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Selection of particle sizes by filter feeding copepods plea for reason



Selection of particle sizes by filter-feeding          copepods:     A plea for reason
    Several recent studies consider the ability   figure 1 were not ingested by the raptorial
of copepods to filter particles of various        processes because they could not be frag-
sizes from the water in which they swim.          mented or pierced.
The conclusions range from statements by              Several workers have approached the
Frost (1972, 1974) that larger particles are      problem of copepod feeding by studying
ingested more efficiently than small ones         the spacing of setules on those mouthparts
to those of Wilson ( 1973) who, observing         that act as sieves. The often cited paper of
that copepods tended to ingest large par-         Marshall and Orr (1960) suggested that
ticles in preference to small ones, attributed    Calanus finmurchicus should be able to re-
to the animals the ability to determine the       tain cells of Chaetoceros that are encount-
size of a particle just filtered; the copepod     ered by the maxilla but the animal would
could then adjust the posture of its filter-      only 0ccasionalIy ensnare particles as small
ing appendages to allow it to capture par-        as Nannochloris. Hargrave and Geen ( 1970)
ticles just slightly larger than that particle.   stated that the intersetule distance of the
Both Wilson (1973) and Poulet (1973,              second maxilla of Pseudocalanus minutus
1974) expressed their results in the form         is 3-5 p, implying that smaller particles
of an electivity index, an index that com-        would not be retained efficiently.        Nival
pares the proportion of particles retained        and Nival ( 1973) h ave measured intersetme
by an animal to the proportion available in       dimensions of the mouthparts of six Calanoid
a particular size category. Mullin ( 1963))       copepods, and pointed out that the second
Hargrave and Geen ( 1970)) and Paffen-            maxilla and first maxilliped, believed to be
hofer ( 1971) all agreed that larger par-         the most important mouthparts involved in
ticles are removed by filter-feeding      cope-   filter feeding, have diverse spacings that
pods in preference to smaller particles, but      can be described by normal statistics.
did not explain the phenomenon.                   Nival and Nival applied measurements of
    Few Calanoid copepods can filter par-         intersetule distances of Acartia clausi to a
ticles smaller than 5 p or larger than 100        population     of naturally occurring phyto-
p, and most grazers filter particles of a         plankton cells and developed calculations
much narrower size range (Gauld 1966).            to predict ingestion based on these mea-
The lower limit of filtration is established      surements ( Nival and Nival 1976).
by the intersetule distance, and the upper            The view advocated here in studying
limit by screening setae on the maxillae          particle-size selection by filter-feeding Crus-
that reject large particles from the filtering    tacea is that mouthparts are rather leaky
processes, though they may be fractured           sieves. The characteristic dimension of a
or pierced and ingested by raptorial food-        commercial sieve is the distance between
handling procedures distinct from filter-         threads or the pore diameter; a sieve of
ing processes (Conover 1966; Richman and          high quality will have a very low variance
Rogers lQ69). (Setules are the fine bristles      of hole diameters. The study of Nival and
that are arranged on the margins of the           Nival (1973) indicated that the particle-
stronger setae that extend from the mouth-        collecting mechanism of several filter-feed-
parts.)    The range of particle sizes ac-        ing copepods can be described in similar
cepted by the filtration apparatus was well       terms; each mean intersetule distance will
shown by Wilson (1973) for various stages         have a variance, and associated with these
of Acartia tonsa; presumably those plastic        statistics will be an estimate of the percent
spheres larger than the upper cutoff of his       area of mouthparts having that mean di-
LIMNOLOGY   AND   OCEANOGRAPHY                175                         JANUARY   1976, V. 21( 1)

                                                 A                                                                  B

                                   I                 I                                                    I              I
    0               IO           20           30                       0                  IO            20               30
                                        lntersetule               Distance          (p)
   Fig. 1. Size-frequency   distributions     of intersetule distances of second maxilla of: A-CaZunus  hel-
gokzndicus and B-Cluusocakrnus         arcuicornis   ( from Nival and Nival 1973 ) . The two curves on each
graph represent two classes of intersetule distances.

mension. Dimensions of two copepods,                              retained, and virtually all particles larger
Calanus hdgolandicus (stage V) and Claus-                         than 20 p will be retained. The matter is
ocalunus arcuicornis are shown in Fig. 1                          complicated, however, because of leakage
and the cumulative curve of these distribu-                       through the setule mesh that results from
tions in Fig. 2 ( data from figure 1: Nival                       distension as particles impinge on it, a
and Nival 1973).                                                  phenomenon well known to plankton biol-
   The cumulative frequency graph (Fig. 2)                        ogists, who term it escapement. No data
is potentially powerful in that it constitutes                    exist indicating the distensibility of setules
a probability function for the retention of                       on copepod mouthparts but the analogous
any particle less than or equal to a specified                    situation of a copepod impinging        on a
size; i.e. only 15% of those particles of a                       plankton net suggests that copepods will
diameter of 5 p or less that impinge on the                       slip through the mesh unless their body
mouthparts of Clausocalunus will be re-                           size (smaller axis) is about 25% larger
tained, 50% of the particles < 8 p will be                        than the mesh size (Saville 1958). Saville


                                            I                I

                                                lntersetule           Distance        (p)
  Fig.   2.   Cumulative   size-frequency       distributions    of intersetule   distances    of second maxilla   of:   A-
Calanus helgolundicus and B-Clausoculunus                urcuicornis; curves have been shifted to the right by add-
ing 25% to the mean intersetule        distances.
                                                     Comment                                                       177

                                                                        +I .
                                               A                                                               6
          yparticles            available                       t

                                               I         -I L
                    IO            20          30            0
                                        lntersetule Distance (p)
   Fig. 3. Size-frequency     distributions      of: A-available        and ingested particles and B-electivity     ob-
tained by applying the cumulative         size-frequency    distribution   of Cihusoculunus urcuicornis to a spectrum
of even-sized food particles.

noted that escapement was a function of dis-                  a variety of particle-size distributions some
tensibility of both the mesh and the object                   interesting results are derived. In Fig. 3
passing through the mesh, and one might                       it is assumed that the Ckzu-socalanus is
expect that escapement would be less for                      feeding on a population       that has equal
rigid diatoms than for naked flagellates. In                  numbers of particles in each size category.
making the following calculations I have                      The quantity of food ingested in a size
added 25% to the mean intersetule distances                   category may be calculated as the product
of the probability function as the best esti-                 of the number of particles available in that
mate of escapement (realizing the inade-                      size category, the probability function for
quacy of the estimate); this constant has                     particles in that size category, and the
been incorporated in the probability func-                    volume of water passing through the mouth-
tions shown in Fig. 2.                                        parts. The resulting spectrum of particles
   If ones applies the probability function to                ingested and the electivity index would

                                           A                                                                   B
                                                                50                                  .
                                                                                                    .              1
                                                                w                                               30

                    IO            20          30
                                        lntersetule          Distance (p)
  Fig.   4.   As in Fig. 3; food particles     constitute   a die-off      curve.

                                       lntersetule           Distance (p)
  Fig.   5.   As in Fig. 3; food particles   have a normal    size-frequency   distribution.

generally be interpreted as a tendency for filtration efficiency might be more appro-
the animal to “select” or “elect” larger par-   priate than an electivity index.
ticles; the curves can be explained more            This scheme does not consider the rate
simply and more credibly by considering         at which the animals beat their maxillae,
the mechanical aspects of the sieve.            but only the spacing of setules on the max-
     Fig. 4A and 5A are more typical of nat-    illae, and assumes that volumes of water fil-
ural particle-size distributions where size is tered are identical in each example. A
expressed as equivalent spherical diameter      mechanistic approach to feeding, however,
 ( Sheldon et al. 1972) ; if the probability    would suggest that copepods feeding on
function is applied to either of these distri-  small particles might beat their maxillae at
butions, unimodal spectra of ingested par-      a faster rate than the same animals feeding
ticle sizes result. Figure 5 is representative  on large particles to obtain the same ration.
of grazing experiments in which one pre- The regulation of beating could be based
sents a monospecific algal culture or a sus- on ingestion of material into the gut as
pension of more-or-less uniform plastic         sensed by a stretch receptor of the type
spheres to a copepod. The modal size of found in blowflies by Dethier and Boden-
particles ingested will be to the right         stein ( 1958); the animal then regulates its
  (larger) of the mode of the particles avail-  beating according to its degree of satiation
 able, a feature which follows from the prob-    and does not need to sense particle size.
 ability function. The simple concept of the        B. Hargrave and S. Poulet (personal
probability     function will always result in communications) have both suggested that
the mode of ingested particles being shifted    the motions of the mouthparts as they beat
to the right of the mode of offered particles   back and forth in their filtering action will
 if the size of the food particles falls within  alter the mesh distance of the setules,
 the sigmoid section of the probability func-   thereby increasing the variance of the in-      .
 tion; there is no need to credit the animals    tersetule distances.     Two other factors
 with the ability to scan the particle-size      would tend to distort the shape of the prob-
 distribution. The shift will also be observed   ability function. The highly serrated margin
 in the “electivity index.” Electivity, under    of a mouthpart would allow it to capture
 this assessment, would not be regarded as large particles with an efficiency not esti-
 an active process, but as a passive result of mated from considerations of mouthpart
 a mechanical feeding system. An index of area alone, for large particles would tend
                                                      Comment                                                        179

                                                              modes, but work of several investigators
 d)           r      intersetal                        .      suggests that particles larger than 100 p
                                                              are processed raptorially by Calanus. Hence
                                                              it is impossible to distinguish in Fig. 6
                                                              whether large particles are retained on the
                                                              setules, between the setae, or are captured
                                                                  The simplest approach to the study of
                                                              filter feeding is to regard the filtering ap-
                                                              paratus as a sieve with a rather wide range
                       25   50    75                 100      of pore sizes. Almost certainly the mouth-
                        Mesh Size (p)                         parts have sievelike properties and it is
                                                              only logical that ingestion reflects these
    Fig. 6. Curve of efficiency      of filtration    rela-   properties. A copepod using a tool of this
tive to the mesh size of mouthnarts          of CaZu~us.
The graph was synthesized by ckculating            the ef-    sort would obtain larger particles more ef-
ficiency   of retention of particles in several size          ficiently than smaller particles, a phenom-
categories. A comnonent of mesh size that includes            enon that will explain in mechanistic terms
interseta retention of large particles was added to           several sets of data in the literature that
the intersetule dimensions from Nival and Nival.
                                                              must be otherwise explained by less obvious
                                                              behavioral phenomena.
to catch in the gaps between setae and along
                                                                                                      Carl M. Boyd
the margins of mouthparts. The importance
of the maxilliped as a food-collecting mech-                  Department of Oceanography
anism is also not known in quantitative                       Dalhousie University
terms; this appendage, which is usually                       Halifax, Nova Scotia
coarser than the second maxilla, is believed
to pass particles on toward the mouth. The                    References
general effect of these considerations would
                                                              CONOVER, R. J. 1966. Feeding on large particIes
be to displace the probability curve toward                       by Calanus hyperboreus ( Kroyer),             p. 187-
the right and to alter its slope as the coarser                   194. In H. Barnes [ea.], Some contemporary
components of the maxillipeds          and the                    studies in marine science. Allen and Unwin.
mouthpart margins are added to the rather                     DETJXIEZI, V. G., AND D. BODENSTEIN. 1958.
fine intersetule component of the maxilla.                        Hunger in the blowfly.           Z. Tierpsychol.    15:
    Frost’s data (1972: figure 5) indicate that
                                                              FROST, B. W.        1972. Effects of size and con-
Calanus pacificus retains large particles                         centration    of food particles      on the feeding
with an efficiency not anticipated by appli-                      behavior    of the marine planktonic          copepod
cation of the probability function used here.                     Calanus pacificus. Limnol.           Oceanogr.      17 :
Frost’s filtration  curve can be simulated
                                                              -.         1974. Feeding processes at lower tro-
 (Fig. 6) however by adding a component                           phic levels in pelagic communities,          p. 59-77.
to the probability function that would in-                        In C. B. Miller         [ed.], The biology       of the
corporate intersetal retention of large par-                      oceanic Pacific.      Oregon State.
                                                              GAULD, D. T. 1966. The swimming and feeding
ticles, though the addition of such a com-                        of planktonic     copepods, p. 313-334.           In H.
ponent may be fallacious. Evidence from                           Barnes [ed.], Some contemporary             studies in
Richman and Rogers (1969) and Conover                             marine science. Allen and Unwin.
 ( 1966) suggests that large particles are not                HARGRAVE, B. T., AND G. H. GEEN. 1970. Ef-
                                                                  fects of copepods grazing on two natural phy-
removed by filtration but are grasped by                          toplankton     populations     (A. tonsa).     J. Fish.
raptorial feeding modes before ingestion.                         Res. Bd. Can. 27: 1395-1403.
One cannot categorize particles into these                    MARSHALL, S. M., AND A. P. Onn.              1960. Feed-
                                                                  ing and nutrition, p. 227-258.          In T. H. Wa-
two modes of feeding with certainty be-                           terman [ea.], The physiology of Crustacea, v.
 cause there is a gradation between the two                       1. Metabolism       and growth.      Academic.
180                                                    Comment

MULLIN, M. M.           1963. Some factors affecting           -.        1974.    Seasonal grazing of Pseudocakz-
    the feeding of marine copepods of the genus                     nus min&us     on particles.  hlar. Biol. 25:
     Calanus.      Limnol.    Oceanogr. 8: 239-250.                 109-123.
NIVAL, P., AND S. NIVAL.            1973. Efficacite      de   RICHMAN,S., AND J. N. ROGERS. 1969. Thefeed-
     filtration   des copkpodes planctoniques.         Ann.        ing of Calanus helgolandicus on synchronously
    Inst. Oceanogr. 49 ( 2 ) : 135-144.                             growing   populations  of the marine diatom
-,            AND -.           1976. Particle    retention         Ditylum brightwellii.    Limnol. Oceanogr. 14 :
    efficiencies of an herbivorous copepod, Acartia                701-709.
     c2ausi ( adult and copepodite stages) : Effects           SAVILLE, A. 1958. Mesh selection in plankton
     on grazing.       Limnol.   Oceanogr. 21: 24-38.              nets. J. Cons., Cons. Int. Explor. Mer 23:
PAFFENH~FER, G. A. 1971. Grazing and inges-                         192-201.
    tion rates of nauplii, copepodids,         and adults      SHELDON, R. W., A. PRAKAsH, AND W. H. SUT-
    of the marine planktonic           copepod Calanus             CLIFFE, JR. 1972. The size distribution       of
    helgolandicus. Mar. Biol. 11: 286-298.                         particles in the ocean. Limnol. Oceanogr. 17 :
POULET, S. A. 1973. Grazing of Pseudocalanus                        327340.
    minutus on naturally           occurring   particulate     WILSON, D. S.     1973. Food size selection   among
    matter.      Limnol.   Oceanogr.      18: 564-573.             copepods.     Ecology 54: 969-914.

A comment          on rate measurements                in open      system?

    It is often necessary to measure the rate                  condition is usually not difficult to achieve
of production or consumption of some ma-                       in practice. In this case the concentration
terial, p, in a flow system such as that il-                   of p in the tank becomes spatially uniform
lustrated schematicahy in Fig. 1, when p                       and equal to C, and we can apply mass
is present as a variable natural constituent                   conservation to write
of the fIuid. Examples may be found in
measurements of respiration        rates (e.g.                          wi(t) + f@>l - [ioG(m
Winberg 1960; Galtsoff 1964; DiSaIvo and                                      = d/dt[VC,(t)].                  (1)
Gundersen 1971), feeding rates (e.g. Walne
                                                               In words, the rate p enters plus the produc-
 1972; Tenore and Dunstan 1973), and else-
                                                               tion rate minus the rate p leaves equals the
where. To be specific we assume that a
                                                               rate of change of p in the tank. If we de-
current i0 ( liter s-l) flows through a tank
                                                               fine the flushing time r = (V/i,) we have
of volume V (liters). Our measured quan-
tities are the concentrations of p at the in-                  p(t) = jo[co(t>-G(t) ++G/dt)l,                  (2)
put and output, C( and C, ( g liter-l).  From
these we wish to obtain the rate at which                      where the right-hand        side contains only
p is produced in the tank, 9 ( g s-l ) .                       measured quantities.
    In the simplest case, Ci and $J are inde-                     It appears that, as in all work cited pre-
pendent of time and we have p = iO( C,                         viously, the contribution      of the derivative
- Ci). When Ci, or p, or both, are func-                       or storage term is quite commonly ignored.
tions of time the relation is considerably                     It is tempting to argue that decreasing r
more complicated. In general, C,(t) must                       by increasing i0 would justify its neglect,
be written as a convolution which explicitly                   but this is not always true; in fact, in some
involves the past history of Tj and Ci as well                 circumstances just the opposite may be
as the dynamical properties of the system.                     true. Consider for example a case in which
Fortunately there is one situation in which                    p is constant and Ci( t ) = A + B cos ot,
the time dependent case also has a simple                      where B and o are independent of iO. This
solution, and that is if the mixing time in                    could perhaps represent a tidal component
the tank is short in comparison to all other                   of p on the incoming water. The fractional
characteristic times in the problem. This                      error produced by neglect of the derivative
                                                               term, 6 ( t) = ( jOr/p) dC,/dt has a maximum
  ’ Supported    by EPA contract       803143-01-2.            value a,,, = (BoV/fI) (1 + 02V2/j,2)-x for

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