Physical Constraints in Sensory Ecology
13
Fig. 3 A, B. (On the previous two pages). Contour plots of possible fitness components for
equal-volume ellipsoids of all shapes, with axes a, b, c. The values of the contours are
relative to an equal-volume sphere. All possible equal-volume ellipsoidal shapes not too
distorted from spherical are represented in these plots. The sphere (a= b =c) is at the
center, and the distance from the center is proportional to the negative log of the minimum
radius of curvature occurring in each ellipsoid compared to the radius of the equal-volume
sphere. At the outer edge of the plots, the ellipsoids are most distorted from spherical and
have a minimum radius of curvature of I% that of the sphere. The three axes of the plots
encompass shapes in which two axes of the ellipsoid are identical (ellipsoids of revolution).
At one end of each axis, prolate ellipsoids, with semiaxes equal to some permutation of(lO,
10. 112 , 10- 112 ), resemble rods, with axial ratios of 32; and at the opposite end oblate
ellipsoids, with semiaxes (10- 415 , 10 215 , 10 215 ) resemble disks with axial ratios of 0.063.
Where swimming occurs, it is along the a axis. For clarity, boxes are illustrated that are just
large enough to contain the optimal ellipse. (Data from Dusenbery 1998a)
4.3 Constraints on Pheromone Use
At small size scales, diffusion transports chemicals faster than does flow. This
permits a simple calculation of the range at which the pheromone released by a
small organism can be detected (Dusenbery and Snell 1995). Making a best
estimate of the cost of pheromone production, the benefits of producing
pheromone to attract a mate can be compared to the benefits of allocating the same
energy to swimming.
Pheromone production can increase the search rate several orders of magnitude
for sufficiently large organisms (Fig. 4). But there is again a sharp size limit below
which pheromone production is a complete waste. The pheromone diffuses away
faster than it can be produced and a threshold concentration never builds up.
The actual value of the size limit depends on the values of several parameters
that are poorly known, but the best estimates suggest a size limit on the order of
lmm, and available information is consistent with this (Dusenbery and Snell
1995).
Crustaceans use mate attractant pheromones but are larger than 1 mm. Rotifers
are smaller and do not employ attractant pheromones. One ciliate is known to
employ attractant pheromones, but it usually stays in contact with surfaces. No
bacteria are known to employ pheromones for mate attraction, although
pheromones are used for regulating genes where more time is available (Surette et
al. 1999).
13
Fig. 3 A, B. (On the previous two pages). Contour plots of possible fitness components for
equal-volume ellipsoids of all shapes, with axes a, b, c. The values of the contours are
relative to an equal-volume sphere. All possible equal-volume ellipsoidal shapes not too
distorted from spherical are represented in these plots. The sphere (a= b =c) is at the
center, and the distance from the center is proportional to the negative log of the minimum
radius of curvature occurring in each ellipsoid compared to the radius of the equal-volume
sphere. At the outer edge of the plots, the ellipsoids are most distorted from spherical and
have a minimum radius of curvature of I% that of the sphere. The three axes of the plots
encompass shapes in which two axes of the ellipsoid are identical (ellipsoids of revolution).
At one end of each axis, prolate ellipsoids, with semiaxes equal to some permutation of(lO,
10. 112 , 10- 112 ), resemble rods, with axial ratios of 32; and at the opposite end oblate
ellipsoids, with semiaxes (10- 415 , 10 215 , 10 215 ) resemble disks with axial ratios of 0.063.
Where swimming occurs, it is along the a axis. For clarity, boxes are illustrated that are just
large enough to contain the optimal ellipse. (Data from Dusenbery 1998a)
4.3 Constraints on Pheromone Use
At small size scales, diffusion transports chemicals faster than does flow. This
permits a simple calculation of the range at which the pheromone released by a
small organism can be detected (Dusenbery and Snell 1995). Making a best
estimate of the cost of pheromone production, the benefits of producing
pheromone to attract a mate can be compared to the benefits of allocating the same
energy to swimming.
Pheromone production can increase the search rate several orders of magnitude
for sufficiently large organisms (Fig. 4). But there is again a sharp size limit below
which pheromone production is a complete waste. The pheromone diffuses away
faster than it can be produced and a threshold concentration never builds up.
The actual value of the size limit depends on the values of several parameters
that are poorly known, but the best estimates suggest a size limit on the order of
lmm, and available information is consistent with this (Dusenbery and Snell
1995).
Crustaceans use mate attractant pheromones but are larger than 1 mm. Rotifers
are smaller and do not employ attractant pheromones. One ciliate is known to
employ attractant pheromones, but it usually stays in contact with surfaces. No
bacteria are known to employ pheromones for mate attraction, although
pheromones are used for regulating genes where more time is available (Surette et
al. 1999).