Domeier et al.: Tracking Thunnus thynnus onentalis with the aid of an automated algorithm 



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tions that a fish can occupy when swimming in a fixed 

 direction from the starting point of a track is the locus 

 of points forming a circle whose center is at the starting 

 point and whose radius is the product of its maximum 

 swimming speed and the length of the time interval. 

 Likewise, the farthest positions from which a fish can 

 swim in given direction and reach the end point of the 

 track is the locus of points forming a circle whose center 

 is at the end point and whose radius is the product of its 

 maximum swimming speed and the length of the time 

 interval. The intersection of loci originating from either 

 the start point or end point with a reference to longitude 

 defines the most northern and southern extent of the 

 search area for that reference longitude. 



Because the distance of arcs whose center lies at the 

 start point increases with time, whereas the distance of 

 arcs whose center lies at the end point decreases with 

 time, the latitudinal range of the search area is usually 

 smallest at the start of the time series and at the end of 

 the time series and is usually largest midway through 

 the time series. The long time series obtained from 

 the recovered archival tags creates a situation where 

 the latitudinal extent of the search areas is largely 

 determined by the northern and southern bounds of 

 the habitat rather than by swimming speed. Swimming 

 speed does, however, constrain east-west movement on 

 a daily basis because the reference longitudes anchor 

 the search areas. 



Step 2: Selection sets for tag data The second step 

 of processing involves selecting SST records (from the 

 tag data set) that are coincident in time with the daily 

 search area. The user can define the sea surface layer 

 by entering a maximum depth of this layer; for this 

 study the surface layer was defined as 0-1 m. The user 

 can also determine how many values from the selection 

 set should be used to search for SST matches. We chose 

 a selection set consisting of three individual values 

 for PSAT tags; however, because of the much higher 

 frequency of measurements from the archival tags, we 

 chose a selection set that consisted of a single average 

 SST value for each day. The temperatures found in the 

 selected set of points for a given daily search area would 

 be used to calculate the location of pixels within the 

 search area that the tag most likely visited. 



Step 3: Choosing candidate points Selecting candidate 

 points from which a best track will be chosen begins by 

 assigning a temperature cost to pixels within the search 

 area. The temperature cost for a given pixel, j, with a 

 search area referenced by time, t{i), AT\J, Hi)], is simply 

 the absolute value of the difference in its temperature, 

 Tsatij, t(i)), and that of its closest match, k, from the 

 selected set of tag points, Ttag\k, Hi)]: 



AT[j,t(i)} = \Tsat[j,tii)-Ttag[k,t(i)]]\. 



The temperature cost, AT \j. Hi)], is an inherited trait 

 of a pixel and will be applied to all further calculations 

 of the best track(s). If the temperature cost of any pixel 



examined in a search area exceeds the cutoff value 

 entered by the user, that pixel will be removed from 

 further consideration. Pixels will also be removed if 

 they lie over land. 



Those pixels that remain are next subjected to an 

 evaluation to determine if they qualify as candidate 

 points. This evaluation is based upon the value of a cost 

 function that weighs both the pixel's temperature cost 

 described above, AT[j, t{i)], and the pixel's contribution 

 to spreading coverage over the search area: 



Cost[jMi >] = AT[j,t(i)] + Spread Factor x AL[j,t( i >]. 



AL [j, Hi)] is the relative contribution a pixel makes to 

 providing even latitudinal distribution along the refer- 

 ence longitude and search lines of the daily search area; 

 the Spread Factor weights the relative importance of 

 temperature costs with the benefit of obtaining an even 

 distribution. Although the primary criterion for selecting 

 candidate points is how well tag SST matches satellite 

 imagery SST, we have found that this criterion alone can 

 cause all the selected candidate points to be bunched 

 together. Such aggregation will force the computed track 

 into small regions of the search area without regard 

 to the distribution of matching pixels in proceeding 

 or succeeding search areas. To avoid this problem the 

 Spread Factor function spreads candidate points in a 

 north-south direction thereby providing smoother and 

 more economical tracks. The degree to which the Spread 

 Factor function spreads candidate points is controlled by 

 the user by entering a weighted value. For this study we 

 chose an intermediate value (5000 out of a possible 9999) 

 and this value was constant for all evaluations. 



The number of candidate points finally determined is 

 determined by the user. For this study, five candidate 

 points were identified for each search area. When the 

 user defines the number of points to be evaluated in the 

 search areas, pixels having the lowest cost are ranked 

 and selected accordingly. 



Step 4: Enumerate and calculate the cost of arcs After 

 the candidate points have been chosen, the best track! s) 

 is computed by choosing a single candidate point from 

 each of the daily search areas in the time series. The 

 best track is selected from all possible tracks by choosing 

 the one of least cost. Thus, the solution is global rather 

 than serial. The computation begins by calculating the 

 cost of arcs between candidate points from adjacent 

 search areas, and ends by summing the cost of all the 

 arcs of a given track (Figs. 3 and 4). 



The cost of an arc is a function of the temperature 

 match for the pair of candidate points that define the 

 arc, AT\j, t(i)\ and AT[k, t(i+D], as defined above. It also 

 depends upon the minimum swimming speed required 

 of the fish traveling between the two candidate points, 

 arc velocity min, where 



arc velocity min 



distance between candidate pixels 



{t(i + l)-t(i)) 



