Connectivity among Nearshore Marine Ecosystems: The
Stochastic Nature of Larval Transport
D.A. Siegel1*, S. Mitarai1, C.J. Costello1, S.D. Gaines1, B.E. Kendall1, R.R.
Warner1 and K.B. Winters2
1- University of California, Santa Barbara, Santa Barbara, CA 93106-3060, USA.
2- Scripps Institution of Oceanography, University of California, San Diego, La Jolla,
CA 92093-0209, USA.
Draft: August 24, 2005 – DV & Satoshi
One sentence description:
Coastal stirring makes larval transport stochastic on intraseasonal to annual time scales
which introduces an inherent and unavoidable source of uncertainty in the management
of nearshore ecosystems.
Abstract:
Bio-physical models illustrate that the connectivity of coastal habitats via larval transport
will be intermittent and heterogeneous on intraseasonal to annual time scales even in
an unstructured environment. Stochasticity in larval transport is driven by the interaction
of the organism’s life cycle with its advection by turbulent coastal circulation. This differs
from previous approaches that assume that larvae simply diffuse from one site to
another or that complex connectivity patterns are created by spatially complicated
habitat configurations. Connectivity characteristics can be explained knowing the
space-time statistics for settling larvae. The stochastic nature of larval transport creates
unavoidable uncertainty in fish recruitment complicating the management of nearshore
ecosystems.
*Corresponding author (Email: davey@icess.ucsb.edu; Phone: 805-893-4547; Fax:
805-893-2578)
1
Text:
Nearshore ecosystems provide resources and habitats for a wide variety of marine
organisms, and are among the most productive environments on Earth. However, many
harvested species are in decline and are officially listed as overfished (Pauly98,
Botsford99). Well over 90% of the groundfish, reef fish and invertebrates that are
harvested from nearshore environments have a characteristic life cycle that includes a
pelagic larval stage that can last up to months and an adult stage where they are nearly
sessile (Thorsen50, Roughgarden88). Thus, larval transport plays a key role in the
structuring and dynamics of nearshore ecosystems.
The typical life history for a nearshore organism starts when adults release hundreds to
millions of larvae. These larval releases can occur continuously over months or in a few
short discrete events. Larvae are passively advected by ocean currents as they
develop competency to settle, although biotic factors, such as active swimming and
vertical migration, can also contribute to movement patterns (Metaxas01). Relatively
few larvae settle at a suitable site and an even smaller fraction successfully recruit to
adult stages where they reach reproductive age, enabling the cycle to repeat itself. At
some point, individuals will reach harvestable size and contribute to regional fishery
yields.
Nearshore ecosystems and the fisheries they support have long been known to vary on
interannual time scales associated with climate oscillations (Chavez03, Ware05). Biophysical coupling is also important on the intraseasonal time scales that typify the
processes of larval transport. In the coastal ocean, time scales for the stirring of surface
water parcels (i.e., Lagrangian decorrelation time) range from 2 to 5 days (Poulain89,
Swensen96). Assuming a stirring time scale of 3 days, a given sub-population
continually producing larvae over a 90 day period will have only 30 statistically
independent larval releases each season, of which only a small fraction will be
successful (Siegel03). This implies that connectivity of nearshore populations will be an
intermittent and spatially heterogeneous process driven by the stirring of planktonic
larvae. This differs from previously published approaches which either assume that
larvae simply “diffuse” from one site to another (Jackson81, Roughgarden88, Gaines03)
or that complex connectivity patterns arise from spatially complicated habitat
configurations (Cowen00, James02).
Here, we illustrate the episodic and intermittent nature of larval transport using an
idealized coastal circulation model patterned after the Central California coast during a
typical July (details in the supplemental information S1; Mitarai05). The model assumes
homogeneity in the alongshore direction and is forced by stochastic winds and a
horizontal pressure gradient, all derived from observations. The model simulations
reproduce the basic statistics of surface water parcel dispersion assessed from surface
2
drifter data sets providing a useful tool for assessing the time/space scales of larval
transport (see supplemental information S1).
As a base case, we model transport of pelagic larvae with a settlement competency
window between 20 and 40 days which roughly typifies ground and reef fish that inhabit
the nearshore ecosystems of California (Kinlan03). Larvae are assumed to follow
surface water parcels and are released daily for 90 days from sites spaced every 2 km
apart within the inner 20 km. The exaggerated offshore extent of suitable habitat (at
least for the California coast) was selected to account for potential active swimming
towards suitable habitat in the last stages of larval development. Biological sources of
larval mortality are not included and larval death only occurs when larvae do not
encounter suitable habitat during their settlement time window. Example trajectories
(Figure 1; supplemental information S2) show the advection of larvae by the simulated
currents (mostly along lines of constant sea level) and these patterns evolve rapidly as
the sea level patterns change in response to the stochastically forced winds. The
nearshore eddies sweep larvae together into “packets” which stay together through
much of their planktonic stage.
Settlement occurs after the larvae have developed competency for their next life stage
and if they find suitable habitat. Here, we consider settlement successful if a larva is
found within suitable habitat (the inner 20 km) within its settlement competency time
window (20 to 40 days after release). The stochastic nature of arriving settlers is
apparent as larvae settle in infrequent pulses at a given location (Figure 2). These
settlers come from a variety of locations including both nearby and distant sources, and
often both. For this realization, settlement pulses last from 5 to 30 days and originate
from source distances from 0 to 400 km upstream (Figure 2a). Sometimes arrival
events occur coincident with reversals in the alongshore winds (Figure 2b), which would
advect surface water parcels onshore (Parrish81). However, onshore Ekman transport
is clearly not the only process by which larval settlement occurs. More often than not,
eddies advect larvae to suitable habitats. Larval settlement is episodic and spatially
localized: alongshore settlement shows characteristic time scales of 12.7 (7.3 s.d.) days
and alongshore spatial scales of 29.5 (16.9 s.d.) km (Figure 2c).
Connectivity matrices are often used to illustrate source-destination relationships for
larval dispersal in complex environments (Cowen00, James02). The present modeling
domain is homogeneous in the alongshore direction; however connectivity matrices
demonstrate that connectivity is highly heterogeneous (Figure 3a). Some sites export
larvae, while others do not. Similarly, some sites receive no settlers, while others
receive pulses from a wide array of source locations. The present connectivity matrices
do not look like those predicted by larval diffusion theory (Figure 3b; Jackson81,
Siegel03); but rather they are made up of “hot spots” that connect sites in an otherwise
unstructured domain. At a few locations, a settlement hot spot occurs on the “self-
3
settlement” line suggesting that eddy processes alone can lead to self settlement
(Siegel03). Different realizations (simulated using a different initial random seeds)
produce connections among nearshore habitats that are still spatially heterogeneous
(Figure 3c), but the locations and intensities of the “hot spots” have changed (other
examples are given in Supplemental Figure S2). This suggests that larval settlement is
not expected to be consistent from one year to the next, even in identical climatic
regimes. Ocean stirring makes larval connections among nearshore sites a stochastic
process that is both spatially heterogeneous and temporally intermittent.
These results suggest that larval settlement can be modeled conceptually as a
superposition of arrival packets where the nature of connectivity is regulated by the total
number of settlement events for the domain, Nev, and the spatial scale (relative to
domain size) over which each event acts, ev. Many events, each providing settlers
over large spatial scales, will result in a smooth connectivity matrix (like Figure 3b);
whereas few events, each providing settlers on smaller scales, will result in a noisy
pattern. The spatial coefficient of variation in number of settlement packets, CVset, is a
useful measure for the nature of the larval settlement pattern. The probability that a
given packet lands on a given site is ev, the expected number of packets arriving at a
given site is (ev Nev), and -- if events are independent and small (ev << 1) -- CVset can
be approximated (using binomial sampling theory) as
CVset = sqrt[ (1 - ev) / (ev Nev)]
(1)
Thus as Nev or ev decreases, the nature of connectivity should be more stochastic.
For the present case, ev is set solely by the flow field. From Figure 2c, ev is 0.115 (=
29.5 km / 256 km). Other factors can influence ev, including bathymetric variations that
influence nearshore flow patterns as well as the spatial scales of suitable habitat (see
below). Scale estimates for Nev, the total number of settlement events for the domain,
can be derived knowing the number of independent releases (parameterized as the
larval release duration, T, normalized by the characteristic time scale for each release,
), the number of larval packets that each coast-wide release are divided into, 1/ev, and
the survival probability for each packet, fsv, or
Nev = (T / ) (1/ev) fsv
(2)
Equation (2) states that a season’s larval releases (T/) are swept together into
coherent packets at a scale 1/ev and only a few of them survive to settlement (fsv). For
continuous spawning over the interval T, values for the characteristic time scale, , will
be set by the time scale at which discrete packets of larvae are created in the flow
(which will be related to eddy time scales). For periodic releases, such as those timed
to lunar phase, a better estimate is the release period itself. The survivability fraction,
fsv, will be controlled by a variety of processes (cf., larval development time course,
4
larval mortality, flow, active swimming, habitat suitability, etc.). Using equation (2), the
normalized spatial variance in settlement can be expressed as
CVset = sqrt[ (1 - ev)  / (T fsv)]
(3)
Thus, the character of larval settlement will become smoother (CVset decreases) as ev,
T or fsv increase or as  decreases (see Table 1). CAN THE PARAEMTERS OF EQ 3
BE ESTIMATED AND THE CALCULATION COMPARED TO THE REALIZED CV,
BOTH FOR THE BASE CASE AND THE MODIFICATIONS?
The present simulation provides a useful point of departure for discussing the character
of connectivity as the simulated biological parameters are approximate upper bounds
for the spatial extent and duration of larval releases for typical nearshore fish species.
Equation (3) indicates that if the spawning season is shortened the connectivity matrix
will become more heterogeneous. In Figure 4a, the spawning season is reduced from
90 to 30 days which shows a more heterogeneous connectivity matrix (i.e., fewer hot
spots) than are found in the base case (Figure 3a). Other moderate changes in the
frequency and density of larval releases appear to have little role in changing the
character of the connectivity matrix (see Supplemental Figure S3). Increasing the
density of releases has only a small effect because adjacent larval releases are swept
together into initial packets. Reducing the frequency and density of releases from the
base case increases the stochastic nature of connectivity, particularly if the time
between releases is much larger than the characteristic time scale  (see Supplemental
Figure S3; Table 1).
Altering the larval settlement competency window can have an important effect on the
connectivity matrix. Reducing the settlement competency time window from 20 to 40
days to 5 to 10 days (both shortening the duration during which settlement can occur
and the average pelagic duration) makes connectivity more regular (Figure 4b). This is
because a much greater fraction of larvae “survive” (are in the nearshore environment
during their settlement competency window) compared with the base case (increasing
fsv; Table 1). This also shows that very different connectivity matrices can result from
the same flow field if the settlement competency windows differ.
The inclusion of larval mortality in the simulations will only increase the stochastic
nature of connectivity as this will act to reduce the number of independent trajectories.
Estimates of larval survival are quite small; a typical larval mortality (Cowen00) of 0.2 d-1
results in ~1.8% survival after 20 days, dramatically reducing the number of successful
releases. However, we are modeling groups of larvae not individuals and the character
of connectivity may not change much – rather, the cohort represented by the connection
will simply be smaller than the number of larvae originally released. Further larval
mortality is likely to increase both closer to onshore and near the benthos
5
(Strathmann85, Gaines87). In all, larval mortality is likely to increase the stochastic
nature of connectivity (Table 1).
Movement by individual larvae, both ontogenetic vertical migrations and late-period
active swimming towards suitable habitat, can also have a role in shaping the
connectivity matrix. Ontogenetic vertical migrations affect larval transport by moving
larvae from high speed surface flows to deeper, slower conditions. Here, we model
ontogenetic changes in depth by setting the vertical depth range that simulated larvae
occupy during their development. This depth is fixed to be at the surface initially and
after 10 days slowly sink to 30 m. The resulting matrix shows somewhat more
connectivity compared with the base case (Figures 4d and 3a). This occurs as larvae
now remain longer in the settling habitat region which increases the survivability factor,
fev. However, other important biological processes (e.g., larval mortality) may act to
work against this process.
The role of late-period larval swimming can be simulated by altering the offshore extent
of suitable habitat. The baseline simulations assume that suitable habitat extends more
than 20 km offshore which is much larger than typical California nearshore
environments. This large habitat was selected in order to account for active swimming
in the late stages of larval development. Reducing the extent of offshore habitat again
increases the stochastic nature of larval connectivity as the number of independent
successful releases has been reduced. (see Supplemental Figure S3D).
The base case simulation models larval transport at the height of upwelling conditions
which results in a strong alongshore jet advecting larvae south (Figures 1 & 3a). In the
winter, upwelling favorable winds are greatly diminished along with the strength of the
mean currents (Chelton84; Pickett03). The same larval release schedule applied to a
perpetual January flow field (see Supplemental Information Section 1) still shows a
stochastic pattern of connectivity although the mean displacement of settling larvae is
slightly reduced compared with the base case (Figures 4d and 3a). This is due to lower
mean and variable currents for the low wind case keeping more released larvae within
the region of suitable habitat.
The present simulations show that alongshore larval connectivity is a stochastic process
even in a spatially unstructured domain. Bathymetric variability and regional variations
in wind patterns can create consistent steering of ocean currents which enable
nearshore sites to be on the average hot spots for larval export or settlement (Signell91,
Graham97, Gaines03, Bassin05). This complexity will be superimposed upon the
stochastic settlement patterns modeled here. Its relative importance on intraseasonal
larval settlement patterns will depend on the magnitudes of bathymetrically steered
currents and the fluctuating currents which are ultimately driven by the time-varying
wind field. This said, bathymetrically driven current variability will do little to reduce the
6
stochastic nature of settlement only to focus it onto and away from particular nearshore
sites. Clearly, this is a fertile area for future research.
A listing of the potential processes that regulate the stochastic nature of connectivity
among nearshore populations is given Table 1. For example, we expect highly
stochastic settlement patterns in organisms with long average pelagic larval durations,
with short and periodic spawning seasons that coincide during periods of maximum
upwelling, and with little active swimming ability. Other scenarios can be developed
using the conceptual model introduced here (Table 1).
The stochastic nature of larval settlement has many important implications for the
dynamics of nearshore ecosystems and their management. While the nature of these
settlement pulses will depend on a variety of factors (Table 1), the connectivity of
nearshore subpopulations on these time scales cannot be modeled using diffusionbased formulations (Siegel03). Further, local rates of larval settlement will be largely
decoupled from local stock abundances. This provides an unexplored source of
uncertainty in observed stock-recruitment relationships commonly found for many fish
stocks (Hilborn92). Last, the stochastic nature of connectivity will make it difficult to
assess the effectiveness of no-take marine reserves on fishery yields and profits on
short time scales. This is because it may take years to detect the spatial closure signal
from the inherent quasi-random fluctuations of recruitment driven by stochastic
settlement. Clearly, more work is required to understand these interactions among
variable coastal circulations, nearshore organism life cycles and the management of
these important ecosystems and fisheries.
7
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L12604, doi:10.1029/2005GL023017 (2005).
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Chelton, D., J. Geophys. Res., 89, 3473, (1984).
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Dynamics and Uncertainty. Chapman and Hall, New York. 570 p., (1992).
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2079–2086 (2002).
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Metaxas, A., Can. J. Fish. Aquat. Sci. 58: 86–98 (2001)
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Pauly, D., V. Christensen, J. Dalsgaard, R. Froese, F. Torres, Science 279, 860 (1998).
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(2003).
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8
Table 1 – Processes regulating the stochastic nature of connectivity among nearshore populations
Forcing that will lead to increased
stochastic connectivity
Magnitude of
effect*
Expected Effect
Increase of upwelling favorable winds
Moderate
Leads to decreased survivability as larvae are advected
from inshore regions
Decrease in wind field variability
Moderate?
Provides fewer independent flow field circulations
Coastline & bathymetric variability
Moderate?
Decreases in spatial scale or frequency of
larval releases
Moderate to
large
Moderate to
large
Moderate to
large
Small to
moderate
Inclusion of larval mortality
Moderate?
Larval mortality increasing towards the shore or
within the benthos
Moderate?
Longer planktonic larval duration
Reducing duration of larval settlement window
Shortening of reproductive season
Reduction of suitable habitat scales
Reduction in the effectiveness of late larval
stage swimming
Moderate to
large
Moderate to
large
Adds additional length scales in the flow & allows spatial
persistence in settlement to occur
Reduces abiotic-induced survival - Are larvae in the right
place at the right time?
Effect upon
conceptual
model (Eq. 3)
Decreases fsv
Can decrease 
Maybe
decrease ev
Decreases fsv
Reduces the time that larvae can find suitable habitat
Decreases fsv
Decreases number of independent releases
Decreases T
Makes releases more sporadic / rare
Decreases ev
&
Reduces number of surviving larvae – depending upon the
assumptions used can eliminate entire trajectories
Reduces survivability of nearshore larvae making it less
likely they can remain within settlement habitat
Decreases fsv
Decreases fsv
Decreases effective habitat size
Decreases fsv
Decreases effective habitat size
Decreases fsv
* - Number of question marks attempts to put uncertainty bounds based on present knowledge.
MANY OF THESE EFFECTS HAVE NOW BEEN TESTED WITH SIMULATIONS – CAN THEY BE MADE MORE PRECISE? SEE MY EARLIER
QUESTION ABOUT ESTIMATING THE CONCEPTUAL PARAMETERS. ADMITTEDLY, THIS WOULD ONLY BE BASED ON SINGLE
REALIZATIONS, SO WOULD BE PRELIMINARY – BUT IT WOULD BE NICE TO REDUCE SOME OF THE UNCERTAINTIES IN THE
MAGNITUDE
9
Figure 1: Depictions of the sea level distribution (color contours in cm) and the trajectories of larvae for simulated days
80, 90 and 100. For clarity, the number of the released larvae is reduced; larvae are released every 8 km and every 4
days. The simulated domain is 256 km on a side (only the inner 200 km are shown in the cross-shore direction). The
circles show the location of the larvae while the white trails behind each show their previous 2 day trajectories. The
vertical dashed red line indicates the boundary for the nearshore habitat where from which larvae are released and to
which settlement can occur. The red arrow in the 80 day panel shows the location of the site where settlement is sampled
in Figure 2a. The flow field is modeled after conditions found in the central coast of California (CalCOFI line 70) during a
typical July (high upwelling conditions). Model development, forcing and validation details can be found in supplemental
information section 1. Low sea level features correspond to cyclones and support counter-clockwise geostrophic currents.
Anti-cyclones, high sea level features, create clockwise circulations. An animated time-lapsed depiction of this flow field
and associated larval transport is provided in supplemental information section 2.
10
Figure 2: Time series showing a) the density and alongshore source locations of
settlers with a settlement window between 20 and 40 days arriving to a single 4
km wide site (centered at an alongshore location of 96 km), b) the alongshore
wind speed forcing the model (- is upwelling favorable) and c) the arrival density
of settlers from all sources with a settlement competency time window between
20 and 40 days as a function of settlement location and time. The timing of the
simulations is as follows (see supplemental information S1); the circulation model
is driven to a quasi-stationary state and larvae are released starting on day 0.
The first larvae are able to settle on day 20 (left vertical dashed line). Larval
releases stop at day 90 (middle vertical dashed line) and settlement is possible
until day 130 (right vertical dashed line). Densities are calculated as the number
of the settlers at a site divided by the number of the larvae released per site.
Length & time scales for settlement are calculated using by the variogram range
(Rossi92) of the arrival density with arrival time (or location) held constant.
Resulting time scales from Figure 2c are 12.7 (3.3 s.d.) days and alongshore
spatial scales are 29.5 (16.9 s.d.) km.
11
Figure 3: Connectivity matrices for larval dispersal for a) the simulation shown in
Figures 1 and 2, b) a diffusion model assuming the same statistics of the
simulation and c) another realization of the simulation model. These depictions
are single realizations of the probability density function of the relationship
between source and destination locations along a coastline. Source locations
(vertical axis) and destination locations (horizontal axis) are identified by their
alongshore location. The connectivity matrices are normalized so that the
summed probabilities equal one. The dashed slanted line represents selfsettlement, i.e., where source locations are identical to destination locations. The
broad extent of the source locations in the above diagrams takes advantage of
the periodic boundary conditions in the alongshore direction. The two
realizations of the simulation model illustrate two different connectivity matrices,
showing the intermittency of larval transport. The diffusion example is
constructed from statistics from panel a) using a mean offset of 133 km and a
spread of the Gaussian distribution of 88 km.
THESE AXES SEEM REVERSED TO ME – IF WE WERE TREATING THESE
AS MATRICES TO MULTIPLY A VECTOR OF SOURCE DENSITIES THEN
THE ROWS WOULD BE DESTINATION AND THE COLUMNS SOURCE
LOCATIONS.
LIKEWISE IT SEEMS TO ME THAT THE NORMALIZATION SHOULD BE SUCH
THAT THE DISTRIBUTION FROM A SINGLE SOURCE SUMS (ON AVERAGE)
TO ONE.
12
Figure 4: Connectivity matrices for larval dispersal examining the role of different
processes. A) Connectivity matrix when the release duration is for 30 days
instead of 90 days. B) Connectivity matrix when the larval settlement
competency window is set to 5 to 10 days. C) Connectivity matrix for the low
upwelling case (January at CalCOFI line 70). D) Connectivity matrix when the
larval depths are set to mimic ontogenetic migration from the surface to 30 m
(after 10 days at the surface). Source locations (vertical axes) and destination
locations (horizontal axes) are identified with the alongshore locations. The color
indicates the number of the settlers from a source location transported to a
destination location. The number shown is normalized so that the summed
probabilities are equal to one. The broad extent of the source locations in the
above diagrams takes advantage of the periodic boundary conditions in the
alongshore direction. The dashed slanted line represents self-settlement, where
source and destination locations are the same. With the exception of panel C
(the low upwelling case), all of these connectivity diagrams are created using the
exact same flow field used in the base case (Figure 3a).
13
Supplemental Online Material
1. Oceanographic Model Development & Forcing
The 3-D flow fields for typical California Current conditions were simulated using
the Regional Ocean Modeling System (ROMS;
http://marine.rutgers.edu/po/index.php?model=roms). The simulated flow fields
are designed to satisfy statistical stationarity and homogeneity in the alongshore
direction while the forcings and boundary conditions are derived from observed
conditions. This provides a numerical system capable of addressing the
fundamental processes affecting larval dispersal.
The domain size is 256 km in alongshore direction, and 288 km in cross-shore
direction. The bathymetry has steep continental slope modeled after CalCOFI
line 70 and no bathymetric variations are considered in alongshore direction. The
minimum depth is set to 10 m at the coast, while the maximum depth is set to
500 m offshore. The domain is discretized by 2-km-resolution grid points
horizontally; 20 vertical levels are considered with enhanced resolution near the
top and bottom boundaries. The eastern boundary is set to free-slip boundary
condition while an open boundary condition (Marchesiello et al., 2001) is used on
the western boundary. Northern and southern boundary conditions are set to
periodic. Consistent with this condition, an f-plane approximation (corresponding
to 38N latitude) is used. Alongshore pressure gradients can not naturally
develop in a periodic domain, which can lead to unrealistically fast alongshore
currents (Dinniman and Klinck, 2002). Here, an alongshore pressure gradient is
imposed as an external body force, estimated using January and July mean
dynamic height differences between CalCOFI hydrographic sections off Pt. Arena
and Pt. Conception (lines 60 and 90) (Lynn et al. 1982).
Initial fields are generated using CalCOFI hydrographic data at line 70 for a
climatological July and January (Lynn et al. 1982). The primitive equations are
integrated with 450-s time step for baroclinic mode and 15-s time step for
barotropic mode. Here, horizontal mixing is given by biharmonic Laplacian
diffusion (Lesieur, 1997), while vertical mixing is described with K profile
parameterization of Large et al. (1994). After the simulation fields reach
equilibrium (or statistically stationary), passive or active particles are added to
simulate the motions of individual larval releases.
Wind forcing is modeled assuming that the wind field varies on spatial scales
much larger than the alongshore scale of the simulated domain while its
magnitude decreases towards the shore (Brink et al., 1987; Capet et al., 2004).
Wind stress is calculated using a standard bulk formula. Each component of the
14
wind vector is modeled as a Markov Chain (Uhlenbeck and Ornstein, 1954) given
the statistics obtained from hourly buoy wind data (NDBC station 46028) and the
spatial wind observations of Pickett and Paduan (2003). Further details of model
set-up and validation of the physical flow fields using CalCOFI observations can
be found in Mitarai et al. [2005].
The larval release protocol is modeled after typical rocky reef benthic fish found
in California nearshore waters. Nearshore habitats (where larvae are released
and settle) are defined as all waters shallower than 150 m in depth. Larvae are
released every day for a season (90 days) near the sea surface every 2 km in
nearshore habitat. Larvae settle when they are found within the nearshore habitat
within their competency time window. For most of the results presented here, the
settlement competency time window is assumed to be 20 to 40 days, which is
typical of many nearshore fishes (Kinlan and Gaines, 2003).
Simulated larvae are modeled as Lagrangian particles and are advected by the
modeled horizontal currents. They are assumed to stay within the upper 5 m of
the model domain. vertical migration in included, larvae remain at the surface for
the first 10 days and then slowly sink to 30 m depth over the next 10 days after
which time they remain at 30 m. Further details and validation of the Lagrangian
trajectories using surface drifter observations can also be found in Mitarai et al.
[2005].
2. Movies of Lagrangian Particle Trajectories
Movie S1: Time-lapsed views of the high upwelling (July) flow field illustrated in
Figure 1 of the text. The time evolution of sea level is shown in color contours (in
cm) and a sampling of the total number of larval trajectories are plotted. The
location of each larva is given by the white circles and the tails show the previous
two day trajectories. See the caption of Fig. 1 for more details.
http://www.icess.ucsb.edu/~satoshi/f3/movies/trajectories1.mpg
Movie S2: Time-lapsed views of the low upwelling (January) flow field patterned
after Figure 1 of the text. The time evolution of sea level is shown in color
contours (in cm) and a sampling of the total number of larval trajectories are
plotted. The location of each larva is given by the white circles and the tails show
the previous two day trajectories. See the caption of Fig. 1 for more details
(except that now the January case is shown).
http://www.icess.ucsb.edu/~satoshi/f3/movies/trajectories2.mpg
15
3. Additional Connectivity Matrix Examples
Figure S1: Connectivity matrices for larval dispersal for different realizations of
the base case simulation shown in Figures 3a and 3c. These depictions are
single realizations of the probability density function of the relationship between
source and destination locations along a coastline. Source locations (vertical
axis) and destination locations (horizontal axis) are identified by their alongshore
location. The connectivity matrices are normalized so that the summed
probabilities equal one. The dashed slanted line represents self-settlement, i.e.,
where source locations are identical to destination locations. The broad extent of
the source locations in the above diagrams takes advantage of the periodic
boundary conditions in the alongshore direction. The four realizations of the
simulation model illustrate four different connectivity matrices, showing the
intermittency of larval transport.
Figure S2: Connectivity matrices for larval dispersal examining the role of
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different processes. A) Connectivity matrix when the density of the releases is
reduced from every 2 km to every 4 km. B) Connectivity matrix when frequency
of the releases is reduced from every day to every 4 days. C) Connectivity matrix
when frequency of the releases is reduced from every day to every 30 days. D)
Connectivity matrix when the nearshore habitat size is reduced from 20 km to 10
km. Source locations (vertical axes) and destination locations (horizontal axes)
are identified with the alongshore locations. The color indicates the number of the
settlers from a source location transported to a destination location. The number
shown is normalized so that the summed probabilities are equal to one. The
broad extent of the source locations in the above diagrams takes advantage of
the periodic boundary conditions in the alongshore direction. The dashed
slanted line represents self-settlement, i.e., where source and destination
locations are the same. All of these connectivity diagrams are created using the
exact same flow field as the base case example (Figure 3a).
17
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