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BULLETIN OF MARINE SCIENC E, 86(2): 439–459, 2010
439
Bulletin of Marine Science
© 2010 Rosenstiel School of Marine and Atmospheric Science
of the University of Miami
REPRESENTATION OF MULTISTANZA LIFE HISTORIES
IN ECOSPACE MODELS FOR SPATIAL ORGANIZATION
OF ECOSYSTEM TROPHIC INTERACTION PATTERNS
Carl Walters, Villy Christensen,
William Walters, and Kenneth Rose
ABSTR AC T
e Ecospace model for spatial organization of trophic interactions has seen
limited use for evaluation of policies such as marine protected areas, partly because
of concern about representing key indicator populations only by spatial biomass
distributions. e software has been improved to include spatial representation of
age structure for such species, by means of the Ecosim “multistanza” population
submodel, which assumes similar diet compositions, predation risk, and vulnerability
to fishing over blocks or stanzas of fish ages. A computationally efficient version
of Ecospace now preser ves the multistanza age structure over spatial habitat and
ecosystem biomass maps, evaluating body growth and mortality rates as spatial
averages weighted by relative biomass use of each model spatial cell. A more
computationally intense version divides each multistanza population into spatial
packets (an individual-based model approach) for more precise analysis of how
movement patterns and movement histories over mosaics of trophic opportunities
and risks affect population performance and variability. e two approaches give
surprisingly similar predictions of abundance patterns over both time and space,
agreeing well in case-study applications to the Gulf of Mexico and California coast
with each other and with nonspatial Ecosim predictions.
e Ecopath with Ecosim (EwE) software is widely used for synthesis of informa-
tion on trophic interactions and for screening of ecosystem-management options
that may alter trophic interactions (Christensen and Walters, 2004). e Ecopath
component of the software is used to manage basic input data (abundances, diet
compositions, productivity) and to provide static mass-balance analyses. e Ecosim
component provides dynamic predictions and capabilities similar to those of single-
species assessment models for parameter estimation by statistically based fitting to
historical time-series data. e realism of Ecosim models has recently been improved
dramatically through inclusion of “multistanza” population-dynamics accounting.
Multistanza accounting replaces the simple biomass-dynamics relationships of Eco-
path and early Ecosim versions with detailed, age- and size-structured population-
dynamics relationships for key species within the ecosystem. e different age ranges
(stanzas) can be represented as having distinct diet preferences and vulnerabilities
to predation and fishing mortality (Walters and Martell, 2004; Walters et al., 2008).
e EwE software package also includes a spatial modeling scheme called Eco-
space, which replicates the Ecopath-Ecosim biomass variables over a grid of spatial
cells and represents mixing of biomass (diffusion, advection, and seasonal migra-
tion) among the cells (Walters et al., 1999; Walters, 2000). Ecospace was originally
intended to provide only crude equilibrium predictions of how spatially oriented
management policies and spatially explicit distributions of fishing effort might alter
trophic-interaction patterns (e.g., through trophic-cascade effects within protected
areas). Ecospace can also make dynamic predictions (see Walters and Martell, 2004:
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
440
279, box 11.2) and has been used to explore spatial management options for a wide
variety of ecosystems (see, e.g., Pitcher et al., 2002; Gribble, 2003; Martell et al., 2005;
Le Quesne et al., 2008), but when the multistanza population dynamics capability
was added to Ecosim, only a crude, equilibrium approximation for age structure
was included in the Ecospace software. At the time, we assumed that representing
full age- and size-structure dynamics on each of the many grid cells (1000 or more)
typically used in Ecospace representations would require massive computational and
memory capacity and prevent rapid simulations needed in workshop situations. e
crude-approximation approach that was implemented allowed very fast solutions but
was recognized to limit severely the ability of Ecospace to represent the spatial habi-
tat shifts that typically accompany trophic ontogeny (different stanzas very often use
different spatial cells). ese ontogenetic shifts can be critical in evaluating impacts
of policies, such as marine protected areas, that often only affect certain stanzas in
the life cycles of the key species. e inclusion of multistanza dynamics will permit
tracking of the changes in abundance and growth of key species over both space
and time, while representing other ecosystem functional groups by means of simpler
biomass-dynamics equations with spatial mixing processes.
Here, we describe two approaches to integration of multistanza population-dy-
namics predictions into the Ecospace framework. Full representation and solution of
multistanza dynamics will allow for more realistic, and yet still computationally ef-
ficient, Ecospace models. e first approach is based on making multistanza age- and
size-structured predictions for an overall spatial region, then predicting distribution
of stanza biomasses over spatial cells by means of predicted proportional cell use
from continuous spatial mixing models. e second, much more detailed, approach
is to divide each multistanza age cohort into a large number of subcohorts or “pack-
ets,” essentially an individual-based modeling approach (Van Winkle et al., 1993),
then to predict movement patterns of these packets over the spatial map. e first
approach is computationally efficient and therefore facilitates multiple model runs
in policy-screening and gaming situations, whereas the second is intended mainly to
check scenarios developed with the first approach for impacts of complex spatial ef-
fects such as differential body-growth rates of fish in different cells or in subareas of
the spatial grid. ese two new multistanza approaches greatly improve the capabil-
ity of Ecospace to deal with policy questions not only about marine protected areas
but also about changes in essential fish habitat available to each stanza for species
with complex spatial and trophic ontogenies.
A R M
L H E
R G E M S B D.—
For functional groups not represented by multistanza population dynamics account-
ing, Ecospace represents biomass (B) dynamics over a set of spatial cells (k) with the
spatially discretized rate formulation
dB dt e Q Z B m B m B
ik i ik ik ik ikk
kik ik k ik
k
= - - +
l l l
l
^ h
/ /
(1)
where Bik is the biomass of functional group i in spatial cell k; ei is conversion ef-
ficiency of food intake by group i into net production; Qik is total food consumption
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 441
rate by group i in spatial cell k; Zik is total mortality rate of group i biomass due to
predation, fishing, etc.; mikk΄ is instantaneous movement rate of group i biomass from
cell k to cell k΄; and mik΄k is movement rate of group i biomass from cell k΄ to cell k.
All of the terms on the right hand side of Eq. 1, except ei, are treated as dynamically
variable over time so as to reflect changes in food availability (Qik), fishing effort and
predation risk (Zik), and seasonal changes in movement patterns (mikk΄). Food con-
sumption rates Qik are calculated as sums over prey types j (i.e., Qik = ΣjQjik). Likewise,
total mortality rates are calculated as sums over predator types and fishing fleets f:
Zik = Moi + Σf Fifk + ΣjQijk/Bik , where Moi is unexplained mortality rate, the fishing rate
components Fifk by fleets f are predicted from spatial distributions of fishing effort for
each “fleet” f over the grid cells k, and the Qijk/Bik ratios represent predation rate com-
ponents of M (i.e., Mijk = Qijk/Bik) calculated from predator j consumption rates Qijk.
e Ecospace grid cells are arranged as a rectangular grid with rows r and columns c,
so that each cell k exchanges biomass directly only with those cells k΄ that are in ad-
jacent rows and columns. If cell k represents row r, column c, then k΄ is restricted to
cells (r – 1,c), (r + 1,c), (c – 1,r), and (c + 1,r). Exchanges at the map perimeter are set to
zero, except for groups that are assumed to be advected across the map, in which case
biomasses at the map boundary are set to constant (Ecopath base estimate) values.
A critical feature of Ecospace is that trophic interactions are not treated as occur-
ring randomly over space within each grid cell. e Ecosim “foraging arena” formu-
lation (Walters et al., 1997; Christensen and Walters, 2004) is used for predicting
the Qijk, and the formulation is based on the assumption that animals can exhibit
highly organized patterns of space use at much finer spatial scales than the size of
typical model cells used for Ecospace simulations. e idea is that behavior (e.g.,
seeking of safe microhabitats) leads to the exchange of individuals between “safe”
and “vulnerable” behavioral states, either continuously over time or in temporally
restricted feeding bouts (Walters and Christensen, 2007). e Ecosim equations for
predicting Qijk allow for classic predator-prey functional response types—type I if no
handling time or foraging time adjustment is needed, type II if handling times and
or foraging time adjustments limit per-capita food-consumption rates, and type III if
predator rates of search decrease when prey densities are low or prey spend less time
foraging when their densities are low—but the foraging-arena equations depart from
classical functional response predictions in calculating prey densities not as average
total biomass in each cell but rather as effective biomass densities in the restricted
arenas where foraging typically occurs and where such local densities can be strongly
affected by densities of competing predators (ratio-dependence effect). Local depres-
sion of available prey biomass can occur whether or not predation affects overall
grid-wide prey densities.
e default assumption for spatial mixing in Ecospace is for the mikk΄ rates to be
equal over all active (nonland) cell faces, representing simple group- or species-spe-
cific diffusion processes. Ecospace allows users to improve upon this assumption
in four important ways. First, passive advection by currents can be represented by
modification of the m’s by means of vertically averaged velocity fields provided by
physical models. Second, each spatial cell can be assigned a distinct user-defined
habitat type, and each group can be designated to use one or more such types. Given
these designations, dispersal rates are modified so as largely to prevent movement
into cells with “bad” habitat types, and movement rates for animals currently in bad
cells are increased in the direction of more suitable cells. is convention is particu-
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
442
larly important for simulation of behaviors that move larval and juvenile fishes from
offshore spawning areas into coastal nursery areas, which can often involve using
behavioral tactics such as vertical migration and movement only on incoming tides
in conjunction with oriented swimming. ird, dispersal rates can be modified to
represent movements oriented toward seasonally varying preferred spatial positions;
movement can be more strongly oriented (m’s reduced more in directions away from
preferred positions) to simulate seasonal migration patterns. Under this option, scal-
ing parameters for north-south and east-west orientation can be specified by model
users to concentrate biomasses more or less tightly around the preferred locations.
Fourth, movement rates (and optionally directions) can be linked to indices of fitness
(food consumption rate Q/B, mortality rate Z) to concentrate animals in more favor-
able cells (Martell et al., 2005). Fitness-driven dispersal typically causes dispersal
rates to be density dependent, leading to large-scale patterns such as range contrac-
tion when overall abundance declines.
Typical Ecospace models developed to date have represented 20–60 functional
groups (denoted i) on spatial grids with 20–50 rows and columns (k cells) and simu-
lated time horizons on the order of 50 yrs, commonly run with monthly time steps.
e Eq. 1 system therefore has on the order of 10,000–150,000 i,k elements and must
be solved by some very efficient implicit numerical procedure so that new results
can be generated quickly for management-policy comparisons and gaming. We have
chosen to use a fully implicit, second-order backward differentiation algorithm. Such
implicit algorithms have the valuable property of being numerically stable even at
very large time steps and even when some of the system variables can change very
rapidly (when the system is numerically “stiff”). e “fast” variables therefore do
not force the whole solution method to use a very short time step (e.g., minutes to
hours for models with high spatial mixing rates and fast variables like small phy-
toplankton); instead, the implicit integration method “discards” fast variation, es-
sentially treating fast variables as remaining near a moving equilibrium with respect
to changes in the slower variables that affect them (e.g., phytoplankton is treated as
remaining near equilibrium with respect to changes in zooplankton biomass). at
is, the moving equilibria for fast variables are assumed to be good estimates of aver-
age variable values over whatever complex, cyclic patterns such variables may exhibit
over time if shorter solution time steps were used.
R E M P D A.—Se-
lected biomass groups can be designated life-history stanzas within single-species
populations. In such cases, the Ecosim differential equation representation for bio-
mass change (Eq. 1) is replaced by a monthly-difference equation system, with full
age-structured accounting for population age and size structure at monthly age in-
crements. e basic accounting relationships are
expN N Z 12
, , ,a t a t s t1 1 = -
+ +
^ h
(2)
W q W
, , ,a t a a t a t1 1 a t= +
+ + (3)
B N W
, , ,
( )
( )
s t a t a t
a a s
a a s
1
2
=
=
=
/ (4)
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 443
Here, Na,t is number of age a (in months) animals in calendar month t, Wa,t is mean
body weight of age a animals in month t, and Bs,t is the biomass of stanza s, defined as
the mass (numbers × weight) of animals aged a1(s) through a2(s) months. Zs,t is the
total mortality rate of stanza s animals, defined the same way on the basis of fishing
and consumption as for other model biomass groups i as Zs,t = Mos + ΣfFsf + ΣjQsj/Bs.
All animals in stanza s are treated as having the same predation risk and vulner-
ability to fishing. e aggregated bioenergetics parameters aa and r are calculated to
make body growth follow a von Bertalanffy growth curve (with length-weight power
3.0) with user-defined metabolic parameter K. Exact von Bertalanffy growth occurs
when predicted per-capita food intake qa,t is equal to a base food intake rate that
is calculated from the consumption per biomass parameter (Qs/Bs) provided by the
user for each stanza. e metabolic parameter r, which equals exp(–3K/12), is based
on the assumption that metabolism is proportional to body weight (Essington et al.,
2001). Actual or realized food intake qs,t at each time step is calculated from the total
predicted food-intake rate for the stanza (Qs,t) as qs ,t = Qs, twa,t
2/3/Ps,t, where Ps,t is the
relative total area searched for food by stanza s animals and is computed as Ps,t =
ΣaNa,twa ,t
2/3. For foraging-arena food-intake and predation-rate calculations involving
stanza s, Ps,t is used instead of Bs as the predictor of total area or volume searched for
food per unit time. e assumption that area searched and food intake vary as the
2/3 power of weight (i.e., as the square of body length) is a basic assumption that also
underlies the derivation of the von Bertalanffy growth function.
For notational simplicity, Eqs. 2–4 above are presented without a species index.
Typical Ecosim models developed to date have included multistanza accounting for
2–10 species, each divided into 2–5 stanzas that capture basic ontogenetic changes
in diet, predation risk, and vulnerability to fishing. e first age for stanza 1 is always
set to a1(1) = 0 (hatching), and a2(1) is usually set to 3–6 mo of age to represent the
larval and early juvenile periods separately. en a2(2) is most often set at 12–24 mo
(to represent older juveniles), and additional stanza breaks are set at key ages like
maturity and first vulnerability to fishing.
Recruitment rates N0, t+1 for Eq. 2 (i.e., animals entering the first stanza) are as-
sumed to be simply proportional to total egg production Et = ΣaNa ,t fa,t, where age-
specific fecundity fa,t is assumed to be zero for fish with body weights less than weight
at maturity Wmat and proportional to weight above Wmat, fa ,t = Wa,t – Wmat for larger,
older fish. Model users can also define monthly relative egg-production multipliers
to represent seasonality in reproduction. Note that this age-0 recruitment formula-
tion for newly entering animals proportional to egg production does not explicitly
account for density dependence in early mortality rates (i.e., an explicit stock-recruit-
ment function is not used). Density-dependent effects occur through (1) impacts of
animal density on food consumption, growth, and fecundity (a time-lagged effect
that can result in violent population cycles) and, more importantly and commonly,
(2) density dependence in Zs,t caused by foraging-time adjustments in the Ecosim
foraging-arena model for Qs,t. Foraging-time adjustments typically result in emergent
stock-recruitment relationships of Beverton-Holt form (Walters and Korman, 1999;
Walters and Martell, 2004).
e Ecosim multistanza model has been fitted to many time series of population
abundances that were reconstructed from single-species age-structure data by meth-
ods like VPA (Sparre, 1991) and stock-reduction analysis (Walters et al., 2006). Spe-
cies fitted range from tunas to groupers to small pelagics like menhaden. For large,
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
444
relatively long-lived species (piscivores, benthivores), behavior of the multistanza
population model is typically indistinguishable from those of other age-structured
models commonly used for stock assessment. For small-bodied species subject to
high and temporally varying predation-mortality rates (e.g., small tunas, herrings,
menhaden), Ecosim can sometimes capture effects such as relative stability of Z as
F increases (decreases in M with increasing F) that are typically missed by single-
species models that assume stable natural mortality rate M (see, e.g., Walters et al.,
2008).
O R M S E.—When the
multistanza option was originally developed for Ecosim, it was not incorporated
directly into Ecospace. Instead, each stanza was treated as its own higher-order
functional group for Ecospace biomass-dynamics calculations (Eq. 3), without ac-
counting for age structure within the stanza. Rather, the age-structure of each stanza
was assumed to be in equilibrium. Body weight was computed grid-wide (not cell-
specifically) for each stanza. Feeding rates were assumed proportional to a relative
search-area index Ps calculated from a prediction of the numerical abundance of the
stanza Ns as ,P N P
s s s
=
r
where Ps
r
is the initial (t = 0) per-capita mean of the relative
area-searched index Ps ,t, i.e.,
.P N w N
, ,
/
,s a a
aa
a
0 0
2 3
0
=
r/ /
Dynamics of the numbers in each stanza Ns were computed for each cell by a differential
equation similar to Eq. 1:
dN dt R Z N m N
sk sk sk sk ik k sk
k
= - - l
l
^ h
/
(5)
where Rsk is an approximate difference between recruitment (incoming) rates and
exit (to next stanza) rates for stanza s in spatial cell k. If the age structure within the
stanza is assumed to remain near equilibrium, the Rsk term in Eq. 5 can be approxi-
mated as
1expR E Z a for s1 1 12
k tk sk1 2
= - =
^^^ hh h
6 @
(6a)
1expR N Z Z a s a s s1 1 12 1 for >
, , ,sk s k s k s k1 1 1 2 1
= - - - -
- - -
^ ^^^ h hh h
6 @
(6b)
Eq. 6a represents egg production rate minus survival rate to the age at exit from
stanza s = 1; egg production is assumed to be approximately proportional to biomass
Bsk of the oldest (adult) stanza s in cell k. Eq. 6b is derived from the equilibrium of
the delay-differential equation for Ns that results from assuming spatial gain and loss
rates to be approximately balanced, so that the dominant effects on Ns are gains from
individuals progressing from the previous stanza and from losses of individuals as
they progress to the next stanza and mortality within the stanza.
e equilibrium assumption needed for derivation of Eq. 6 can lead to inaccurate
predictions because it can result in incorrect size distributions if incoming and out-
going numbers are not in balance, and size then affects the predation-rate param-
eters (areas searched, maximum prey-consumption rates). Eq. 6 is a relatively poor
approximation for both egg production and net rates of numbers gained through
graduation from younger stanzas and loss to older stanzas, so this early version of
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 445
Ecospace tended to predict incorrect absolute values for cell-specific numbers Nsk
relative to Ecospace-predicted cell-specific biomasses Bsk, but the predicted spatial
distributions of abundances were at least qualitatively reasonable. In past applica-
tions, Ecospace generally predicted that Nsk was relatively high in cells with high
egg production, in cells with favorable habitat, and in cells near seasonally varying
optimum migration positions for migratory stanzas.
N A : P S D O A-
B C M-R M.—In an effort
to avoid the large computer-memory requirements and massive accounting calcula-
tions (for typical models, on the order of 103 more calculations per time step) re-
quired for replicating the full age-structure accounting of Eqs. 2–4 for every grid cell
of large Ecospace models, we developed a simple approach based on combining the
overall population accounting of Eqs. 2–4 with the relatively simple Eq. 6 diffusion
model for predicting relative spatial abundances by stanza. is approach depends
on two key assumptions: (1) that Eqs. 2–4 can be applied for each multistanza popu-
lation as a whole (totaled over all Ecospace grid cells), given reasonable estimates of
mean food consumption rates qs ,t and mortality rates Zs,t averaged over the grid cells
(a basic assumption that is made anyway in the nonspatial Ecosim representation of
any large area) and (2) that the diffusion model, Eqs. 5–6, gives reasonable predic-
tions of the relative distribution of the biomass of each stanza over grid cells whether
or not the absolute numbers Nsk are predicted correctly, hence preserving effects of
complex spatial-overlap patterns among stanzas.
We then perform the Ecospace time solution on monthly time steps using the fol-
lowing four-step procedure. First, we use the results from integration of Eqs. 5–6 to
apportion the spatial distribution of total stanza biomass Bst (Eq. 4) over spatial cells
k to give Bsk cell biomasses comparable to those from integration of Eq. 1, using Bsk =
BstNsk/ΣkNsk . Second, the spatial Bsk biomasses (and relative predator-search areas Psk
= Pst Nsk/ΣkNsk) are then used in the Ecosim foraging arena and fishing rate calcula-
tions for each cell k to predict food-consumption rates Qsk and mortality rates Zsk.
ird, biomass-weighted average food-consumption rates q,s t
r and mortality rates
Z,s t
r
for the whole population are calculated as
.q B q B Z B Z Band
, ,s t sk sk st s t sk sk s t
kk
= =
r
r//
Fourth, the system-scale multistanza accounting is done by means of Eqs. 2–3 with
the biomass-weighted averages ,q Z
, ,s t s t
r
r
^ h
to give predicted total population age and
size structure and total stanza biomasses Bs ,t+1 at the start of the next month.
is procedure retains some information about predicted changes in spatial abun-
dance patterns due to mixing processes and spatial variation in mortality rates Zsk
because Zs k is included in the prediction of relative numbers Nsk by cell from Eqs.
5–6, but it discards information about spatial variation in growth rates qsk in favor of
using a single system-scale prediction of body growth (Eq. 3 with consumption rate
qs,t represented by q,s t
r).
Further, it fails to account for the cumulative divergence that can take place in
both age and size structure for relatively sedentary species resident in spatial cells
that are protected from fishing. at is, for “adult” stanzas containing many age
classes, it fails to represent the potential accumulation of older, more fecund animals
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
446
in protected areas, considered by some to be a key benefit of marine protected areas
(MPAs; see, e.g., Gaylord et al., 2005). One possible solution to allowing accumula-
tion of large adults in specific areas is to split the oldest stanza group into a number
of stanzas, but doing so is an approximate fix rather than a solution.
For resident species, the mixing-model approach also fails to account for regional
variation in growth rates associated with spatial cells that have higher basic (pri-
mary and lower-trophic-level) productivity or reduced intraspecific competition due
to limited recruitment. For these reasons, the mixing-model approach is best suited
to analyses of pelagic systems, where relatively high mobility results in averaging of
feeding and mortality rates over substantial areas. When used for systems with many
resident or sedentary species, the approach is potentially misleading and should be
used only to provide computationally “quick-and-dirty” policy screening for options
such as size and spacing of MPAs, to be followed by more careful screening according
to the more detailed individual-based approach described below.
N A : I-B A P S
P G, S, D.—Most regional popula-
tions exhibit at least some degree of localized or cell-scale variation in recruitment,
body growth, and survival rates, and erosion of this local structure has serious im-
plications for maintenance of both biodiversity and overall productivity. e origi-
nal and mixing-model approaches described above cannot adequately capture such
local structure, which can result from the cumulative effects of the development of
a fishery or from MPAs. We therefore decided to develop a much more detailed and
realistic approach to the representation of localized trophic-interaction effects based
on concepts of individual-based modeling (IBM).
In the IBM approach, we retain the spatial biomass-dynamics accounting for non-
multistanza species represented by Eq. 1 and the multistanza population-dynamics
accounting of Eqs. 2–4, but rather than solving Eqs. 2–4 once for each stanza us-
ing spatially averaged (grid-wide) food-consumption and mortality rates, we divide
the age-0 recruits for each multistanza population (N0,t) into a large number np of
packets (cohorts). Each packet is assumed to represent some number of identical in-
dividuals of the population, and all packets from the monthly recruitments start out
with the same individual biomass and numbers at recruitment (Np,0,t = N0,t/np). Each
packet is then followed independently as it moves among spatial cells on the grid.
is approach is similar to that recommended by Rose et al. (1993) and Scheffer et
al. (1995). e growth-survival Eqs. 2 and 3 are then solved for each packet, yielding
its predicted age and size dynamics (Np,a, t and Wp,a, t). Packets are discarded from the
overall population when they reach a maximum age (denoted ama x) beyond which
Np,a,t is negligible. Each packet p is assigned an initial spatial position Xp,0, t,Yp,0,t, and
movements of the packet over time are predicted from both random (diffusive) and
oriented (migratory) changes in position. At each simulation time step, the ecologi-
cal conditions (food intake rates, mortality rates) for the spatial cell in which each
packet is located are used in Eqs. 2–3. e overall accounting for Bs,k and Psk needed
for trophic-interaction predictions (impacts from and on biomasses of nonstanza
species in each cell k) then involves simply summing Bp,k,t and Pp,k,t packet biomasses
and predation search areas over those packets present in each cell k, before foraging-
arena predictions of Qsk, Zsk are performed for that cell.
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 447
e obvious advantage of the IBM approach is that it retains the cumulative his-
tory of each packet’s space-use pattern, in the form of the packet’s numerical (worth)
and body-size (weight) states. For sedentary species, local differentiation in growth
and accumulation of older animals is represented by how packets in different local
areas (cells) fare over time. Further, through use of restricted movement rules, col-
lections of packets can easily be made to form distinctive local populations, presum-
ably key units of local adaptation and biodiversity.
A disadvantage of the approach is that it requires massive computation, both
for the survival-growth calculations and for movement of a sufficient number of
packets over the simulated grid to permit realistic spatial distributions and varia-
tion. is number must be determined by trial and error; the number of packets
must be increased until results stop changing. Most of the computational effort
(typically about 90%) ends up being in the simulation of movement as changes in
the locations Xp,a ,t, Yp,a ,t.
Monthly survival-bioenergetics updates for each packet are based on food intake
and mortality rates predicted for the spatial cell where the packet is located at the
start of the month. No attempt is made to integrate q or Z rates over times within the
month spent in different cells; doing so would be prohibitively computationally in-
tensive. is omission amounts to assuming either that cell sizes are set large enough
that most movements over any month occur within a single cell or that spatial cor-
relation in productivity and predation risk among nearby cells there is reasonably
high, so movements over such cells would result in the same predicted food intake
and mortality rates obtained from the initial cell. Effects of violating this assumption
could be tested if the model were run with varying grid cell sizes.
e initial or spawning position for each packet (Xp,0,t , Yp,0,t) is set to the center of
a cell k, where the probability of recruiting to cell k is set equal to Ekt/ΣkEkt and Ek t is
the predicted total egg production in cell k for month t summed over all packets that
are in cell k at the start of the month. is procedure allows spawning to occur well
away from locations of larval settlement or juvenile growth because larval disper-
sal and juvenile migration can be explicitly represented, through either different or
similar movement-simulation rules as used for packets of older fish. In particular, the
IBM approach “encourages” formation of local stock structure; recruitment tends to
occur near centers of egg production. In the context of MPAs, lower mortality rates
Z in designated cells can result in the accumulation of older, more fecund fish, and
those cells can thus become local areas of high reproduction.
Monthly movements by each packet are simulated as a set of ns increments to the
X,Y values that determine location on the grid. e user specifies an average an-
nual movement distance, which implies an average monthly movement distance. e
number of moves ns each month is then set so that the distance per increment can-
not exceed the width of one cell. Each movement is made only in a cardinal direction
(N,S,E,W), so that only X or Y (not both) changes for each move. e probability of
choosing each of the four directions, k΄, is set to ms kk΄/Σk΄mskk΄, where ms kk΄ is the in-
stantaneous movement rate from cell k to k΄ calculated for the continuous biomass
model (see Eq. 1). As noted above, the mskk΄ can be set equal for all k΄, to represent
purely diffusive movement, or biased to represent avoidance of cells with unsuitable
habitat, movement toward preferred habitats, or seasonal migration patterns. is
method for choosing movement directions allows users to employ the same user
interface for entering assumptions about movement distances and orientation for
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448
multistanza populations as for groups represented only by biomasses, and it ensures
that the multistanza movement patterns are broadly comparable with predictions
from the computationally faster continuous mixing-model version of Ecospace.
C E
Realistic representation of ontogenetic shifts in habitat usage and migration and
dispersal patterns is critical to proper evaluation of MPAs. In both cases presented
here, conservation groups have exerted considerable pressure in favor of relatively
large MPAs for protection of biodiversity and for the restoration of depleted fish pop-
ulations. e assumption is that traditional fisheries-management approaches (e.g.,
harvest regulation and habitat protection) are inadequate to the task.
In both cases, currently available population-dynamics and ecosystem-response
data are clearly recognized to be inadequate to provide unambiguous predictions of
response to various policy options, and clearly, therefore, protected-area plans must
be implemented as adaptive-management experiments with the expectation that
considerable adjustments will be needed as response information becomes avail-
able. e Ecospace models being developed are specifically intended to provide only
broad “policy-screening” predictions. Such screening helps to eliminate proposals
that would clearly be inadequate to meet various management objectives or would
create substantial risks though unintended dynamics such as shifting effort into ar-
eas that remain open to fishing.
ese two case studies should be viewed as works in progress, where the EwE
modeling framework is intended to act as a focus for scientific communication, data
synthesis, and progressively refined policy testing over a number of years. Further
development of useful ecosystem models will require active involvement and partici-
pation by quite large teams of scientists with diverse interests and knowledge. e
case-study models represent what practitioners of adaptive environmental assess-
ment and management (Holling, 1978; Walters, 1986) would call “straw man” results,
intended specifically to cross the initial intellectual hurdle of getting some model
working that can be used as a basis for future improvement and to attract scientific
and management interest in that improvement.
Here, we do not provide details about the Ecopath and Ecosim parameters (bio-
masses, Zs, QBs, diet compositions, prey vulnerability exchange rates, etc.) used in
the simulations. Databases containing all parameter values for the two models, along
with the EwE software needed to read the databases and run the Ecosim and Eco-
space model scenarios described below, are freely available for download at http://
www.ecopath.org (model references Gulf of Mexico, California MLPA).
S F C G M.—e Gulf of Mexico has
some of the more valuable fisheries of North America, in particular for shrimp,
northern red snapper [Lutjanus campechanus (Poey, 1860)], and Gulf menhaden
(Brevoortia patronus Goode, 1878). Controversy has developed over impacts of the
shrimp trawl fishery on the red snapper (Gallaway and Cole, 1999). By-catch esti-
mates of age 6- to 24-mo-old juvenile red snapper have exceeded 20 million fish
per year (Ortiz et al., 2000), far larger than the number of older fish caught in com-
mercial and recreational fisheries (SEDAR, 2005). Management proposals for the red
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 449
snapper have called for by-catch reduction to promote the recovery of red snapper
from historical overfishing.
During development of a demonstration Ecosim model for the Gulf of Mexico
Fishery Management Council, Walters et al. (2008) obtained very good fits to histori-
cal stock-assessment data using a multistanza Ecosim population model for a variety
of important commercial fish species in the Gulf (Fig. 1). e demonstration model is
quite complex, including 63 Ecopath biomass pools of which 31 represent life-history
stanzas for multistanza population modeling of 10 commercially and recreationally
important species, so perhaps not surprisingly, we were able to fit historical data for
some species quite well despite very limited information on details of ontogenetic
changes in diets, mortality rates, and predation risk, but when model scenarios were
run that assessed possible responses of the red snapper to reductions in by-catch
mortality of its age 6- to 24-mo juveniles in the Gulf shrimp trawl fishery, we found
Figure 1. Time trends of harvestable biomass for key indicator stocks in the Gulf of Mexico
(GoM) and central California coast (CA), estimated from single-species stock-assessment mod-
els (stock reduction analyses) and simulated time trends predicted by Ecosim’s multistanza age-
structured approach and by two Ecospace methods for predicting spatial distribution of size-age
stanzas. The y-axis indicates relative abundance, scaled to the same mean for each simulation (all
simulations started with the same absolute biomass).
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450
that model predictions diverged dramatically depending on details of the protocol
followed in selecting Ecosim parameters for inclusion in model fitting to the histori-
cal assessment data. Some apparently credible parameter combinations (based on fit
to the data) resulted in dramatic increases in red snapper recruitment after by-catch
reduction, but other combinations led to predictions of practically no recruitment
increase, because of increases in competitor and predator species that are also as-
sumed to be subject to shrimp trawl by-catch (Walters et al., 2008).
We found that this divergence of model predictions resulted from differences in
modeled dynamics of several “minor” fish species like marine catfishes, for which
very few historical data are available to inform the model-fitting procedures. at is,
we cannot resolve uncertainty about how such species would respond to by-catch re-
duction simply by building more models and including more available data in model
parameterization; data critical for model testing were simply not collected during
development of the shrimp trawl fishery.
Now, therefore, two basic management options are available. One is to proceed
with plans for by-catch reduction, in hopes that various single-species model pre-
dictions, and the more optimistic Ecosim predictions, will turn out to be correct.
e other is to proceed with an experimental adaptive-management approach, in
which some areas are first closed to trawling (or where by-catch reduction devices
are required) and are monitored for improvement in red snapper juvenile produc-
tion, before the decision is made whether to proceed to large-scale trawl closures or
by-catch-reduction requirements.
e Ecospace models being developed for the Gulf of Mexico offer an opportunity
to provide at least broad, qualitative predictions about likely abundance responses
of a range of species to implementation of MPAs aimed at testing effects of trawl
closures. Accordingly, we are developing a suite of alternative models for the Gulf
region, differing in spatial resolution (grid cell size) and model complexity (number
of functional groups) so as to determine which model predictions are robust to these
modeling details.
e crudest spatial representation uses 0.5° × 0.5° (~50-km × ~50-km) cells and
is therefore capable of looking only at very large closed areas; this model gives fits
to historical abundance trend data that are comparable to the nonspatial Ecosim
model fits (Fig. 1). e crude spatial version predicts that large closed areas (100 km
wide onshore-offshore bands spaced evenly along the coast) would result in dramatic
increases in abundance of a number of species that are heavily exploited (Fig. 2). In-
terestingly, the model predicts quite strong trophic-cascade effects within such large
protected areas, involving substantial increases in demersal piscivores (groupers,
snappers) at the expense of small planktivores (menhaden) and nearshore pelagic pi-
scivores (mackerels). We note though that both of these prey groups exhibit seasonal
migration beyond the MPA borders, which may result in a lowering of the cascading
effects if incorporated.
Extreme scenarios like the closure pattern in Figure 2 are probably not practical
to implement from a political, economic, or monitoring-cost perspective, but they at
least provide a benchmark against which to evaluate more modest adaptive-manage-
ment proposals. For example, using finer spatial grids (e.g., 0.125° × 0.125°, 25-km ×
25-km cells), we find with reasonable estimates of spatial dispersal rates that small
protected areas (e.g., 25 km wide onshore-offshore strips, widely spaced around the
Gulf coast) would probably not produce measurable responses except in a few rela-
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 451
Figure 2. Spatial distributions of some indicator biomasses for the Gulf of Mexico, as predicted by Ecospace for calendar year 2005 (end of simulations in Fig.
1). Spatial cells are 0.25° × 0.25° (approximately 25 km × 25 km); cells designated as marine protected areas (MPAs) are shown in grey. Modeled ontogenetic
habitat shifts are represented as successive biomass distributions of (A) juvenile (0–12 mo old) menhaden Brevoortia t yrannus (Latrobe, 1802), (B) adult men-
haden (age 12+ mo), (C) juvenile (age 0–5 mo) red snapper (Lutjanus campechanus), (D) juvenile (age 6–24 mo) red snapper, and (E) older (24+ mo old) red
snapper. Individual-based modeling (IBM) results with MPAs are not shown because these were indistinguishable from results shown in the MPA column.
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
452
tively sedentary species (groupers) and probably not in the key experimental target
species, red snapper.
When we repeated the simulations with the crude Ecospace model using the IBM
approach to multiple stanzas, rather than the mixing-model approach, we were
somewhat surprised to see very little difference between model predictions. In par-
ticular, the IBM representation typically predicts spatial patterns very similar (Fig.
2) to those obtained with the much simpler, computationally efficient approach of
allocating stanza biomasses over grid cells according to simple biomass mixing-rate
predictions and spatially averaged mortality and feeding rates.
To increase the possibility of divergence between the mixing-model and IBM
versions, we forced the Ecospace model to have a strong spatial pattern of prima-
ry production. We scaled phytoplankton production rates for each cell to mean
model-derived primary production estimates based on the approach of Platt and
Sathyendranath (1988) tuned to Sea-WiFS satellite data. Such data show that a high
proportion of the Gulf ’s primary production occurs near the mouth of the Missis-
sippi River, obviously a massive nutrient-loading source. A high proportion of the
total shrimp and fish harvest of the Gulf also comes from this very productive area;
Ecospace correctly predicts this pattern for both the mixing-model approach and the
IBM approach to multiple stanzas (Fig. 2).
P C C F C.—From the 1970s
through the 1990s, intensive commercial and recreational fisheries along the Cali-
fornia coast apparently led to severe depletion of a variety of demersal fish species,
especially long-lived rockfishes (Starr et al., 2002, but see also Stephens et al., 2006).
In federal waters (outside California’s 3-mile limit of jurisdiction), this depletion has
led to severe restrictions on commercial fishing and, in particular, to closure of large
areas as rockfish conservation areas (RCAs). In state waters, a key public reaction to
the perception of widespread overfishing has been passage of the Marine Life Pro-
tection Act (MLPA). e MLPA mandates development of a network of MPAs along
the coast with broad objectives including protection of fish habitat, restoration of
ecosystem function, and restoration of natural population size and age structures for
long-lived species. e MLPA resulted in a complex planning process that included
extensive consultation with the scientific community for development of size and
spacing guidelines for MPAs. ese guidelines presently call for protected areas to
be at least 10 km in long-shore extent, to extend offshore to at least the limits of
state jurisdiction, and to be no more than 50 km apart so as to ensure “connectivity”
through larval dispersal processes.
Single-species, one-dimensional spatial population-dynamics models of MPA
plans developed to date under the MLPA indicate that the size and spacing guide-
lines will provide effective protection only for the most sedentary demersal fish spe-
cies (Walters et al., 2008) and will have almost no impact on ecosystem “function”
as measured by fish biomass or production. is lack of impact arises because over
90% of the production involves species whose annual dispersal or migration rates are
far too high for small inshore MPAs to have any impact on their exploitation rates.
We hope that Ecospace models will be able to provide improved policy screening
(development of size and spacing guidelines needed to provide effective protection
of ecosystem function) in two regards: (1) we will be able to examine two-dimen-
sional spatial dynamics (i.e., inshore-offshore mixing effects and federal and state
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 453
MPA policies), and (2) we will be able to account for trophic-interaction effects (e.g.,
trophic-cascade dynamics) that previous Ecospace modeling has indicated may sub-
stantially reduce the efficacy of small protected areas (Walters et al., 1999; Walters
and Martell, 2004).
We have developed an initial Ecospace model using most of the Ecopath functional
groups and parameter estimates developed by Field et al. (2006) for the large-scale
dynamics of the Northern California Current region off California, Oregon, and
Washington (Cape Mendocino to Cape Flattery). e Field et al. model included 63
functional groups, but no multistanza components. We aggregated some lower-tro-
phic-level biomasses and left out species (e.g., marine mammals) that are not likely to
be affected by MLPA plans to produce a model with 35 functional groups. We then
selected six representative demersal species or life-history types (lingcod, thorny-
heads, shortbelly rockfish, nearshore rockfish, widow rockfish, and abalone) to rep-
resent with multiple stanzas using the mixing-model approach. Common features of
the modeled life histories of all of these species are that the first life-history stanza
represents pelagic larvae and early postsettlement juveniles that are dispersed more
or less widely along the coast, that the second stanza represents juveniles that migrate
into and grow in inshore (shallow) waters, and that the third stanza represents older
(> 4-yrs) juveniles and adults that either remain in shallow areas (abalone, inshore
rockfish, lingcod) or migrate offshore to reside in deeper reef and canyon areas. e
three-stanza representation allows us to examine “connectivity” among protected
areas by larval dispersal, impacts of protection from fishing and other disturbances
on juveniles inshore, and impacts of federal management policies in offshore waters.
As for the Gulf of Mexico case, and as did Field et al. (2006), we obtained good
agreement between simulated trends in decline of major species and estimates of
these trends from single-species stock assessments. e multistanza models predict
quite long recovery times (20–50 yrs) to productive stock levels (e.g., stock sizes for
maximum sustainable yield) for the depleted species even given complete protection
from fishing. A comparison of Ecospace predictions for three spatial protection poli-
cies (Fig. 3), using 2" × 2" (3.3-km × 3.3-km) grid cells for the MLPA’s North Central
Coast planning unit, indicated that only abalone, with its very short larval and older
animal dispersal rates, was likely to increase greatly under the protection afforded by
MPAs developed under current size and spacing guidelines, unless the federal RCAs
are maintained for at least 20 yrs. Ecospace predicted that implementing the federal
RCAs alone would lead to more rapid depletion of inshore species (like lingcod and
nearshore rockfishes), because of concentration of fishing effort inshore after closure
of offshore grounds. Anecdotal reports and hints in catch statistics imply that this
shift actually did start to occur when the RCAs were implemented, but the shift was
at least partially countered by introduction of other fishing restrictions like trip lim-
its and license reductions (R. Parrish, NMFS retired, Pebble Beach, CA, pers. comm.).
We then repeated the baseline Ecospace simulation that was previously fitted to
the time-series data, but we used the IBM version of the multiple stanzas. We did
not try to refit the IBM version to the same time-series data used to fit the mixing-
model version. e California Current model generated larger differences between
the mixing-model and IBM versions than the Gulf of Mexico model. In particular,
the IBM formulation predicted more severe declines of the long-lived rockfishes than
were estimated from single-species assessments, from nonspatial Ecosim, or from
the mixing-model Ecospace version. e divergence is caused by two factors: (1) con-
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No MPAMPA and RCAMPA Only
A
0.05 22.02
A
A
B
0.18 176.14
B
B
C
0.28 53.58
C
C
D
0 0.46
D
D
Figure 3. Spatial distributions of biomasses of indicator species for an area of the central California coast, calculated by Ecospace for the year 2035 as a future
reference point. Maps show three alternative MPA congurations. Species distributions shown are for (A) lingcod (Ophiodon elongatus Girard, 1854) adults
age 36+ mo, (B) cabezon (Scorpaenichthys marmoratus Girard, 1854) adults age 48+ mo, (C) widow rocksh [Sebastes entomelas (Jordan and Gilbert, 1880)]
harvestable juveniles plus adults age 36+ mo, and (D) abalone (Haliotis spp.) harvestable juveniles plus adults age 36+ mo. Cabezon and abalone represent spe-
cies largely restricted to inshore waters within California’s state jurisdiction, whereas lingcod and widow rocksh are more widely distributed and subject to
impact from recent U.S. federal regulations (RCAs, rocksh conservation areas).
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 455
centration of Ecopath base biomasses on a much smaller proportion of the total habi-
tat than in the Gulf of Mexico case, causing more severe intraspecific competition for
food (and therefore reduced growth rates and fecundities wherever IBM packets are
concentrated through chance movements), and (2) greater concentration of fishing
effort on cells where more packets are concentrated by chance at each model time
step.
Ecospace includes a procedure for adjusting prey-vulnerability and fishing-mor-
tality rate parameters for concentration of abundance in cells with favorable habi-
tats, but the adjustments are apparently not great enough to prevent reduced mean
productivity and higher overall fishing mortality in the IBM version. is problem
could, in principle, be remedied by refitting of the model, but with present comput-
ing capability, making the many IBM simulation runs that would be necessary for the
nonlinear search procedures used in Ecosim model fitting is not practical. One com-
forting point is that, although the IBM representation overestimates stock depletion,
it still predicts the same relative response to spatial closure patterns as does the sim-
pler Ecospace representation, indicating that the simpler representation can be used
effectively for rapid policy screening.
D
e two new approaches presented complement each other and should be used
in tandem. e faster and less expensive mixing-model version can be used for data
fitting and gaming, and periodic comparison of predictions with those of the more
computationally intensive IBM version can ensure high confidence in the overall
results.
Although Ecospace now has the accounting procedures needed for realistic rep-
resentation of multistanza life histories, the case examples illustrate a key gap in
information that suggests caution in interpreting model predictions. For both case
models, the first or early juvenile stanzas are assigned high annual natural mortal-
ity rates Z on the order of 1–3, and small changes in these rates can cause large
changes in predicted recruitment rates. Presumably most of this juvenile mortality
is due to predation, but modeled “ecotrophic efficiency” (proportion of Z caused by
modeled predators, calculated from predator abundances, food consumption rates,
and diet compositions) is low for most juvenile groups. Early juvenile biomass is typi-
cally low, and high mortality rates can be caused if the juveniles make up only a
tiny proportion of the diet of abundant predators. Diet data are typically inadequate
even to detect, let alone to estimate accurately, such tiny proportions. Low ecotro-
phic-efficiency values in the models mean that juvenile mortality rates do not vary
substantially with changes in abundance of modeled competitors and predators, so
the models may greatly underestimate effects of changes in community structure on
recruitment rates. A major and unfortunately very common problem is that we have
only very incomplete information about causes of mortality for juvenile fishes, and
this is an area that should see increased research focus.
Individual-based or packet models for fish dynamics have typically represented
dynamics at much finer scales (hours to days, meters to kilometers) than is usual for
Ecospace models (see, e.g., Van Winkle et al., 1993; Tyler and Rose, 1994; Ault et al.,
1999; Werner et al., 2001). e main emphasis in those models has been on capturing
effects of individual variation in foraging and predation circumstances on growth
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
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and survival patterns. To date, few IBMs (e.g., that of Ault et al., 1999) have includ-
ed dynamic calculations on fine enough time and space scales (minutes, meters) to
capture the predation-risk-management effects (spatially and temporally restricted
foraging, bout feeding dynamics) that have been found to be critical for represent-
ing recruitment relationships, long-term predator-prey stability, and maintenance of
biodiversity in Ecosim models (Walters and Martell, 2004).
Comparison of IBMs for very fine-scale spatial behavior (K.A.R., unpubl. data)
with Ecospace reveals a key structural limitation in the Ecospace formulation. In
assuming that the Ecosim foraging-arena equations (for exchange of prey biomass
between vulnerable and invulnerable behavioral states) apply within each Ecospace
cell, we implicitly assume that each model cell is at least large enough to contain all
of the “routine” (diurnal, feeding and resting) activities for each individual. We do
not allow for the possibility that individuals use one spatial cell or habitat type for
resting and hiding and other cells for foraging (and exposure to increased predation
risk). For example, suppose we set up an Ecospace model with small enough grid cells
to display a mosaic of reef habitat cells and a corresponding mosaic of soft (sandy or
mud) bottom areas between these reefs. Any model species that is treated as using
only reef habitat is then restricted to spend all its time in the reef-type cells, when
in reality many such species make periodic, extensive (and risky) foraging excur-
sions onto open bottom areas. In restricting such species to the reef cells, Ecospace
underestimates food resources available to them, as well as exposure to some preda-
tors and fishing pressure, and their local impact on abundances of food organisms
on adjacent soft bottom areas. We can crudely represent such use of multiple habitat
types by creating a new habitat type called something like “soft bottom near reef,”
and placing a “halo” of such cells around each reef, but this arbitrary approach as-
sumes that we can predict the sizes of such habitat halos a priori rather than as part
of the Ecospace IBM movement dynamics. Further, Ecospace provides no simple way
to predict the proportion of time that animals choose to spend in relatively safe (reef)
cells as opposed to relatively risky foraging (soft-bottom) cells. For larger Ecospace
cells, where daily movements are contained within cells, that time allocation is au-
tomatically estimated from Ecopath base feeding rates and maximum feeding rates,
and changes in time allocation are calculated automatically (when desired) as relative
time spent feeding and at risk to predation.
Although this structural limitation may be seen as a weakness of Ecospace by sci-
entists concerned with understanding how the details of fine-scale behavioral ecol-
ogy contribute to limitation of trophic interaction rates, it is also a strength in the
sense of allowing use of large spatial cells for exploration of policy options like MPAs
over large regions (e.g., Figs. 1–2). Representing such large regions with spatial cells
and time steps small enough to represent resting-foraging behavioral exchanges
explicitly—while still making long-term ecosystem response predictions quickly
enough to allow for model fitting and comparison of multiple policy options in plan-
ning settings like management gaming workshops—is presently impractical, limited
by insufficient data and computational speed. Further, running highly detailed mod-
els over very large spatial grids is an invitation to generation of pathologically large,
cumulative errors in model predictions. e challenge is to meld the detailed IBMs
with the broad-scale Ecospace model to be able to scale small-scale IBM results to
more ecologically meaningful regional scales and to increase our confidence in how
fine-scale dynamics are approximated in Ecospace.
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 457
Another potential weakness in the current Ecospace formulation is that habitat
structure (habitat “type” for each spatial cell) is treated as constant over time. Some
temporal changes in cell habitat type can be accommodated. If cell habitat is defined
by biologically produced habitat features like macrophyte biomass, then the vari-
able can be included as Ecopath/Ecosim variables and linked to trophic interactions
through “mediation functions.” Model users can introduce arbitrary changes in the
habitat type map as simulations proceed, but the capability has not yet been devel-
oped to model how such changes might happen dynamically over time as a result of
processes like industrial development and land subsidence (as occurs in the Gulf of
Mexico near the Mississippi River mouth). Further, no easy way is available to model
dynamics of physical-chemical variables like turbidity, salinity, and dissolved oxygen
as defining variables for habitat type or habitat quality. Time series of spatial salinity
fields and relative primary production rates can be input to the software as spatial
forcing fields and then linked to feeding and mortality rates, but this approach does
not allow complete flexibility in how the input variables affect habitat quality.
Much modeling of ocean ecosystems has focused on understanding linkages be-
tween physical dynamics (hydrodynamics), chemistry (nutrient cycling), and lower
trophic levels (phytoplankton, zooplankton), by means of “nutrient-phytoplankton-
zooplankton” models like ERSEM (Baretta et al., 1995) and NEMURO (Werner et
al., 2007), and efforts have been made to link these models with Ecosim (Aydin et al.,
2005) and with IBMs (Megrey et al., 2007) and, more recently, to real-time coupling
of Ecosim to biogeochemical models (B. Fulton, CSIRO, pers. comm.; S. Mackinson,
CEFAS, pers. comm.). Such efforts will eventually lead to synthetic models that over-
come at least some of the limitations of Ecospace related to habitat structure and
productivity, but as for most IBMs, such models are not yet computationally efficient
enough to be useful for interactive policy analysis.
Clearly, we need to view Ecospace not as a fixed, completed modeling application
but rather as an evolving framework, subject to continuing improvement as the mod-
el is challenged with new “what-if” questions and with opportunities for integration
with other modeling approaches. We hope the steps we have taken to improve the
population-dynamics representations in Ecospace will be just one component in a
much larger process of further model development and testing.
A
We especially thank R. Ahrens for help with the spatial map figures. Financial support for
this work was provided by NSERC Discovery Grants to Walters and Christensen, and by the
Sea Around Us Project, a scientific cooperation bet ween the University of British Columbia
and the Pew Environmental Group.
L C
Ault, J. S., J. Luo, S. G. Smith, J. E. Serafy, J. D. Wang, R. Humston, and G. A. Diaz. 1999. A
spatial dynamic multistock production model. Can. J. Fish. Aquat. Sci. 56(Suppl 1): 4–25.
Aydin, K. Y., G. A. McFarlane, J. R. King, B. A. Megrey, and K. A. Myers. 2005. Linking oceanic
food webs to coastal production and growth rates of Pacific salmon using models on three
scales. Deep-Sea Res. II 52: 757–780.
Baretta, J. W., W. Ebenhöh, and P. Ruardij. 1995. e European Regional Seas Ecosystem Mod-
el, a complex marine ecosystem model. Neth. J. Sea Res. 33: 233–246.
BULLETIN OF MARINE SCIENC E, VOL. 86, NO. 2, 2010
458
Christensen, V. and C. Walters. 2004. Ecopath with Ecosim: methods, capabilities and limita-
tions. Ecol. Model. 172: 109–139.
Essington, T. E., J. F. Kitchell, and C. J. Walters. 2001. e von Bertalanffy growth function,
bioenergetics, and the consumption rates of fish. Can. J. Fish. Aquat. Sci. 28: 2129–2138.
Field, J. C., R. C. Francis, and K. Aydin. 2006. Top-down modeling and bottom-up dynamics:
linking a fisheries-based ecosystem model with climate hypotheses in the Northern Cali-
fornia Current. Prog. Oceanogr. 68: 238–270.
Gallaway, B. J. and J. G. Cole. 1999. Reduction of juvenile red snapper bycatch in the U.S. Gulf
of Mexico shrimp trawl fishery. N. Am. J. Fish. Manage. 19: 342–355.
Gaylord, B., S. D. Gaines, D. A. Siegel, and M. H. Carr. 2005. Marine reserves exploit popula-
tion structure and life history in potentially improving fisheries. Ecol. Appl. 15: 2180–2191.
Gribble, N. A. 2003. GBR-prawn: modelling ecosystem impacts of changes in fisheries man-
agement of the commercial prawn (shrimp) trawl fishery in the far northern Great Barrier
Reef. Fish. Res. (Amst.) 65: 493–506.
Holling, C. S. (ed.). 1978. Adaptive environmental assessment and management. Wiley Inter-
national Series on Applied Systems Analysis, Vol. 3. Wiley, Chichester. 377 p.
Le Quesne, W. J. F., F. Arreguín-Sánchez, M. Albañez-Lucero, H. Cheng, V. H. Cruz Escalona,
G. Daskalov, H. Ding, E. González Rodríguez, J. J. Heymans, H. Jiang, et al. 2008. Analysing
ecosystem effects of selected marine protected areas with Ecospace spatial ecosystem mod-
els. Fisheries Centre Research Reports 16(2). Fisheries Centre, Univ. British Columbia. 67 p.
Martell, S. J. D., T. E. Essington, B. Lessard, J. F. Kitchell, C. J. Walters, and C. H. Boggs. 2005.
Interactions of productivity, predation risk, and fishing effort in the efficacy of marine pro-
tected areas for the central Pacific. Can. J. Fish. Aquat. Sci. 62: 1320–1336.
Megrey, B. A., K. A. Rose, R. A. Klumb, D. E. Hay, D. L. Eslinger, and S. L. Smith. 2007. A bio-
energetics-based population dynamics model of Pacific herring (Clupea harengus pallasi)
coupled to a lower trophic level nutrient-phytoplankton-zooplankton model: description,
calibration, and sensitivity analysis. Ecol. Model. 202: 144–164.
Ortiz, M., C. M. Legault, and N. M. Erhardt. 2000. An alternative method for estimating by-
catch from the U.S. shrimp trawl fishery in the Gulf of Mexico. Fish. Bull., U.S., 98: 583–599.
Pitcher, T. J., E. A. Buchary, and T. Hutton. 2002. Forecasting the benefits of no-take human-
made reefs using spatial ecosystem simulation. ICES Mar. Sci. Symp. 59: S17–S26.
Platt, T. and S. Sathyendranath. 1988. Oceanic primary production: estimation by remote sens-
ing at local and regional scales. Science 241: 1613–1620.
Rose, K. A., S. W. Christensen, and D. L. DeAngelis. 1993. Individual-based modeling of popu-
lations with high mortality: a new method based on following a fixed number of model
individuals. Ecol. Model. 68: 273–292.
Scheffer, M., J. M. Baveco, D. L. DeAngelis, K. A. Rose, and E. H. Van Nes. 1995. Super-individ-
uals: a simple solution for modeling large populations on an individual basis. Ecol. Model.
80: 161–170.
SEDAR 7. 2005. Assessment summary report, Gulf of Mexico red snapper. Available from:
http://www.sefsc.noaa.gov/sedar/
Sparre, P. 1991. An introduction to multispecies virtual analysis. ICES Mar. Sci. Symp. 193:
12–21.
Starr, R. M., J. M. Cope, and L. A. Kerr. 2002. Trends in fisheries and fishery resources associ-
ated with the Monterey Bay National Marine Sanctuary from 1981–2000. California Sea
Grant Program, Univ. California. San Diego, La Jolla, California, Pub. T-046. 158 p.
Stephens, J., D. Wendt, D. Wilson-Vandenburg, J. Carroll, R. Nakamura, E. Nakada, S. Reinecke,
and J. Wilson. 2006. Rockfish resources of the south central California coast: analysis of the
resource from partyboat data 1980–2005. CalCOFI Rep. 47: 140–155.
Tyler, J. A. and K. A. Rose. 1994. Individual variability and spatial heterogeneity in fish popula-
tion models. Rev. Fish Biol. Fish. 4: 91–123.
Van Winkle, W., K. A. Rose, and R. C. Chambers. 1993. Individual-based approach to fish
population dynamics: an overview. Trans. Am. Fish. Soc. 122: 397–403.
WALTERS ET AL.: MULTISTANZA LIFE HISTORIE S IN ECOSPACE MODELS 459
Walters, C. 1986. Adaptive management of renewable resources. Blackburn Press, Caldwell.
374 p.
_________. 2000. Impacts of dispersal, ecological interactions, and fi shing eff ort dynamics on
effi cacy of marine protected areas: how large should protected areas be? Bull. Mar. Sci. 66:
745–757.
_________ and V. Christensen. 2007. Adding realism to foraging arena predictions of trophic
fl ow rates in Ecosim ecosystems models: shared foraging arenas and bout feeding. Ecol.
Model. 209: 352–350.
_________ and J. Korman. 1999. Revisiting the Beverton-Holt recruitment model from a life
history and multispecies perspective. Rev. Fish Biol. Fish. 9: 187–202.
_________ and S. J. D. Martell. 2004. Fisheries ecology and management. Princeton Univ. Press,
Princeton. 399 p.
_________, V. Christensen, and D. Pauly. 1997. Structuring dynamic models of exploited eco-
systems from trophic mass-balance assessments. Rev. Fish Biol. Fish. 7: 1–34.
_________, ____________, and _______. 1999. ECOSPACE: prediction of mesoscale spatial pat-
terns in trophic relationships of exploited ecosystems. Ecosystems 2: 539–544.
_________, S. J. D. Martell, and J. Korman. 2006. A stochastic approach to stock reduction
analysis. Can. J. Fish. Aquat. Sci. 63: 212–223.
_________, S. J. D. Martell, V. Christensen, and B. Mahmoudi. 2008. An Ecosim model for ex-
ploring ecosystem management options for the Gulf of Mexico: implications of including
multistanza life history models for policy predictions. Bull. Mar. Sci. 83: 251–271.
Werner, F. E., J. A. Quinlan, R. G. Lough, and D. R. Lynch. 2001. Spatially-explicit individual
based modeling of marine populations: a review of advances in the 1990s. Sarsia 86: 405–
410.
_________, S.-I. Ito, B. M. Megrey, and M. J. Kishi. 2007. Synthesis of the NEMURO model
studies and future directions of marine ecosystem modeling. Ecol. Model. 202: 211–223.
A O: 10 March, 2010.
A: (C.W., V.C., W.W.) Fisheries Centre, University of British Columbia, Vancouver,
British Columbia V6T 1Z4, Canada. (K.R.) Department of Oceanography and Coastal Sciences,
Louisiana State University, Baton Rouge, Louisiana 70803. C A: (C.W.)
E-mail: <c.walters@fi sheries.ubc.ca>.
