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SUPPORTING INFORMATION
Invasion in tidal zones on complex coastlines: modelling larvae of the non-native Manila
clam, Ruditapes philippinarum, in the UK
Roger J.H. Herbert, Jay Willis, Elfed Jones, Kathryn Ross, Ralf Hübner, John Humphreys,
Antony Jensen and John Baugh
Journal of Biogeography
Appendix S1 Supplementary details of models and additional figures (Figures S1–
S6).
Details of models
A video of the model instantiation in Fig. 3 in the main paper is available at:
http://www.youtube.com/watch?v=17ezKfP0a34
Variables and scales
The time step of the results stored by the hydrodynamic and water quality sub-models
was 900 s and they were run for 32 model days. The minimum time increment
interpolated from the output of these models was 1 s. The salinity water quality model
was calibrated in psu (standard salinity scale equivalent to parts per thousand). The
larval sub-model ran for 15 days, with larvae released at various tidal states from five
500 m square areas in the harbour for which we have field records of inhabitation by
the Manila clam in either 2002 or 2009. The time step of the larval model was 5 s in
the vertical and 50 s in the horizontal. During the model run we stored a number of
different results as output data, including after 12 days, when the model larvae were
assumed to be in a settlement state (pedi-veliger), their positions inside any of the five
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zones was recorded as a ‘hit’. The numbers of particles that had left the harbour at the
end of 15 days were recorded. Also the number that had crossed the (arbitrarily
placed) target lines to the east or south of the harbour at least one time was recorded
(Fig. 2). All the particle positions were recorded at hourly intervals throughout the 3
day settlement period and all these positions were used to build dispersion kernels
across the modelled area. Particles that had left the model boundaries at any time were
removed from the model. This does preclude the possibility of us accurately
modelling real particles in the ocean that do leave the harbour and which are
transported further than the model wet boundary and which do then, in the actual
ocean, get transported back to the harbour – our general exploration of the model
suggests this transport link would be a very small possibility considering the model
run time
Process overview and scheduling
At each time step the water velocity was interpolated at each point at which there was
a larva, and the larvae were advected in that direction using the accepted Runge Kutta
4th order integration iterative method to re-position the particle, which requires three
further interpolations of velocity (Ramsden & Holloway, 1991; North et al., 2009).
The present depth of the larvae as a proportion of total depth was converted to actual
depth (in metres) by interpolation of the depth at the new position. The salinity model
was queried to get the salinity for the new point. The change to depth as a result of
settlement, buoyancy, or swimming was calculated. The particle’s new position was
tested for model integrity (i.e. to check it was not on land or in an area that was dry, or
out of the model domain); if the new position was valid the proportional depth was
recalculated and the larval position renewed. If the move was not possible (or logical)
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the larvae was either returned to the original position, or removed from the model (if
it left the wet boundary of the model it did not participate further in the model). Once
the new position was validated, output data were recorded for crossing the lines (east
or south) and for being inside the target zones if the time step indicated that this
required, i.e. if it was at the pedi-veliger stage.
Initialization
The model was initialized with up to two groups of 2500 particles randomly placed
inside any one or two of the five zones. The zones were 500 m squares centred
approximately on the following decimal latitude and longitude points numbered in
sequence outlined in Fig. 2 (1. 50.668, -1.977; 2. 50.704, -2.059; 3. 50.72, -1.997; 4.
50.69, -1.995; 5. 50.679, -2.002). The reason for allowing two groups to exist in the
model simultaneously was so that visual assessment of progress and differences was
possible in the output figures. Multiple instantiations of similar parameter set-ups (up
to 12) were used to calculate confidence intervals for results which demonstrated that
2500 larvae in each run, which was convenient from a computational resources
perspective, was adequate to provide a consistent result.
We analysed our results to estimate the likely variance of the results on any target of a
single run of 2500 particles. There was a correlation between the log mean hits (of a
set of at least five similar runs) and the log standard deviation as a percentage of the
mean. The linear regression was best fit by:
y = 75.357 x-0.4857
(1)
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Where y is the standard deviation as a percentage of the mean and x the mean (R2 =
0.8, P < 0.0001, N = 59). This shows that for very small hit levels (~1), the standard
deviation of the mean is likely to be around 100% of the mean, whereas if a target is
hit by many particles (1000) the standard deviation of the mean is likely to be around
3% of the mean. This is consistent with theoretical considerations (Brickman &
Smith, 2002) and we used this relationship to estimate standard deviations of low
numbers of replicates of full model run (i.e. less than 3 runs) (supplementary Table 2
in main paper).
Sub-models
The model incorporated a set of sub-models: the hydrodynamic water model, the
salinity model, the method for advection of Lagrangian particles and the larvae
behavioural model. These are each explained below.
Water model
The water model was designed to simulate the tidal hydrodynamics and sediment
transport processes in Poole Harbour and its approaches (HR Wallingford, 2004). The
model was composed of three parts, a regional 2D model, a local 2D model and a
detailed 3D model of the harbour entrance where 3D effects associated with
secondary currents occur. The regional scale model was used predominantly to drive
the local model with realistic tidal forcing, by coupling the model output at the
boundaries of the local model. In the original developmental application the smaller
scale water models were then used in conjunction with a wave model to drive a
Lagrangian drifting model of sediment movements and deposition. The output of the
hydrodynamic model includes velocity fields (u (x, y) and v (x, y)) and water depth at
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a series of stored time steps. Velocities and other quantities can be interpolated from
the stored timesteps to produce output at any time during the model simulation, with
the minimum time step of 1 s. Thus the output of the hydrodynamic model is ~800
Mbytes of data and each layer is a 2D matrix at a point in time for the output data
(velocity, depth, etc.) for every node on the triangular grid. The model we used ran for
32 days (two spring and two neap tidal cycles). It had 28,658 triangular elements,
14,968 nodes and 3073 output time steps (one every 900 s).
The water model was built and calibrated using a variety of existent and newly
surveyed bathymetric and flow data and as part of the Poole Approach Channel
deepening studies was validated against newly surveyed tidal flow data observed
using a vessel mounted Acoustic Doppler Current Profiler (ADCP) across three
transects at the harbour entrance (HR Wallingford, 2004). The spatial resolution of the
unstructured triangular mesh used by the model in Poole Harbour is variable between
about 20 m and 100 m (Figure S2). Spatial resolution of the larvae model was
effectively unlimited, in that linear interpolation can be used to estimate the velocity
or depth at any point within the model domain to double precision (16 decimal
places). Hydrodynamic conditions in the study area were simulated using the 2D,
depth averaged flow model TELEMAC-2D (http://www.opentelemac.org).
TELEMAC-2D uses an unstructured triangular grid that allows variable model
resolution and the direct incorporation of observational data regardless of how it is
distributed.
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Salinity model
The temporal and spatial variation of depth-averaged salinity was modelled using
DELWAQ transport modelling tool. This was originally developed as part of the
Delft-3D modelling system (http://delftsoftware.wldelft.nl/) but has been configured
to use TELEMAC flow model results. This takes flows from a TELEMAC-2D
simulation and solves the advection-diffusion equation over a hexagonal mesh based
on the TELEMAC mesh. It can be used to simulate a wide range of water quality
parameters, but in this case only salinity was used.
A single source point was used to represent the freshwater inputs from the Rivers
Piddle and Frome in the western end of Poole Harbour (Figure S1). Based on data
from the National River Flow Archive, flows were identified corresponding to median
flow (8.8 m3/s), and the 10th percentile flow (17 m3/s). The input of water from the
rivers was included in the TELEMAC water model and the model was run for a
spring-neap cycle. The DELWAQ salinity was set up with the seaward boundary
condition and initial condition for salinity set to the sea value of 35 psu throughout the
model area. A source of water with zero salinity was used to represent the input of
freshwater from the rivers. The salinity model was then run for several spring-neap
cycles by repeating the salinity simulation through the same water model results until
the variation in the distribution of salinity within Poole Harbour due to the mixing of
sea and river waters repeated over a cycle (Figure S4). We used the median flow
model in all simulations but a salinity variation model may be used in the future to
predict seasonally alternative dispersion patterns related to the two annual spawning
events recorded in Poole Harbour for Manila clam (Jenson et al., 2004; Humphreys et
al., 2007).
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Larval advection model
The particles in the model, individual larvae, were assumed to have no inertia and
consequently get pushed along by the water current, at the speed of the current, at the
point at which they reside at each time step. The two-dimensional water model was
converted into a three-dimensional model by an assumed vertical velocity profile
(Quasi-3D model). This is a standard logarithmic profile (the law of the wall)
appropriate to water models in relatively shallow channels (< 30 m) (Table 2). The
velocity near the bottom is assumed to be zero and increase in a U-shaped profile to a
maximum at the surface. This method has advantages of computational simplicity
over a fully three-dimensional model in shallow estuaries. In shallow channels the
depth changes rapidly, and relatively large areas of the model are subject to drying
throughout the tidal cycle, which leads to potential solution difficulties for 3D models.
Although a fully three-dimensional model was available of the deeper sections of the
harbour we felt that the marginal additional accuracy was not worth the additional
computational investment. Likewise we did not incorporate forcing by wind and wave
coupling so as to maintain clarity in the final results being dependent on tidal forcing
alone. Poole Harbour is relatively small (5 km by 10 km), shallow (~5 m) and
homogeneously mixed (Humphreys, 2005). With short fetch lengths, and a narrow,
relatively shallow entrance (0.3 km wide, 30 m deep) tidal currents predominate. This
is confirmed through in situ measurements used to calibrate the water model (HR
Wallingford, 2004). Wind advection is a predominant factor in Manila clam larval
advection in other situations, for instance Tokyo harbour (Hinata & Tomisu, 2006)
which is much bigger (50 km by 20 km, average depth 15 m), vertically stratified
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(i.e. a complex vertical profile) and with a much wider and deeper entrance (10 km
wide, 130 m deep) (Wolanski, 2006).
Dispersion
Dispersion is usually added into Lagrangian models to represent the turbulent flow
which occurs at a scale less than the resolution of the hydrodynamic model and
therefore is not captured in the output velocity field. The simplest and most common
method for incorporating dispersion is a random walk defined by the coefficient of
diffusivity. The physics around spatially variable diffusivity and random walks were
clearly outlined when Lagrangian models were first used (Hunter, 1987; Hunter et al.,
1993). This is not usually a problem in the horizontal dimension where discontinuities
in diffusivity are rare, and it is common practice to use a single coefficient of
diffusivity throughout the model domain. However, diffusion is variable in the
vertical in shallow channels (Fischer et al., 1979), and we used a parabolic profile of
diffusion coefficient to model this effect. Hunter et al. (1993) showed how a variable
diffusivity could cause particles to aggregate in a model where they did not in real
systems and therefore we used a (differential) drift term to counteract the effect in the
vertical dimension (Hunter et al., 1993; North et al., 2009). Also when a random walk
is used the length of the time step in the model can cause resolution errors around
diffusivity discontinuities (Ramsden & Holloway, 1991). This can be an issue in the
vertical dimension, because of discontinuities in diffusivity at the surface or bed. To
overcome this potential issue, we used a variable time stepping scheme, with subtimesteps (5 s) for vertical dispersion coupled with longer timesteps for the horizontal
(50 s) (Mead, 2008). We used a coefficient of diffusivity of 0.01 m2 s -1 in the
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horizontal and 0.001 m2 s -1 in the vertical and report sensitivity tests related to these
values.
Behaviour model
Ishida et al. (2005) conducted laboratory experiments with the Manila clam in order
to provide data and correlative relationships for use in predictive models of
dispersion. We have used their data to inform our model. Ishida et al. (2005) showed
that Manila clam larvae respond to salinity gradients by swimming and appear to
target specific salinities. We do not know if different larvae consistently target
different salinities, or if all larvae target the range of salinities at different times. We
modelled the former case as it is a more simple interpretation of their results and
requires no more estimated parameters such as behavioural switch over frequency or
other cues for the behavioural changes. As the larvae grow and develop they become
more capable swimmers and Ishida et al. (2005) provided a linear correlation between
larval age and swimming speed; we used this relationship for the default swimming
capabilities of larvae in the model (see Table 1 in the main paper). Their experiment
showed no change in response due to daylight so we did not model any response to
day/night cycle. They also showed that in the early stages of development (< 6 days)
the salinity response was variable, but after 6 days the swimming response was strong
and directed. In our model we wished to postulate the simplest possible behavioural
response, thus we modelled a larval response of ‘swim up’ if salinity at present
location is higher than the target salinity, ‘swim down’ if it is lower, and remain
neutral if it is in the target range. The default starting salinity target was 23 psu, with
neutral behaviour between 21 psu and 25 psu to match Ishida et al. (2005). We do not
specifically model any vertical salinity structure other than the implied assumption
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that it is less saline at the surface than the bed. For the first 3 days we modelled slow
settling of the larvae to mimic some of the behaviour described by Ishida et al.
(2005). The larvae were also subject to an additional random perturbation in the
vertical using a similar dispersion coefficient and method to the above Lagrangian
modelling methods (but without a parabolic profile, and associated drift terms) in
order to model general variability in swimming capability and directedness. Thus the
two random walks in the vertical were calculated in sequence. We explored changes
to these perturbations in the sensitivity testing as well as random variation added to
the swim speed relation recorded by Ishida et al. (2005).
Sensitivity analysis
As the behaviour response to salinity was assumed to be a major factor in the
potential dispersion of the Manila clam, and because we had good laboratory data to
hand, we experimented with many different target salinities from and to each of the
target zones. The data in Ishida et al. (2005, their Fig. 3) shows that the target salinity
for larvae in the laboratory is not normally distributed – there are noticeable heavy
tails in the distribution showing that some of the population may target lower salinity
(down to 17 psu) or higher up to 29 psu while the majority target 23 psu. The mean
salinity in Mikawa Bay is 29 psu at 3 m depth, where the experimental larvae were
gathered. This is similar to most of Poole Harbour (Humphreys, 2005) with the
exception of the Wareham Channel.
To test non-salinity behaviour we ran the model with two different behavioural
modes, random distribution (in the vertical) and a tidal response, in which the larvae
swam up and down according to the state of the tide. This was designed to model the
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kind of tidal response that has been observed in the larvae of other bivalves (e.g.
Knights et al., 2006; North et al., 2008). The behaviour was designed to retain larvae
in the harbour as is assumed to be the target for the behaviour in other animals (Zeng
& Naylor, 1996). We did this by making the larvae swim up when the tide was in
flood and down during ebb tide; they responded to the state of the tide at their initial
launch point regardless of where they were in the model. This kind of behaviour has
been observed for crab larvae and it is assumed they respond to pressure differences
(Zeng & Naylor, 1996) and continue with this cycle wherever they are (including in
the laboratory). The random vertical distribution was a null behavioural case.
Interestingly, studies of Manila clam larvae in natural settings show that they are often
distributed evenly through the water column (Hinata & Furukawa, 2006), although
this may be an effect of turbulent dispersion and perhaps a swimming response to
unknown salinity structure, or a lack of significant variation in salinity.
We ran sensitivity analysis for some of the other variable parameters including: tidal
state at initialization, (flood to ebb, and spring to neap), settlement rate during initial 3
day period, dispersion coefficients in horizontal and in vertical, variation in swim
speed, and multiple instantiation of the same parameters to check potential error due
to random dispersions (12 max, 255,000 particles).
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Supplementary figures (Figures S1–S6)
Figure S1 Intertidal habitats and the benthic sampling grid in Poole Harbour. Eighty
sampling sites were established across the entire intertidal area of the harbour on a
500 m × 500 m grid between Mean High Water and Mean Low Water Spring tide
mark. Five sediment core samples (10 cm diameter) were obtained to a depth of 15
cm from each sampling site. © Crown Copyright and database right (2010) Ordnance
Survey Licence Number 1000022021. Sediment data from East Dorset Habitat map ©
Environment Agency, 2010.
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Figure S2 Spatial resolution of medium scale hydrodynamic model which was used
for the larval advection modelling and which was parameterized using a larger scale
model of the surrounding area. Colour scale is square root of element area in metres.
The spatial resolution is lowest around the dredged channel in and around the
entrance to the harbour, which reflects the purpose for which the model was originally
built. There are 31,847 triangular elements and 16,342 nodes.
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Figure S3 Water depth at reference point (centre of area of initial introduction of
Manila clam). Panel A shows 32 days through 2 spring-neap cycles, and panel B
several days. The red line indicates the emergence of larvae and the red shaded area
indicates the time during which the settlement of larvae was recorded. Grey bars are
similar to red for sensitivity tests.
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Figure S4 Salinity model of Poole Harbour, A flood, B mid ebb, C ebb, and D mid
flood. This is a 2D Eulerian water quality model based on the output velocity fields of
the hydrodynamic model used in the study. The yellow colour indicates the
approximate band of salinity favoured by Manila clams from Tokyo Harbour when
placed in a vertical salinity gradient. In situ salinity measurements, in the harbour,
confirm the pattern and have been employed in calibration.
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Figure S5 Dispersal matrices showing mean number of initial 2500 model larval
particles initiated from zones 1-5 in Poole Harbour that then cross these zones during
days 12-15 of the model run under different behavioral parameters. Diagram A shows
particles with neutral buoyancy (no behaviour); B, particles tracking salinity of 17 psu
and C, particles tracking 23 psu. For further details see Table 2 in the main paper.
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Figure S6 Stock assessment of Manila clams at two locations within zones 2 and 5 in
October 2002–2005, prior to commencement of fishing season. Note log-scale. O+
Class between 5-20 mm (Jensen et al., 2004; Humphreys et al., 2007; R.J.H.H.,
personal observation).
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REFERENCES
Brickman, D. & Smith, P.C. (2002) Lagrangian stochastic modelling in coastal
oceanography. Journal of Atmospheric and Ocean Technology, 19, 83-99.
Fischer, H.B., List, E.J., Koh, R.C., Imberger, J. & Brooks, N.H. (1979) Mixing in
inland and coastal waters. Academic Press, New York.
Hinata, H. & Furukawa, K. (2006) Ecological network linked by the planktonic larvae
of the clam Ruditapes phillipinarum in Tokyo Bay. The environment in Asia
Pacific harbours (ed. by E. Wolanski), pp. 35-45. Springer, Dordrecht,
Netherlands.
Hinata, H. & Tomisu, K. (2005) Numerical simulation on advective process of
planktonic larvae of the clam Ruditapes philippinarum in Tokyo Bay. Bulletin
Fisheries Research Agency, Supplement 3, 59-66.
HR Wallingford (2004) Poole Harbour approach channel deepening: hydrodynamic
and sedimentation studies. HR Wallingford, UK.
Humphreys, J., Caldow, R.W.G., McGrorty, S., West, A.D. & Jensen, A.C. (2007)
Population dynamics of naturalised manila clams Ruditapes philippinarum in
British coastal waters. Marine Biology, 151, 2255-2270.
Hunter, J.R. (1987) The application of Lagrangian particle-tracking techniques to
modelling dispersion at sea. Numerical modelling: applications to marine
19
systems (ed. by J. Noye), pp. 257-269. Elsevier Science Publishers B.V, North
Holland.
Hunter, J.R., Craig, P.D. & Phillips, H.E. (1993) On the use of random-walk models
with spatially-variable diffusivity. Journal of Computational Physics, 106,
366-376.
Ishida, M., Ogasawara, M., Murakami, C., Momoi, M., Ichikawa, T. & Suzuki, T.
(2005) Changes in the behavioural characteristics in relation to salinity
selection and vertical movement at different growth stages of the planktonic
larvae of the Japanese littleneck clam Ruditapes philippinarum. Bulletin of the
Japanese Society of Fisheries Oceanography, 69, 73-82.
Jensen, A.C., Humphreys, J., Caldow, R.W.G., Grisley, C. & Dyrynda, P.E.J. (2004)
Naturalization of the Manila clam (Tapes philippinarum), an alien species, and
establishment of a clam fishery within Poole Harbour, Dorset. Journal of the
Marine Biological Association of the United Kingdom, 84, 1069-1073.
Knights, A.M., Crowe, T.P. & Burnell, G. (2006) Mechanisms of larval transport:
vertical distribution of bivalve larvae varies with tidal conditions. Marine
Ecology Progress Series, 326, 167-174.
Mead, C.T. (2008) Timestep splitting in Lagrangian marine dispersion models. 5th
International Conference on Marine Waste Water Discharges and Coastal
Environment and 3rd International Exhibition on Materials, Equipment and
Services for Coastal Environmental Projects, 27–31 October 2008, Cavtat
(Dubrovnik, Croatia). MWWD (http://www.mwwd.org).
20
North, E.W., Schlag, Z., Hood, R.R., Li, M., Zhong, L., Gross, T. & Kennedy, V.S.
(2008) Vertical swimming behavior influences the dispersal of simulated
oyster larvae in a coupled particle-tracking and hydrodynamic model of
Chesapeake Bay. Marine Ecology Progress Series, 359, 99-115.
North, E.W., Gallego, A. & Petitgas, P. (2009) Manual of recommended practices for
modelling physical - biological interactions during fish early life. ICES
Cooperative Research Report No. 295, International Council for the
Exploration of the Sea (ICES), Copenhagen.
Ramsden, D. & Holloway, G. (1991) Timestepping Lagrangian particles in two
dimensional Eulerian flow fields. Journal of Computational Physics, 95, 101116.
Wolanski, E. (2006) The environment in Asia Pacific harbours. Springer, Dordrecht.
Zeng, C. & Naylor, E. (1996) Endogenous tidal rhythms of vertical migration in field
collected zoea-1 larvae of the shore crab Carcinus maenas: implications for
ebb tide offshore dispersal. Marine Ecology Progress Series, 132, 71-82.