SHORT
COMMUNICATIONS
Evaluating Models of Crop Emptying in Hummingbirds
F. REED HAINSWORTH
Departmentof Biology,Syracuse
University,Syracuse,
New York 13244-1270USA
Hummingbirdshave receivedconsiderableattention in studiesof feeding and energy regulation becauseof their smallsize, frequentfeeding,and their
use of energy-richsugarsolutions(e.g. Diamond et
al. 1986,Ewald and Carpenter 1978,Hainsworth 1981).
They storenectarin a crop,and this internal reservoir
suppliesenergy betweenforagingbouts(Hainsworth
and Wolf 1972,Karasovet al. 1986).The rate of crop
emptying, therefore,should influenceforaging frequency (Karasovet al. 1986, Wolf and Hainsworth
1977).Becausethe crop is a major interfacebetween
feeding input of energy and outflow for energy use,
there has been interest in the determinantsof crop-
emptyingrates(DeBenedictis
et al. 1978,Hainsworth
1981, Hainsworth et al. 1981, Diamond et al. 1986,
Karasov et al. 1986).
Karasovet 02. (1986) report measurementsof apparent crop volumes for seven Rufous Hummingbirds (Selasphorus
rufus)at various times after they
were fed 100/•1of 0.585 molal sucrose.Approximately
26/•1remainedin the cropfollowing prolongedtimes
after feeding, so subtracting26/•1 from apparentvolumes adjustedvolumesrelative to the amount fed.
The authorsused a negative exponential and a linear
regressionto characterizethe pattern of crop emptying. A negativeexponentialregressiongavehigher
correlation coefficients for 5 of the 7 birds (Karasov
et al. 1986).
et al. 1984).An obviousappeal for this model is that
it producesdecreasingratesof emptying with time,
but there are other models with this feature.
Hopkins (1966) suggestedan alternative to a negative exponential model to describestomachemptying in humans.A betterdescriptionrelatedthe square
root of volume to time. This could be explained functionally with the law of Laplace(Tension = Pressure
x Radius), where circumferential tension in the wall
of the emptying structureis proportionalto the radius
of the compartment(Hopkins 1966).If outflow is proportional to tension and the structureapproximates
an elastic cylinder, radius would be proportional to
the squareroot of volumeand volumewould change
asa negativequadraticfunction of time. In this model,
rates of emptying decreaseover time with a functional basisin how elasticstructuresempty.
A fourth model, also basedon the law of Laplace,
relates the cube root of volume
to time. This would
apply to the casewhere the emptying structureapproximatesan elasticsphere.
A fifth model
relates the inverse
of volume
to time
(hyperbolicfunction)basedon empiricaldescription
of stomachemptying, and the sixthmodel relatesthe
inverse
cube root of volume
to time based on a com-
bination of Laplace's law, Hooke's law, and Poiseuille'sequationapplied to stomachs(Stubbs1977).
I usedapparentvolumesminus 26/•1(from Karasov
et al. 1986)to comparethesemodelswith linear least
The interpretations for these regressionsare inadequatelytested,and there are other modelsthat squaresregressions
(Fig. 1). The cuberootregression
may describecropfunction.Sixalternativemodelscan gavenearlythe samecalculated
volumesasthesquare
be comparedbasedeitheron studieswith otherspecies root regression. The hyperbolic regression is not
or physical features of elastic emptying structures
(Smith et al. 1984, Stubbs 1977). The models involve
lOO
(1) a linear, (2) an exponential, (3) a squareroot, (4)
a cube root, (5) a hyperbolic, or (6) an inverse cube
root changein volume with time.
A linear model describesstomachemptying of glucoseloads in monkeys(McHugh and Moran 1979)
and laboratoryrats(McCannand Stricker1986).Negative feedback mechanismshave been suggestedto
producethis pattern from detectionof fluid properties in the duodenumwith subsequentadjustmentof
stomachemptying (Hunt 1983,McHugh and Moran
80
20
0
1979).
A negativeexponentialmodel, where the logarithm of volume decreaseslinearly with time, was
used to describeemptying in a variety of animals
where the rateof emptyingdecreased
with time (Sibly 1981).This pattern appearswhen feedbackmechanismshave a minimum impacton emptying(Smith
724
Minutes
Fig. 1. Crop volume as a function of time after
feeding 100/d of 0.585 molal sucrose(data from Karasov et al. 1986). Lines are shown for (1) linear, (2)
squareroot,(3) exponential,and (4) inversecuberoot
regressionequations.
October1989]
ShortCommunications
TABLE1. Regressionequationsand statistics.Residual sum of squares(RSS) for untransformeddata
wascalculatedby solvingeachequationfor y when
x = 0, 2, 5, i0, 15, and 20 rain, subtractingeach
predictedvaluefrom observedvalues,squaringthe
difference,and-adding the squares.
Equation
t
RSS
Linear
7.94
7,354
4.17
26,300
8.04
6,289
7.03
6,745
3.15
>130,000
4.53
7,178
y0.• = 4.54 - 0.17x
Hyperbolic
y • = -0.019 + 0.012x
cube root
y-0.•3= 0.205 + 0.016x
evidence
for feedback
in hum-
informationon cropemptyingwith differentconcentrationsand bird energy stateswould be useful to
understandhow feeding and digestioninfluencethe
precisionof energy regulation.
shownbecauseit predictednegativevolumesat zero
time and gave a poor fit to the transformeddata (see
below).
Two statistics were calculated to compare the
regressions.
The firstwasa "t" statisticbasedon slope/
standard error of slope calculatedfrom r.•/n - 2.
•-•
is indirect
mingbirdsbecauseincreasingfood concentrationreducesfeedingfrequency(Wolf and Hainsworth1977).
Changesin crop functionare alsosuggestedbecause
the energy condition of hummingbirdsinfluences
their feeding frequency(Hainsworth et al. 1981).More
Cube root
Inverse
nonnutritious fluids are emptied from the stomach
with a pattern best describedby an exponential or
squareroot model (Smith et al. 1984). This has been
called the "intrinsic" emptying pattern of the stomach (Smith et al. 1984). However, this changesto a
linearpatternwith high-qualityfoodsbecauseof negative feedback mechanismsthat modify the "intrinsic" pattern (Hunt 1983,McHugh and Moran 1979).
There
y = 85.3 - 4.4x
Exponential
y = 148.1e-ø.3x
Square root
y0.5= 9.43 - 0.39x
725
(Hopkins1966;Table1). Because
thisis
based on correlation
transformed,
coefficients after data had been
it indicates how well the data fit the
models once volumes
had been transformed.
LITERATURE CITED
DEBENEDICTIS,P. A., F. B. GILL, F. R. HAINSWORTH,G.
H. PYKE,& L. L. WOLF. 1978. Optimal meal size
in hummingbirds.Am. Nat. 112:301-316.
DIAMOND, J. M., W. H. KARASOv,D. PHAN, & F. L.
CARPENTER. 1986. Hummingbird
digestive
physiology,a determinantof foragingbout frequency. Nature 320: 62-63.
EWALD, P. W., & F. L. CARPENTER. 1978. Territorial
responsesto energy manipulationsin the Anna
Hummingbird.Oecologia31: 277-292.
F.R. 1981. Energyregulationin humregression
(Table1,RSS).Thisprovidesa waytojudge HAINSWORTH,
mingbirds. Am. Sci. 69: 420-429.
howwell eachregressiondescribedthe measuredvolumes because transformation
of the volumes influ--,
M. L. TARDIFF,& L. L. WOLF. 1981. Proporencescorrelationcoefficients(Jobling1986).I usedan
tional control for daily energy regulation in
hummingbirds.Physiol. Zool. 54: 452-462.
ANOVA of squaredresidualswith multiple comparison (Scheffe'stest) to comparethe models.
--,
& L. L. WOLF. 1972. Crop volume, nectar
The exponentialand hyperbolicregressionsproconcentration, and hummingbird energetics.
Comp. Biochem.Physiol. 42A: 359-366.
ducedhigh residualvariation that was statistically
greaterthan residualvariationwith other regressions HOPKINS,
A. 1966. The pattern of gastricemptying:
(P < 0.05,Scheffe'sF >- 5.143).The remainingmodels
a new view of old results.J. Physiol. 182: 144-
The secondstatisticwasthe residualsumof squares
(RSS) calculated from untransformed data for each
could not be discriminated
as different
based on re-
149.
sidual variation (P > 0.05, Scheffe'sF --- 0.017). The
exponentialandhyperbolicregressions
gaveverylarge
RSS mainly becauseof poor prediction of volumes
HUNT,J.N. 1983. Doescalciummediateslowingof
gastricemptyingby fat in humans?Am. J. Phys-
for untransformeddata closeto zero time. The neg-
JOBLING,
M. 1986. Mythical modelsof gastricemptying and implications for food consumption
ative exponentialregressionpredictedan initial volume of 148 •1, and the hyperbolic regressionpredicted- 53•1. The linearregression
predictedan initial
volume of 85 •1, the squareroot 89 •1, the cube root
94 •1, and the inverse cube root 116 •1.
iol. 244: G89-G94.
studies. Environ.
Biol. Fishes 16: 35-50.
KARASOV,W. H., D. PHAN, J. M. DIAMOND, & F. L.
CARPENTER.
1986. Food passageand intestinal
nutrient absorptionin hummingbirds.Auk 103:
453-464.
A negative exponential model for crop emptying
doesnot appearto apply to thesedata as originally MCCANN,M. J.,& E. M. STRICKER.
1986. Gastricempsuggestedby Karasovet al. (1986). Their conclusion
tying of glucoseloadsin rats: effectsof insulinwas based on correlation coefficients for individuals
inducedhypoglycemia.Am. J.Physiol.251:R609R613.
consideredseparately.
More than onemodelmayapplyto cropemptying MCHUGH, P. R., & T. H. MORAN. 1979. Calories and
dependingon circumstances.
In humans,for example,
gastricemptying: a regulatory capacitywith ira-
726
ShortCommunications
plicationsfor feeding. Am. J. Physiol.236:R254R260.
[Auk,Vol. 106
S•VBBS,
D. F. 1977. Modelsof gastricemptying.Gut
18: 202-207.
SIlkily,R. M. 1981. Strategiesof digestion and defecation. Pp. 109-139 in Physiologicalecology:an
evolutionary approach to resource use (C. R.
WOLF,L. L., & F. R. HAINSWORTH.1977. Temporal
patterning of feeding by hummingbirds. Anim.
Behav. 25: 976-989.
Townsend and P. Calow, Eds.). Sunderland, Mas-
Received3 January 1989, accepted6 April 1989.
sachusetts, Sinauer Assoc.
S•tIT•I, J. L., C. L. JIANG,& J. N. HVNT. 1984. Intrinsic
emptying pattern of the human stomach.Am. J.
Physiol. 246: R959-R962.
Incubation of Dead Eggs
DANIEL AFIK AND DAVID WARD
MitraniCentrefor DesertEcology,
Jacob
Blaustein
Institutefor DesertResearch,
BenGurionUniversity
of theNegev,SedeBoqerCampus
84993,Israel
Prolongedincubationhasbeenrecordedin a number of bird species(Drent 1975). We discusstwo types
orated in the following manner. The five heaviest
eggs(shownby candlingto be live eggs)were left in
of prolongedincubation:birdsthat incubatea single
the nest and all the others were removed.
clutchfor an extendedperiod, and birds that lay sev-
eggsdied,two moreclutches(totalingnine eggs)were
laid in sequence,eachone after the eggsof the precedingclutchhad died. A plot of massagainstvolume
for these 14 eggs revealed three clustersthat corre-
eral discrete
clutches
in the same nest and incubate
all the clutchestogether.We provided an exampleof
eachtype in the Negev Desert,Israel,with particular
emphasison the secondtype, and we attempted to
provide explanations for the occurrence of this be-
When
these
spondedwith the three clutches.Massdecreasedwith
age of clutch. Thus, a total of six clutcheswere laid
in the samenest and none was successful.
The eggs
We observedthe first type of prolongedincubation of the different clutcheswere arrangedin no obvious
in a pair of StoneCurlews(Burhinus
oedicnemus),
which patternin the nest(determinedby markingeggs).On
incubateda clutchof two eggscontainingdead em- three occasions,
a brokenegg was removedfrom the
bryos (determined by candling) for 75 days (1 June nest by the birds and placed some30 cm away.
to 14 August 1988)at Sede Boqer(30ø52'N,34ø46'E).
Toexaminethe possibilitythatthe retentionof eggs
Incubation was terminated when all the Stone Curwith dead embryosin the nest actedas a heat buffer
lews in the vicinity of SedeBoqermigrated. The sec- to the other eggs that containedlive embryos,we
ond type was observedin a pair of Hoopoes(Upupa measuredtemperaturesin the nest (T•) and in the
epops),alsoat SedeBoqer,from June to August 1988. surroundingspacewithin the ceiling. We usedcopOn 20 June 1988,the Hoopoeshad an inordinately per-constantanthermocouples(calibratedagainst a
large clutch (23 eggs)in a nest locatedbetweenthe mercurythermometerapprovedby the U.S. National
ceiling and roof of an unusedbuilding. The nestwas Bureau of Standards) with an error of +0.1øC. One
enclosed,exceptfor a small hole (ca.4-cm diameter) thermocouple connected to a Campbell model 21 x
through which the adults entered. Over the study dataloggerwas placed between the eggs (to record
period,the Hoopoeslaid 32 eggsin the nest.A normal T•) and a secondwas placed 0.5 m from the nest to
clutch for this speciesis 4-10 eggs, rarely up to 12 recordtemperaturebetweenthe ceiling and roof (Tc;
(Crampand Simmons1985).In Israel,the usualclutch hereafter known as ceiling temperature).Temperasize is 5-6 eggs(Paz 1987).When we candiedthese tureswere recordedevery 5 s and averagedevery 15
eggs,manycontained
deadembryos(henceforth
called min. We compared the mean T• with all the live and
deadeggs).We plotted egg massagainstegg volume deadeggs(n = 23) in place(for two daysand nights)
and found four clustersof egg mass.These clusters to mean T• of nestswith all dead eggs(n = 18) recorrespondedwith eggshellcolor; the darker eggs moved (for three days and nights).
Ceiling and nest temperatures approximated siweighedless.The eggshellspresumablydarkenwith
age as the result of dirt accumulationin the nest. nusoidal curves over time. We divided these data into
Becauseeggslosewater continuouslywith age,with two groups (for temperaturesrecorded both before
an increasedrate of water lossin dead eggs(Rahn and after dead-eggremoval).One group had increasand Ar 1974),we assumedthat the eggsbelongedto ing T• and the other decreasingT•. We separatedthe
four different clutches.This assumptionwas corrob- two groupsat the crestsand troughsof the sinusoidal
havior.