The Effects of Flow on Polyp-Level Prey Capture in an Octocoral, Alcyonium siderium

10 Pages·1991·4.1 MB·English

by  M R Patterson

Reference: Bwl Bull 180: 93-102. (February, 1991)
The Effects of Flow on Polyp-Level Prey Capture in an
Octocoral, Alcyonium siderium
MARK PATTERSON
R.
Division ofEnvironmental Studies, University ofCalifornia, Davis. California 95616
Abstract. Particlecaptureby individual polypsandten- wasrecognized (Bell, 1974). Particlecapture mechanisms
tacles ofthe octocoral, Alcyonium siderium, was investi- used by biological niters include direct interception (the
gated in flowsofdifferent speed and turbulence intensity. particlecomeswithin oneparticleradiusofafilteringsur-
In low flow (Umean = 2.1 cm/s; u' = 1.2 cm/s. where u' is face), inertial impaction (the particle contacts the filter
theroot mean squareofthe fluctuations from Umean),ten- because particle inertia causes it to deviate from a fluid
tacles on the upstream side ofa polyp capture the most streamline around the filter), diffusive deposition (both
prey. In intermediate flow (Umean = 12.2 cm/s; u' = 6.0 Brownian and eddy-enhanced the motion ofthe particle
cm/s).downstream tentacleswithinapolypcatch themost acrossstreamlines leadstocontact with the filter), sieving
prey. In high flow (Umcan = 19.8 cm/s; u' = 4.0 cm/s), (the particle is too large to pass through gaps in the filter
polyps are bent downstream, eddies form over the ten- geometry), electrostatic attraction (requires net surface
tacularsurfaces,andthecapturedistributionovertentacles charges ofopposite sign on filter and particle), and grav-
becomes radially symmetric. At all flow speeds tested, itational deposition (a particle denserthan the fluid sinks
particles are caught with increasing frequency nearer the and contacts the filter). Aerosol filtration theory allows
tip ofthe tentacle relative to locations near the pharynx. estimation ofthe relative importance ofthese mechanisms
At the highest flow speed tested, no particles are caught by calculating the ratios ofrelevant forces acting on par-
on the segment ofeach tentacle closest to the pharynx. ticles of different charge, size, and density, in flows of
The per polyp capture efficiency is low and drops mark- different velocity and viscosity (LaBarbera, 1984).
edly with increasing Reynolds number. The capture Recentwork in organismsasdiverseasconifers(Niklas,
mechanism for this species appears to be direct intercep- 1982a.b), dipteran larvae (Ross and Craig, 1980), poly-
tion;inertial impaction isshown tobeunimportant. Flow chaetes (Taghon el a/.. 1980; Merz, 1984), veliger larvae
modulation of particle capture by polyps is probably a of mollusks (Strathmann and Liese, 1979), ophiuroids
general phenomenon among octocorals. (LaBarbera, 1978), bryozoans (Okamura, 1984, 1987),
hydroids (Harvell and LaBarbera, 1985; Hunter, 1989),
Introduction and crinoids (Holland el al. 1987) has extended our
knowledge of how biological filters work and how flow
The application of modern engineering theory to the speed can affect the geometric pattern ofparticle capture
analysis ofparticle capture by suspension feeding organ- at the level of the colony or individual. An important
isms began with a review of the engineering and fluid generalization from these works is that the coupling be-
mechanics literature by Rubenstein and Koehl (1977). tween an organism's filter morphology and the resulting
The medical community has long been interested in the flow field, whether generated actively or passively, is ex-
related problem ofhow particles are deposited in the tra- tremely important in the particle capture process.
cheobronchial tree ofmammalian lungs(Findeisen, 1935; Few studies have examined the mechanics of zoo-
Landahl, 1950, 1963). The theory invoked was the same plankton captureby passivesuspension feedingcnidarians
(McMahon el a/.. 1977), and importance offlow pattern atthelevelofthe filteringelementsthemselves,thepolyps
in affecting the location of particle capture inside lungs composedoftentacles. Lewisand Price(1976)investigated
mucus feedingin corals. Hunter(1989)demonstrated that
Received 30August 1989; accepted 6 November 1990. feeding effectiveness ofhydroid polyps was greater in os-
93
94 M. R. PATTERSON
dilatory flow compared to steady, unidirectional flow. higher turbulence in the flow tank and a closer approxi-
Harvell and LaBarbera (1985) examined how flexibility mation tothe flowseen overthecoloniesin the field (Pat-
affects local flow speeds over polyps in hydroid colonies. terson and Sebens, 1989). Seawater forthe flume was ob-
Best (1988) has investigated prey capture in the sea pen, tained from the MSC seawater system and was filtered
Ptilosarcusgumeyi, aspeciesthat hasthepolypsarranged twice(sand, cotton mesh) to remove particlesgreater than
at the ends ofcantilevered support tissue through which 20 jim diameter or was made fresh using InstantOcean,
flowingseawaterpasses. She found that thedeformability and adjusted to a salinity of34%o.
ofthe organism strongly affected nitration efficiency and Flow speeds and turbulence intensities were measured
volumeofwaterfiltered; ineffecttheorganism couldtune with a twochannel thermistorflowmetercircuit modified
itsfeedingperformanceby maintainingavariableporosity from LaBarbera and Vogel (1976). The frequency re-
filter. sponse ofthe probe plus circuit is 5 Hz at 6 dB down
While some workers have investigated the location of from maximum response. Theturbulence intensitiesmay
prey capture on the surface of cnidarian colonies (Lev- underestimate the true turbulence in the flume, ifthere
ersee, 1976; Lasker, 1981; Patterson, 1984), no studies issignificant energy at frequenciesabove 5 Hz;thisaspect
have addressed the location ofprey capture within indi- offlumeflowregimewasnotevaluated.Thevelocitysignal
FM
vidual polyps or tentacles. Alcyonium siderium Verrill is was converted into an signal for transmission over a
a planktivorouscolonial octocoral common on hard rock distance ofseveral meters to a frequency-to-voltage (f/v)
substrate in the New England subtidal (Sebens, 1986). Its converter. The output ofthe f/v converter was sent to a
diet consists largely of small zooplankton; invertebrate signal conditioner(custom-made)andeightbitsuccessive
eggs, foraminiferans, ascidian larvae, nematodes, harpac- approximation A/D converter (Mountain Computer)
ticoid and calanoid copepods, barnacle nauplii and cy- connected to an Apple He microcomputer. The sampling
prids, ostracods. and crustacean fragmentswere common, rate was 10 Hz.
althoughalgal material isoften present(Sebensand Koehl, Octocoral colonies attached to mussels (Modiolus mo-
1984). It readily captures and eats live zooplankton and diolus) were collected subtidally. Mussel shell fragments
Artemiacystsinalaboratory flume(Patterson, 1984). Prey bearing Alcyonium were mounted securely in the flow
capture events by individual tentacles are easily observed tank working section. The prey offered to the colonies
by the naked eye. The subtidal habitats it occupies can were cysts ofthe brine shrimp, Artemia. Characteristics
differ greatly in water motion (Sebens, 1984; Patterson, ofthe cysts are described in Patterson (1984). The cysts
1985), and there is a change in colony morphology of are about the same size as the mean prey size taken by
local populationsthat iscorrelated with flow regime, with Alcyonium in the field (Sebens and Koehl, 1984).
finger-likecolonies found in slowerflowareas, and lobate
ellipsoids and roughly spherical forms found in higher Location ojpreycapture
flows(Patterson, 1980). The present study tested whether The spatial location ofprey capture on individual po-
the location ofprey capturewithin individual polypsand lypsofAlcyonium wasstudied in flowsofhigh turbulence
tentacles ofthe boreal octocoral, Alcyonium siderium. is levels and differing mean flow speeds. Colonies used
affected by flow patterns over the colony. ranged from 2 to 8 cm in greatest dimension when ex-
panded. Colonies were all roughly spherical. Prior to an
Materials and Methods observation period, a single colonywas introduced to the
flow tank and allowed to acclimate to the flow regime
Colony collection, maintenance, andflowgeneration and expand its polyps. A standard volume of seawater
andmeasurement
(11) and weight ofhydrated cysts (0.45 g) were added to
Polyp feeding experiments were conducted at the Ma- the flow tank at the beginning ofthe observation period.
rine ScienceCenter(MSC), Northeastern University, Na- The flow 1 cm above the observed polyp was adjusted to
hant, Massachusetts, and at the University ofCalifornia, have a mean value of2.7, 12.2, or 19.8 cm/s (4 saverage
Davis. Colonies ofA. siderium were collected and main- achieved through an electronic integrator) by adjusting
tained in flowing seawater tables or recirculating chilled the speed control on the flume motor. Five minutes into
aquaria. A recirculating Plexiglas flume (98 liters; 15 cm theexperiment, three 60-ml sampleswerewithdrawn iso-
X 15 cm working section; 1.9 m long) patterned after a kinetically (Brodkey and Hershey, 1988) using a Cole-
design published by Vogel and LaBarbera (1978) and Parmer peristaltic pump(model no. 7568) smoothed with
equipped with a chiller (Aquanetics) enabled colonies to hydraulic capacitors. Each sample was filtered onto grid-
feed in flows ofvarious speeds and turbulence intensities ded Millipore filters, the cysts counted, and the mean
at 15C. Patterson (1984)givesaquantitativedescription concentration ofparticlescalculated. The range ofparticle
offlow inthisparticular flume. All experimentswere per- concentrations encountered by the colony among exper-
formed with the flow straighteners removed, resulting in iments ranged from 0.13 to 0.53 cysts/ml.
POLYP-LEVEL PREY CAPTURE EVENTS 95
Figure 1A shows a typical top view ofa polyp after a Results
feeding bout and the coordinate system used to assess Prey capture around theperiphery ofapolyp
location of capture around the polyp's circumference.
Note that the coordinate system for the top projections Figure 1C shows the distribution of particle capture
paired tentacles from the bilaterally symmetric halves of aroundthe polypson thedifferent tentaclesasone moves
the polyp (Fig. 1A). The coordinate variable (x) used for in the downstream direction; the histograms have been
describing capture along individual tentacles is shown in adjusted fortheamount ofsurfacearea available forprey
=
Figure IB; note that the distance along the tentacle (x) is capture. At low flow speeds(Umean 2.7 cm/s), prey cap-
normalized to the tentacle length (L). Capture events on ture is remarkably asymmetric, with upstream tentacles
individual polypswere observedat a magnification of35X capturingthe most prey [Kolmogorov-Smirnov (K-S)test;
throughadissectingmicroscopesuspendedovertheflume. P< 0.001; df= 207]. At intermediate flow speeds(Umean
A watch glass floating on the water and anchored over = 12.2 cm/s), the distribution is again asymmetric, but
thecolony prevented blurringofthe image from capillary in the opposite direction, with downstream tentacles fa-
waves at the air/water interface. As a feeding bout pro- vored in particle capture (K-S test; P < 0.001; df= 205).
gressed, composite maps of capture sites of cysts from At the highest flow speed tested (Umean = 19.8 cm/s), the
individual polyps were made (Fig. 1A). All polyps cen- distribution is indistinguishable from an even distribution
susedwere located nearthe topofthecolony; polypscho- ofprey capture around the tentacles (K-S test; P > 0.5;
sen forobservation had theirtentacles oriented to the flow df= 70). The distribution ofcapture events isthus mark-
(Fig. 1A). edly affected by flow speed. Only at the highest speeds
An ocular micrometer permitted measurement ofrel- can capture be modeled by a Poisson process.
ative position of capture along the length of a tentacle.
Only particlescaughton theoral sideofthetentacleswere Prey capture by tentacles
noted; particles were very rarely captured on the aboral When prey captureeventsareexamined overthe length
side ofthe tentacles. The tentacle capture maps were di- ofindividual tentacles, an additional pattern emerges(Fig.
vided into five non-dimensional length sectors. Particle 2). At low speeds (Umcan = 2.7 cm/s), the distribution is
counts in the tentacle length sectors were normalized significantly asymmetric, with the outer segments ofthe
within atentacletothe projected areaavailableforparticle tentaclescapturing the most prey (K-S test; P< 0.001;df
capture. Surface areas ofpolyps were computed using a = 207). The same pattern is found at intermediate flow
camera lucida and an interactive digitizing tablet (Apple speeds (Umcan = 12.2 cm/s), with the asymmetry shifted
Graphics Tablet). The area ofthe pinnules was not mea- even further in the direction away from the pharynx (K-
sured in calculatingareasavailable forcapture. Projected S test; P < 0.001; df = 205). Finally, at the highest speed
surface area ofthe entire colony was measured similarly. used in the flume (Umt.an = 19.8 cm/s), the distribution is
still asymmetric with a bias toward the tentacle tips (K-S
FeeAdidnigmeenfsfiicoinelnecsys measure offeeding effectiveness, the tteusrte; Pin<th0e.00i1nn;edrfm=os7t0)2,0b%utowfitthhesotmenetadcilfef'esrelnecnegs.thCahpa-s
efficiencyofpreycaptureatthepolyplevel wascomputed disappeared, and the outermost 20% experiences much
asfollows: thenumberofparticlescaught perpolypduring more variable prey capture success.
a standard feeding bout was divided by the number of
particles passingthrough thecross-sectional area occupied Feeding efficiency
by the colony (divided by the number of polyps), ifthe When the efficiency offiltration for individual polyps
colonywere notthere. Thisresultisthestandarddefinition is examined with respect to Reynolds number (Re) com-
offiltration efficiency from engineering theory (Dorman, puted for flow around a polyp, a significant inverse rela-
1966). The number passing through the cross-sectional tionship is found (P < 0.05; df =11), and the efficiency
areawascalculated by integratingthe flowovertheheight is remarkably low at all speeds tested forfeeding in dense
and width ofthe colony and multiplying by the sampled concentrations ofprey (Fig. 3). Re = Umeand/i', where d
particle concentration. Feeding rate in the dense concen- = polyp oral disk diameter, and v = kinematic viscosity
trations of prey used in the flume is not constant, but ofseawater. Because polyp size is relatively constant. Re
decreases with time (Patterson, 1991). These concentra- can be viewed as a dimensionless flow speed.
tions were similar to zooplankton patch concentrations
in the field. Hence, efficiency is a function oftime. For Discussion
purposes of comparison, efficiency was computed over
the time necessary to reach saturation. Saturation is de- Mechanisms ofparticle impaction
fined as the point at which capture events drop to less Rubenstein and Koehl (1977) presenteddimensionless
than one prey item caught per 5-min period percolony. indicesforvariousmechanismsofparticlecapturebysus-
96 M. R. PATTERSON
3
2 4
A. B.
flow L
5
x
2
C.
Umean =2-7cm/s Umean =12-2cm/s Hnean = 19'8
45
40- n =207
35 1
30
S 25-
I
20- o
15- T a.
JO- 1
S'
Upstream Tentacles > Downstream Tentacles
Figure 1. Coordinatesystem usedtoquantifypreycapturein individual polypsincoloniesofAliyonium.
(A)Quantification inthecircumferential directionaroundthepolyp. Notethepairingoftentaclesfromthe
bilaterallysymmetric halvesofthepolyp, ;.t'.. preycaughtontentacleswiththesameidentification number
werepaired.Thefiveconcentricringsdelineatethedimensionlesslengthcoordinateusedforassessingcapture
by individual tentacles. (B) The distance from the pharynx toward the tentacle tip (X) is divided by the
overall length ofthe tentacle (L) to generate the dimensionless distance (X/L) used as the independent
variable (abscissa) in Figure 2. (C)Circumferential position ofprey capture events in individual polypsof
Alcyoniumatthreedifferent flowspeeds. Datafrom thebilateral halvesofthecolonyarepooled;seeFigure
1A forinterpretationofabscissa.Capturefrequenciesarenormalized relativetotheamountoftentaclearea
assigned to the numbersone through five. Data werearc-sine transformed and then back-transformed for
graphical portrayal. Vertical barsare95% confidence intervals. For flow speeds of2.7, 12.2. and 19.8 cm/
s, thetotal numbersofcystscaughtwere 207, 205,and 70. respectively.
pension feeding organisms. Table I gives these values for is contrary to the pattern observed. A formulation ofthe
polyps ofAlcyonium feeding on Anemia cysts. Note that model more appropriate to aqueous suspensions invokes
direct interception or "geometric" interception (Chang, the importance of short-range (London-van der Waals)
1973) has the highest value and is thus most likely to be forces and does not ignore the hydrodynamic resistance
the dominant mechanism ofparticle capture. For a rigid that occurs as the particle squeezes fluid from the space
filter, the efficiency of capture by direct interception between itself and the filter element (Chang, 1973; La-
should be independent offlow speed (Fuchs, 1964): this Barbera, 1984). This more refined theory predicts an in-
POLYP-LEVEL PREY CAPTURE EVENTS 97
Umean = 2-7 cm/s LI
60
50 '
40
1 30 '
u
01
ft, 20
10 '
98 M. R. PATTERSON
the convection of unfiltered water to the vicinity ofthe
filtershould beconsidered. Methodsofcarefully releasing
dyeand studyingits motion nearfilter feedersusingimage
processingtechniquesare beingdeveloped toallow better
investigation ofmicroscale turbulent diffusive deposition
(unpub. obs.).
Rates of particle encounter and possible capture by
gravitational deposition are independent of flow speed
but directly proportional to settling velocity. The settling
velocity for Anemia cysts is absolutely low, so the total
flux ofparticlesto the polyps via this mechanism is much
lower than the contribution provided by direct intercep- Figure 4. Streamlines of fluid How near the upstream stagnation
tion. It isunlikely that natural food particleshavesettling pointofatiller(Birdelal.. 1960),whereinertialimpactionismostlikely
cveolnotcriitbiuestioanpporfeciinaebrtliyalgiremaptaecrtitohnantoAtnheemciaaptucrysetso.fTpahre- dtdoiecvoaictacetuderd.byfXrXoamn)dthmeYarsaktrrseeawdmihlreiernceetisopdanrautleicctlooeosrtdheieainrrantieensde.rtbiTyah.etSheeuepfstlthoreweAahpmapvepelnadnnioetx(yfieont-r
ticles at higher Reynolds number could be a potentially a derivation showing how inertial impaction is not likely tobe an im-
important mechanism if particle inertia is appreciable. portant capture mechanism forcnidanans that use passive suspension
The upstream side ofan individual tentacle will have a feeding.
stagnation point and the flow will split at this point (Fig.
4) and flow around the tentacle at low flow speeds or up
and over the tentacular crown at higher Re (Patterson, A/croniiim tentacles are not trapped; relatively few are
1984). A calculation in the Appendix demonstrates that lostifthey initiallyadhere,althoughJ. Miles(Northeastern
this mechanism is highly unlikely to be an important Univ. pers. comm.) found that adhesion and losswassig-
mode ofparticle capture by polyps in this octocoral. nificantly affected by flow speed in the sea anemone, Me-
tridium senile, and Leonard et al. (1988) found that flow
Feeding efficiency ofcnidarian filters speedaffectedcaptureprobabilitiesinacrinoid. Mystudy
ofcapture at the level of the polyp addresses successful
The filtration efficiency as calculated per Dorman prey capture events only.
( 1966)isvery lowforindividual polyps(Fig. 3);apossible Future work on the mechanisms ofparticle capture by
explanation involves partitioning capture efficiency into cnidarians should investigate the role of unsuccessful
collection efficiency and adhesion efficiency (Weber et ai. adhesions. In particular, the importance ofLondon-van
1983). Many particles that appear to strike the surface of der Waals forces versus nematocyst firing should be ex-
Table I
\'alliesofditnensionlessparametersforfourpotentialmodesojparticlecapture(cf. Rubenstein andKoehl. 1977) intheoctocoralAlcyonium
siderium feedingon Artemiacystsal twodi/lerenl flowspeedscommonlyencounteredinnature
Gravitational
deposition
POLYP-LEVEL PREY CAPTURE EVENTS 99
plored,ascurrentdataare insufficient toaddressthisissue. more rigid than those ofOhelia. and hence it is not clear
The subject bears further attention because Best (1988) without furtherexperimentation whetheroscillatory flow
also found that feedingefficiency wasan inverse function would result in enhanced feeding in Alcyonium. Thus
of flow speed (read Reynolds number) in the sea pen, these results should be applied only to feeding in the field
Ptilosarcusgumeyi. She attributed thisdecline tothepre- under steady flow conditions when wind-driven oscilla-
dicted behavior ofparticles that are caught by direct in- tions have a small contribution to the flow field.
terception (Spielman, 1977), perhaps aided by a defor- The distribution ofparticle capture over the length of
mation ofthe filter elements as the hydrodynamic drag an individual tentacle is also in agreement with a geo-
increased. Alcyonium polypson the upstream side ofcol- metric (direct) interception model. Parts ofthe tentacle
onies deform in strong flows while polyps in the wake furthest out ofthe boundary layer ofthe polyp intercept
undergo little deformation (Patterson, 1984). The octo- the mostprey. Patternsofpreycapturediscernedthrough
corals she studied are more efficient than Alcyonium by flume experiments using non-motile particlessuch asAr-
a factor of five at a similar flow speed. This study used lemia cysts may be different from those measured using
only polypslocated nearthe topofthecolony. Increasing live prey, but only if the loss rate of captured particles
mechanical deformation ofthis subpopulation ofpolyps differs between the two types of food or the motility of
occurred at higher flows, resulting in less surface area live prey causes the diffusive deposition mechanism to
available forprey capture, but the reduction wasdetected increasecapturepreferentiallyata locationdifferent from
in the measurements of projected colony surface area. directinterception. Lossofcaptured particlesismostlikely
The reasons for this interspecific difference in feeding ef- causedby hydrodynamicdrag forcesexceedingthebreak-
fectiveness are presently unknown. ing strength ofthe attachment between particle and ten-
tacle. Live zooplankton prey and Anemia cysts will ex-
Paniclecapture locations perience very similar amounts ofdrag because size and
shape are similar. The motility oflive zooplankton should
The patterns ofprey capture seen (Figs. 1C, 2) are in result in an increase in the diffusive particle flux relative
agreement with a direct interception model ofprey cap- to Anemia cysts, but it should not affect the geometric
ture. Polypsresemble inverted umbrellas(see photograph location ofcapture on tentacles ifmovement is random
in Sebens and Koehl, 1984); they do not hold their ten- in all directions.
tacles in a flat canopy as the top view in Figure 1A might Thisstudy hasshown how flow regimecan dramatically
imply. At low speeds, the first tentaclesto encounter par- affectpatternsofparticlecaptureatthelevelofthefiltering
ticles are the upstream ones, and here capture is more elements in an octocoral. Variation in feeding ability at
likely. As the flow speed increases, the polyps are bent by the level ofthe polypcaused by hydrodynamics may help
the flow (cf. Patterson, 1984). and the aboral side ofthe explain the variation Lasker(1981)observed in prey cap-
upstream polypsispresentedtothe flow. Forpreyparticles ture between polyps and branches in colonies oftropical
the size ofAnemia cysts (ca. 200 ^m; close in value to gorgonians. Capture events in the three species Lasker
the mean size of natural zooplankton prey, Sebens and studied did not fit a Poisson distribution, and he invoked
Koehl, 1984), few particles are caught on these upstream differential feeding ability of the polyps as the cause of
tentacles because particles do not adhere to the aboral thevariation. Heoffered noexplanation forthedifferential
side. The downstream tentacles then begin feeding. In feeding ability other than to note that other authors had
strong flows, the polyp is severely bent downstream, and also seen asymmetric patterns in prey capture by cnidar-
a small eddy forms over the tentacular disk (pers. obs.); ians (e.g., Leversee, 1976). I have demonstrated that mo-
the distribution becomes roughly symmetric again. The mentum transport (fluid flow) directly affects masstrans-
relativerolesthatattachededdyformulation and turbulent port(particlecapture)atthelevel ofthe individual feeding
diffusion play in thissmoothingout ofthe particlecapture elements, polyps. Upon closer inspection, other passive
distribution are unknown. suspension feeding cnidarians may exhibit similar pat-
Theseexperimentswereconducted underturbulent but terns.
steady flow conditions. Alcyonium occursovera range of
depths and habitats in the shallow subtidal; it is exposed Acknowledgments
to both oscillatory flow from wind-driven waves and to
steady tidal flows (Patterson, 1984, 1985). The particle This paper has benefited from discussionswith P. Bas-
capturebehaviorofindividual polypsandtentaclesmight ser, T. Givnish, M. Koehl, M. LaBarbera, T. McMahon,
be quite different in an oscillating flow. Hunter (1989) R. Olson, S. L. Sanderson, K. Sebens, and R. Turner. T.
found that the feedingeffectivenessofthe hydroid Obelia McMahon provided inspiration and insight into the me-
longissimawas muchgreaterin an oscillating flowrelative chanicsofparticledeposition through hisgraduatecourse
to a steady current. Alcyonium colonies are inherently on fluid flow in the human body. P. Rudy, Acting Di-
100 M. R. PATTERSON
rector. Marine Science Center, Northeastern University, Landahl, H. D. 1950. On the removal ofair-borne droplets by the
Nahant, Massachusetts, kindly provided laboratory space. human respiratory tract: 1. The lung. Bull. Math. Biophys. 12: 43-
C. Alexander provided technical assistance. Financial 56.
support for this project was provided by the Richmond Landoanhlt,heH.reDm.ov1a9l63.ofaPiarrbtoirclneerpeamrotivcaullabtyesthbeyrtehsepirhautomraynsyrsetsepmi:rantoortye
Fund of Harvard University, the Lerner-Gray Fund for tractwithparticularreferencetotheroleofdiffusion.A M.A.Arch.
Marine Research of the American Museum of Natural Ind. Hyg Occup. Med. 25: 29-39.
History, a Faculty Research Award from UC Davis, and Lasker, H. R. 1981. A comparison ofthe paniculate feedingabilities
NSFOCE87-16427. ofthreespeciesofgorgonian softcoral. Mar. Ecol. Prog. Ser. 5:61-
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802.
Gibbs,R.J. 1985. Estuarinefloes:theirsize,settlingvelocity,andden-
Glauseirtyt.,/M.Ge1o9p4h0y.s. ARemset90h(oCd2)o:fc3o2n4s9t-r3u2c5t1in.gthepathsofraindropsof OkuMbood,elAs..1(9B8i0o.mathDei/mfautsiicosn,aVmoli.E1c0o)l.ogSipcrailngPerroVbelrelmasg:. NMaetwheYmoartki.cal
different diameters moving in the neighbourhood of(Da circular Patterson, M. R. 1980. Hydromechanical adaptations in Alcyonium
cylinder. (2) an aerofoil, placed in a uniform stream ofair: and a .sulerium(Octocorallia). Pp. 183-201 inBiofluidMechanics2. D.J.
determination oftherateofdeposit ofthedropsonthesurfaceand Schneck, ed. Plenum, New York.
thepercentageofdropscaught.Aeronaut. Res Council. Reportsand Patterson, M. R. 1984. Patterns ofwhole colony prey capture in the
MemorandaNo. 2025. London. octocoral. Alcyonium siderium. Biol. Bull. 167: 613-629.
Harvell, D., and M. LaBarbera. 1985. Flexibility: a mechanism for Patterson, M. R. 1985. The effects offlow on the biology ofpassive
control oflocal velocity in hydroid colonies. Biol. Bull 168: 312- suspension feeders: prey capture, feeding rate, and gasexchange in
320. selected cnidarians. Ph.D. dissertation. Harvard University. Cam-
Holland, N. D., A. B. Leonard, and J. R. Strickler. 1987. Upstream bridge. Massachusetts.
and downstream capture during suspension feeding by Oligometra Patterson,M.R.,andK.P.Sebens. 1989. Forcedconvectionmodulates
serripinna(Echinodermata:Crinoidealundersurgeconditions.Biol. gas exchange in cnidarians. Proc. Nat. Acad. Sci. USA 86: 8833-
Bull. 173: 552-556. 8836.
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colony morphologyandflowregimeon planktoncapturebythehy- planktonpatches:empiricaltestofamathematicalmodel.Biol.Bull
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foodcaptureatlow Reynoldsnumber.Limnol. Oceanogr 26: 1062- neighborgraph. Proc. Roy. Soc. LondonA 110: 709-727.
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POLYP-LEVEL PREY CAPTURE EVENTS 101
Sebens, K. P. 1984. Water flow and coral colony size: mterhahilal The velocitycomponents in the y- and z-directionsare
comparisonsoftheoctocoralAlcyoniwnsidenum Proc. Nat. Acad. V and W, respectively, and the equations ofmotion are
Sci (i'SA)Sl: 5473-5477.
Sebens, K. P. 1986. Spatial relationships among encrusting marine similar. IfI define:
organismsintheNewEnglandsubtidalzone. Ecu!. Monogr. 56:73-
96. (Eq.2)
Sebens, K. P., and M. A. R. Koehl. 1984. Predation on zooplankton
Mbyettrhiedibuenmthsiecnilaent(hAocztoianinasr.iaA)lcinyotnhiewnNeswideErniugnlian(dAlscuybotniadcale.a)Maanrd then (Eq. 1) becomes:
Biol 81: 255-271.
Spielman. I.. A. 1977. Particlecapturefrom low-speed laminarHows. ko-^ -Up (Eq.3)
Anna Re\ l-'liiu/Mec/L 9: 297-319.
Strathmann, R. R., and E. Liese. 1979. On feeding mechanisms and and other directions can be transformed
Svercdlreuapr,anHc.eUr.a,teMs.oWf.moJlolhunsscoann,avenldigRe.rsH..BiFolle.miBnulgl.-1195472:.52T4h-5e3O5c.eans: The equations ofmotion must be solvesdimsiulbajrelcyt.to the
TheirPhysics, Chemistry, andBiology Prentice-Hall, New York. initial conditions. Let me introduceascaled timevariable.
Taghon, G. I,., A. R. M. Nowell, and P. A. Jumars. 1980. Induction
ofsuspension feedingin spionid polychaetes by high particle fluxes. (Eq.4)
Science210: 562-564.
Taylor, C. I. 1940. Notes on possible equipment and technique for
experiments on icing on aircraft. Aeronaut Res Council. Report\ and the differential operator,
andMemorandaNo. 2024. London.
Vogel, S., and M. LaBarbera. 1978. Simple flow tanks for research = l (Eq.5)
and teaching. BioScience 10:638-643. dt
Webaenri,smM.otEs.c,aDve.nCg.inBgloafnwcahtaredr,boarnndebLa.ctDe.riSaybzydeakr.is1in9g83b.ubblTeh,el.mtemcnohl- Now (Eq. 3) becomes
Oceanogr. 28(1): 101-105. dU
n
Zerbe, VV. B., and C. B. Taylor. 1953. Sea water density reduction (Eq.6)
tables. Pp. 18-19 in Coast and Geodetic Survey. Special f'uhl no
298. U. S. Dept. ofCommerce, Washington. DC. and similarly for the other directions.
Flow near the upstream stagnation point ofthe filter
Appendix will look like Figure 4 (Bird c/ a/.. 1960). The velocity
field near the stagnation point is given by:
The following derivation, developed from the work of U = -ex
(Eq.7)
Glauert (1940) on raindrop capture by airfoils and from
and
Taylor ( 1940) on aircraft icing, shows how unlikely it is
that inertial impaction will be an important mechanism V =
cy (Eq.8)
forpassive suspension feedingcnidarians forthe range of
velocities normally encountered in the field. Substituting into (Eq. 6), I obtain:
Considerthe motion ofasolid particle(e.g.. aplankter), d:x + -dx + cM =
moving with a velocity relative to the seawater, as it ap- ^3 (Eq.9)
proaches the upstream end ofa filtering organism (Fig.
4). In otherwords,theparticledoes not followthestream- Itisreasonabletoassume that upstream ofthetentacle
linesperfectly. Ifthe Reynolds number(Re) ofthe particle a certain distance, X , the flow field is not distorted by
ison the orderofone orless, as it would be for plankton- the presence ofthe tentacle and the particle is following
size particles(Koehl and Strickler, 1981), the forces acting the streamlines ofthe moving seawater(see Fig. 4). Ifthe
o1n983t)h.eTpharetiecqlueatarieondguoevesorlneilnygttohethmeotStiookneso'fdthreagpa(rBteircgl,e tstirmeeamaltinwehsiocfhfltohweispacratlilceldeTst=art0s, tIoobdteaviina:te from the
in the x-direction is: x(0) = - X (Eq. 10)
dU
3 dtp _= 67rrM(U - UD) (Eq. 1) dt (Eq.ll)
winnhaemtriheecrvxi-=sdciorpseaicrtttyii,ocnlU,epra=anddivuesUl.ocp=istyv=eclpooamcripttioycnlceeondmtepnosofintteyh,netnpaor=ftidtcyhle-e ttehreiAsftrioceraemsqouxna(attb)iloe=ngAiuseetsphls,utswo.htehreesAolu=tiocnonosfta(nEtq.. T1h1)eischoanreaco-f
seawater in the x-direction. p: + p + = (Eq.12)
102 M. R. PATTERSON
The roots ofthe equation are: 2p rRU
s
(Eq. 15)
9pR2v
- -
PL: = 1 VI (Eq. 13) where R = radius ofthe filter, and v = n/p, the kinematic
viscosity ofthe seawater.
Usingreasonable values forflow around anAlcyonium
= =
When oneofthe roots isimaginary, the solution tothe colony, I obtain k<jC 0.003, forp 1.024g/cm\ (Zerbe
eelavqteuonarttyu,iaoiln.le.y.oftchomeionptcaiirotdineclo(exfpto=hsei0t)pi.aosnTshaiinnsgdptcahorentdifiicltlteierownpiollswiilbtleioonocswcciiullrl- ac=nnrd1/0sT0aXyfolro1r0s,~e4a1cw9am5t,3e)rR, ap=t, 5=1c0m1,C.0U4(9c=algc5/ucclmma/t3se,d,(Gvfi=rbobms1,.S3v169eX8r5d1)r0,u~pr:
when: el til.. 1942). Ifthe flow speed increasesbyan orderofmag-
nitude to U = 50 cm/s, then koC = 0.034. Appreciable im-
paction will not occur until U = 185 cm/s, far above the
4ck<, (Eq. 14) rangeofspeedsnormallyencountered nearthisspecies(Pat-
terson and Sebens, 1989). Such a flowwould only be found
Glauert (1940) showed for a cylindrical geometry that understormy conditions in the subtidal orin tidal currents
a negligible numberofparticleswill impact ifk^c^s0.125, in fjords. Alcyonium contracts its prey-capturing surfaces
where c = 2 and the definition ofko is as follows: long before this flow speed is obtained (Patterson. 1980).