mobile objects (artificial fish) 

 were allowed separate variances. The resulting model 

 was 



L,f= 1.1 + pL* + o, + f^ -t-f,,. 



(1) 



where L, ^ = length measured by observer / of an object 

 of class J=|fixed, mobile! and of true size 



L*; 

 o, ~ iV(0,a(o)); and 

 e,j ~ N(0,a), whereas /", ~ N(0, a,(/;)). 



The model was fitted to the data from the eight observers 

 who had measured all objects with the laser method. 



Accuracy and precision for artificial objects An extended 

 linear model including heteroscedastic variance terms 

 was used to compare the precision and accuracy of 

 the two methods. The model included fixed effects for 

 true length and the measurement method. The esti- 

 mated fixed effects allow assessment of the potential 

 measurement bias of each method. The measurement 

 errors for fixed and mobile artificial objects were mod- 

 eled separately for each method. This allowed us to 

 compare the precision of the methods. Thus, the fitted 

 model was 



measurements. The model included a fixed individual 

 fish effect (each fish had a different, unknown size) 

 and a random observer effect; and fish species were al- 

 lowed heteroscedastic variances to account for species 

 behavior differences (Lepidion versus Bathypterois). 

 The stationary species, B. dubius, is easier to measure 

 compared to the more lively L. eqiies. The model was 



^,,.,.1 = ^'n +0, +S, + £„,, 



(3) 



where Z>,, , ^ = the length measurement obtained by ob- 

 server / for individual fish n belonging 

 to species /; 

 o, ~ MO, a(o)); and 

 f,„, ~ MO, a), whereas s, ~ N(o, a, (s,)). 



Unfortunately, it was not possible to carry out a direct 

 comparison between the precision of size estimates 

 of fish and artificial objects because the latter were 

 measured seven to 11 times, whereas the former were 

 measured only two to seven times. Random subsamples 

 could be carried out to obtain comparable sample size; 

 unfortunately, subsamples from large samples would 

 still have a larger variance than small samples. 



All models were fitted by using Splus 6.0 for Unix 

 (MathSoft, Seattle, WA). For heteroscedastic models, be- 

 cause of identifiability constraints, the fitting algorithm 

 provided estimates of the ratio between the standard 

 deviations of each class in relation to the standard 

 deviation of a specified class instead of the full set of 

 standard deviations. 



Results 



H + PL* + f,k + f,*. 



(2) 



where k = the measurement method and j the object 

 class as before. As in model 1, f^,, ~ N(0, o). In contrast, 

 f^i. ~ N(0, o^f^if^i.)) allowed for separate variances for each 

 object-type and method pair. Only two trained observ- 

 ers used both measurement methods for all objects. 

 Because there was no significant difference between 

 their measurements, and in order to reduce the number 

 of parameters to be estimated, no observer effect was 

 included in this model. 



Precision of fish measurements The precision of fish- 

 length estimates was compared for two species, Bathyp- 

 terois dubius and Lepidion eques. These species were 

 selected for this analysis because they are abundant and 

 relatively easy to measure, compared to other species 

 that move faster or flex their body more often. Twenty- 

 four individuals belonging to these two species were 

 measured repeatedly by up to five observers using the 

 real-time laser measurement method. 



Because true fish size was unknown, measurement 

 accuracy could not be estimated. For estimating the pre- 

 cision of fish measurements, an extended linear model 

 with heteroscedastic errors was fitted to the fish length 



Precision and accuracy of measurements varied among 

 objects and methods (Table 1). The best precision was 

 obtained with the video-replays of laser measurements, 

 whereas METRAU generally did not perform very well, 

 especially on snapshots. The precision was generally 

 much lower for mobile objects than for rigid objects. Mea- 

 surement bias was generally low for the laser method, 

 whereas the METRAU method systematically under- 

 estimated the size of objects. A variety of fish species 

 with various sizes were measured. CVs for individual 

 fish measurements varied from 3% to 23% (Table 2). 

 Species were grouped according to their motion behavior 

 (l=sitting on bottom motionless, 2 = station holding or 

 drifting, 3 = slow swimming, 4=fast swimming [Lorance 

 and Trenkel-]). CVs were found to differ between groups, 

 increasing with mobility (mean CV in group 1: 8.9%; 

 group 2: 9.7%; group 3: 12.9%; group 4 was excluded 

 because there was only one individual, P<10"''). 



- Lorance, P., and V. Trenkel. In preparation. Natural 

 behaviour and reaction to an approaching ROV of large 

 mid-slope species. IFREMER, Centre do Brest, B.P. 70, 

 29280 Plouzane. France. 



