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Structurally complex sea grass obstructs the sixth sense of a
specialized avian molluscivore
Jimmy de Fouw
a
,
*
, Tjisse van der Heide
b
,
c
, Thomas Oudman
a
, Leo R. M. Maas
d
,
Theunis Piersma
a
,
e
, Jan A. van Gils
a
a
Department of Coastal Systems, NIOZ Royal Netherlands Institute for Sea Research, and Utrecht University, Den Burg (Texel), The Netherlands
b
Groningen Institute for Evolutionary Life Sciences (GELIFES), University of Groningen, Groningen, The Netherlands
c
Aquatic Ecology and Environmental Biology Group, Institute for Water and Wetland Research, Radboud University Nijmegen, Nijmegen, The Netherlands
d
Department of Physical Oceanography, NIOZ Royal Netherlands Institute for Sea Research, and Utrecht University, Den Burg (Texel), The Netherlands
e
Chair in Global Flyway Ecology, Conservation Ecology Group, Groningen Institute for Evolutionary Life Sciences (GELIFES), University of Groningen,
Groningen, The Netherlands
article info
Article history:
Received 20 June 2015
Initial acceptance 31 August 2015
Final acceptance 27 January 2016
MS. number: 15-00530R
Keywords:
Calidris canutus
obstruction
prey detection
sea grass
searching efficiency
Predators have evolved many different ways to detect hidden prey by using advanced sensory organs.
However, in some environmental contexts sensory information may be obscured. The relation between
sensory organs, obstruction and searching efficiency remains little explored. In this study we experi-
mentally examined the ways in which a sensory system (‘remote detection’), which enables red knots,
Calidris canutus, to detect hard objects buried in wet soft sediments, is obstructed by plants. At an
important coastal nonbreeding site of this species, the Banc d'Arguin (Mauritania, West Africa), most of
the intertidal foraging area is covered by sea grass. The structurally complex networks of belowground
roots and rhizomes and aboveground sea grass may obstruct information on the presence of buried
bivalves and thus affect searching efficiency. Under aviary conditions we offered red knots buried bi-
valves in either bare soft sediments or in sea grass patches and measured prey encounter rates. Red knots
detected prey by direct touch in sea grass but remotely in bare sediment. Physical modelling of the
pressure field build-up around a probing bill showed that within a layer of sea grass rhizomes,
permeability is reduced to the extent that the pressure field no longer reveals the presence of an object.
In bare sediment, where searching efficiency is constant, red knot intake rate levelled off with increasing
prey density (described by a so-called type II functional response). In the sea grass beds, however, prey
density increases with sea grass density and simultaneously decreases searching efficiency, which will at
some point lead to a decrease in intake rate when prey densities increase (i.e. a type IV functional
response). Clearly, prey detection mechanisms dictate that the combined effects of prey density and
habitat complexity should be taken into account when predicting forager distributions and habitat
preference.
©2016 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.
Insights into the morphology and functionality of sensory or-
gans in animals have contributed to our basic understanding of
habitat selection and foraging distribution of animals searching for
prey (Cunningham et al., 2010; Miller &Surlykke, 2001; Piersma,
2012; Sleep &Brigham, 2003). Predators have evolved multiple
ways to detect their prey other than by sight. For example, bats
detect their prey in the dark by ultrasonic signalling (Schnitzler &
Kalko, 2001), owls use high acoustic sensitivity to detect their
prey by sound in the dark (Martin, 1986) and cetacean species often
use echolocation to detect their prey in the water column (Au,
Benoit-Bird, &Kastelein, 2007; Madsen, Kerr, &Payne, 2004). Us-
ing their sensitive bill tip, shorebirds (Scolopacidae) have evolved a
variety of ways to detect prey buried out of sight in soft sediments,
including smell, taste, detection of prey vibrations, direct touch and
even ‘remote detection’(Gerritsen &Meiboom, 1986; Hulscher,
1982; Nebel, Jackson, &Elner, 2005; Piersma, van Aelst, Kurk,
Berkhoudt, &Maas, 1998).
In some environmental contexts, sensory information may be
obscured. For example, vegetation cover on the water surface ob-
structs echolocation-based prey detection in insectivorous bats
*Correspondence: J. de Fouw, Department of Coastal Systems, NIOZ Royal
Netherlands Institute for Sea Research, and Utrecht University, P.O. Box 59, 1790 AB
Den Burg (Texel), The Netherlands.
E-mail address: jimdefouw@gmail.com (J. de Fouw).
Contents lists available at ScienceDirect
Animal Behaviour
journal homepage: www.elsevier.com/locate/anbehav
http://dx.doi.org/10.1016/j.anbehav.2016.02.017
0003-3472/©2016 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.
Animal Behaviour 115 (2016) 55e67
(Boonman, Boonman, Bretschneider, &van de Grind, 1998), and
underwater sea grass meadows may serve as an acoustic refuge for
fish from echolocation sounding by dolphins (Wilson, Wilson,
Greene, &Dunton, 2013). Yet, the relation between sensory or-
gans, obstruction and searching efficiency remains little explored
(Piersma, 2011). In this study we experimentally examined
whether sea grasses can obstruct prey detection by red knots,
Calidris canutus. Red knots are highly specialized molluscivorous
birds that usually forage on bivalves buried in the soft sediments of
intertidal mudflats (Piersma, 2007, 2012). They have a sensory or-
gan in the tip of the bill to detect hard-shelled prey buried in soft
wet sediments without direct contact (Piersma et al., 1998). As is
the case for other shorebirds, the tip of the bill contains numerous
tiny pits with clusters of Herbst corpuscles, which in red knots
enable the detection of self-induced pressure differences during
repeated probing in wet soft sediments. Using this form of ‘remote
prey detection’, red knots detect buried prey faster and more effi-
ciently than if they had to rely on direct touch (Piersma et al., 1998;
Piersma, van Gils, de Goeij, &van der Meer, 1995). A similar mode of
prey detection has been described for kiwis (Apterygidae) and
ibises (Threskiornithinae) (Cunningham et al., 2010; Cunningham,
Castro, &Alley, 2007; Cunningham, Castro, &Potter, 2009).
This model of prey detection is applicable to red knots foraging
on hard-shelled prey in bare soft sediments (van Gils, Spaans,
Dekinga, &Piersma, 2006; Piersma et al., 1995). However, at Banc
d’Arguin (Mauritania, West Africa), the subspecies C. c. canutus
mostly encounters and uses sea grass habitats (Altenburg,
Engelmoer, Mes, &Piersma, 1982; van Gils et al., 2015). These
habitats consist of structurally complex networks of belowground
roots and rhizomes and aboveground leaves (Larkum, Orth, &
Duarte, 2006). We hypothesized that searching efficiency, i.e. the
standardized rate at which foragers encounter their prey (Holling,
1959), will be negatively influenced by these structures, because
the remote detection system requires unobstructed passage of
water between the sediment particles (Piersma et al., 1998). To test
this idea, we measured searching efficiency in red knots by offering
them buried prey either in bare sediment or in sea grass-covered
sediment. Here, the bare sediment treatment served as a control
to verify whether red knots were able to find prey remotely
(Piersma et al., 1998). Additionally, we developed a model to show
the obstructing effect of sea grass rhizomes on the pressure field
build-up by the probing bill. We briefly discuss the implications of
this effect on the predicted relationship between prey density and
intake rate (i.e. the functional response).
METHODS
Birds
The experiment was conducted in January 2011 at the research
station of the Parc National du Banc d'Arguin, Mauritania, West
Africa (19
53
0
N, 16
17
0
W). Six red knots were caught with mist nets
on a nearby shoreline high-tide roost and colour-ringed for indi-
vidual identification. All birds were successfully released after the
experiments. Average bill length was 35.1 mm (range
33.6e37.0 mm) and body mass just after catching was 129 g (range
118 e144 g). Birds were kept as a group in a small aviary
(2.0 0.6 m and 0.4 m high) with sand on the floor, freshwater ad
libitum, and with local natural daylight cycles and temperatures
(varying between 18 and 24
C). Every morning, the birds were
weighed and their health status assessed. Birds were fed com-
mercial trout feed (Trouvit; Skretting, Stavanger, Norway) and live
bivalves that were collected locally on a daily basis. To keep birds
motivated to feed during the trials, daily portions were adjusted to
keep body mass just above 100 g (e.g. van Gils &Ahmedou Salem,
2015; Oudman et al., 2014).
Experimental Design
Feeding trials were conducted in the housing cage, in which a
feeding patch (10 cm depth and 15 cm radius) was created with
either bare sediment or sea grass (Fig. 1cee). Loripes lucinalis
(8.5e10.5 mm length), the most common bivalve in our study area
(Honkoop, Berghuis, Holthuijsen, Lavaleye, &Piersma, 2008), was
used as prey. Per patch, either 20 or 40 prey items were offered (283
and 566 individuals/m
2
). All prey were buried at a fixed depth at
either 1, 2 or 3 cm. For practical reasons all trials of each combi-
nation were offered in the same patch in which prey items were
replaced after each trial. All density and depth combinations were
offered twice to each bird (although never on the same day).
Densities and depths of bivalve prey were well within the range
reported for the field (Ahmedou Salem, van der Geest, Piersma,
Saoud, &van Gils, 2014; van der Geest, van Gils, van der Meer,
Olff, &Piersma, 2011; van Gils et al., 2015; van Gils et al., 2013;
Piersma, de Goeij, &Tulp, 1993). Patches were filled with sand
(mean medium grain size ±SE (N¼6): 248.0 ±2.7
m
m) collected at
the nearby intertidal beach (19
53.026
0
N, 16
17.573
0
W). Penetra-
bility of the sea water-saturated sand was kept constant by adding
sea water until 2 mm of water remained on top of the surface.
Sea grass was collected on a tidal flat (19
53.051
0
N, 16
17.367
0
W)
500 m east of the field station. Sea grass densities were within the
range reported from the field (range 2200e130 00 shoots/m
2
;van
Lent, Nienhuis, &Verschuure, 1991; Vermaat et al., 1993). A 15 cm
high sharpened PVC ring (15 cm radius) was pushed gently into the
sea grass (mean shoot density ±SE (N¼5): 8842 ±700 per m
2
).
The ring with the sea grass bed was taken out. Metal pins were
pushed in horizontally from the side of the ring through the sea
grass rhizome mat forming a 2.5 2.5 cm mesh holding the sea
grass mat intact. Next, the sediment was carefully sieved out, a
time-consuming process that was needed to remove all prey living
in the sea grass in order to be able to offer precise experimental
prey densities. Eventually, a ‘clean’intact sea grass mat (rhizomes,
roots and leaves) remained in the ring, which was then placed in a
15 cm radius,10 cm high container, thereafter filled with wet sand,
after removing the metal pins. Next, a plastic rod with a scale was
used to insert prey in their natural position into the sediment at the
aimed depth, at random spatial positions. The hole was filled and
the sand was smoothed (Piersma et al., 1995, 1998).
After a trial ended, the remaining prey items were counted. We
never noticed prey movements or any other signs of their presence
(i.e. the bivalves showing a siphon or extending a foot). Each trial
was conducted with one bird at a time, with each bird being
involved in at least one trial per day. Within each combination
offered on a given day, the order of the birds in the trials was
randomly chosen by rolling a dice. The five remaining birds were
held in a separate part of the cage such that they were in vocal and
visual contact with the experimental bird. A trial stopped after six
prey items were encountered or after 15 min.
Searching Efficiency and Touch Model
A digital video camera (CANON Powershot G9) recorded each
trial. Timing of prey encounters and ingestions were scored digi-
tally with Etholog (Ottoni, 2000), and the recordings were played
back in slow motion to confirm that we had not missed a prey
encounter. In a randomly searching forager, the interval between
two prey encounters, search time (T
s
), is inversely related to the
product of searching efficiency (a) and current prey density (D;
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e6756
initial prey density minus the number of prey removed; van Gils,
Schenk, Bos, &Piersma, 2003):
1
T
s
¼aD (1)
which can be rewritten as:
logðT
s
Þ¼logðaÞlogðDÞ(2)
In this relationship, a slope of 1 thus indicates random search,
while the intercept, elog(a), reflects the negative of searching ef-
ficiency (van Gils &Piersma, 2004; Piersma et al., 1995). A searching
efficiency that does not vary with prey density, together with a
handling time that is constant across prey densities, leads to Hol-
ling's type II functional response (Holling, 1959). In this well-known
equation, the intake rate of a forager increases as a function of prey
density, initially at a rate given by searching efficiency until it levels
off due to the handling time constraint. Hence, when red knots use
remote prey detection the functional response has a steeper slope
than with direct touch (Piersma et al., 1995).
To test to what extent red knots remotely detect buried prey, we
compared the experimentally observed searching efficiency with
the calculated searching efficiency based on a direct touch model
(see for details Hulscher, 1982; Piersma et al., 1995; Zwarts &
Blomert, 1992). We predicted a strong relation with prey depth
for the observed searching efficiencies in sea grass, following the
touch model (Piersma et al., 1995). The touch model was deter-
mined with the touch area of the prey (surface projection of prey
area), enlarged by the surface area of the bill tip multiplied by the
probe rate at each depth (1 cm classes; Appendix 1;Zwarts &
Blomert, 1992). Probe rates were scored during five time intervals
(ca. 10 s) for a selection of trials (all six birds equally distributed
over the two habitat treatments and three prey depths, N¼36), by
slowing down digital video recordings (1/8th of the recording
speed). Probe depth was measured five times in each interval by
freezing the digital video image at a probe's maximum depth and
using an individual's bill length as a reference.
Statistics
Average search and handling times (each denoted by Y
i
)were
calculated for every trial, with individual bird as a random effect
(bird
i
):
20
10
5
2
1
0.5
0.2
1.4
1.2
1
0.8
0.6
0.4
(b)
12
Pre
y
de
p
th (cm)
Handling time (s) Searching efficiency (cm2/s)
3
(a) (c)
(d)
(e)
Figure 1. (a) Searching efficiency as a function of prey depth of knots foraging on prey in bare (black) and sea grass (green) habitat. The grey lines indicate the touch model with
confidence interval (95%). (b) Prey handling time as a function of prey depth of knots foraging on prey in bare (black) and sea grass (green) habitat. (c) Bare patch, (d) sea grass patch,
(e) knot swallowing a prey during an experimental trial on a sea grass patch.
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e67 57
logðY
i
Þ¼aþb
1
prey depth
i
þb
2
logðprey density
i
Þþhabitat
i
þbird
i
þε
i
where ε
i
Nð0;s
2
Þ:
Search and handling times were log-transformed to meet model
assumptions (when Holling's type II functional response holds then
the predicted values for
b
2
are 1 and 0 for search time and
handling time, respectively). We used a one-sample ttest for a
difference between the observed and the estimated (touch-model)
searching efficiency. All statistical analyses were done in R (package
nlme for mixed-effect models; R Development Core Team, 2014).
The Physical Model
We developed a physical model to get mechanistic insight into
how sea grass may obstruct the remote detection of red knots (for
mathematical descriptions see Appendix 2). Observations and ex-
periments by Piersma et al. (1998) showed that knots are able to
remotely sense the presence of shells in wet bare sediment, and
that their sensory capacity fails in dry but also in very liquid mud.
However, a belowground sea grass mat, consisting of a network of
roots and rhizomes, reduces the sediment layer's permeability. This
may reduce the effective porosity of the soil and obstructs the
pressure field built up by the probing bill of red knots. We consider
first the response to a shell in a mud layer without a rhizome mat,
qualitatively discussed in Piersma et al. (1998), and second, the
response to a shell buried in the lower layer containingthe rhizome
mat.
The probing of the bill will produce pressure variations in wet
sediment (pore size 180
m
m). Red knots rapidly probe in the sedi-
ment over a depth of about 0.5e1 cm, usually in series of five to 10
probes at a rate of about 6e9Hz(Piersma et al., 1998). The property
of the medium at hand determines in what way it responds to
pressure variations. In dry sediments it can either be supported by
normal stresses (pressure) in the rigid sediment structure or be
released instantaneously when it surpasses a certain threshold. In
fluids, on the other hand, the pressure cannot be built up, as it will
immediately respond by means of flows and waves on the water
surface that will quickly remove the added energy towards infinity
(see Appendix 2). In wet sediment, however, there is enough water
in the pores to produce a flow through it driven by pressure dif-
ferences. But as the pores are tiny channels whose sides exert a drag
on the flow along them, this local increase in pressure needs time to
relax and can be maintained for a while, which is the property
employed by the birds.
The classical description of flow through wet sediment is one in
which the pressure gradient is balanced by friction, proportional to
the flow velocity. Because of the complexity of the sand skeleton
this is necessarily an empirical relation, known as Darcy's law (e.g.
Sleath, 1984). Since the fluid is nearly incompressible, this implies
the pressure field is governed by a Poisson equation (Lamb, 1932;
for details see Appendix 2).
The knot's sense of remote prey detection involves repetitive,
shallow probing, followed by a single deep probe in another di-
rection, apparently used to build up residual pressure near the bill
tip. Very likely, compaction is of dominating influence. This refers
to the continuous increase in residual pore pressure, owing to the
‘shaking’of the muddy sand by the probing action of the bill, which
may lead to a (local) compaction of sediment due to a rearrange-
ment of sand grains in closer packing and an associated increase in
pore pressure. This process plays a dominant role in liquefaction
and the formation of quick sand (Sleath, 1984). For knots, the
important aspects of this are that the residual (i.e. time-averaged)
pressure pattern is affected by the presence of a shell and that
this pattern becomes increasingly ‘visible’due to its increase at
each successive cycle of the probing motion. Together with the
directionality offered by the set of pressure sensors (Herbst cor-
puscles), present over the whole circumference of the bill, this
should offer the knot the ability to sense both prey direction and
distance (for details see Appendix 2).
For knots foraging in sea grass, however, the permeability of the
lower rhizome layer will be less than that of the upper mud layer.
This is due to the decrease in the effective porosity of the sediment.
We assume that the rhizome root structure is so small that we can
represent its presence in the form of a reduced effective perme-
ability which will affect the radial pressure distribution discussed
above. For simplicity, we assume the permeability to be constant
within the rhizome layer. Hence the pressure will again be
inversely proportional to radial distance, but with reduced ‘trans-
mitted’amplitude. In fact, the semipermeable interface between
the mud and rhizome layers acts as a partial mirror. This will result
in an augmented pressure field in the upper sediment layer.
Ethical Note
All possible efforts were made to minimize physical and mental
impact on the experimental animals. Each bird was weighed and
visually inspected for general condition daily. All experimental
animals were released in the wild in healthy condition after the
experiment with an average body mass of 147 g (range 136e16 0 g)
after 2 days of ad libitum food. The experiment was performed
under full permission by the authorities of the Parc National du
Banc d'Arguin. No animal experimentation ethics guidelines exist
in Mauritania but the experiments were performed in accordance
with Dutch animal experimentation guidelines. The NIOZ Royal
Netherlands Institute for Sea Research has been licensed by the
Dutch Ministry of Health to perform animal experiments under
licence number 80200.
RESULTS
Searching Efficiency and Holling's Type II Functional Response
Search time decreased with increasing prey density with an
estimated slope of 0.947 (95% confidence interval: 1.172
to 0.722) which did not differ from 1 (i.e. random search),
showing that searching efficiency was independent of prey density
(Table 1). Likewise, handling time was independent of prey density
(Table 1). Thus, both assumptions of Holling's type II equation were
met. Searching efficiency differed significantly between bare sedi-
ment and sea grass and decreased with depth (Table 1)inboth
habitat treatments, with the decrease being stronger in sea grass
than in bare sediment (significant interaction between depth and
habitat treatments: Table 1,Fig. 1a). Handling time increased
significantly with prey depth in both habitat treatments and was
higher in the sea grass (1.01 ±0.05 s; mean ±SE) than in the bare
patches (0.82 ±0.05 s; Table 1,Fig. 1b).
Touch Model
There was a significant effect of depth on the probe rate
(Table 2), but no effect of habitat treatment (bare sediment versus
sea grass) or prey density (Table 2). In bare sediment, there was a
significant difference between the predicted searching efficiency
based on the touch model and the observations (Fig. 1a; at 1 cm:
difference
observed-predicted
¼1.58 cm
2
/s, t
23
¼2.98, P<0.01; at
2 cm: 4.30 cm
2
/s, t
24
¼5.98, P<0.001; at 3 cm: 3.52 cm
2
/s,
t
23
¼11.22, P<0.001). In sea grass, however, the predicted
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e6758
searching efficiency based on a touch model did not differ from the
observations when prey were buried at greater depths (Fig. 1a; at
1 cm: difference
observed-predicted
¼3.78 cm
2
/s, t
23
¼5.31,
P<0.001; at 2 cm: 0.16 cm
2
/s, t
22
¼1.53, P¼0.14; at 3 cm:
0.11 cm
2
/s, t
24
¼0.84, P¼0.41; observed estimates: bias-
corrected back-transformed; Sprugel, 1983). This implies that red
knots were unable to use remote detection when foraging in sea
grass.
The Physical Model
The physical model shows that the pressure patterns produced
by the probing knot's bill, located at the interface between air and
sediment, and the flow through the pores, driven by pressure dif-
ferences, are influenced by the presence of a spherical shell deeper
in the sediment (see Fig. 2a,b for details). The pressure pattern
induced by the presence of the shell is defined by subtracting the
response of the initial pulse with the spherical shell in place from
that without it. It is this difference that we argue is sensed and
informs the knot about the presence of a prey, at some radial dis-
tance and direction (Fig. 2b). In sea grass, however, the pressure
field is changed (see Fig. 2c). When we again subtract the response
pulse with the spherical shell in place from that without it, we see
that the pressure field no longer reveals the presence of the shell
(Fig. 2d).
DISCUSSION
Searching efficiency of red knots foraging in sea grass was much
lower than when foraging in bare sediment, especially for prey
buried at greater depths, and was better explained by the touch
model than by remote detection (Fig. 1a). The present estimates of
searching efficiency on bare sediment were similar to previous
estimates (5.8e26.2 cm
2
/s; van Gils &Piersma, 2004; Piersma et al.,
1995). Nevertheless, we found a small negative effect of depth in
bare sediment, an effect not found by Piersma et al. (1995). How-
ever, as searching efficiencies in bare sediment were higher than
predicted by the touch model, and were quantitatively in line with
previous estimates, we conclude that red knots used remote prey
detection in bare sediment at all depths (Fig. 1a). Our finding of the
low searching efficiencies (even lower than in the direct touch
model) at the shallower prey depths (Fig. 1a) is probably the result
of invisible prey rejections below ground. Searching efficiency is
derived from number of prey encountered, so that when prey are
detected but rejected below ground without being noticed by the
observer, searching efficiency will be underestimated (van Gils
et al., 2015; Piersma et al., 1995; Wanink &Zwarts, 1985). This
bias is likely to become more systematic at high prey densities or at
shallow depths when prey are more easily found (Wanink &
Zwarts, 1985; T. Piersma, personal observation).
Handling time increased with prey depth and was higher in sea
grass, an effect also found by Piersma et al. (1995). In addition,
handling time increased more strongly with depth in sea grass
which may well be caused by the difficulty for red knots of pulling a
prey out of a dense network of rhizomes. Theaverage handling time
was 0.92 ±0.04 s, which is close to a mean handling time of 0.7 s
measured in the field (van Gils et al., 2015).
Why do red knots lose their ability to remotely detect hard-
shelled prey when foraging in sea grass? The outcome of the
physical model shows that when the spherical shell is situated
within a layer of rhizomes, the permeability of this substrate is
reduced; the pressure field is changed at the interface between the
sediment and the rhizomes (Fig. 2c). This overwhelms the much
weaker pressure difference due to the reflection by the shell and
obscures the directional prey information. Therefore, red knots can
no longer rely on their remote detection to encounter the hard-
shelled prey ‘hidden’by the rhizome layer. It also falsely suggests
the presence of a prey item at a certain distance right below the bill
tip. This indicates that, relative to the vertical, the angular spread of
successful deep probes of knots feeding over a rhizome mat should
be significantly less than that over a mud layer without a rhizome
mat, a hypothesis that deserves testing (see a detailed discussion on
the sensitivity of the pressure gradient to the permeability in
Appendix 2). All of the pressure differences, of course, also depend
on the actual change in permeability due to the rhizome mat, on the
location of that layer and on its depth (here assumed to be of
infinite extent). But the dramatic change in the pressure difference
that we see because of the rhizome layer (compare Fig. 2b,d) will
not depend too much on these details.
Table 1
Mixed-effect models: test statistics and parameter estimations
Estimate SE tP
Search time (s)
Fixed effects
Intercept 0.983 0.172 5.725 <0.0001
Prey depth (1, 2, 3 cm) 0.135 0.030 4.535 <0.0001
Habitat (sea grass) 0.024 0.091 0.261 0.773
Prey density 0.945 0.114 8.320 <0.0001
Habitat)prey depth 0.170 0.042 4.053 <0.001
Random effects
Individual bird 1.2010
5
(SD)
Residual 0.202 (SD)
Searching efficiency (cm
2
/s)
Fixed effects
Intercept 1.111 0.065 16.961 <0.0001
Prey depth (1, 2, 3 cm) 0.135 0.030 4.517 <0.0001
Habitat (sea grass) 0.026 0.091 0.290 0.773
Habitat)prey depth 0.172 0.042 4.061 <0.001
Random effects
Individual bird 0.015 (SD)
Residual 0.209 (SD)
Handling time (s)
Fixed effects
Intercept 0.351 0.065 5.388 <0.0001
Prey depth (1, 2, 3 cm) 0.095 0.016 5.872 <0.0001
Habitat (sea grass) 0.097 0.049 1.984 <0.05
Prey density 0.001 0.001 1.373 0.172
Habitat)prey depth 0.001 0.022 0.011 0.992
Random effects
Individual bird 0.135 (SD)
Residual 0.111 (SD)
Mixed-effect model of the log-transformed search time, searching efficiency and
handling time. Models include fixed effects prey depth (continuous), prey density
(continuous), habitat (categorical; sea grass or bare sediment) and individual bird as
a random effect.
Table 2
Mixed-effect model results for probe rate: test statistics and parameter estimations
Estimate SE tP
Probe rate (per s)
Fixed effects
Intercept 15.277 1.401 10.882 <0.0001
Prey depth (1, 2, 3 cm) 4.977 0.397 12.548 <0.0001
Habitat (sea grass) 1.562 0.916 1.705 0.1
Prey density 0.032 0.049 0.654 0.512
Random effects
Individual bird 1.062 (SD)
Residual 1.946 (SD)
Mixed-effect model of probe rate, with fixed effects prey depth (continuous), prey
density (continuous), habitat (categorical; sea grass or bare sediment) and indi-
vidual bird as a random effect.
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e67 59
Implications for Predictions on Intake Rates and Habitat Use
Insights into nonvisual sensory systems may give tantalizing
opportunities to actually predict habitat selection rules and even
foraging distributions (Cunningham et al., 2010; van Gils et al.,
2006; Piersma, 2011, 2012). In this study, the remote detection
ability of red knots was obstructed by sea grass resulting in
decreased searching efficiencies, an important parameter to predict
intake rates with a functional response. The functional response is a
commonly accepted function to predict spatial distributions and
habitat use of foragers (van Gils et al., 2015; Piersma et al., 1995;
Stephens &Krebs, 1986). However, in bare sediment, where
Figure 2. (a) The pressure field build-up by the bill of the knot in bare wet sediment of a hypothetical mudflat. The imposed pressure gradient is displayed by a spherically
symmetric radial decay decreasing from high pressure (densely packed isobars near bill tip) to low pressure (wider spaced isobars to right). (b) The isobars are obstructed in the
vicinity of the shell, and the disturbance pressure field (shown here) is sensed and informs the knot about the presence of a prey, in the form of radial distance and direction. (c)
When the spherical shell is situated within an infinite rhizome layer (below the interface between bare wet sediment and infinitely deep rhizome layer, dashed line), which reduces
the permeability, the rhizome layer changes the apparent strength of the source at the origin. The change in the pressure field at the interface between wet sediment and rhizome
layer is visualized by a changing isobar inclination. (d) Here, the pressure difference is nearly symmetric at the bill tip, at the origin, and no longer offers any clues on the direction
(or distance) at which the prey can be found (for details see Appendix 2).
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e6760
searching efficiency is a constant, red knots obey the assumptions
of Holling's type II functional response, implying that intake rate in
relation to prey density levels off at high prey densities (this study;
Holling, 1959; Piersma et al., 1995). Based on our experimental and
physical model results we argue below that in sea grass beds the
relation between intake rate and prey density will be dome-shaped
(so called type IV functional response; Holling, 1961; Jeschke &
Tollrian, 2007), implying that above a certain prey density, the
intake rate goes down with increasing prey density.
It is known that sea grass has a positive effect on prey density
and abundance (van Gils et al., 2015; Honkoop et al., 2008; Orth,
Heck, &van Montfrans, 1984). In Banc d'Arguin, sea grass and
lucinid bivalve densities are tightly linked due to their mutualistic
relationship (van der Heide et al., 2012). While at first sight the
increase in prey density would be an advantage for knots, ‘simul-
taneously’increasing sea grass density leads to decreasing
searching efficiency (Fig. 3a). Hence, with an increasing sea grass
biomass, the searching efficiency decreases faster than the increase
in prey densities, so that the functional response will become
dome-shaped, and this goes for all depth distributions (Fig. 3b; see
mathematical details in Appendix 3).
Thus, on the Banc d'Arguin, red knots encounter high searching
efficiencies at low prey densities in little or no sea grass, and low
searching efficiencies with high prey densities in dense sea grass
beds. This shows that in sea grass habitats knots may maximize
intake rates by feeding on intermediate prey densities and
moderately dense sea grass beds (which is indeed what has been
found by van Gils et al., 2015). In other words, in this case the
functional response may not be a simple function of prey density
but also of sea grass density. Note that in herbivores a type IV
response is commonly observed, often because digestive quality
decreases with increasing biomass (Fryxell, 1991; Heuermann, van
Langevelde, van Wieren, &Prins, 2011). However, in predatoreprey
interactions a type IV functional response has not received much
attention. Only a handful of recent studies have shown that
density-dependent defences, and nutritional quality of the prey,
lead to a decline in intake rate at high prey densities (Bijleveld et al.,
2016; Bressendorff &Toft, 2011; Liznarova &Pekar, 2013; Vucic-
Pestic, Birkhofer, Rall, Scheu, &Brose, 2010), again suggesting
that in many foraging contexts animals should aggregate at inter-
mediate prey densities.
In the Wadden Sea, spatial prediction of foraging red knots was
better with than without the refinement of the functional response
based on remote detection (Piersma et al., 1995). In sea grass beds,
when sea grass-dependent searching efficiency is not taken into
account this may lead to an overestimation of intake rates at high
prey densities. The notion of a sea grass-dependent searching ef-
ficiency offers a quantitative working hypothesis for future research
in diet and habitat preference of red knots foraging on sea grass-
covered ecosystems.
Acknowledgments
We thank the staff of the Parc National du Banc d'Arguin for
their permission to work and use their facilities in the park. We
especially thank Lemhaba Ould Yarba, Mohamed Ahmed Sidi
Cheikh and the local crew at Iwik station: Amadou Abderahmane
Sall, Mohamed Camara, Hacen Ould Mohamed Abd, M'Bareck Ould
Sangu
e and Sidi Ould Ely. We thank Bernard Spaans for catching
birds, Jeroen Onrust, Mohamed Vall A. Salem and Laura L. Govers
for field assistance and the latter also for advice on sea grass
collection. Dick Visser prepared the final figures. Two anonymous
referees gave helpful comments on the manuscript. This work was
largely supported by an NWO-VIDI grant (no. 86 4.09.002) to J.A.v.G,
but also by an NWO-WOTRO Integrated Programme grant
(W.01.65.221.00) to T.P. and an NWO-VENI (no. 863.12.003) to
T.v.d.H. Appendix 2 was written by L.R.M.M., J.d.F. and T.P.
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Appendix 1. Determination of the effective touch area of the
prey
To calculate the effective touch area we need to determine the
touch area of the prey, because the probability of prey being
touched depends on the surface area of the prey, measured in the
horizontal plane (Zwarts &Blomert, 1992). The touch area, deter-
mined from digital pictures of Loripes, is an allometric function of
shell length (N¼27; see inset of Loripes touch area, Fig. A1a) and
was analysed with a nonlinear model based on least-squares esti-
mates (function nls; Fig. A1). Red knots probe with a slightly
opened bill, apparently to increase the effective touch area
(Piersma et al., 1998; Zwarts &Blomert, 1992). Therefore, the touch
area is enlarged by the average surface area of the bill tip of the red
knot, with t(thickness of bill) ¼0.3 cm and w(width of bill) ¼
0.7 cm (bill parameters taken from Zwarts &Blomert, 1992). The
effective touch area is written as: wt þ2wr þ2tr þ
p
r
2
, with r
derived from the average touch area from this study based on the
allometric function with average prey length of 0.9 cm used in the
experiment (see Zwarts &Blomert, 1992 for details). Finally, the
effective searching efficiency (‘touch model’) was calculated by
multiplying the effective touch area by the effective probe rate at
each depth (1 cm classes; Fig. A1b).
Appendix 2. Physical mechanism of remote touch
Observation and experiments by Piersma et al. (1998) show that
knots are able to sense the remote presence of shells (or pebbles), of
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e6762
some 1 cm diameter, in muddy sand. Knots can sense hard-shelled
objects, buried over distances up to their bill length (approximately
3cm).Itissignificant that their sensory capability fails in dry sand, in
very liquid mud and, what is of particular interest here, when there is
a rhizome mat shielding their prey (see main text for description).
Observation also shows that the tip of the knot's bill is (uni-
formly) covered with many tiny pressure sensors (Herbst corpus-
cles), whose threshold sensitivity (the minimally detectable
pressure perturbation) and response time are unknown. We make a
few assumptions concerning the bill that will be convenient in its
physical modelling. We assume that the probing depth is very
small, so that the probe, in its ‘emitting’(forcing) mode, acts as a
point source of pressure fluctuations (located at the surface). This is
also an accurate description when the emission is produced by a
finite-sized spherical object, as long as the same mass flux is
affected. For the conical shape of the bill this should be modified at
a later stage. During its detection mode, we assume that the bill
penetrates to its true depth.
We first address the following questions related to the pressure
detection mechanism of probing bills and the specific demands
posed on the mud and hydrodynamic environment. (1) What is the
role of fluid in the mud, and why does the detection mechanism fail
in dry or very liquid circumstances? (2) What is the role of the re-
petitive character of the probing? (Why is a single probe not suffi-
cient?) (3) What is the role of the rhizome layer in the detection
mechanism?
Role of Fluid in the Mud Layer
The probing of the bill will produce pressure variations in the
mud. The properties of the medium at hand determine in what way
it responds to pressure variations. In dry sandy sediments, for
instance, pressure perturbations can, to a large extent, simply be
supported by increased or decreased normal stresses of one sand
grain upon another, without the necessity of having to yield. In
other words, for tiny pressure perturbations, the sand, except in the
very vicinity of the bill, acts as a solid. Fluids, on the other hand are
unable to support pressure differences and always have to ‘yield’.
Consequently, they will immediately start to flow, thereby relaxing
the pressure difference. Moreover, when forcing is at a liquid sur-
face, the fluid will also respond by means of waves on that surface
that will quickly remove the added energy towards infinity. In a
muddy environment, however, there is enough water in the pores
to produce a flow through it, while the absence of a free, liquid
surface eliminates the ability to remove energy by means of surface
wave propagation. The pressure perturbation generated is, in other
words, trapped in the forcing location.
The flow through pores is driven by pressure differences. The
pores are tiny channels whose sides exert a drag on the flow along
them. Indeed, side wall friction is the dominating mechanism
which impedes the flow through the pores. The classical descrip-
tion of flow through mud is therefore one in which the pressure
gradient is balanced by friction. Because of the complexity of the
sand skeleton this is necessarily an empirical relation, known as
Darcy's law (e.g. Sleath, 1984):
u¼kVp;
where u¼ðu;v;wÞis the fluid velocity in direction x¼ðx;y;zÞ
respectively, zpointing upwards, against gravity, pis the pressure,
V¼ðv=vx;v=vy;v=vzÞthe gradient operator, and kan empirical
constant proportional to the mud's permeability (proportional to
the porosity of the mud), and inversely proportional to the viscosity
of water. Although the pores may contain a substantial amount of
air, which will make the aggregate of air and water within the pores
susceptible to compression, we adopt the simplistic viewpoint that
the pores are entirely filled with water, which is (nearly) incom-
pressible. Hence the fluid is nondivergent:
V·u¼0
(Accounting for the slight compressibility of water, or of the
watereair mixture, would enable us to describe acoustic waves. For
the range of probing frequencies given, however, these waves
would have length scales of some hundreds of metres, far outside
the range of interest of 5 cm, say.) Incompressibility of the pore
water (adopted here) means that pressure variations will instan-
taneously be felt throughout this domain of interest. The probing
bill will bodily displace sand and water and thus will also act as a
mass source. This is modelled by introducing a source term at the
right-hand side of the last equation. In the approximation that this
is a point source this will take the character of a Dirac delta function
0.6
0.5
0.4
0.3
Touch area (cm2)
Effective searching efficiency (cm2/s)
0.2
0.1
0.5 0.6 0.7 0.8
Lori
p
es len
g
th (cm) Pre
y
de
p
th (cm)
0.9 1 1.1 1.2 1.3
(b)
15
10
5
0123
(a)
Figure A1. (a) Touch area as a function of shell length: 10
a
L
b
.(a¼0.486 ±SE 0.006, t¼84.36, P<0.001, b¼2.145 ±0.083, t¼25.88, P<0.0 01). Average shell length Lin the
experiments was 0.9 cm. (b) Estimated searching efficiency based on the touch model. The horizontal line in each box plot shows the median value, the bottom and top of the box
show the 25th and 75th percentiles (middle 50% of the data), respectively, and whiskers show 1.5 times the interquartile range of the data.
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e67 63
dðxÞ,a‘distribution’whose integral value only has physical signif-
icance representing the mass flux.
Role of Repetitive Probing
Assuming the permeability kto be spatially uniform, the pre-
vious two equations, with the addition of a point source, can be
combined into a Poisson equation for the pressure:
Dp¼dðxÞe
2pift
;(1)
where the Laplacian operator D¼d
2
=dx
2
þd
2
=dy
2
þd
2
=dz
2
.Note
that this only determines a spatial relationship for the pressure. Its
time (t) dependence (introduced by the repetitive probing with
frequency f) is parametric: pfexpð2piftÞ. Omitting the time
dependence (see below) the Poisson equation, (1), is solved by
p¼1=r, where r¼ðx
2
þy
2
þz
2
Þ
1=2
represents radial distance. The
pressure in an infinite medium (for the moment disregarding the
upper surface) is thus simply inversely proportional to the distance
to the source.
The knot's ‘sixth sense’for remote detection of prey (Piersma
et al., 1998), employing repetitive, shallow probing, followed by a
single deep probe in another direction, apparently uses the build-
up of residual pressure near the knot's bill tip. Compaction may
be responsible for this pressure build-up. The periodic ‘shaking’of
muddy sand by the probing action of the bill may explain the
continuous increase in residual pore pressure. Each shake may lead
to a (locally) more compact rearrangement of sand grains when the
stirred-up sand grains fall back under the action of gravity. This
process may lead to an associated increase in pore pressure and
plays a dominant role, for example, in liquefaction and the forma-
tion of quick sand (Sleath, 1984). But the pressure field is not only
changing in the vicinity of the bill. The residual (time-averaged)
pressure pattern in the vicinity of a nearby shell will be affected as
well, and in consequence this will in turn affect the pressure dis-
tribution around the bill. The intensity of this spatially modified
pressure pattern will increase at each successive cycle of the
probing action, revealing the prey's location by making it, in every
cycle, more clearly ‘visible’.
Response due to a Rhizome Layer with or Without a Shell
At the top of the rhizome layer, situated at depth z¼d;the
pressure, p, and the vertical velocity, w¼kdp=dz;perpendicular to
that plane, have to be continuous. The permeability, k, of the lower
rhizome layer, k
l
;is less than that of the upper mud layer, k
u
:This is
due to the decrease in the effective porosity of the sediment, and we
assume that the rhizome root structure is so small that we can
represent its presence in the form of a reduced effective
permeability.
We next describe the response due to a localized pressure pulse
induced by repetitive probing of a knot's bill, at z¼0. We consider
three cases: first, the response in the absence of a shell, when a
mud layer rests on top of a layer containing a rhizome mat; second,
the response to a shell in a mud layer without a rhizome mat,
qualitatively discussed in Piersma et al. (1998); third, the response
to a shell buried in the lower layer containing the rhizome mat. In
the latter case we give particular attention to the pressure gradient
sensed at the position of the knot's bill.
Response due to a rhizome layer without a shell
Even in the absence of a prey (or stone) the change in perme-
ability between a mud layer and a layer containing a sea grass root
system (rhizome mat) will affect the radial pressure distribution
discussed above. Assuming the permeability to be constant within
the rhizome layer, the pressure will again be governed by a Laplace
equation. Hence the pressure will also be inversely proportional to
the radius, but with a reduced ‘transmitted’amplitude T. The
semipermeable interface between the mud and rhizome layers acts
as a partial mirror. Therefore it augments the pressure field in the
mud layer, where the knot senses the pressure difference relative to
the uninhibited pressure field it knows it has been producing. This
augmented field in the mud layer seems to come from a mirror
source situated in the rhizome layer at adistance from the interface
at z¼dequal to that of the source (the bill), at the surface and the
interface. Therefore, the pressure is written as
pðx;y;zÞ¼8
>
>
>
<
>
>
>
:
p
u
¼1
r
0
þR
r
1
;z2ðd;0Þ
p
l
¼T
r
0
;z<d
(2)
where r
n
≡ðx
2
þy
2
þðzþZ
n
Þ
2
Þ
1=2
, denotes the distance with
respect to source (n¼0) or images, located at Z
n
¼2nd for
n¼(1,2,…). At the interface between mud and rhizome
layer, z¼d, we require continuity of the pressure p
u
¼p
l
, (sub-
scripts denoting upper (u) and lower (l) layer, respectively), and
also continuity of vertical velocity k
u
dp
u
=dz ¼k
l
dp
l
=dz. This de-
termines reflection and transmission coefficients Rand Tin terms
of k≡k
l
=k
u
<1:
R¼1k
1þk;T¼2
1þk:(3)
The resulting pressure field is displayed in Fig. A2a.
In this computation, the top layer ðz>dÞis treated as being of
infinite extent. Therefore, the normal derivative of the pressure,
dp=dz, and hence the vertical velocity, w, do not vanish at the water
surface, z¼0:Fig. A2a shows a weak inclination of the isobars
relative to the vertical. The presence of the water surface, however,
leads to a subsequent reflection of our virtual source at z¼2d;
which creates a new mirror image above the water surface, at
z¼2d:This mirror source, in turn, will produce a subsequent
mirror source in the rhizome layer at z¼4dand so on, ad infin-
itum, and the pressure field due to this infinite sequence of source
and mirror images is given by
pðx;y;zÞ¼8
>
>
>
>
<
>
>
>
>
:
p
u
¼X
∞
n¼0
R
n
r
n
þR
nþ1
r
ðnþ1Þ
!;z2ðd;0Þ
p
l
¼TX
∞
n¼0
R
n
r
n
;z<d
(4)
Taking, for example, 50 mirror sources into account, the isobars
indeed approach the water surface practically orthogonally (see
Fig. A2b). When we subtract the initial pulse, we find the pressure
perturbation as sensed by the knot (Fig. A2c), which the knot may
take to indicate the presence of a prey straight below its bill.
Perturbation due to a spherical shell
We now consider the impact of a shell (Piersma et al., 1998). For
conveniencethisisassumedtobeofsphericalshapeorradiusa<1,
located at a radial distance r¼1 from the bill tip, at an oblique angle q
from the horizontal. In an infinitely extended mud layer, an appro-
priate array of image sources and sinks, located within the shell, will
be able to generate a pressure and corresponding motion field such
thattheisobarsareeverywhereperpendicular,andthustheflow is
parallel to the shell's boundary (Lamb, 1932; p. 129; Fig. A3a). We let
thesourcebeattheoriginandthecentreoftheshelldefines the
x;z-plane. The residual pressure field is then most easily expressed in
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e6764
a coordinate system in which the x;z-coordinates, rotated to x;z-co-
ordinates, with x¼xs þzc;z¼xc þzs;and ðs;cÞ≡ðsin q;cos qÞ,are
such that the line connecting bill tip and prey is now defined as the
new horizontal x-axis, and the line perpendicular to this as the new
vertical z-axis. Then the residual pressure reads
pðx;y;zÞ¼1
rþa
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1a
2
z
2
þr
2
qþ1
asinh
1
1a
2
z
r
sinh
1
1z
r;
where r¼ðx
2
þy
2
Þ
1=2
is a horizontal radial coordinate. Subsequent
figures show the y¼0 plane only (the plane containing bill tip and
prey), in which the response is strongest. When we subtract the
initial pulse, we find, however, that the isobars of the perturbation
pressure field are not perpendicular to the water surface, z¼0,
suggesting a flow through the surface (Fig. A3b) but this does not
happen since the water surface is impenetrable. The surface acts as
areflector leading to another change in the pressure field. This is
produced by a mirror image of the virtual sources produced by the
shell. Adding this contribution, the isobars are correctly perpen-
dicular to the water surface (Fig. A3c), but at the bill tip, at the
origin, ðx;zÞ¼ð0;0Þ, this difference is sensed and informs the knot
about the presence of a prey at q¼60
relative to the horizontal, at
a radial distance r¼1. Note that these image sources (located
above the water surface) would require another perturbation
pressure field in the vicinity of the shell, as the flow induced by that
field would equally need to avoid penetrating the shell. In theory,
an infinite sequence of virtual sources within the shell and above
the water surface would be needed to exactly satisfy the impene-
trability at shell and water surfaces. In practice, here and in what
follows, we truncate this sequence after a few terms. When the
shell is buried in a half-infinite rhizome layer of permeability
k¼0:25 (leading to a reflection coefficient, R¼0.6) below a mud
layer of depth d¼0:3, the rhizome mat changes the apparent
strength of the source at the origin by a factor T¼1R
2
. The
change in the pressure field at the interface between mud and
rhizome layer is clearly visible in a changing isobar inclination
(Fig. A4a). Subtracting the influence of the source (Fig. A4b) shows
that the pressure field in the mud layer no longer reveals the
presence of the shell, even if we take the mirroring aspect of the
surface into account (Fig. A4c). In both cases, the pressure differ-
ence is very nearly symmetric at the bill tip, at the origin x¼0, and
no longer offers any clues on the direction (or distance) at which
the prey can be found (compare Fig. A4c with Fig. A3c). In fact,
while not exactly symmetric, it is clear that the pressure difference
p
0
¼pr
1
between the induced ðpÞand the imposed pressure
ðr
1
Þ;the difference sensed by the knot, is dominated by the direct
reflection due to the presence of the rhizome layer. This over-
whelms the much weaker pressure difference due to the reflection
by the shell and obscures the directional prey information.
Perturbation pressure gradient
Thepressuredifferencebelowthetoplayerofdepthd,ofcourse,
also depends on the actual change in permeability, k, due to a
0
–0.4
–0.6
–0.8
–1
–1.2
–1.4
0
–0.2
–0.4
–0.6
–1
–1.2
–1.4
0
–0.2
–0.4
–0.8
–1
–1.2
–1.4
–0.2 0 0.2 0.4 0.6 0.8 1
(a) (b) (c)
1.2 –0.2 0 0.2 0.4 0.6
x
0.8 1 1.2 –0.2 0 0.2 0.4 0.6 0.8 1 1.2
–0.2
z
–0.8
–0.6
Figure A2. Rhizome layer without a shell. Pressure distribution, p(x, z), for k¼0.25 taking in the summation (a) only the n¼0 term into account, or (b) up to n¼50. The top of the
rhizome layer is indicated by a dashed line. (c) Pressure perturbation, p0ðx;zÞ≡p1=r, af ter eliminating the forced pulse at the source.
0
–0.2
–0.6
–0.8
–1
–1.2
–1.4
00
–0.2
–0.4
–0.6
–0.8
–1
–1.4
–0.2
–0.4
–0.6
–0.8
–1
–1.4
–0.2 0 0.2 0.4 0.6 0.8 1 1.2
(a) (b) (c)
–0.2 0 0.2 0.4
y
x
0.6 0.8 1 1.2 –0.2 0 0.2 0.4 0.6 0.8 1 1.2
–0.4
–1.2 –1.2
Figure A3. Shell without rhizome layer. (a) Pressure distribution, pðX;zÞ, due to shell in infinitely deep mud layer without rhizomes. (b) Perturbation pressure, p;ðX;zÞwithout the
source. (c) As (b), but with reflecting water surface.
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e67 65
rhizome mat below, on shell size, a, and on shell angle, q, relative to
the horizontal. (We here assume the rhizome mat to be of semi-
infinite extent.) The strength of the pressure gradient as sensed by
the knot's bill is estimated by taking only the influence of the rhizome
layer and of a shell into account. Thus we discard the subsequent
contribution consisting of mirror images due to the presence of the
surface. The reason to do so is that the vertical component of the
pressure gradient (proportional to the vertical velocity) vanishes at
the surface. Since the knot's bill penetrates the mud layer over a few
millimetres, the knot also senses this difference below the surface,
where this component is not annihilated. In this way, the pressure
gradient at the origin,ðx;yÞ¼ð0;0Þ, affected by the sea grass roots
and a shell, contains, apart from its magnitude, directional informa-
tion, f, which can be computed analytically. It is given by
Vp
0
≡jVp
0
jðcos f;sin fÞ¼1R
2
a
3
1a
2
2
ðcos q;sin qÞ
þ0;R
4d
2
:
Without a rhizome layer, the permeability ratio k¼1, and thus
there is no reflection, R¼0, and the pressure gradient decreases with
decreasing shell size, a. In the vertical plane this points towards the
shell position, f¼q. With a rhizome layer, but without a shell
ða¼0Þ, the perturbation pressure gradient points simply
downwards, towards the image source. This may falsely suggest the
presence of a shell at a depth 2d, twice the thickness of the sediment
layer on top. For a single depth ðd¼0:3Þand shell diameter ða¼0:2Þ,
the magnitude jVp
0
jand direction f, relative to the horizontal, are
displayed in Fig. A5a,b. The figure reveals that even under a small 4%
drop of permeability in the lower rhizome layer, the perturbation
pressure gradient magnitude increases by a factor of 10 (see the left
side of Fig. A5a). Obviously, the contribution to the perturbation
pressure by the shell is dwarfed by that due to the virtual image
source. Most significantly, the angular information on the position of
the shell is almost lost, since fz90
for any shell direction q
(meaning the knot believes the prey to be buried vertically below the
bill). This sensitive dependence on permeability remains present for
other surface layer depths, d, and shell diameters, a.
Appendix 3. Functional response
To investigate how searching efficiency affects intake rates (IR)
of knots, we integrated the sea grass density-dependent searching
efficiency into the type II functional response where his the con-
stant handling time of the prey (s), ais the constant searching ef-
ficiency (m
2
/s) and Dis the prey density (no./m
2
):
IR ¼aD
1þaDh
0
–0.2
–0.6
–0.8
y
–1
–1.2
–1.4
0
–0.2
–0.4
–0.6
–0.8
–1
–1.2
0
–0.2
–0.4
–0.6
–0.8
–1
–1.2
–0.2 0 0.2 0.4 0.6 0.8 1 1.2
(a) (b) (c)
–0.2 0 0.2 0.4 0.6 0.8 1 1.2 –0.2 0 0.2 0.4 0.6 0.8 1 1.2
–0.4
x
–1.4 –1.4
Figure A4. Shell within a rhizome layer. (a) Pressure distribution, pðX;zÞ, due to shell in infinitely deep rhizome layer located below mud layer. The interface between the layers is
indicated by a dashed line. (b) Pertur bation pressure p;ðX;zÞwithout the source. (c) As (b), but with reflecting water surface.
80 0.06
0.05 0.01
0.04 0.03
0.02
60
40
θ
20
0
80
p
40
20
0
0.96
(a) (b) 50
10
20
30
70
40
60
80
0.97 0.98
kk
0.99 1 0.96 0.97 0.98 0.99 1
φ
60
θ
Figure A5. Perturbation pressure gradient sensed at the bill tip ðx¼ð0;0;0ÞÞ: (a) magnitude, jVpj, (dimensionless units and colours) and (b) direction, f, (labelled contours in
degrees and colour) as a function of shell angle to the horizontal, q, and of permeability ratio, k.
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e6766
Because searching efficiency is negatively dependent on sea
grass density (Fig. 3a) and prey density increases with sea grass
density, we introduced a dynamic searching efficiency A(S) that is
negatively related to sea grass density S:
IR ¼AðSÞDðSÞ
1þAðSÞDðSÞh
We described the relation between searching efficiency and
prey density by the exponential function A(S)¼A(S¼0) e
cS
,
where the constant cand A(S¼0) (the searching efficiency on bare
sediment) are fitted to the results of this study. Because the
detectability of the prey is depth dependent, all parameters were
estimated for all three depth classes separately by a nonlinear
model based on least-squares estimates (function nls in R, Fig. 3a; R
Development Core Team, 2014). The relationship between prey
density and sea grass biomass was recently quantified as non-
linearly dependent on sea grass (D(S)¼256.6 S
0.24
,de Fouw et al.,
2016). We use depth-specific prey density fractions from the field
(based on Piersma et al., 1993) and length specific energy content of
Loripes (van Gils et al., 2012). The estimated amount of energy
gained based on the functional response becomes dome-shaped
and the effect becomes stronger with prey depth (Fig. 3b).
J. de Fouw et al. / Animal Behaviour 115 (2016) 55e67 67
