jf. Exp. Biol. (1965), 43, 257-269
With 4 text-figures
Printed in Great Britain
257
REGULATION OF TRANSPIRATION IN THE CLOVER MITE
BRYOBIA PRAETIOSA KOCH (ACARINA: TETRANYCHIDAE)
BY PAUL W. WINSTON AND V. EUGENE NELSON*
University of Colorado, U.S.A.
(Received 22 February 1965)
INTRODUCTION
The rigorous limitation of evaporative water loss is essential for the survival of
small arthropods normally exposed to low humidities. Such animals, particularly the
Acarina, contain limited amounts of water that can be lost and a relatively large
surface area from which to lose it. Evaporation is limited primarily by physical
barriers in the exoskeleton, the chitin-protein complex of the endo- and exocuticles
(Beament, 1961) and a thin surface layer of oriented lipid molecules (Wigglesworth,
1945; Beament, 1945). The intact lipid layer provides a high degree of waterproofing
but is characterized by loss of effectiveness above critical temperatures or upon
treatment with solvents (Beament, 1959).
In addition, active mechanisms in the respiratory system and within the living
portions of the cuticle may further reduce and control water loss (Edney, 1957). Of
these, control of spiracular opening has been shown by many workers to be highly
effective for water conservation in insects. Mellanby (1935) greatly increased water
loss in Tenebrio by preventing spiracular closure with excess CO2, while it has recently
been shown that the degree of opening of these organs is influenced directly by
humidity in tsetse flies (Bursell, 1957) and by water balance in dragon flies (Miller,
1964). Browning (1954) and McEnroe (1961) showed the importance of the mechanism
to ixodid ticks and to the spider mite Tetranychus telarius.
Another active principle, a restrictive mechanism in the general body cuticle, seems
to be of secondary significance in most insects (Wigglesworth, 1945), but it was shown
in ticks (Lees, 1946; Browning, 1954) to be equally as important as respiratory control.
It has been called 'active retention' by Edney (1957) and others; and Lees' (1947)
hypothesis that the epidermal cells are able to secrete water inward seems to offer the
best explanation, although it has not yet been experimentally confirmed. As the result
of this proposal, Edney (1957) and Beament (1961) suggested that the mechanism
might be one which would result in the uptake of atmospheric water at high humidities.
It would remove the need for a different mechanism to explain this puzzling phenomenon which is known to occur in a limited number of arthropods, e.g. T. molitor
(Buxton, 1930) and many ticks (Lees, 1946).
These active mechanisms in the cuticle and in the respiratory system may also
contribute to at least one of the two forms of regulation that are apparent in the water
balance of some hardy insects and arachnids. Certain insects are able to regulate
their percentage of body water, maintaining it at essentially constant levels both with
• Present address: Department of Entomology, University of Kansas, Lawerance, Kansas, U.S.A.
17
Exp. Biol. 43, a
258
PAUL W. WINSTON AND V. EUGENE NELSON
time and over a wide range of humidities, e.g. T. molitor (Buxton, 1930). In addition
a very few animals, e.g. nymphs of the grasshopper Chortaphaga viridifasciata
(Ludwig, 1937) and a locust Oedipha coeruliens (Jakovlev & Kriiger, 1953), have been
shown to regulate their water loss, keeping it at nearly constant rates over a substantial
portion of the humidity range. The only specific studies on the mechanisms by which
these regulatory functions are accomplished have been on the first type in which it has
been shown, especially in Tribolium confusum and Dermestes vulpinus (Fraenkel &
Blewett, 1944), that metabolism, and thereby the production of metabolic water, is
adjusted to differences in humidity. More food is consumed in dry air than in moist
and the extra water produced is enough to maintain the water level in the body. Each
of these controls is such as to keep an internal variable at an essentially constant level
in the face of changing external conditions, thus conforming to the usage of the term
'regulation' by Prosser & Brown (1961).
The clover mite Bryobia praetiosa is active on warm walls and tree trunks from late
September to early June in Colorado, and the ability of these very small animals
(< 1 mm.) to thrive at the low humidities commonly measured on such exposed
surfaces prompted studies on their humidity tolerances and behaviour (Winston,
1963 a). These have been followed in the present work by the measurement of water
loss in both living and dead mites over a wide range of humidities. Because an
active mechanism was indicated by the earlier studies, it could be expected that dead
mites would show a higher rate of loss than living ones throughout the humidity range,
Furthermore, it seemed likely that a comparison of weight changes in living mites at
various humidities would reveal the existence of mechanisms for the control and
restriction of water loss and for the uptake of atmospheric water in different portions
of the humidity range. Since preliminary studies on water loss in living mites
(Winston, 1964) indicated the ability to regulate over a substantial part of the range,
the nature and location of the underlying mechanisms was made the primary objective
of this investigation.
MATERIALS AND METHODS
The mite used in this study is the Bryobia praetiosa Koch of Anderson & Morgan
(1958), and a brief description of its life-cycle in Colorado appears in Winston (19636).
For most of the winter and spring, a plentiful supply of these parthenogenetic animals
from a natural population was maintained on bean plants growing on flats in the
windows of the Laboratory. A 'conditioning' or pre-experimental treatment was
adopted to assure a more uniform experimental animal than could be obtained directly
from a wild population. Adult mites were taken from the leaves rather than from the
windows, ensuring that the majority had fed for some time. They were then held
without food or water for 48 hr. at 29% R.H. and 25° C. This allowed ample time for
defecation of the copious, watery faeces and for most of the egg-laying. No faeces
were found after tests that had been preceded by this conditioning and there were
usually fewer than two eggs per mite.
Groups of sixteen mites were lightly anaesthetized, weighed as a group, and placed
in screen-topped vials for exposure to air of a specified humidity. This treatment was
carried out in a water-bath at 25 ±0-5° C. in small chambers in which the humidity
was controlled by saturated salts as described by Winston & Bates (i960). The mites
Regulation of transpiration in clover mite
259
were exposed to humidities of o, 12, 29, 43, 52, 62, 76, 85, and 93%; none higher was
used because the mites easily drown in condensed droplets and because their activity
is greatly reduced at very high humidities. Because all the work was done at one
temperature, relative humidity (R.H.) and saturation deficit are equivalent, and the
former term will be used throughout this paper. After 24 hr., later 18, the mites were
again anaesthetized, weighed, dried for 24 hr. at 900 C , and weighed again. These
treatment periods were long enough to result in measurable weight-changes at high
humidities, but short enough to reduce mortality to a minimum at the low. No
differences in the calculated rates of loss were noted between the two testing periods.
The water and dry-matter content of both feeding and conditioned mites were
measured at intervals to check for any seasonal effect on these variables and none was
found. Feeding animals were removed from the plants, anaesthetized, weighed and
dried to constant weight. The conditioned animals were treated similarly except for the
48 hr. starvation period at 29% R.H. and 250 C. prior to weighing.
A correction factor of 1-5 /jg. each was obtained for the few eggs laid during the
tests by calculating the volume of an egg from the diameter and assuming the density
to be about 1-02. Measurements of many eggs with an ocular micrometer showed
them to be of nearly uniform size, so a reasonably accurate correction could be made
for the loss of weight by counting the number of eggs laid. For the dry weights a
correction of 0-4 fig. per egg was used. These factors were multiplied by the number
of eggs laid per mite in each group and the result added to the average weight. Any
water loss resulting from the process of oviposition was so slight as to be undetectable
with the methods employed.
Ether was used instead of other standard anaesthetics throughout these experiments
because its ill-effects were much less than any others tested. The possible effect of this
lipid solvent on the water-proofing layer was of some concern to us, but tests indicated
that stronger doses of the anaesthetic than that used in practice did not increase
mortality even in dry air.
Water loss in dead mites was measured after they had been killed by exposure for
2 hr. to hydrogen cyanide fumes in a water-saturated atmosphere. The greatly increased
rate of loss at death made it necessary to expose these animals for only 4 hr., to prevent
low water content and decay from influencing the results.
For measurement of the effects of high concentrations of CO2 on weight loss the
mites were exposed to atmospheres containing 10% of the gas at various humidities.
An approximation to the lowest concentration which would produce a maximum effect
was obtained by determining the water loss in 5, 10, and 15% mixtures of the gas in
air at one humidity. The two higher concentrations produced essentially the same loss
while at 5% it was significantly lower; the 10% mixture was therefore used throughout
the tests. No anaesthetic effect was observed at these concentrations. Humidity in
this series of experiments was controlled by appropriate concentrations of sulphuric
acid (Solomon, 1951) because, unlike many of the saturated salts, these solutions
absorb very little CO2.
A Cahn Electrobalance, model Mio, was modified to obtain a sensitivity of less
than 1 fig. with a range of 1 mg. Changes in weight of individual mites were quite
small, and to obtain greater accuracy we weighed them in groups of sixteen and
calculated the average loss per mite. Standard weights approximating the weight of
17-2
260
PAUL W. WINSTON AND V. EUGENE NELSON
a group of mites were weighed frequently to check for drift in the balance circuit.
Single adult mites averaged 36±n/<g. in weight; and, to counteract the wide
variations found, groups were made up of animals as close to the same size as possible.
Standard deviations and standard errors of the means of all values were calculated
by the methods of Arkin & Colton (1955) and the significance of the difference between
means of adjacent values was tested by the use of the t-test of Fisher (1950).
In these experiments weight loss was determined on 560 groups of 16 mites, about
9000 individuals. Each group was weighed at least twice, and most three times, to
obtain an initial weight, a final weight, and a final dry weight.
RESULTS
Water content
The water content of the mites was calculated as a percentage of the final total
weight and plotted against R.H. in Fig. 1. The freshly fed animals have a much higher
water content than that of conditioned ones, a result to be expected from the large
amount of water in the plant cells on which they feed. Much of this water is lost
rapidly soon after feeding, but the remaining water is only slightly reduced during
78
r
74
Feeding mites
20
40
60
Relative humidity
80
100
Fig. 1. The water content of untreated mites and of mites treated with 10% CO^ expressed
as a percentage of the final weight, was plotted against the various humidities to which they
were exposed. As freshly fed mites were not exposed to any specific humidities their average
water content is indicated by the dotted lino. Vertical lines represent the standard errors of the
means.
Regulation of transpiration in clover mite
261
the subsequent treatment periods of 18 or 24 hr., indicating a form of regulation in
relation to time. It can also be seen that there is very little effect of R.H. on the water
content of control mites throughout the humidity range. They are thus able to regulate
the percentage of body water despite different rates of water loss over a wide range of
humidities.
The water content of CO2-treated mites falls below that of the controls (Fig. 1) and
is essentially proportional to the R.H. AS the dry weights are the same in both groups,
the reduction in water is probably due to loss through the opened spiracles, which
would indicate that the mechanism for regulation is based in the control of these
structures. In addition, the differences in rate of loss of solids in control mites were
so slight (Fig. 4) that it does not appear possible that maintenance of a constant water
content could be the result of adjustments in metabolic rate in response to water loss.
This problem is really tangential to the present one of regulation of water loss, however,
and further study must be deferred for the present.
Water loss
Though the object of this study was to determine water loss in groups of mites, it
was obviously possible to obtain only the loss in total weight. The final weight was
easily resolved into solids and water by obtaining the dry weight and then subtracting
this value from the total to get the water. For the initial weight, however, these had
to be calculated by using the percentage of water and of solids in the conditioned
mites. Water and dry-weight losses were then obtained by subtracting the final from
the initial values. The results of these calculations are plotted in Fig, 4 and show that
water loss follows total weight loss quite faithfully, and that the latter is not affected
by the slight changes in dry weight. We will, therefore, use both terms interchangeably
in the remainder of this paper even though the values presented will actually be of
total weight loss. These animals vary so much in size that only relativecomparisons are
possible, and because of this we have expressed weight changes as percentages of the
initial total weights, in percentage per hour per mite.
There are four avenues for the escape of water in Bryobia: urine and faeces,
oviposition, cuticular transpiration, and spiracular loss. In our work the 48 hr.
conditioning period eliminated urine, faeces, and most of oviposition as factors; and
only water loss through the cuticle and through the spiracles remained to account for
that which was measured.
The nature of the barriers to transpiration from these two areas was studied by
the measurement of water loss in living mites, in those killed by HCN gas, and in
others killed in chloroform vapour (Fig. 2). As the lowest rates of loss were from
living mites, rates above these can be considered due to the removal or disruption of
one or more of these barriers. By far the highest rates of loss were from the chloroformtreated animals, demonstrating changes in the lipid waterproofing layer. Gibbs &
Morrison (1959) recently showed the same kind of layer for another tetranychid, the
spider mite Tetranyckus telarius. In both this species and Bryobia the cuticle underlying the wax layer is so thin that it is difficult to see how it could be much of a
barrier, but Beament (1961) has shown that, though very permeable, such a layer
would reduce evaporation considerably below that from a free-water surface. It can
be seen that the passive barriers provide the major reduction of evaporation, but the
262
PAUL W. WINSTON AND V. EUGENE NELSON
substantially higher rates of loss in dead mites over those in living ones suggest the
presence of an active mechanism which further restricts water loss.
The respiratory system is considered to be a primary site of evaporative water loss
in many terrestrial arthropods (Wigglesworth, 1953), and the relatively simple technique needed to demonstrate this offered an obvious starting-point for the problem
70 r
Dead mites-chloroform treated
10 -
20
•40
60
80
100
Relative humidity
Fig. 2. The average loss in weight in percentage per hour per mite was measured at various
humidities for mites killed in chloroform vapour and in cyanide fumes (lower line). Vertical
lines represent the standard error of the means.
in Bryobia. Since CO2 at concentrations of 5-10% is known to maintain the spiracles
in an open position in most arthropods (Wigglesworth, 1953) including ticks (Browning,
1954), the rates of loss of CO8-treated and untreated mites were compared (Fig, 3).
Tests atfivehumidities indicated that a CO2-sensitive mechanism, presumably control
of the respiratory openings, would account for about half the difference in the rate of
water loss between live, untreated animals and dead ones; thus about half the loss is
considered to be through the spiracles and half through the cuticle. Lees (1946) and
Browning (1954) found a similar relationship in ticks.
There is no doubt of the existence of organs acting as spiracles in clover mites and
many other Acarina, but little is known of their behaviour and controls (Winston,
Regulation of transpiration in clover mite
263
1964). Bryobia is usually very active in dry air and one would expect this to result in
high rates of water loss through necessarily opened spiracles. There is higher loss at
0% R.H. than in more humid air, but it is so small that these animals can survive for
relatively long periods under dry conditions. It must be that they, like the tsetse fly
24-r
20
40
60
Relative humidity
100
Fig. 3. The average loss in weight in percentage per hour per mite was measured at various
humidities for those killed in cyanide fumes, for living mites treated with 10% CO,, and for
untreated animals. Vertical lines represent the standard errors of the means.
{Bursell, 1957), can obtain enough oxygen for activity through nearly closed spiracles
and thus make gas exchange subordinate to control of water loss in these organs. It
has been reported that the respiratory organs of spider mites are exposed to the air to
a greater or lesser extent in response to changing levels of activity (Blauvelt, 1945),
humidity, and water content (McEnroe, 1961). Observations in this laboratory have
failed, however, to show any visible positional changes of these organs in Bryobia that
would indicate a control function. They have been seen to be exposed only when the
mites were actively feeding.
Since the differences between living and killed mites cannot be explained wholly
on the basis of a CO2-sensitive respiratory mechanism an additional one is indicated.
PAUL W. WINSTON AND V. EUGENE NELSON
264
This is most likely some form of active retention of water by the general body cuticle,
though Beament's (1961) suggestion of a rapid change in the cuticle at death still
remains a remote possibility.
The better to show important deflexions in the curves for water loss, the rates for
living mites are given on a larger scale in Fig. 4. The general tendency of the curve,
Total weight loss
\
20
40
60
80
100
Relative humidity
Fig. 4. The average loss in weight in percentage per hour per mite was measured at various
humidities for untreated (control) mites (solid line). Calculated values for water loss and for
loss of solids are shown by the dotted lines. Vertical lines represent the standard errors of the
means.
as shown by the broken line between 0% and 85% R.H., indicates an overall inverse
relationship between water loss and R.H. The deviation from this straight line between
53% and 85%, however, indicates that the mites are able to modify the relationship
in this part of the range. Between these humidities, loss is maintained at a nearly
constant rate, showing that the mites can regulate water loss in the face of considerable
differences in the evaporating power of the air.
Despite the slight influence of humidity in the zone of regulation, the differences
between adjacent means were found to be not significant to the 0-05 level, though that
between the two extremes was close to it. At humidities above and below this region
Regulation of transpiration in clover mite
265
the differences between adjacent means were found to be highly significant, at least to
the 001 level. It is to be noted that cyanide-treated mites do not exhibit this plateau,
and so it can be assumed to be the result of an active process. The sharp breaks at
either end of this zone of regulation are indications that some distinct changes in the
active process take place between 85 and 93% and between 43 and 53% R.H.
In contrast, the greater slope of the line between 43 and 0% shows that loss depends
more on the humidity, but this slope is still much less than was found in dead mites.
Thus the sudden increase in rate of loss from 53 to 43% is not to a condition which is
completely dependent on the evaporating power of the air. Instead, there is evidence
of an active mechanism functioning at low humidities that restricts, but does not
regulate, water loss.
The apparently insignificant effect of R.H. on dry-weight losses (Fig. 4) does not
support the hypothesis that energy is expended for the retention of water, as any
change in respiratory activity should produce a corresponding change in the loss of
solids. Other evidence for an active principle is too strong to be ignored, however.
Furthermore, it is quite probable that the amount of energy used is too small to be
shown by measuring the very slight changes in solid matter in these animals.
The mechanism for this regulation could be based either in the respiratory system
or in an active component of the cuticle. If it were in the cuticle the regulatory pattern
should still be evident after CO2 treatment, but if it were in the spiracles, which
presumably were wide open, the line should show inverse proportionality to the
humidity over its entire length. It is evident that the line for average rates of loss in
the treated mites (Fig. 3) shows the same deviation as that for the control animals,
indicating a zone of regulation. This is good evidence that the mechanism is indeed a
part of the cuticular activity rather than being based in the respiratory system. Treated
animals showed a much greater water loss than did the controls, but this is to be
expected when the spiracles were kept open. Moreover, if this were a spiracular
mechanism, one would not anticipate the sharp breaks at either end of the zone of
regulation found in untreated mites. Spiracular control would probably require
hygroreceptors of some sort, and such abrupt changes are not characteristic of receptors
in general.
DISCUSSION
The restriction of water loss by active work of some mechanism in the cuticle,
possibly the epidermal cells, has been shown to be an important factor in only a few
other animals, notably in several species of both ixodid and argasid ticks (Lees, 1946).
This mechanism is thought to be of only slight importance in most insects (Wiggleworth, 1945), and it may be that it is more significant in the Acarina because of the
relatively greater surface area for water loss in these small animals. Little has been
done on the very small hardy insects, however, and this approach might lead to other
ideas on the subject.
It would be convenient to assume that the active cuticular restriction of loss below
50% R.H. and the regulation above it are part of the same mechanism, if for no other
reason than simplicity. There is little or no evidence for either one mechanism or two
at this time, and a second ought not to be assumed if it is not necessary. This can be
better justified by postulating that above 50% R.H. the mechanism can regulate water
266
PAUL W.
WINSTON AND V. EUGENE NELSON
loss, causing the deviation from proportionality to humidity that we have shown. In
all humidities below this zone of regulation, though, it would be working at the same
rate, its full capacity. Hence, differences would be due to variations in the drying
power of the air. The mechanism would only be restricting transpiration in the lower
humidities.
The mechanism by which regulation and restriction of water loss are accomplished
is unknown, but Edney's (1957) and Beament's (1961) suggestions, that it might be the
same as the one that produces active uptake of atmospheric water at high humidities
in some arthropods, should be considered. Beament (1954) hypothesized that uptake
is based on the active transport of water; and, to follow this same line of thought,
regulation and restriction would then be based on active transport. If this were so, one
would expect a sharp change such as that between 43% and 53% R.H., indicating a
breakdown of the mechanism at lower vapour pressures. It would mean that the
regulation of transpiration at humidities below 50% R.H. requires more energy than
is available to the system, and the rate of loss rises at 43 % to become proportional to
the evaporating power of the air. Such an abrupt change between these two humidities
is also typical of several other aspects of the humidity relations of B. praetiosa,
especially of survival (Winston, 1963 a); and Edney (1945) and Beament, NobleNesbitt & Watson (1964) found that the lower limits for uptake were near 50% R.H. in
prepupae of rat fleas and in the common firebrat. It is possible that these changes are
the result of the breakdown of a mechanism common to many species.
Though regulation is apparent, we have been unable to demonstrate active uptake
in the clover mite by any of the techniques used successfully on other acarines and
insects. One might expect to find it in this mite, though it is the first tetranychid to be
studied in this way, because the other Acarina which have been properly tested have
shown the phenomenon quite readily—for example, ticks of several species (Lees, 1946;
Belozerov & Seravin, i960), grain mites (Kniille, 1962; Solomon, 1962), spiny rat
mites (Wharton & Kanungo, 1962) and rabbit ticks (Camin, 1963). None of these is
as well adapted to dry air as are clover mites, however, except for some of the argasid
ticks, and it may be that uptake is not present in some hardy forms such as Bryobia.
Water loss is slow enough to make it possible for them to replenish their water
supply by drinking or feeding well before their water content has dropped to acute
levels, and uptake would not be of any particular survival value. Thus the function
may have either been lost completely or masked so that the usual techniques would not
reveal it.
To show that there is regulation of water loss one must expose the experimental
animals to a wide range of humidities, and very few workers have used this approach.
Of these, only Ludwig (1937) and Jakovlev & Kriiger (1953), working with two
orthopterans, were able to demonstrate regulation. It is probably only because so few
animals have been tested in this way that the regulation of transpiration is not more
commonly known among terrestrial arthropods.
Such a regulatory system would be a major factor in the maintenance of a stable
internal environment over a major portion of the humidity range. Even though many
arthropods are apparently able to withstand wide variations in their internal medium,
there must be an advantage to having as much constancy of the blood as possible. The
development of homeostatic mechanisms has usually brought advances for the
Regulation of transpiration in clover mite
267
fortunate species that had them, and, in general, fluctuating humidities represent
much more of a stress factor for small animals than for large ones. This ability to
control and restrict evaporative water loss in all but the highest humidities, coupled
with broad temperature tolerances (Anderson & Morgan, 1958), may be the primary
factors that make it possible for these mites to be almost the only arthropods active
in numbers above the soil surface during the winter months when competition and
predation are essentially nil. They carry on their life-cycle in normal fashion during
a long period of the year in which daytime humidities in this region may range down
to 5% or below and in which temperatures commonly vary between 250 and — io° C.
They are to be found on sun-warmed walls all during this period, limited in their
activity by low light intensities and extremely low temperatures.
The humidities encountered by this mite over most of its distribution in the North
and South Temperate Zones (Morgan, i960) are almost always within or above the
zone of regulation. Presumably, they evolved under such conditions where life would
seem to be easiest for them from the standpoint of humidity. There is no question,
though, from the data presented in this paper, that the mites can cope without difficulty
with the occasional periods below 50% R.H. which would be experienced. Drier
areas, such as this one at Boulder, Colorado, where the humidity during the day is
almost always below the zone of regulation and the evaporating power of the air is
high, represent nearly marginal habitats that must tax their control mechanisms
considerably. Nevertheless, they are able to thrive under such conditions.
SUMMARY
1. Groups of sixteen mites were starved for 48 hr. at 29% R.H. and then exposed
for 18 or 24 hr. to one of nine humidities, from 0% to 93% R.H. They were weighed
as groups before and after the treatments to determine total weight loss. Dry weights
were also obtained to find water content and for the calculation of water and dry-weight
losses. All work was done at 250 C.
2. Water loss, considered equivalent to total weight loss, was also obtained under
several other conditions; and at all humidities it was found to be highest in mites
killed in chloroform vapour while it was considerably less in those killed in HCN gas.
Mites with spiracles kept open by air with 10% CO2 lost weight at rates midway
between those for dead and those for living animals.
3. There is apparent regulation of body-water content as a percentage of the final
weight over the whole humidity range.
4. Water loss is restricted by a CO2-sensitive mechanism, presumably the spiracles.
5. Active regulation of water loss by a cuticular mechanim was shown between
53% and 85% R.H., while at humidities below this, loss was actively restricted but not
regulated.
6. It is postulated that both restriction and regulation are brought about by the
same mechanism, which might be a form of active transport.
7. Uptake of water from unsaturated air was not found with any of the methods
used.
8. Regulation such as was found here would help to maintain the internal environment of these mites as nearly constant as possible in the face of fluctuating humidities.
268
PAUL W.
WINSTON AND V.
EUGENE NELSON
The authors wish to acknowledge support of this research by the University of
Colorado and by Research Grant no. G14517 to the senior author from the National
Science Foundation.
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