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Behavioral observations and computer simulations of blue crab movement to a chemical source in a controlled turbulent flow

Marc J. Weissburg^* and David B. Dusenbery

School of Biology, Georgia Institute of Technology, Atlanta, GA 30332-0230, USA

View larger version (6K): [in a new window]   Fig. 1. Illustration of a simulated searcher in the chemical plume. The searcher's ten sensors are located at the ends of the `spokes'. The dark patches are areas where the chemical stimulus is above threshold. The image is to scale, with the plume extending approximately 150 cm downstream of the source and the diameter of the searcher equal to 10 cm.

View larger version (34K): [in a new window]   Fig. 2. Performance of center-of-gravity (A) and best-receptor (B) models with different weightings of rheotaxis and tropotaxis. For each weighting, 1000 searchers were simulated for up to 1500 time steps (30 s), as described in Materials and methods. The vertical lines span the range of time steps taken to reach the source, while the horizontal lines indicate the median time taken. The closed circles indicate the number of searchers that reached the source. Few searchers reached the source with a weighting of less than 0.5, whereas weightings greater than 0.8, resulted in some searchers reaching the source while others never did. All searchers reached the source in close to the minimum time with intermediate weightings. For comparison, the average crab found the source in approximately 1500 time steps (30 s).

View larger version (16K): [in a new window]   Fig. 3. Distance from the source as a function of time is shown for an arbitrary sample of three simulations at four different rheotaxis weightings. (A) Searchers with a weighting of 0.4 eventually move downstream, away from the source, following blobs of chemical stimulus. All searchers with a weighting of 0.5 move upstream to the source, displaying varying periods of little movement, as stimulus blobs move downstream of the searcher. Searchers move upstream to the source at close to maximum speed, when rheotaxis weightings are 0.7 (the 3 tracks overlap) (B). With a weighting of 1.0, searchers blessed with a low bias in determining flow direction move directly upstream to the source, while others veer cross-stream of the source and move upstream of it, or move out of the plume and rarely progress.

View larger version (42K): [in a new window]   Fig. 4. Comparative performance of searchers with different numbers of sensors and different integration areas (big or small). Sensor arrays are illustrated by `spokes' from the array center to the center of each sensor and by a filled area of integration (top). With all models, performance falls off rapidly outside the 0.5-0.9 range of weighting rheotaxis. With any weighting within this range, at least 70% of searchers reached the source within the 10,000 time steps simulated (A,B). However, the median time taken to reach the source varied 20-fold (C,D). All models with the large integration area outperformed all those with the small integration area. In addition, models with more sensors were better than those with fewer. With the two-sensor models, the larger array was marginally superior. The more complicated center-of-gravity models (B,D) are not superior to the simple best-sensor models (A,C).

View larger version (16K): [in a new window]   Fig. 5. Typical search paths of real and simulated searchers. (A) Real crab, (B) simulated crab with a rheotaxis weighting of 0.5, (C) simulated crab with a rheotaxis weighting of 0.7. Values represent the coordinates of the animal rendered at 5 Hz.

View larger version (21K): [in a new window]   Fig. 6. Typical velocity records in real and simulated searchers. (A) Real crab, (B) simulated crab with a rheotaxis weighting of 0.5, (C) simulated crab with a rheotaxis weighting of 0.7.

View larger version (21K): [in a new window]   Fig. 7. Path kinematic parameters of real and simulated searchers. Values are means per path (N=14 paths for each treatment). Analysis of variance (ANOVA) indicates that speed and path efficiency are significantly different across these groups (F2,39>39.07, P<<0.001 for both comparisons), whereas the ANOVA analysis of stop time indicates a marginally significant effect (F2,39=3.02, P=0.06). Horizontal lines join pairs that are statistically indistinguishable based on Scheffe's test, for speed and path efficiency. Path efficiency is the total distance traveled relative to the shortest distance from the origin to the destination, and is unity when the searcher takes the shortest, most direct route to the source. Data are from real (hatched bars) and simulated crabs (open and filled bars; rheotaxis weighting in parentheses).

View larger version (18K): [in a new window]   Fig. 8. Distributions of movement speed and turning angles of real and simulated searchers. Data from all paths in a particular group were pooled. Turn angle is the absolute difference between the heading measured over successive frames (crabs) or simulation steps. Values are from real (open triangles) or simulated crabs (filled squares and circles; rheotaxis weighting in parentheses). Sample sizes, representing the number of video frames in all 14 paths in each group, were 758, 2100 and 2504 for simulated searchers with a rheotaxis weighting of 0.7, simulated searchers with a rheotaxis weighting of 0.5 and real crabs, respectively.