J. Exp. Mar. Biol. Ecol., 1987, Vol. 113, pp. 231-245
231
Elsevier
JEM 00974
Lift as a mechanism of patch initiation in mussel beds
Mark W. Denny
Hopkins Marine Station, Department of Biological Sciences, Stanford University, Pacific Grove, Cal$oomia.
U.S.
(Received 10 February 1987; revision received 29 July 1987; accepted 26 August 1987)
Abstract: The mussel hfytilus caZ@nianur is the dominant competitor for space in the mid-intertidal zone
of wave-swept rocky shores in the Pacific Northwest where it forms extensive tightly packed beds. The rate
at which patches are formed in these beds, can play an important role in community ecology by controlling
the establishment and persistence of fugitive species. Despite the biological importance of physical
disturbance, the mechanism of patch initiation has not been adequately explained. Battering by logs can
create patches, but is the predominant mechanism only on shores near active logging sites. In other areas,
it has been speculated that the hydrodynamic forces associated with storm waves somehow cause patches
to form. However, the forces acting along the direction of Bow - drag and the acceleration reaction - are
unlikely to initiate patch formation. Here, it is suggested that fluid-dynamic lit? forces imposed on mussel
beds by breaking waves are sufficient to dislodge individual mussels and trigger patch formation. Arguments
are presented suggesting that the likelihood of dislodgment by lift is consistent with the observed rate of
patch formation in the absence of log battering.
Key words: Hydrodynamic force; Lift; Mussel; Myth
calijixnianuc; Patch dynamics; Patch formation
INTRODUCTION
The mussel M_~tiZuscalij3mianus is the dominant competitor for space in the
mid-intertidal zone of wave-swept rocky shores in the Pacific Northwest (Paine, 1974,
1976; Dayton, 1971; Paine & Levin, 1981). The biological interactions among mussels,
their predators, and their competitive subordinates play a key role in structuring
intertidal communities (Dayton, 1971, 1973; Levin & Paine, 1974, 1975; Paine, 1974,
1976; Suchanek, 1979; Paine & Levin, 1981, others). Of particular interest, is the role
played by physical disturbance of mussel beds. The ecological consequences of
disturbance in mussel beds have been well-documented (Dayton, 1973; Levin & Paine,
1974, 1975; Paine & Levin, 1981; Sousa, 1985). For instance patch formation, the
clearing of areas in the bed, is a controlling factor in the establishment and persistence
of local populations of fugitive species, such as the sea pahn Postelsia palmaefomzis
(Dayton, 1973; Paine, 1979).
Despite the biological importance of physical disturbance, the mechanism of patch
initiation (i.e., the initial dislodgment of one or a few mussels from the substratum) and
Correspondence address: M. W. Denny, Hopkins Marine Station, Department of Biological Sciences,
Stanford University, Pacific Grove, CA 93950, U.S.
0022-0981/87/$03.50 0 1987 Elsevier Science Publishers B.V. (Biomedical Division)
232
M. W. DENNY
subsequent short-term expansion in mussel beds has not been carefully examined.
Dayton (1971) has shown that battering by logs can create patches in mussel beds, but
this is probably the dominant mechanism only on shores near active logging sites. Paine
& Levin (198 1) found that patch formation by log battering was infrequent at several
open-coast sites in Washington. Along shores where log battering is rare, it is clear that
the hydrodynamic forces associated with large storm waves are somehow responsible
for patch formation. However, the nature of these forces is vexing. A priori, the
formation of tightly packed beds would seem to be an ideal strategy for avoiding damage
from wave-induced hydrodynamic forces. Each mussel in the bed shields its downstream neighbor from the prevailing flow and thereby from the hydrodynamic forces
acting along the direction of flow [drag and the acceleration reaction (Denny, 1982,
1983, 1985, 1987, in press; Denny et al., 1985)], and the tightly packed bed provides
physical support in resisting these forces.
Special circumstances can affect the hydrodynamic forces imposed on mussel beds.
For example, Dayton (1973) showed that mussels to which P. palmaeformis is attached,
are often dislodged in storms. Witman & Suchanek (1984) have shown that macroalgal
epizoites can substantially increase the drag imposed on a mussel, suggesting a
mechanism for the dislodgments noted by Dayton (1973). Unfortunately, the measurements of Witman & Suchanek (1984) may not be applicable to the problem of patch
initiation. First, mussels in the low-intertidal zone on exposed shores (or in the midintertidal zone if the slope of the shore is gradual, e.g., the benches studied by Sousa,
1984) commonly have algal epizoites and would thereby be subjected to increased drag.
However, large-bladed macroalgae (other than P. palmaeformis) are rarely found
attached to mussels in mid-intertidal beds on steeply sloping shores, such as those
studied by Paine & Levin (1981). Certainly, the algal epizoites studied by Witman
& Suchanek (1984) (Laminaria saccharina and Alaria marginata) as-e virtually absent
from the mid-intertidal beds on steeply sloping exposed shores. The vast majority of
patches studied by Paine & Levin (1981) were initiated at sites without large epizoic
macroalgae (Paine, pers. comm.). Secondly, an extrapolation from the drag measurements made by Witman & Suchanek (1984) shows that drag alone is not sufficient to
dislodge mussels. An average of the data shown in their Fig. 3 suggests that drag (N)
increases as 0.93 [velocity (m/s)]“.6’. At the extreme water velocity they estimate at
Tatoosh Island (16 m/s), this would result in a drag force of only 5 N, an order of
magnitude lower than the lowest force of dislodgment they measured for M. cal$wniunus
at this site. Further, they measured the mussels’ ability to resist forces applied
perpendicular to the substratum, while drag acts parallel to the substratum. The support
provided by neighboring mussels makes it much more difficult to dislodge a bed mussel
parallel to rather than perpendicular to the substratum, making it even less likely that
an increase in drag alone will be sufficient to initiate a patch. Only if a portion of the
bed is initially detached by being pulled away from the substratum can drag and the
acceleration reaction effectively act to dislodge mussels in the midst of a bed.
Once a patch is initiated, it is not difficult to understand how the disturbance is
LIFT ON MUSSELS
233
propagated by subsequent waves. Bed mussels attach to each other as well as the
substratum, forming a cohesive fabric; once a small area is ripped free from the
substratum and allowed to flap in the flow, drag can act to peel up adjacent areas much
as one would peel a rug from the floor. The patch wilI expand in the course of a few
waves until halted by some structure on the substratum (e.g., a crevice or protruding
rock) or by a group of mussels more firmly adherent to the substratum than to their
neighbors. In this scenario, epizoites, although ineffective in initiating patches, could
serve to enhance subsequent patch expansion by increasing drag.
The mechanistic problem in patch formation, then, is not how patches are enlarged
but how the initial rip is formed in the bed fabric. This study examines the possibility
that lift can initiate patch formation by locally detaching mussels from the substratum.
Extrapolations from field measurements of lift-producing pressures suggest that lift can
act to initiate patches and thereby can provide a mechanistic explanation for disturbance
in mussel beds.
The long-term expansion of patches has been addressed by Dayton (1971), who
suggested that patches can continue to grow for years, and by Paine & Levin (1981),
who in a more comprehensive study found that after the initial formation of a patch its
size grew only slowly or not at all. Witman & Suchanek (1984) report that mussels near
the edges of patches are more strongly attached to the substratum, providing an
explanation for the lack of patch growth noted by Paine & Levin (198 1). These issues
will not be addressed here.
LIFT
Lift is defined as any hydrodynamic force which acts perpendicular to the direction
of fluid motion. It is most familiar as the force that keeps birds, insects, and airplanes
aloft. In these cases, lift acts upward in opposition to gravity, but in the present context
we are concerned with the lift that can act to pull mussels away from the substratum.
Lift is caused by a difference in pressure between opposite sides of an object. In general,
this pressure difference is associated with a difference in fluid velocity. For instance,
air moves faster across the top of a wing than across the bottom, and, in accordance
with Bernoulli’s principle, there is a lower pressure above the wing than below (for a
complete explanation, see Prandtl8z Tietjens, 1934, Sabersky et al., 1971, or any other
standard text in fluid dynamics). This difference in pressure (a net force per area) acts
over the area of the wing, resulting in lift. The same general concept applies to a mussel
bed. As a wave surges up the shore, there is a higher velocity above the bed than in the
bed’s interstices. Although the turbulent nature of the flow and the proximity to a solid
surface do not allow for a direct application of Bernoulli’s principle in this case, it is
nonetheless reasonable to expect that the pressure near the substratum is higher than
the pressure in the flow above the bed, resulting in a force tending to pull mussels away
from the rock.
In general, the pressure difference responsible for lift is proportional to the square of
velocity (U).
234
M.W.DENNY
Pressure difference = (l/2 p v”) C, ,
(1)
where p is the density of the fluid (in this case seawater, p = 1025 kg/m3) and C, is the
coefficient of lift (for a full explanation, see Vogel, 1981, or any standard text in fluid
dynamics). Eqn. 1 is used to define the lift coefficient
C, = 2 (pressure difference)/(@).
(2)
When multiplied by the cross sectional area of a mussel (Ap, projected perpendicular
to the substratum), the pressure difference yields the lift on the mussel,
lift = (l/2 p v’) C, A,.
(3)
METHODS
Experiments were conducted in March 1985 on the mussel beds of Tatoosh Island,
Washington (48”24’N : 124”44’W), the site of many of the beds described by Levin &
Paine (1974,1975), Paine (1974,1976), Paine & Levin (1981), and Witman & Suchanek
(1984).
The tenacity of mussels in beds was determined as follows. A small hole was drilled
through the shell of a mussel near the posterior lip using a high speed drill. A hook was
inserted through the hole and attached to a recording spring scale similar in principle
to that described by Jones & Demetropoulos (1968). The scale was used to pull on the
mussel in a direction normal to the substratum, and the force required to dislodge the
mussel was noted. The dislodging force was applied rapidly (over l-2 s), but not as an
abrupt jerk. The length, maximum width, and maximum thickness of the shell were
measured with vernier calipers, and the projected area of the shell (A,) calculated by
assuming the width and thickness to be the axes of an ellipse. Tenacity is expressed as
dislodgment force per projected area (N/m*). A total of 99 mussel tenacities was
measured at four sites on the exposed southern and southwestern shores of Strawberry
Island, a subisland of Tatoosh Island. Within each site, mussels were selected
haphazardly for tenacity measurements, the only criterion being that each individual
was deemed far enough away from the location of previous tests (x 30 cm) as to be
unaffected by any resulting disturbance of the bed. The beds where these measurements
were taken were < 6-8 yr old (Paine, pers. comm.), and were one or two mussels thick.
The majority of mussels were attached directly to the rock substratum. The application
of results from these relatively young beds to older multilayered beds is addressed in
the discussion.
Direct measurement of hydrodynamic forces on mussels in a bed is problematic.
Most force transducers measure force by measuring the deflection of a beam or spring
in response to the force imposed on the test object, and thus require that the object be
free to move. Because mussels in a bed are held relatively immobile both by their byssal
LIFT ON MUSSELS
235
attachments and by friction among the tightly packed shells, the use of standard force
transducers is precluded. Here, this problem is circumvented by measuring the pressure
difference which causes lift.
The voltage signals from two absolute pressure transducers (Sensym 1603A) were
compared by a differential amplifier to provide a voltage proportional to the difference
in pressure between the ports of the transducers. The transducers were housed in a
water-tight container and their ports connected to the mussel bed by z l-m lengths of
g-mm i.d. oil-filled copper tubing. The two tubes were insinuated into the mussel bed
with minimal disturbance of the mussels, and were held in place by the mussels
themselves. The end of one tube was situated near the surface of the bed and the other
on the substratum at the base of the bed (Fig. 1); the vertical distance between the two
I
VOLTAGE-
FREOUENCY
TO TAPE RECORDER
CONVERTER
FLOW
A
DIFFERENTIAL
PRESSURE
AMPLlFlER
TRANSDUCERS
Fig. 1. A schematic diagram of the apparatus used to measure tram-bed pressure differences acting on a
mussel bed.
was z 7 cm. The transducer housing was secured to the rock and the signal carried via
cable to a voltage-to-frequency converter (LaBarbera & Vogel, 1976) housed well above
the splash zone. The frequency modulated signal was recorded on tape cassette using
a Sony TC-D5M recorder. The second channel of the recorder was connected to a
microphone and used to annotate the pressure record. The taped records were returned
to the laboratory, the original voltage signal reconstructed via a frequency-to-voltage
converter (National Semiconducter LM2917) and recorded on an oscillographic chart
recorder (Gould 220) for further analysis.
The pressure transducer/recording system was calibrated in the laboratory prior to
traveling to Tatoosh Island by imposing a series of accurately known static pressure
hea’ds on each of the pressure ports. The O-force frequency of the frequency-to-voltage
236
M.W. DENNY
converter was set at 1150 Hz, sufficient to provide a flat response to input signals with
a frequency of < z 10 Hz.
The pressure transducer was installed at a site near the north end of the Glacier
mussel bed, the study site of Paine (1974). The Glacier bed borders a broad surge
channel, and incident swell from the southwest results in the propagation of turbulent
bores over the test site. Pressures were recorded near high tide on the evening of
5 March 1985 and the following morning. In neither instance were large (i.e., storm)
waves present, but the surf on 5 March was more energetic and these records are used
here. During the recording period, the bores incident on the test site were visually
estimated to have a height of 1 m. It is assumed that this visual estimation corresponds
to the significant bore height (Kinsman, 1965; U.S. Army Corps of Engineers, 1984)
and is approximately equal to the average of the highest l/3 of the bores present. The
wave period during recording was 10-l 1 s.
RESULTS
Pressure differences corresponding to lift were recorded on 120 of the 160 bores
which passed the test site during the recording period. The 40 bores which did not result
in lift were the smallest observed, and in most cases did no more than till the interstices
of the bed without resulting in substantial mainstream flow above the bed.
Three typical pressure records are shown in Fig. 2. The initial pressure difference
tending to force mussels into the substratum is attributable to the face of the bore
SECONDS
Fig. 2. Three typical records ofpressure
differences recorded on Tatoosh Island. Pressure
could result in lift are arbitrarily shown as positive pressures.
differences
which
237
LIFT ON MUSSELS
crashing onto the pressure port at the surface of the bed. Subsequent flow results in a
pressure difference tending to pull mussels away from the substratum; the magnitude
of the pressure difference decreases as the bore moves beyond the site. The mean
lift-producing pressure difference was 2457 N/m’ (SD = 1689 N/m*) and the maximum
pressure difference was 7498 N/m*.
A cumulative probability distribution (the “exceedance” distribution) of the 120
lift-producing pressure differences is shown in Fig. 3. This figure shows the probability
that a wave, chosen at random from those present during the test, will exert a pressure
difference greater than a specified value.
0
2
4
PRESSURE DIFFERENCE
6
(N/m”4
8
000)
Fig. 3. The exceedance distribution of the 120 lift-producing pressure differences. The solid curve is the
Rayleigh distribution calculated from the mean pressure difference. This is the distribution which could
theoretically be expected on the basis of the wave height distribution in the nearshore (see Thornton &
Guza, 1983, and Denny, 1985, 1987). The deviations from the Rayleigb distribution are similar to those
noted for forces on exposed limpets (Denny, 1985).
A cumulative probability distribution of mussel tenacities is shown in Fig. 4, where
in this case the ordinate is the probability of a mussel having less than a specified
tenacity. The mean tenacity measured in the study for bed mussels (1.27 * lo5 N/m*,
SD = 6.3 * lo4 N/m*) is not significantly difTerent from that measured by Denny et al.
(1985) for solitary mussels on Tatoosh fsland (2 = 1.25 * lo5 N/m*, SD = 4.0 * lo4
N/m’). Tenacity increases slightly with mussel size (and thereby, presumably, with age)
(see Fig. 5), but the dependence of tenacity on size explains < 10% of the variance in
tenacity and may not be biologically significant.
M. W. DENNY
238
2
IO
6
IS
14
22
26
30
TENACITY (Nlm2-I 041
Fig. 4. The cumulative probability distribution of mussel tenacities at four sites on Tatoosh Island. The
ordinate is the probability that a mussel chosen at random will have less than the tenacity specified on the
abscissa.
30
26
"0
22
6
4
6
6
MUSSEL LENGTH
IO
12
(cm)
Fig. 5. The relationship between mussel length and tenacity. The solid line is the least squares fit to the data:
tenacity (N/m2) = 3.362. lo4 + 1.202. lo4 length (cm). Although the regression line has a slope statistically
signiticant from 0 (r = 0.303, P < O.OOS),
the regression exphtins < 10% of the variance in tenacity and may
not be biologically significant.
DISCUSSION
The results of this study indicate that wave-induced water motion can impose lifts
on bed mussels. Are these lifts suffkient to initiate patch formation? Unfortunately, the
measurements made during this study did not coincide with a storm large enough to
LIFT ON MUSSELS
239
cause damage to the mussel bed, so it is necessary to extrapolate from these results.
Eqn. 1 provides a means for this extrapolation, if (1) the water velocities present during
storms can be estimated, and (2) an appropriate lift coefficient can be calculated.
Carstens (1968) proposed that the maximum water velocity associated with breaking
waves is approximately equal to that at the wave crest as the wave breaks. At breaking,
the water velocity at the crest is equal to the wave celerity, the speed with which the wave
form is propagated (Carstens, 1968, U.S. Army Corps of Engineers, 1984). To a first
approximation (from solitary wave theory) this speed is
u
rnax
=
MD + m11’2,
(4)
where g is the acceleration due to gravity (9.81 m/s2), His the wave height (the vertical
distance from still water level to the wave crest) and D is the water depth (below still
water level) at which the wave breaks. On steep shores such as those of Tatoosh Island,
waves break when H is approximately equal to D (Galvin, 1972). Thus,
u
umax
max
=
(2g w*
2=2gH.
(5)
The maximum water velocity associated with a turbulent bore surging over the
substratum is the same as that associated with a breaking wave. Denny (1985) has
shown that this value of maximum water velocity can be used to provide an accurate
estimate of maximum forces on intertidal organisms, and it is used in the present
calculations. At the test site during this study D = 0 (the site was very near still water
level) and H was visually estimated at 1 m, implying that maximum water velocities were
w 3 m/s.
The estimate of H = 1 m is assumed to be the average height of the l/3 largest bores.
By further assuming that these large bores caused the largest l/3 of the recorded
pressures, an estimate of the lift coefficient can be calculated. The average of the l/3
largest pressure differences is 4431 N/m* (SD = 1230 N/m’). Inserting this value and
the estimated water velocity of 3 m/s into Eqn. 2 yields an estimated C, of 0.88. This
C, and the maximum velocity calculated from Eqn. 5 can be inserted into Eqn. 1 to
estimate the maximum lift per area imposed on bed mussels,
maximum pressure difference = lift/A, = (8.9 * 103) H,
(6)
when pressure difference is expressed in N/m’, A, in m*, and H in m. Thus, a wave 5 m
high at breaking is accompanied by velocities sufficient to exert a maximum lift per area
of = 4.4 * lo4 N/m2. Such waves are common in winter storms on Tatoosh Island (U.S.
Navy, 1973; pers. obs.). From Fig. 4 it can be seen that this pressure difference would
be sufficient to dislodge z 7.5 % of the mussels to which it was applied. Waves of > 9 m
240
M. W. DENNY
height have been recorded in the vicinity of Tatoosh Island (U.S. Navy, 1973), and
should be capable of imposing a lift/area > 8 - lo4 N/m*. This pressure would be
sufficient to dislodge ~22% of the mussels to which it was applied.
Patch formation is a relatively rare occurrence. Paine & Levin (198 1) report that only
0.32-8.15 % of mussels are dislodged per month during the winter on Tatoosh Island.
Yet, the dislodgment percentages calculated above suggest that a single application of
the pressure difference caused by a storm wave could dislodge 7.5-22% of mussels. Can
these calculated dislodgment percentages due to lift be reconciled with the observed
rates of patch formation? In answering this question, three factors must be taken into
account.
(1) The maximum velocity associated with the breaking wave will not be applied to
all mussels in a bed. A breaker or bore slows down as it loses energy to turbulence and
as it surges up the shore against the acceleration of gravity, and only those mussels
closest to the point where the breaker first strikes the shore will be exposed to the
maximum velocity. Thus, a 5-m breaker can dislodge 7.5% of the mussels in the
portion of the bed nearest where the wave hits, but will dislodge a much smaller
percentage of the entire bed. The portion of the bed exposed to the largest velocities
depends on the still water level, and will thus vary with the tides (see Denny, 1985, for
a model of this process).
(2) The destructive actions of waves are not strictly additive. If one wave dislodges
7.5 % of the mussels in the bed, a second identical wave will not dislodge an additional
7.5%. Consider the tenacity distribution for Tatoosh mussels (Fig. 6A). A wave
imposing a uniform pressure difference of 4 * lo4 N/m* will dislodge the 7.5 y0 of mussels
having the smallest tenacities, resulting in the new distribution shown in Fig. 6B. An
identical pressure difference applied to these remaining mussels would cause no further
A
6
TENACITY
Fig. 6. For legend,
see opposite
page.
(N/m24
00)
241
LIFT ON MUSSELS
I590
TENACITY
TENACITY
2365
(N/m2.
3160
100)
(N/m’.1
00)
Fig. 6. The distribution of mussel tenacities. A, observed. B, after the imposition of a lift pressure of 4. 10“
N/m*. Several low-tenacity mussels have been dislodged, shifting the distribution slightly to higher tenacity
values. C, the net changes in the percent of mussels having various tenacities required to change distribution
(B) to distribution (A).
dislodgments, all the susceptible mussels having been eliminated by the first wave.
Repeated application of the same pressure will only dislodge those mussels whose
tenacity has sufficiently decreased since the last pressure was applied. For example,
Fig. 6C shows the net changes in the percent of mussels having various tenacities
required to return the distribution of Fig. 6B to that of Fig. 6A. Thus, the rate at which
individual mussels are dislodged by the repeated large lift forces imposed during a storm
will be determined both by the magnitude of the forces applied and by the net rate at
which high-tenacity mussels become less tenacious. The net rate of change of mussels’
242
M.W. DENNY
tenacities will in turn depend on two factors. (a) Mussels may be weakened, but not
dislodged, by a wave, and thereby become susceptible to the next force imposition. For
instance, there may well be a local effect of the removal of one individual mussel by lift
-the mussels surrounding the removed individual are deprived of an area to which they
can attach byssal threads and their tenacity consequently may be lowered. This type of
decrease in tenacity can occur rapidly (i.e., during a single wave). Alternatively, a
decrease in tenacity due to degradation of byssal threads or the substratum may take
considerably longer (days to years). (b) Mussels can respond to an increase in applied
force by increasing their tenacity. For example, Witman & Suchanek (1984) found that
mussels at the edge of a bed (where drag forces are presumably relatively large) have
a greater tenacity than mussels in the middle of a bed where drag forces are small. Price
(1980) found that mussels M. edulis have a greater tenacity in the winter than the
summer, presumably in response to imposed forces. An increase in tenacity through the
attachment of more byssal threads requires minutes to days to accomplish. The relative
rates at which these two counteracting processes occur will determine the net rate at
which a bed becomes susceptible to the repeated imposition of lift forces.
(3) The rate at which individual mussels are dislodged will be greater than the rate
at which patches are initiated. Even allowing for the local decrease in tenacity described
above, the dislodgment of one mussel in the midst of others may not provide sufficient
disturbance to allow drag and the acceleration reaction to “grab” the bed and form a
patch. More likely, the dislodgment of several adjacent mussels is necessary to initiate
patch formation. If we assume that the dislodged mussels are scattered randomly
through the bed, the probability of several adjacent mussels being dislodged can be
calculated. Consider a wave which dislodges 5% of all mussels. At the test site on
Tatoosh Island, there are z 20 mussels in each lo-cm square of the bed. Thus, for this
particular force imposition, there is on average one mussel dislodged in each lo-cm
square (100 cm’) of the bed. The probability of multiple mussels being dislodged by a
single wave in a particular IO-cm square is calculated from the Poisson distribution,
probability of X mussels being dislodged in a lo-cm square = iZx/(euX!),
(7)
where U is the mean number of mussels dislodged (in this case, 1). The probabilities of
multiple mussels being dislodged are shown in Fig. 7. Even when as many as 5% of
mussels are dislodged by a single wave, the probability of seven to eight mussels being
in close proximity to each other is quite small, and the probability of patch initiation
may be similarly small.
Unfortunately, at present it is not possible to specify the number of mussels which
must be removed simultaneously from a small area to initiate patch formation. The
validity of this calculation could be affected by the possibility that the removal of an
individual affects the susceptibility of those around it (noted above). If this is the case,
the random dislodgment assumed in calculating the Poisson distribution will not be
found. Similarly, the time-varying tenacities described above preclude the use of the
243
LIFT ON MUSSELS
Poisson distribution to describe the removal of multiple mussels from a small area at
different times.
Further work must be done before these three factors can be quantified. However,
each of these qualitative considerations provides a reason why the rate of patch
o-
.
-I
.
-
Mean Number
L
=
I
.
i -2 E
$
o-3
E
Dislodged
l
.
-
.
8 -4 _
.
?
l
-5 -
.
-6 -
-7
L
I
I
I
I
2
3
NUMBER
I
4
OF MUSSELS
I
5
I
I
I
I
l
6
7
8
9
IO
DISLODGED
PER
IO0
CM ’
Fig. 7. The probability of multiple dislodgments in a IO-cm square area of the mussel bed when the mean
number of dislodgments is one. Calculated from the Poisson distribution (Eqn. 7) assuming that the
dislodgments are scattered randomly through the bed.
formation should be slow even though an individual wave may locally dislodge a
substantial fraction of mussels. Thus, the suggestion that lift forces can be responsible
for patch initiation appears consistent with the observed low rate of patch formation
on Tatoosh Island.
Although lift provides one likely mechanical explanation for the initiation of patches,
there is no reason to assume that it is the sole mechanism by which patches form. Two
possible alternative mechanisms, log battering and drag from epizoans, have already
been mentioned. Further, in older mussel beds, it is not uncommon to find “hummocks”,
small groups of lo-20 mussels, which have become detached from the rock and forced
upwards above the bed surface. These hummocks could serve as initiation sites for
patch formation, and may be formed by mussel-mussel pressures as individuals grow
in a tightly packed bed. There also may be underlying biological mechanisms which
predispose certain beds to being dislodged by lift. Paine & Levin (198 1) note that there
is a certain length of time (7-10 yr) during which a recovering mussel bed is immune
to patch formation, suggesting that either the tenacity of mussels becomes weaker after
this period or that some property of the aging bed enhances lift. The present data cannot
be used to decide between these possibilities. It does seem likely, however, that the
244
M. W. DENNY
degradative action of infauna and the propensity for mussels in an old multilayer bed
to attach to each other rather than the substratum (Harger & Landenberger, 197 1) could
progressively decrease the tenacity of older beds, rendering them increasingly susceptible to patch initiation via lift.
A final note can be made regarding the distribution of lift pressures recorded in this
study (Fig. 3). Eqn. 6 suggests that on steeply sloping shores the pressure difference that
causes lift is a linear function of wave height. Using a combination of wave theory and
empirical measurements, Thornton & Guza (1983) have shown that broken waves have
a particular distribution of heights, known as the Rayleigh distribution. One would thus
expect that lift-causing pressures would similarly have a Rayleigh distribution, shown
as the solid line in Fig. 3. This theoretical distribution has been used as a tool for
predicting the probability that a given organism will encounter forces of a specified
magnitude (Denny, 1987, in press). However, the observed distribution of lift-causing
pressures differs from the expected Rayleigh distribution - there are more small and
large pressures and fewer medium pressures. The distribution observed here is similar
to that reported by Denny (1985) for wave forces imposed on limpets at an exposed site
on Tatoosh Island. If future studies show this non-Rayleigh distribution of forces to be
a general feature of intertidal habitats it will be interesting to examine the mechanistic
basis for the deviation from the expected, Rayleigh distribution.
ACKNOWLEDGEMENTS
This study was supported by NSF Grant OCE83-14591 with logistical support from
NSF Grant OCE77-26901 to R. T. Paine. I thank R. T. Paine, L. Johnson, S. Gaines,
E. Carrington, W. Sousa, and an anonymous reviewer. The U.S. Coast Guard and the
Makah tribe allowed me the privilege of conducting research on Tatoosh Island.
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