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First published online December 1, 2006
Journal of Experimental Biology 209, 4901-4907 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02593
Mechanics of nectar feeding in the orchid bee Euglossa imperialis: pressure, viscosity and flow
Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA
e-mail: bborrell{at}cal.berkeley.edu
Accepted 16 October 2006
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Summary |
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Key words: Apidae, Euglossini, foraging, energetics, biomechanics, tongue
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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;
Kingsolver and Daniel, 1995).
In many insect taxa, the fluid pump is formed from a muscular expansion of the
cibario-pharyngeal chamber (henceforth, cibarium) located in the anterior
region of the head (Snodgrass,
1993). As the airtight pump chamber expands via
contraction of pump dilator muscles, a pressure gradient develops along the
length of the proboscis. Because the external pressure of the atmosphere is
greater than the internal pressure of the pump, fluid is forced through the
feeding canal to fill the expanding pump chamber.
Butterflies, pollen wasps, long-tongued bee-flies and orchid bees are among
the nectar feeding insects that have independently evolved a purely suctorial
feeding mode (Borrell and Krenn,
2006). Because viscosity of floral nectars varies exponentially
with sucrose concentration and ranges over more than an order of magnitude
(Heyneman, 1983), a principal
goal of biomechanical studies has been to understand how viscosity influences
the dynamics of suction feeding (Daniel et
al., 1989; Josens and Farina,
2001; Kingsolver and Daniel,
1979; May, 1985;
Smith, 1979). An early model
of suction feeding assumed that butterflies produce a constant pressure drop
at all viscosities (Kingsolver and Daniel,
1979), and a modification of the Hagen-Poiseuille equation was
used to relate this pressure drop to the rate of nectar flow in the tapering
proboscis. Subsequently, May (May,
1985) falsified this model by measuring nectar intake rate
Q (m3 s-1) in two butterfly species, along with
the length L (m) and radius R (m) of the proboscis, in order
to calculate the pressure drop P (Pa):
 | (1) |
where viscosity µ (Pa s) is a function of sucrose concentration. The
pressure drop increased nonlinearly with sucrose concentration, suggesting a
complex relationship between fluid flow and the physiology of the suction pump
(May, 1985;
Pivnick and McNeil, 1985).
Indeed, an earlier study on the operation of the suction pump in the
blood-sucking bug Rhodnius prolixus demonstrated that at low
viscosities, flow rate departs from the linear dependence on viscosity
predicted by the Hagen-Poiseuille equation
(Smith, 1979). Smith
hypothesized that as the speed of pump contraction increases, the tension of
the muscle will be too low to produce a constant pressure drop
(Smith, 1979). In quantitative
terms, the inverse relationship between the speed of contraction V (m
s-1) and the amount of force developed by a muscle,
Fmuscle (N), is traditionally described by the Hill
equation (Hill, 1938):
 | (2) |
where T0 is the maximum isometric tension of the pump
dilator muscle (N), and Vmax is the maximum shortening
velocity (m s-1). By assuming an equivalence between the pressure
drop in the Hagen-Poiseuille equation and the pressure drop developed in the
cibarium, Daniel et al. (Daniel et al.,
1989) combined Eqn 1 and Eqn 2 to develop a general expression for
the mechanics of suction feeding:
 | (3) |
where Acib is the cross-sectional area of the cibarial
pump (m2). Energy intake rate during feeding,
Emax (W) is then:
 | (4) |
where e is the energy equivalent of nectar, 15.4 J
mg-1, S is sucrose concentration (% w/w), and 
is
nectar density (kg m-3). The Daniel et al. model
(Daniel et al. 1989) predicts
that energy intake rate will be maximized for all suction feeders drinking
nectars between 35-40% sucrose, but the concentration that maximizes the
mechanical power output of the suction pump depends on the configuration of
the nectar feeding system.
Although predictions of the Daniel et al. model
(Daniel et al., 1989) concur
with optima derived from laboratory feeding trials with butterflies
(Boggs, 1988;
May, 1985;
Pivnick and McNeil, 1985),
hawkmoths (Josens and Farina,
2001), orchid bees (Borrell,
2004), bee-flies (Kingsolver
and Daniel, 1995), and ants
(Paul and Roces, 2003), the
predicted relationship between the pressure drop produced in the cibarium and
fluid flow through the proboscis has never been experimentally validated
(Kingsolver and Daniel, 1995).
The relationship between pressure and flow depends crucially on values of
Vmax and T0, which are not easily
measured. Furthermore, a study with hawkmoths has demonstrated that nectar
intake rates depend on behavioral motivation: the sweetness of ingested
solutions influences intake rate independent of viscosity
(Josens and Farina, 2001).
Finally, a third challenge to linking pressure and flow in feeding mechanics
comes from the morphological diversity of the insect proboscis and the
difficulty in distilling morphology into two fixed parameters: radius and
length (Krenn et al., 2005).
In the present study, I used the orchid bee, Euglossa imperialis, to
test the hypothesis that the pressure drop increases with fluid viscosity
alone and that the maximum pressure drop is limited by ambient air
pressure.
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Materials and methods |
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Proboscis morphology
Digital photographs were taken of the proboscis components from three
Eg. imperialis. These images were scaled to a height of 1500 pixels
and the width of overlapping and non-overlapping components of the galeae and
labial palps were measured along their length. The sum of these widths
represents the outer circumference of the proboscis at a given distance, and
the overall radius was calculated by treating the total cross-section as a
circle. In order to estimate resistance to flow in a pipe with an annular
cross-section, the ratio k of the inner radius to the outer radius is
used to calculate a correction factor that can be multiplied by the radius in
the Hagen-Poiseuille equation:
 | (5) |
for Re<2000 (Bird et al.,
2002). Because the proboscis tapers towards the tip and the
resistance of pipes in series is additive, hydraulic resistance should be
calculated from the numerical integration of
Correctionxr4 from the proximal end of the
feeding tube to the distal end (Pivnick
and McNeil, 1985). For simplicity, I refer to the fourth root of
this value as the effective radius because it can be substituted for
r in Eqn 1 and Eqn 3.
A minimum effective radius was derived functionally by plotting viscosity versus the pressure drop (calculated from Eqn 1) for radii ranging from 0.02 mm to 0.06 mm. The viscosity at which nectar intake rate approaches zero corresponds to the maximum pressure that can be developed in the cibarium. By assuming that ambient pressure equals the limiting pressure drop, one may calculate a minimum estimate of the radius.
Feeding protocol
Experimental nectar solutions were placed in 200 µl micropipette tips
sealed at the small end using a drop of cyanoacrylate. Nectar intake rate was
then measured with either starved bees introduced to nectar solutions or from
previously trained bees freely visiting flowers. In short, the mass gain of
the bee (±1 mg) was divided by the time spent feeding
(Borrell, 2004). Volumetric
rate of nectar intake is mass intake rate divided by density of the sucrose
solution (Mathlouthi and Génotelle,
1995), and sucrose intake rate is mass intake rate multiplied by
sucrose concentration.
The temperature of the nectar solution was controlled between 29 and 31°C, by warming it before feeding trials using a 15 W halogen lamp. Ambient temperature could not be controlled, and only trials in which ambient temperature was within 2°C of the experimental nectar solution were included in these analyses.
Viscosity experiments
To independently test the effects of sweetness and viscosity on nectar
intake rates, low concentrations of tylose (Coquinex, Panama City, Panama), an
inert sugar, were used to augment fluid viscosity without significantly
affecting density or energy content. Artificial nectar solutions were prepared
using either laboratory grade or commercially available sucrose, distilled
water, and tylose (Josens and Farina,
2001). A Brookfield Desktop Viscometer (Middleboro, MA, USA) was
connected to a constant temperature water bath to measure the viscosity of
test solutions at 30°C. In the constant sucrose experiment, sucrose
content was held at 25%, while viscosity was increased to the equivalent of
35, 45, 55 and 65% sucrose. Viscosity of experimental solutions matched true
sucrose solutions (R2=0.999). In the constant viscosity
experiment, viscosity was held at the equivalent of 50% sucrose, nominally
10.21 mPa s, at five sucrose concentrations, 5%, 15%, 25%, 35% and 50%. For
pure sucrose feeding trials, 5%, 15%, 25%, 35%, 45%, 55%, 65% and 75%
solutions were prepared. The concentration of all solutions was checked with a
pocket refractometer before each trial.
Hypobaria experiments
To estimate the maximum pressure drop produced by Eg. imperialis,
nectar intake rates were measured as bees fed inside a vacuum chamber (Nalge
Nunc International, Rochester, NY, USA) under reduced ambient pressure. Rubber
housing connected the chamber to an AC powered pump and a series of three-way
valves were employed to switch between pump suction and ambient pressure.
Chamber pressure was monitored using a catheter-style transducer (Millar
Instruments, Houston, TX, USA), which was inserted through a small,
tight-fitting hole at the base of the chamber. The output of the pressure
transducer along with that of a thermistor thermometer were digitized at 10
samples s-1 with a 12 bit A-D converter (Vernier Instruments,
Beaverton, OR, USA).
At the start of each trial, artificial flowers were filled with either 25% or 45% sucrose solution. The 45% solution was selected as the high viscosity treatment because intake rates were high enough that they could be easily measured under reduced ambient pressure. Immediately after bees began to feed, data acquisition was initiated, the pump was switched on, the chamber was placed over the bee, and valves were slowly adjusted to a previously determined set point nominally lowering the pressure in the chamber to 80, 60, 50 or 40 kPa. The pressure reduction required 5-15 s to reach a stable final pressure. Control trials were conducted at ambient pressure (101 kPa) with the pump running but not connected to the chamber. Additional nectar intake rate measurements were made as bees fed from 15%, 35% and 55% sucrose solutions under reduced ambient pressure (40 kPa), but control trials were not conducted for these solutions.
Nectar feeding model
Morphological and kinematic data for orchid bees were used to parameterize
the Daniel et al. model (Daniel et al.,
1989), and the Hill constants Vmax and
T0 along with the cibarium height,
Hcib, were estimated by minimizing the sums-of-squares
error between the model and the nectar intake rate data. Radius and length of
the proboscis were held at 0.045 mm and 17.5 mm, respectively, as measured in
the present study. The maximum flow rate, 1.2 µl s-1, was
divided by the estimated pump frequency of 2.5 Hz to obtain a cibarium volume
of 0.48 µl. Cross-sectional area of the cibarium was calculated by dividing
the volume by the height.
The muscle parameters Vmax and T0
are each the products of two implicit parameters: Vmax is
the product of the length of the muscle and length-specific
Vmax (L s-1); T0
is the product of the maximum isometric stress of the muscle (kPa) and the
cross-sectional area of the pump-dilator muscle, Amuscle.
Length-specific Vmax tends to vary widely among animal
taxa from 1 to 20 L s-1
(Medler, 2002), although 5
L s-1 is probably the upper limit for the cibarium dilator
(Josephson, 1993). The maximum
isometric stress of muscle tends to be relatively conserved among taxa,
ranging from 5 to 12 kN m-2
(Medler, 2002). To avoid
redundant simulations, maximum isometric stress was fixed at 8 kPa
(Daniel et al., 1989) and
Lmuscle was fixed at 1 mm (twice the final estimate of
Hcib). A total of 250 simulations were performed where the
unknown parameters were varied as follows: Hcib
(0.0002-0.002 mm), Vmax (1-5 L s-1),
and Amuscle (0.5-0.9 mm2). The five models with
the lowest sums-of-squares error were examined for convergence.
All analyses and simulations were conducted in JMP (v. 4.04, SAS Institute, Cary, NC, USA) and Matlab (v. 7.1, MathWorks, Natick, MA, USA). Statistical tests were performed using analysis of variance (ANOVA), analysis of covariance (ANCOVA), and ordinary least-squares regressions. Error bars are presented as 95% confidence intervals (CI). Sample sizes varied with treatment but typically ranged from 5-10 individuals.
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Results |
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The maximum pressure drop recorded from freely foraging bees occurred at 65% sucrose. If the cibarial pump were able to produce an absolute vacuum under these conditions, then the mean radius would be 0.039±0.002 mm. Orchid bees have been recorded feeding or attempting to feed at 75% sucrose under laboratory conditions. Using this value as the maximum viscosity, then the minimum radius becomes 0.047 mm (Fig. 1).
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Viscosity experiments
Nectar intake rate declined nonlinearly with increasing sugar concentration
from a maximum of 1.2 µl s-1 to less than 0.1 µl
s-1 (Fig. 2). The
intake rate for starved bees was linearly related to intake rate measured from
freely foraging bees (R2=0.994,
F1,2=343.3, P=0.0029) with a slope of
1.39±0.08 and an intercept not significantly different from zero
(P=0.2801).
When sucrose concentration was held at 25%, nectar intake rate declined with increasing viscosity of tylose treatments (Fig. 3). Nectar intake rate declined with viscosity according to the power relationship: Q=-1.3 µ-0.64 (R2=0.890, F1,31=253.4, P<0.0001) When viscosity was held constant while sucrose concentration was varied from 5% to 50%, nectar intake rate remained constant (Fig. 3)
Hypobaria experiments
The mean pressure drop calculated for intake of 25% and 45% sucrose
solutions (Eqn 1) in the pressure chamber at ambient pressure (control) was
not significantly different than values recorded during typical laboratory
feeding trials (Fig. 4, ANOVA:
F1,56=1.244, P=0.2695). There was no interaction
between sucrose concentration and method (P=0.4517). Pressure drop
declined with decreasing sucrose concentration and reduced ambient pressure
(sucrose: F1,56=9.612, P=0.0030; pressure:
F1,56=27.06, P<0.0001). However, the
interaction effect between sucrose concentration and ambient pressure was not
significant (P=0.6387), suggesting that the pressure drop may not
vary with sucrose concentration.
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Suction feeding model
The sums-of-squares error was minimized when Hcib was
0.5 mm, Vmax was 4.5 L s-1 and
Amuscle was 0.5 mm2. Although a range of values
can lead to an good fit of the model, it was clear that
Vmax must be greater than 1 L s-1 in
order to be compatible with the data from either starved bees or trained bees.
The best fit of the model to the data is shown in
Fig. 5.
Using optimal model parameters, the simulation provided estimates of the pump characteristics of the cibarium. At zero pressure, the flow rate of the pump would be about 3.8 µl s-1. At zero flow, the maximum pressure drop is about 42 kPa (Fig. 5A). Mechanical power of the pump was calculated as nectar flow rate times the pressure drop and is about 1.7x10-5 W when pumping nectars from 5% to 35% sucrose, dropping to zero as concentration increases to 75% sucrose (Fig. 5B).
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).
These authors found that even when viscosity was held constant using tylose,
energy intake rate still peaked at 34% sucrose, suggesting that gustatory
input influences the dynamics of cibarial pumping in those insects. Honeybees
have been shown to respond independently to changes in viscosity and sweetness
during trophallactic (regurgitation) behavior
(Tezze and Farina, 1999), and
in nectar choice experiments Eg. imperialis discriminates among
constant sucrose solutions of variable viscosity (B. J. Borrell, unpublished
observation). Sensors on both the glossa and gut measure the sweetness and
quantity of ingested fluids allowing bees to monitor the profitability of
nectar resources (Blatt and Roces,
2002). It seems, however, that such behavioral assessments do not
influence cibarial pump contraction in Eg. imperialis. Indeed, if
foraging bees are attempting to maximize energy intake, then there is little
reason to feed at sub-maximal rates simply because resources are deemed
nonoptimal.
As has been previously noted
(Kingsolver and Daniel, 1995;
Smith, 1979), flow rate does
not exhibit the linear relationship with viscosity as predicted by the
Hagen-Poiseuille equation. Instead, when ingesting low viscosity solutions
with high frequency contractions of the cibarium, insects may not be producing
adequate force. Owing to the nonlinearity of the force-velocity relationship,
nectar viscosity ranges over nearly two orders of magnitude, but actual flow
rates exhibit a far smaller of a spread. If the radius of the proboscis varies
with flow rate or pressure (see below), then this interaction could prove to
be more complex.
Pressure and flow
The pressure drop appears to be limited by ambient air pressure, but it is
unclear whether it actually increases with viscosity. At all sucrose
concentrations nectar intake rate was significantly affected by a reduction in
ambient pressure. In fact, the relative effect of the pressure reduction was
similar for 15%, 25%, 35% and 45% solutions, and the relative reduction in
nectar intake rate was directly proportional to the relative reduction in
ambient pressure.
Flow through a rigid tube depends on the pressure difference along the
length of the tube, not the absolute pressure at either end of the tube
(Vogel, 1994). Consequently,
nectar intake rate and the associated pressure drop should be independent of a
reduction in ambient pressure until the absolute pressure inside the cibarium
approaches the vapor pressure of the ingested fluid (i.e. a perfect vacuum),
or some negative value if orchid bees are able to avoid fluid cavitation
(Bennet-Clark, 1963).
Calculations using the Hagen-Poiseuille equation indicate that the pressure
drop for bees feeding on a 25% sucrose solution should be about 15 kPa. If the
ambient pressure is lowered to 43 kPa, then the absolute pressure inside the
cibarium will be 28 kPa, meaning that cavitation should not be an issue. Even
if the instantaneous pressure drop peaks at twice the average value, the
absolute pressure inside the cibarium will still be 13 kPa. Because backflow
was not taken into account, these calculations are likely to be underestimates
of the true pressure drop. Quantitative errors, however, cannot explain why
intake of nectar solutions declined by the same fraction at all
concentrations.
The present experiments are more likely to reflect biomechanical effects on
the pumping apparatus rather than physiological effects of limiting oxygen
availability. Post-flight resting metabolic rate of honeybees exhibits a
slight increase as ambient pressure is reduced from 101 kPa to 24 kPa
(Withers, 1981). However,
resting metabolic rate is still less than 1/40th of flight metabolic rate in
free flight, and even flight metabolic rate is not affected by a reduction in
oxygen partial pressure down to 10 kPa, the equivalent of 60 kPa total
pressure (Joos et al., 1997).
The power requirements of the suction pump are only a small fraction of the
power requirements of flight.
Radial expansion: a hypothesis
One possible explanation for the results from the pressure reduction
experiment is that the euglossine proboscis functions as a `collapsible' tube.
The butterfly proboscis is sealed via series of hook-shaped
structures and overlapping cubicula plates, forming a food canal that is
permanently interlocked (Hepburn,
1971). The circumferential stress imposed by an atmosphere of
pressure is insufficient to trigger collapse of the proboscis
(Kingsolver and Daniel, 1979).
By contrast, in long-tongued bees, the food canal is sealed via a
series of tongue-and-groove junctions that permit proboscis components to
slide with respect to each other and even disconnect
(Borrell and Krenn, 2006). The
proboscis is extended via contraction of muscles at its base in
addition to an increase in haemolymph pressure within proboscis components,
particularly the glossa (Paul et al.,
2002). It is unclear how the euglossine proboscis, which is
normally in a flattened configuration, remains open during feeding. Some
critical pressure must be developed before flow is initiated, a phenomenon
that is apparent during the first moments after the proboscis has contacted a
nectar solution. Bees attempting to feed from 75% sucrose solutions often
extend their tongues repeatedly before giving up, suggesting that flow rates
were insufficient for proboscis expansion. During pressure reduction
experiments, bees feeding on all concentrations occasionally retracted their
tongues as ambient pressure fell below 50 kPa, re-extending them when ambient
pressure rose again. The critical pressure required for opening of the feeding
canal must be greater than the pressure drop required during steady flow. Once
fluid is flowing inside the proboscis, the feeding canal may still be
susceptible to partial or total collapse if the external pressure is
sufficient to overcome supporting forces. In collapsed, flexible tubes, either
the flow rate can become pressure drop independent or the pressure drop can be
flow rate independent (Bertram,
1995). These nonlinear phenomena, which are common in the
circulatory system, may be important if fluid forces counterbalance structural
properties of the proboscis during feeding.
Because of the high degree of overlap of proboscis components and the low
Reynolds number of the system, the proboscis will tend to expand in response
to a pressure drop (Vogel,
1994). The hooks on the galeae and labial palps set a minimum
radius of the proboscis, but the maximum radius depends on the degree of
overlap required to maintain an airtight seal. Although the morphological
estimate of the radius was in good agreement with the functionally derived
estimate, small differences in radius can have a large effect on the pressure
drop. For instance, a 10% decrease in overlap will cut pipe resistance in
half, thereby halving the required pressure drop for a given flow rate. Radial
expansion may even prevent proboscis collapse by maintaining a constant
pressure gradient independent of flow rate. Radial expansion would also
explain why flow rate declined with ambient pressure at all sucrose
concentrations.
I performed a series of simulations to see whether a variable radius could be compatible with both the empirical flow data and the suction feeding model. Proboscis radius was set to either increase linearly with sucrose concentration from 0.04 mm to 0.054 mm, increase exponentially with sucrose concentration from 0.04 mm to 0.058 mm, or decrease linearly from 0.054 to 0.04 mm with sucrose concentration. In these three simulations, the optimal nectar concentration always matched the empirical data (30-38% sucrose). Not surprisingly, however, the match of the calculated pressure drop to the model depended strongly on chosen values for the Hill parameters. For the case of the linearly increasing radius, the pressure drop will remain nearly constant at all concentrations, and the simulation is capable of replicating these results with reasonable values for the Hill parameters. This analysis shows that optimal nectar concentrations will be largely independent of radial expansion, but the pressure drop cannot be predicted without more detailed knowledge of the physiological properties of the pump dilator muscle or the dependence of radial expansion on flow rate.
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Acknowledgments |
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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