106
Joseph A. C. Humphrey et al.
earlier investigations, several authors have derived and applied physical models to
describe the behavior of filiform cuticular hairs responding to oscillatory
movements of the surrounding fluid medium in both terrestrial and aquatic
arthropods; see Fletcher (1978), Tautz (1979), Shimozawa and Kanou (1984),
Humphrey et al. (1993, 1997), Barth et al. (1993, 1995), Devarakonda et al.
(1996), Shimozawa, et al. (1998), and Barth (2000). The theoretical component of
that work is numerical in nature. It requires the judicious calculation and plotting
of numerous individual cases in order to elucidate the effects on hair maximum
angular deflection and velocity, and their corresponding resonance frequencies,
resulting from changes in hair diameter and length, the mechanical spring and
damping constants of the hair, and the medium density, viscosity, and velocity.
In spite of its accuracy, the numerical solution approach is not entirely
satisfactory. This is because it does not provide easily usable and interpretable
analytical formulas from which to derive generally applicable conclusions
concerning the expected performance or evolutionary adaptation of filiform hairs
as the result of small changes in hair properties or the environment. The purpose
of this study is to derive such formulas subject to simplifications that render the
mathematics tractable but which, nevertheless, retain the essential physics of the
problem and from which correct qualitative results can be obtained.
The combination of increased understanding and predictive capability allowed
by the present highly integrative analytical approach squarely addresses a major
challenge in sensory ecology explained elsewhere in this book by David
Dusenbery. In the case of arthropod filiform motion-sensing hairs it can be stated
as follows. Biomechanical and physiological studies clearly show that these hairs
are tuned to preferred frequencies (or frequency ranges) and require minimal
deflection, velocity, and acceleration thresholds to detect fluid medium-borne
deflection stimuli originating from other animals (mates, prey, and predators) and
the environment. It seems reasonable to assume that over evolutionary time
periods the hairs have adapted to selective pressures in response to changes in the
frequencies and/or deflection velocities and accelerations detected. As Dusenbery
explains, two types of constraints influence this evolution: the history of previous
evolution through genetic encoding, and the physical-chemical laws that all
systems, animate or inanimate, must obey. We note that the first constraint
evolves with time while the second has been fixed since the beginning of time. It
would advance understanding to determine how the fixed physical-chemical
constraints influence and guide evolutionary adaptation. We explore this problem
here for the case of arthropod filiform hairs.
1.2 Review of Earlier Work
This section summarizes some of the main experimental and numerical findings of
the earlier studies referred to above with emphasis on the trichobothria of spiders.
In the case of Cupiennius salei, the trichobothria appear in clusters of 2-30 hairs
ranging in length from I 00 to 1400 !liD and in base diameter from 5 to 15 !liD.
Aerodynamic drag is favored by the feathery structure of the hairs, which are
Joseph A. C. Humphrey et al.
earlier investigations, several authors have derived and applied physical models to
describe the behavior of filiform cuticular hairs responding to oscillatory
movements of the surrounding fluid medium in both terrestrial and aquatic
arthropods; see Fletcher (1978), Tautz (1979), Shimozawa and Kanou (1984),
Humphrey et al. (1993, 1997), Barth et al. (1993, 1995), Devarakonda et al.
(1996), Shimozawa, et al. (1998), and Barth (2000). The theoretical component of
that work is numerical in nature. It requires the judicious calculation and plotting
of numerous individual cases in order to elucidate the effects on hair maximum
angular deflection and velocity, and their corresponding resonance frequencies,
resulting from changes in hair diameter and length, the mechanical spring and
damping constants of the hair, and the medium density, viscosity, and velocity.
In spite of its accuracy, the numerical solution approach is not entirely
satisfactory. This is because it does not provide easily usable and interpretable
analytical formulas from which to derive generally applicable conclusions
concerning the expected performance or evolutionary adaptation of filiform hairs
as the result of small changes in hair properties or the environment. The purpose
of this study is to derive such formulas subject to simplifications that render the
mathematics tractable but which, nevertheless, retain the essential physics of the
problem and from which correct qualitative results can be obtained.
The combination of increased understanding and predictive capability allowed
by the present highly integrative analytical approach squarely addresses a major
challenge in sensory ecology explained elsewhere in this book by David
Dusenbery. In the case of arthropod filiform motion-sensing hairs it can be stated
as follows. Biomechanical and physiological studies clearly show that these hairs
are tuned to preferred frequencies (or frequency ranges) and require minimal
deflection, velocity, and acceleration thresholds to detect fluid medium-borne
deflection stimuli originating from other animals (mates, prey, and predators) and
the environment. It seems reasonable to assume that over evolutionary time
periods the hairs have adapted to selective pressures in response to changes in the
frequencies and/or deflection velocities and accelerations detected. As Dusenbery
explains, two types of constraints influence this evolution: the history of previous
evolution through genetic encoding, and the physical-chemical laws that all
systems, animate or inanimate, must obey. We note that the first constraint
evolves with time while the second has been fixed since the beginning of time. It
would advance understanding to determine how the fixed physical-chemical
constraints influence and guide evolutionary adaptation. We explore this problem
here for the case of arthropod filiform hairs.
1.2 Review of Earlier Work
This section summarizes some of the main experimental and numerical findings of
the earlier studies referred to above with emphasis on the trichobothria of spiders.
In the case of Cupiennius salei, the trichobothria appear in clusters of 2-30 hairs
ranging in length from I 00 to 1400 !liD and in base diameter from 5 to 15 !liD.
Aerodynamic drag is favored by the feathery structure of the hairs, which are