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



northern offshore stock of spotted dolphins, 

 Stenella attenuata, all have the same number of 

 animals, all are equally visible, and all move in- 

 dependently of each other. All vessels are as- 

 sumed to be identical also; they are the same 

 size, are equally adept at sighting dolphin 

 schools, and do not communicate with each 

 other. Dolphin schools move at speeds varying 

 between 0.5 and 2.4 knots, depending on condi- 

 tions of the local environment (see below). All 

 vessels move at 15 knots continuously. Speeds 

 are based on reported averages for dolphin 

 schools (Perrin 1979) and for vessels (vessel 

 activity records, NMFS data bases). Vessels are 

 assumed to chase and set upon all sighted 

 schools. Vessels that have set on a school are 

 "removed" from the simulation for 5 hours, sim- 

 ulating the average time to chase, set, collect 

 tuna, release dolphins, and get back under way. 

 Sighted schools are removed from the position of 

 sighting and replaced randomly within to 50 

 nmi of the sighting, simulating a variable "rest" 

 period of to 24 hours between one set and the 

 next for sighted schools. 



Dolphin schools move in response to the local 

 height and gi'adient of an "environmental topog- 

 raphy". The topography is a grid of equally 

 spaced peaks of good habitat interrupted by val- 

 leys of low-quality habitat. Habitat quality varies 



between a value of 1 at the peaks for optimum 

 habitats to at the least favorable habitats mid- 

 way between peaks. Topographies are generated 

 as a function of sine waves in two-dimensional 

 space and are either stationary or made to slide 

 from right to left at 1 knot. Two combinations of 

 peak spacing and peak shape were used for the 

 simulations reported here: 1) a simple topogra- 

 phy of 4 equally spaced peaks with relatively 

 gentle slopes (Fig. 2a), and 2) a more complex 

 topogi'aphy of 16 equally spaced peaks with rela- 

 tively steep slopes (Fig. 2b). 



These choices for peak number generate 

 spaces between peak tops of 300 and 600 miles. 

 These spacings were chosen based on approxi- 

 mate distances between clusters of dolphin 

 school sightings from research vessel data^. 

 Peak steepness was chosen to simulate either 

 slow spatial changes in environmental conditions 

 (gentle slope) or rapidly changing conditions 

 (steep slope) such as those which pertain at 

 ocean fronts (Owen 1981). 



Spacings of 600 miles between gently sloping 

 peaks generates distances of 300 miles between 

 maximum and minimum values of the environ- 



"R. S. Holt. Southwest Fisheries Center, National Marine 

 Fisheries Service, NOAA, P.O. Box 271, La Jolla, CA 92038, 

 pers. commun. July 1987. 



SIMPLE TOPOGRAPHY 



^^ 



<^ o 



Figure 2. — Geometric configuration of the simple environmental 



862 



