Appendix D. Methodological details of computer simulation and description of simulation parameters.
We created a computer simulation run in Java to assess the performance of belt, point, and video methods for surveying the abundance of coastal sharks. Prior to implementing the simulation we collected field data on shark movement to help select realistic parameter values with which to define shark behavior in the simulation. On snorkel and SCUBA at Palmyra we followed 8 reef sharks (Carcharhinus amblyrhynchos and C. melanopterus) and tracked their paths of movement by dropping markers at seven timed intervals. From these movement traces we estimated (1) their velocities of linear travel and (2) the tortuosity of their movement defined as the sum of the distances of all component segments in one shark follow divided by the distance between the start and finish points of the follow.
In the simulation we populated a two dimensional circular reef space (radius 1,000 m) with sharks and measured their density in the simulation using belt, point, and video surveys which replicated methods employed in field data collections activities at Palmyra. Initial stocking densities of sharks in the simulation were set to approximate estimated values of shark density observed at Palmyra and fished reef sites. Sharks were programmed to swim in semi-random, irregular paths. Each shark was designed to select and move towards a series of constantly changing target destinations in the simulation. Sharks were programmed to alter their direction of travel approximately every 15 seconds (precise interval selected at random between 10 and 20 sec) while transiting towards these targets and to accelerate towards a set maximum traveling velocity. The direction of travel for these periodic changes in heading was randomly determined from a subset of values that kept the shark swimming on average towards its target destination. The overall tortuosity and velocity of travel for simulation sharks was parameterized to approximate field-measured values (Table D1). Sharks were assigned to overlapping circular home ranges whose size was determined from the literature (Papastamatiou et al. 2009). Sharks were not, however, strictly confined to these home ranges, but were programmed to spend the majority of their time within these boundaries: 95% of all selected target destinations were located within these home ranges. Sharks were programmed to travel either singly or in pairs and the distribution of animals between these two groupings was determined based on field data from video surveys at Palmyra. Sharks moving in pairs traveled along the same path of motion. Sharks did not behaviorally interact with one another or with the simulation observer.
All three survey types (point, belt, and video) were conducted simultaneously at the same location in the center of the simulation. Both the number of individual sharks (number of sharks that the observer believed to be unique individuals) and the total number of sharks (total number of shark sightings; sharks recounted each time they reenter a survey area) were recorded. Provisions were incorporated into the simulation so that observers “forget” sharks that travel > 50m in any direction from them. Any sharks that traveled beyond this 50 m forget radius boundary were subsequently recounted as new individuals if it reentered the survey area. Only numbers of individual sharks were used to calculate predicted shark density estimates for each method.
Observers in the belt count method travel at a constant speed (same as speed used by divers in the field) along the length of the belt transect. They count sharks in a rectangular area with a length limit for shark detection set at 25 m (the approximate limit at which large targets can be detected reliably in the conditions at Palmyra) and width limit that is bounded by the defined borders of the belt. When the belt observer is ≤ 25 m from the end of the survey, the length of the detection area is reduced at a constant rate, eventually collapsing to an area of 0 m² the instant the observer reaches the end of the transect. The circular forget area for sharks travels around the belt observer as they advance. In the point count method, the observer continuously scans a rotating sector of defined width within the observation circle for a defined period of time. The video survey views a circular sector of simulation area and records data 2 sec every 30 sec. Sharks are forgotten and recounted as new individuals using the video methods whenever they leave and reenter the observation area and between all 2 sec counts. The duration of simulation video surveys were set to match mean duration of field video surveys.
In addition to testing the three survey methods field trialed at Palmyra, we also tested one larger belt and point count survey. The dimensions and duration of these five simulation survey methods are summarized in Table 2. The simulation was run under two different shark density scenarios as described in “Methods.” Each method was run for 500 iterations under each of these scenarios. All other parameters utilized for the simulation are summarized in Table D1. Simulation code and associated parameter files are included as supplementary materials in Ecological Archives.
TABLE D1. All parameters utilized for the simulation.
|Min school size / # schools||1/194|
|Max school size / # schools||2/24|
|Min school size / # schools||1/20|
|Max school size / # schools||2/2|
|Max velocity (m sec-1)||0.54|
|Home range (m²)||550000|
|Belt / Belt long|
|Point / Point long|
|Observation angle (rad)||0.2835|
Papastamatiou, Y. P., C. G. Lowe, J. E. Caselle, and A. M. Friedlander. 2009. Scale-dependent effects of habitat on movements and path structure of reef sharks at a predator dominated ecosystem. Ecology 90:996–1008.