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WG-EMM-08/42
7 July 2008
Original: English
Agenda Item No(s): 7
A PRELIMINARY BALANCED TROPHIC MODEL OF
THE ECOSYSTEM OF THE ROSS SEA, ANTARCTICA,
WITH EMPHASIS ON APEX PREDATORS
M.H. Pinkerton1, J.M. Bradford-Grieve1, S.M. Hanchet2,
1
National Institute of Water and Atmospheric Research Ltd
(NIWA), Private Bag 14901, Wellington, New Zealand.
Email: [email protected]
Telephone: +64 4 386 0369 Fax: +64 4 386 2153
2
NIWA, PO Box 893, 217 Akersten Street, Nelson, New Zealand
Yes
No 9
ABSTRACT
We report on the development of a mass balanced carbon-budget trophic model of the Ross Sea as a
step towards investigating ecosystem effects of the fishery for Antarctic toothfish (Dissostichus
mawsoni). The model has 30 trophic groups representing all the major biota of the Ross Sea. Many of
the lower trophic level species in the model are grouped by functional role because information is not
available at greater taxonomic resolution. The model separates the following apex predators by species:
Emperor penguin, Adélie penguin, crabeater seal, Weddell seal, orca, sperm whale, Antarctic toothfish.
A survey of the available literature and both published and unpublished data provided an initial set of
parameters describing the abundance (seasonally and spatially resolved where possible, imports,
exports), energetics (growth, reproduction, consumption), and trophic linkages (diets, key predators)
for each model group. We also estimated the relative level of uncertainty on these parameters. We
describe the method we used to adjust the parameters to give a balanced model taking into account
estimates of parameter uncertainty and the large range of magnitude (>6 orders of magnitude) in
trophic flows between different groups of organisms. Biomass, production, consumption, export and
diet fractions are adjusted simultaneously. We set ecotrophic efficiency to unity for all non-primary
producers. Changes to the initial set of parameters needed to obtain balance were significant, especially
for bacteria. Excluding bacteria, the adjustments required for balance from the parameters estimated a
priori were <46% (biomass), <15% (production, consumption), and <28% (diet fractions). The
balanced model presented here has not yet been validated and should be considered a work in progress.
SUMMARY OF FINDINGS AS RELATED TO NOMINATED AGENDA ITEMS
Agenda Item
7
Findings
Improved information on demersal fish species that are prey of
Antarctic toothfish is urgently needed to assess potential ecosystem
effects of the fishery in the Ross Sea region.
This paper is presented for consideration by CCAMLR and may contain unpublished data, analyses, and/or conclusions
subject to change. Data in this paper shall not be cited or used for purposes other than the work of the CCAMLR
Commission, Scientific Committee or their subsidiary bodies without the permission of the originators and/or owners of the
data.
1
1.1
INTRODUCTION
Ecosystem model of Ross Sea ecosystem
We report here on progress towards developing a balanced trophic ecosystem model of the Ross Sea
shelf and slope. This model is a revised version of Pinkerton et al. (2007) and includes key apex
predators as separate species. The model is an important step towards understanding the potential
effects of the fishery for Antarctic toothfish (Dissostichus mawsoni) on the Ross Sea ecosystem. It is
known that fisheries impact other parts of the ecosystem as well as the target species, both directly
from by-catches, and indirectly by altering the species composition and inter-specific relationships
within the ecosystem. Long-term sustainable use of the fishery resource requires an understanding of
the extents of both the direct and indirect effects of fishing. Investigating the indirect effects requires
an improved understanding of ecosystem dynamics in three areas: (1) the current structure of the
ecosystem; (2) variability of the environmental setting, including factors such as hydrodynamics,
climatic forcing, and sea ice dynamics; and (3) the interactions of biotic and abiotic factors in
constraining population sizes.
As a first stage in modelling the potential indirect effects of the fishery for Antarctic toothfish we set
out to describe quantitatively the structure of the ecosystem in the Ross Sea before fishing started.
Species can be interdependent through various means, but one of the more dominant ways that species
are interconnected is trophically, that is, by one species feeding on another. Mass balance models aim
to provide a quantitative description of the trophic structure of a particular ecosystem (e.g. JarreTeichman et al. 1997, 1998; Arreguin-Sanchez et al. 2002; Wolff 1994; Mendoza 1993). Such models
provide a unifying framework to bring together varied field data and literature information to provide
a self-consistent picture of the trophic structure of a given ecosystem. The trophic model developed
here quantifies the transfer of organic material through a highly stylised view of the ecosystem, and
was based on the main mass-balance identities used by the Ecopath trophic model (Christensen &
Walters 2004; Christensen et al. 2004). This approach is commonly used around the world. In
describing the trophic structure of the ecosystem, we quantify: (1) the species present, and their
abundances; (2) energetics of species i.e. growth rates, production rates, respiration rates, assimilation
efficiencies; (3) trophic interconnections between species through information on diets of predators.
Deficiencies in knowledge of these factors mean that parameters estimated from the primary literature
are unlikely to be self consistent. We describe a method to search for a balanced (feasible) mass
balance model taking into account the huge differences in the magnitudes of trophic flows in the
system, and respecting differences in uncertainty between parameters.
The current formulation of the model has no predictive capability and is not, in itself, sufficient to
assess indirect or ecosystem effects of fishing in the Ross Sea. Ecosystem function and dynamics are
closely but not simply related to ecosystem structure (e.g. Pascual & Dunne 2006) so that the work
described here should be seen as a necessary precursor to developing dynamic ecosystem models of
the Ross Sea. It also gives useful insights into system-level trophic structure and helps to identify
priorities for fieldwork. Time-series monitoring of populations, work on understanding life histories of
organisms, and perturbation experiments to investigate the relative importance of various factors in
limiting the abundance of biota are required to move from a static budget to a dynamic ecosystem
model.
1.2
Validation of the ecosystem model
The balanced trophic model presented here has not been validated and should be considered a work in
progress. We intend to validate this model using information on the stable isotopic composition of
tissues of many organisms in the Ross Sea. The interplay of physical, biological and chemical
processes in the environment produces distinct isotopic signatures in the tissues of biota. These natural
abundance signatures are increasingly used as tracers in environmental studies. Carbon and nitrogen
2
isotope ratios (δ13C and δ15N) can track trophic connections within ecosystems and provide
information on the structure of foodwebs. Carbon isotopes are a powerful tool for identifying primary
sources of organic material within ecosystems and showing benthic reworking (Fry & Sherr, 1984;
Peterson & Fry, 1987). Nitrogen isotope ratios often show distinct enrichments per successive trophic
level and have strong applications in food web and dietary studies (DeNiro & Epstein, 1981;
Minagawa & Wada, 1984; Vander Zanden & Rasmussen, 2001). Together, analysis of carbon and
nitrogen stable isotopes have the potential to quantitatively validate food-web models. Stable isotope
data for many Ross Sea organisms are available now, either in the primary literature (e.g. Burns et al.
1998) or in reports and working papers (e.g. Bury et al. 2008; Thompson et al. 2008), or will become
available soon. Tissue from many organisms relevant to the current trophic modelling were sampled
for stable isotope composition on the recent New Zealand IPY-CAML survey of the Ross Sea and are
will be processed through 2008–2009 (Hanchet et al. 2008).
1.3
Overview of the Ross Sea ecosystem
The Ross Sea is a low primary production system, with irradiance, iron, and macronutrients (nitrate,
silicate) variously limiting algal growth through the year. The high latitude position of the Ross Sea
means that primary production is highly seasonal, driven by the annual light/dark cycle and the
freezing and thawing of the sea surface. Insolation sets the dominant limit on primary production from
autumn through to spring; in summer, macronutrients are not depleted and iron appears to limit
primary production (e.g. Sedwick et al. 2000; Arrigo et al. 2003). Organisms have various strategies
for survival through the winter, including migrating in and out of the region (e.g. some whales, seals,
birds), storing lipids or other high-energy products, going into a quiescent stage, vertically migrating
in the case of zooplankton, having a wider than normal range of feeding styles, and having breeding
cycles that are adapted to the realities of food availability for their young (Battaglia et al. 1997).
Sea ice plays an important structural role in forcing the ecology of the Ross Sea (Thomas &
Dieckmann 2002; Arrigo & Thomas 2004). The mean monthly sea ice cover in the Ross Sea varies
from 5% ice free in winter to 70% ice-free in January and September (Arrigo & van Dijken 2004). Ice
reaches a maximum thickness around November of c. 2 m. In contrast with most polar regions, ice
extent in the Ross Sea is increasing (Comiso 2003). The upper surface of the ice provides a habitat for
a number of sea birds and mammals (Ackley et al. 2003), while at the same time, the ice itself,
especially the lower part which is in contact with the water, constitutes a unique habitat for microalgae
and bacteria which provide a food source for associated microfauna and meiofauna and the
cryopelagic fauna of the surface water layer immediate below the ice (Garrison 1991; Brierley &
Thomas 2002; Arrigo & Thomas 2004).
The input of primary production from the water column and sea ice in the Ross Sea is channelled
mainly through the copepods. The connection may not always be direct as heterotrophic flagellates
and larger heterotrophic microplankton, including dinoflagellates, tintinnids, other ciliates, and eggs
and developmental stages of metazoans, are significant grazers of primary production and are often a
significant part of the diet of many copepods (Umani et al. 1998; Caron et al. 2000). Two species of
krill are found in the Ross Sea Euphausia crystallorophias, and E. superba. Abundances of krill are
apparently much lower in the Ross Sea than in other parts of the Southern Ocean, with E. superba
being found primarily along the continental slope, and E. crystallorophias only over the shelf.
Although they form an important link between the water column, sea ice and larger predators, they are
believed to be less productive and have slower turnover rates than the large epipelagic copepods
(Calanoides acutus, Calanus propinquus, Rhincalanus gigas and Metridia gerlachei) (Voronina 1998;
Tarling 2004). In the relative absence of large krill, Antarctic silverfish (Pleuragramma antarctica)
are a major link between mesozooplankton (mainly copepods) and the larger predators. P. antarctica
are ubiquitous in the diet of all large animals (seabirds, seals, toothed and baleen whales, toothfish,
many other species of fish, squid) (DeWitt 1970; Hubold & Ekau 1987). P. antarcticum have a life
history that is thought to take in the whole Ross Sea shelf and slope (Hubold 1985), and their juveniles
dominate the Ross Sea ichthyoplankton. Abundance of demersal fish species is poorly known, but is
3
thought to be dominated (in terms of biomass) by the macrourid Macrourus whitsoni (c. 70%), the
skate Bathyraja eatonii (c. 10%), and icefish (c. 7%) mainly Chionodraco hamatus and C. antarcticus.
Cephalopods (squid and octopods) are likely to be important components of the Ross Sea ecosystem
but their abundances and trophic roles are poorly known (Okutani 1994).
There are a number of long-lived predators in the Ross Sea. Avian biomass is dominated by penguins,
with an estimated >40 000 pairs of emperor penguins breeding between Cape Roget and Cape Crozier,
and at Cape Colbeck (Young 1981; Ainley et al. 1984; Harper et al. 1984; Kooyman 1994). About
38% of the world population of Adélie penguins reside in the Ross Sea, breeding at 35 rookeries with
a total of about 1 million breeding pairs (Young 1981; Ainley et al. 1984). Seals are the most common
marine mammals in the Ross Sea, with more than 200 000 crabeater seals alone. Weddell seals are
probably the second-most common seal in the Ross Sea, with estimates for the larger Ross Sea region
of 32 000 individuals (Stirling 1969; Ainley 1985; Stewart et al. 2003), or about 45% of the entire
Pacific sector population. There is debate over whether or not Weddell seals are migratory. Some
individuals may remain in residence year round in the fast ice at latitudes as high as 78°S in McMurdo
Sound. Others, particularly newly weaned and subadult animals, move north from the continent in
April and spend the winter in the pack ice. Weddell seals are known to feed on Dissostichus mawsoni,
but its significance in their diet is not clear (Kooyman 1981; Ross et al. 1982; Burns et al. 1998;
Fuiman et al. 2002; Pinkerton et al. 2008).
Baleen whales (minke, fin, humpback, sei, blue) tend to congregate in a feeding zone, out of the pack
ice, where krill are abundant. This narrow feeding zone moves north in winter, south in summer, so
that the baleen whales spend only the summer in the Ross Sea. Information on toothed whales (killer
whale, sperm whale, southern bottlenose whale, Arnoux’s beaked whale) in the Ross Sea is rather
limited, coming primarily from surveys of their distribution and numbers carried out by systematic
surveys (e.g., Bassett & Wilson 1983; Ainley 1985). Recent work has shown that three different types
of killer whale may occur in the Ross Sea (Pitman et al. 2001; Pitman & Ensor 2003; Pitman 2003).
Type-C (fish-eating) orca are considered to be by far the most common form in the McMurdo Sound
region, but the migration and feeding characteristics of this type are poorly known.
2
2.1
MATERIAL AND METHODS
Model structure
The trophic model has the balance currency of biomass presented in units of organic carbon density
(gC m-2). Trophic flows are presented in units of gC m-2 y-1. We used 30 trophic groups which are
described below. The model was not spatially resolved. A time step of one year was used. Horizontal
gradients of planktonic groups are not known, but are likely to be small over the course of a year at the
scale of the study area. Seasonal movement patterns of nekton and birds are taken into account in
model parameterisation where known.
Carbon flow through a given trophic group per year is balanced according to Equation 1 where Bi is
the biomass (gC m-2) of trophic group i, Pi/Bi is the production/biomass ratio (y-1), Qj/Bj is the
consumption/biomass ratio (y-1), Dji is the fraction of prey i in the average diet of predator j
(dimensionless), Ei is the “ecotrophic efficiency” (more on this below), Xi is the net export of material
from the group (due to advection, migrations), Ai is the accumulation of biomass over a year, and (n–
1) is the total number of non-detritus trophic groups. Autotrophs are defined as having exactly zero
consumption (Q/B=0), and their production is net of respiration. For heterotrophs (Q/B>0), carbon
flow is assumed to follow Equation 2. Here, Ui is the fraction of food consumed by component i that is
not assimilated but rather transformed into detritus rather than productive potential due to “messy
eating” and faecal excretion; Ri is the loss of organic carbon in the system due to respiration (gC m-2 y1
). The nth group is assumed to be the only detritus group, and this accumulates all “lost” production
(i.e., that which is not available to other trophic groups) from the other (n–1) non-detrital groups,
according to Equation 3.
4
n −1
⎛P⎞
⎛Q⎞
Bi ⎜ ⎟ Ei − ∑ B j ⎜ ⎟ D ji − X i − Ai = 0
⎝ B ⎠i
⎝ B⎠j
j =1
(1)
Qi (1 − U i ) = Pi + Ri
(2)
⎡⎛ P ⎞
n −1
⎤
⎛Q⎞
n −1
⎛Q⎞
∑ B ⎢⎜⎝ B ⎟⎠ (1 − E ) + ⎜⎝ B ⎟⎠ U ⎥ − ∑ B ⎜⎝ B ⎟⎠
i =1
i
⎣
i
i
i
i
⎦
j =1
D jn − X n − An = 0
j
(3)
j
An implicit assumption of this type of model is that all parts of the ecosystem will be in balance in an
“average” year. This assumption is unvalidated. It may be that the functioning of the system as a
whole relies on the unbalanced dynamics of different trophic groups. Many of the environmental
drivers of the Ross Sea ecosystem are highly variable from year to year, and this variability will be
superimposed on any long-term trend. Sea ice area, for example, has substantial (c. ±25%) interannual
variability in the Ross Sea (e.g. Arrigo & van Dijken 2004; Comiso 2003). The nature of
environmental variability in the Ross Sea will have implications for the biota. For example, long-lived
predators feeding on food sources which are known to vary in abundance between years are likely to
be tolerant of years of poor food supply, perhaps by migrating out of the area for longer than normal.
Animals are also likely to accumulate energy reserves when the food supply is good to be able to
“ride-out” periods where the food supply is poor. For these organisms, carbon flows may be balanced
only on decadal (or longer) scales.
2.2
Study area
The Ross Sea study region is defined for this work as follows (Figure 1). The region is bounded to the
north by the 3000 m depth contour, and by 69°S line of latitude; to the south by the permanent ice
shelf; to the east and west by land, and the 160°W and 170°E meridians. The total area of the study
region is c. 637 000 km2. The bathymetry in the region, taken from Davey (2004), shows that 30% of
the study region is shallower than 500 m, 40% of the region has depths 500–1000 m, and 30% is
deeper than 1000 m.
This region was chosen for a number of reasons. The 3000 m bathymetric contour approximates the
location of the Antarctic Slope Front (Jacobs 1991) which, in part at least, hydrodynamically separates
the study region from the rest of the Southern Ocean. Cross-shelf transport is only partly understood
and appears to be extremely small, based on a modelling study (Dinniman et al. 2003), though there is
considerably more off-shelf volume flux via a relatively strong bottom Ekman layer. Langone et al.
(1998) estimate a residence time in the Ross Sea of 50 years. Transport of water across the boundary
of the study region may be higher in the northern part, under the influence of the narrow Antarctic
Slope Current (Jacobs 1991; Dinniman et al. 2003).
The study region covers the main fishing grounds for adult D. mawsoni, comprising Small-Scale
Research Units (SSRU) 88.1H–88.1L, and some of SSRU 88.2A (Figure 1). Based on commercial
catch data, we estimate that biomass of adult toothfish in the study area is estimated to be 85% of the
modelled biomass of the whole stock given by Dunn et al. (2005). There is no fishery take in the
model as we are representing the ecosystem before fishing started.
The study region encompasses the intense localised burst of primary production associated with the
Ross Sea polynya adjacent to the permanent ice shelf (Zwally et al. 1985; Kurtz & Bromwich 1985;
Arrigo & van Dijken 2004). Finally, the study region is similar to that used in other Ross Sea studies
(e.g. Ichii 1990; Ichii et al. 1998; Anderson 2000; Ainley 2002), allowing us to use published
information even when access to the base data are not available. We exclude the ecosystem below the
permanent Ross ice-shelf assuming that it plays a small role in the ecosystem of the larger Ross Sea
region.
5
2.3
Trophic groups
We assume that living organisms in a marine ecosystem can be grouped usefully into relatively few
functional groups with distinct and stable characteristics. Too few groups will not allow the model to
describe the trophic structure with sufficient subtlety, whereas too many groups can lead to spurious
results because of lack of information to provide good parameterisation. The divisions we use include
taxonomy (species or groups of species), function (e.g. water column primary producers), and
sampling methodology (e.g. benthic organisms by size). Ideally, groups would be chosen so that
organisms combined into groups have similar characteristics such as size, energetics (growth rates,
respiration rates, etc), and similar trophic links (similar prey items, predators). In reality, choice of
groups is often constrained by the available information. It is assumed that the choice of groups does
not affect the fundamental results of the modelling study though this has not yet been tested. The
current groups are as follows.
•
•
•
•
•
•
•
•
•
•
•
2.4
Aves (3 groups): Emperor penguins, Adélie penguins, and flying birds (including Antarctic
petrel, snow petrel, skua, albatrosses)
Pinnipeds (4 groups): crabeater seal, Weddell seal, leopard seal, Ross seal.
Cetaceans (5 groups): minke whale, other baleen whales (fin whale, humpback whale, sei
whale, blue whale), type-C killer whale (orca), sperm whale, other toothed whales (southern
bottlenose whale, Arnoux's beaked whale)
Antarctic toothfish (adults);
Middle-level nekton (4 groups): demersal fish, pelagic fish, juvenile fish, cephalopods;
Zooplankton (3 groups): macrozooplankton (includes krill and salps), mesozooplankton,
microzooplankton (including heterotrophic flagellates, ciliates);
Phytoplankton in water column;
Bacteria, including water column bacteria, sea ice bacteria, benthic bacteria in one group;
Sea ice biota (3 groups): epontic algae, ice metazoa, ice protozoa;
Benthic fauna (3 groups): megabenthos, macrobenthos, meiobenthos;
Detritus, including ice detritus, water column detritus, benthic detritus in one group.
Ecotrophic efficiency
It is known that a substantial part of organic material (especially at lower trophic levels) is not directly
consumed but enters the detrital pool where it is decomposed by bacterial action. This material is
typically accounted for in ecotrophic model using a parameter for ecotrophic efficiency. Ecotrophic
efficiency (E) is defined as the fraction of production that is consumed by other organisms, exported,
fished or accumulated. The remainder of production in such trophic models (the fraction 1-E of
production) is assumed to be remineralized by bacterial action. Whereas small organisms that die from
reasons other than direct predation (e.g., disease, parasites, injury) may be decomposed by bacterial
action, we suggest that larger organisms that die in the sea are more likely to be consumed by
scavenging fauna than decomposed by bacterial action. Remains of these dead organisms should not
therefore be included in the detrital pool, and consequently ecotrophic efficiency should be set to
unity. In the model presented here, we set E=1 for all consumer groups to represent a view of the
ecosystem where bacterial decomposition plays the smallest feasible role. In this preliminary version
of the model we have not separated animals killed by direct predation from those that die from other
causes – there is no “carcass” group. Instead, consumers of a species in the model include its direct
predators and those which are likely to consume its carcasses or remains. For apex predators that have
few direct predators, we assume that they are likely to die in the water so that their remains are likely
to be consumed by megabenthic scavengers. There will still be a substantial flow of material to
detritus in the model because of “unassimilated consumption” from each consumer. Unassimilated
consumption includes faecal material and the results of “messy eating” at lower trophic levels.
6
It is known that a substantial part of primary organic material (i.e. phytoplankton and epontic algae) is
not directly consumed but enters the detrital pool where it is decomposed by bacterial action. Some of
the detritus will be in the form of particulate material in the water column (for example, algae released
as sea ice melts), some as dissolved organic matter (e.g. phytoplankton exude transparent
exopolymers), and some will be deposited to the sea bed in intense sedimentation events (e.g. rapid
sinking of phaeocystis “mats”). Detritus has high spatial and temporal variability so that the proportion
of primary organic matter entering the detrital pool rather than being consumed directly (i.e.
ecotrophic efficiency) is inexactly known. Ecotrophic efficiency for primary producers is hence
estimated after stages 1 and 2 of the balancing process (described below).
2.5
Parameter estimation
There is a huge amount of information on the physical environment of the Ross Sea, and its flora and
fauna, including physiology, life histories, energetics, and ecology. Detailed information on the
estimation of the biomass, energetic parameters, and diets for each trophic group is given in Pinkerton
et al. (2006) which lists over 700 references. Since this report was completed, several sections have
been revised which we summarise below. Detailed information on the estimation of parameters for all
groups in the model will be made available on-line, through the NIWA website
(http://www.niwa.co.nz/rc/antarctica). We think the approach of making the detailed information
available on-line addresses the issue that it is not possible to present or summarise the required
quantity of information in a published paper.
Major changes to model parameters between Pinkerton et al. (2006) and the trophic model presented
to CCAMLR in Pinkerton et al. (2007) include: (1) separating ice microfauna into two groups (ice
metazoa, ice protozoa); (2) performing a detailed literature survey on epontic algae, ice meiofauna and
ice bacteria; (3) revising abundances and diets of some top predators; (4) improving the information
on ice type and extent in the Ross Sea; (5) changing the study area to exclude areas in SSRU 88.1F
which is not in the Ross Sea proper; (6) revising the estimated biomass of demersal fish based on
recent skate and ray tagging data (Dunn et al. 2007). Major changes to model parameters between
Pinkerton et al. (2007) and the present study include: (7) separation of apex predators (from 4 to 12
groups); (8) combining cryopelagic fish and pelagic fish into a single compartment; (9) revising
biomass and energetic parameters for demersal fish; (10) separating heterotrophic flagellates (2–20
μm) and heterotrophic microzooplankton (20–200 μm); (11) including SeaWiFS ocean colour data on
the near surface chlorophyll-a concentration between 2004 and 2007; (12) revising benthic groups of
megabenthos, macrobenthos, meiobenthos.
Work on estimating appropriate model parameters from the literature will continue until July 2009
under funding provided by the Foundation for Research, Science and Technology (New Zealand
government). It is noted that new results from research on various parts of the Ross Sea ecosystem
become available constantly and it is highly unlikely that any trophic model could be considered
“finished”. For example, new information from the IPY-CAML voyage to the Ross Sea, available in
1–2 years time, is likely to provide strong reasons to revise this model. Nevertheless, we feel that the
parameters obtained here represent a detailed summary of the available information.
2.6
Diet fractions
Together with biomass, diet fractions (the proportion of various prey items in the diet of a consumer)
are the key determinants of ecosystem structure in the final trophic model. Unfortunately, information
on diet fractions in an ecosystem is generally poor for a number of reasons: (1) there are often no local
diet measurements for many groups; (2) measurements of diet are often potentially biased (for
example, diet measurements are often only taken in a particular area, for particular sizes of consumers,
or at particular times of year); (3) measurements are often imprecise due to small sample size,
uncertain digestion rates, or due to difficult taxonomic identification of well digested prey items; (4)
measurements only semi-quantitative, for example, where presence/absence or percent occurrence of
7
prey in stomachs of predators are measured. Taking diet fractions from “similar” ecosystems is
unreliable given that fractions of prey in the diet of predators are likely to be affected by the relative
abundances of various prey items in the ecosystem. A starting value for diet fractions can be taken
from the literature, similar studies, and local information but we argue here that it is important that the
process of balancing an ecosystem model allows for these initial estimates of diet fractions to vary.
The facility to allow this to occur is not part of the standard suite of Ecopath/EcoSim/Ecoranger
software, and instead we describe a two stage balancing methodology that facilitates this process.
2.7
Uncertainty
First, we estimated an uncertainty for each parameter in the model. The uncertainty factors are
dimensionless coefficients and are labeled KB (biomass B), KP (production, P/B), KQ consumption
(Q/B), KD (diet fractions, D) and KX (export X). Values of K are higher if the parameter is poorly
known. Having a separate uncertainty coefficient for each parameter in the model allows for that fact
that there is a huge range of variation between parameter types and between organisms. For example,
we have a much better estimate of the biomass of Antarctic toothfish in the Ross Sea than of
cephalopods. We note that there remains some degree of subjectivity in assessing levels of uncertainty
for parameters. Four sets of uncertainty parameters were estimated a priori (KB, KP, KQ, KX) whereas
the diet uncertainty parameters (KD) were estimated after the first stage of balancing as explained
below. Local (Ross Sea) information is lacking for many parameters, including values of B, P/B and
Q/B for many groups and we had to use information from other parts of the Southern Ocean. We
assumed that energetic parameters for a given organism are likely to be less variable between regions
than biomass, so KP and KQ are generally lower than KB. Uncertainty parameters for the model
balancing are given in Table 1.
2.8
Balancing methodology: stage 1
The limits on B, P/B, Q/B, and X parameters were determined based on the uncertainty coefficients as
follows. The upper acceptable limit was calculated as the initial estimate multiplied by a factor, α. The
lower acceptable limit was calculated as the initial estimate divided by α. The factor α is derived from
K according to α=1+2K. Hence, a value of K=0.5 implies that we think the actual parameter may lie
between half and twice our initial parameter estimate. A value of K=0.1 implies that the actual
parameter may be between 0.83 and 1.20 of the initial estimate.
The limits on diet fractions were determined by considering whether we believed an organism was a
trace (0–0.01), minor (0.01–0.1), moderate (0.1–0.5), major (0.5–1), or sole (1) prey item for a given
predator. The values in brackets give the estimated proportion in the diet. For this part of the balancing
procedure we assume that trace prey items may constitute 0–0.2 of the diet, minor prey items may
actually make up 0–0.7 of the diet, moderate prey items may be 0.01–1 of the diet, major prey items
may be 0.2–1 of the diet, and sole prey items always make up the whole diet. These ranges are very
wide by design.
The balance equations (Equation 1 for producers and consumers, Equation 3 for detritus) provide a
number of equality constraints to the system. Other equality constraints are provided by the fact that
diet fractions of each predator sum to unity. The number of variable parameters is greater than the
number of constraints so we have an under-constrained system and may expect a number of solutions.
Some or none of these may be within the feasible parameter space defined by our upper and lower
bounds on variable parameters. The problem at this stage is non-linear and we adopt a two stage
strategy to test whether there are any feasible solutions, and if so, what we are able say about the
feasible ranges of the parameters.
The first step in the balancing methodology is to exclude impossible ranges of diet fractions, using two
tests. First, a diet fraction is impossible if it pushes another diet fraction outside its feasible range. For
example, if a predator can consume two prey groups, and the fraction of one prey is known to be less
8
than 0.1, the fraction of the other prey must be greater than 0.9. Second, we calculate the upper limit
on the amount a given prey item a predator can consume using the highest possible production rate of
the prey and the lowest total consumption of the prey by other predators. The highest diet fraction is
then given by the highest available prey biomass divided by the lowest possible consumption rate of
the predator. A lower limit for the diet fraction is obtained in a similar way.
The feasible range of each diet fraction is adjusted in turn using these two tests and the process
repeated until there are no further changes. Note that the remaining ranges are not sure to be feasible,
but the parts excluded are definitely not feasible. If the entire range of a diet is excluded this implies
that there is no feasible solution to the system. In this case, the initial parameter estimates are
inconsistent with the model structure, and the offending parameter(s) need to be reconsidered. If the
diet range was adjusted, we took our best-estimate as the mid-point of the new diet range adjusted so
that total diets fractions sum to unity. Otherwise, we used our original estimate of diet fraction. The
diet uncertainty parameters KD were set to the fourth root of the difference between the maximum and
minimum acceptable diet fractions.
2.9
Balancing methodology: stage 2
Having obtained an estimate of each energetic parameter and diet fraction that are not inconsistent
within the bounds of estimated uncertainty, we move to stage 2 of the balancing method. Stage 2 uses
Singular Value Decomposition (SVD: Press et al. 1992) to search for the closest solution where all the
equality constraints are fulfilled - the “balance point”. The SVM method simultaneously adjusts
biomass (B), production ratio (P/B), consumption ratio (Q/B), export (X), and all diet fractions (D).
The challenge here is to ensure even adjustment across all groups given that the magnitude of carbon
flows across the ecosystem spanned over 6 orders of magnitude. The system is first linearised and then
the SVD algorithm is applied to find the smallest adjustment vector i.e. the solution which minimises
the cost function, Δ (Equation 4).
2
2
⎡ ⎛P⎞ ⎤
⎡ ⎛Q⎞ ⎤
Δ = ∑ (δBi ) + ∑ ⎢δ ⎜ ⎟ ⎥ + ∑ ⎢δ ⎜ ⎟ ⎥ + ∑ (δDij ) 2 + ∑ (δX i ) 2
all i
all i ⎣ ⎝ B ⎠ i ⎦
all i ⎣ ⎝ B ⎠ i ⎦
all i , j
all i
2
2
(4)
The changes in parameters (δBi, δ(P/B)i, etc) are assumed to be small. These changes are defined by
Equations 5–9. In these equations, using biomass as an example, B’ is the value of biomass that causes
the model to balance, and B is the starting value.
Biomass
B ′ = B ⋅ (1 + K iB ⋅ δB )
i
i
i
(5)
Production
⎛P⎞ ⎤
⎛P⎞ ' ⎛P⎞ ⎡
P
⎜ ⎟ = ⎜ ⎟ ⋅ ⎢1 + K i ⋅ δ ⎜ ⎟ ⎥
⎝ B ⎠i ⎦
⎝ B ⎠i ⎝ B ⎠i ⎣
(6)
Consumption
⎛Q⎞′ ⎛Q⎞ ⎡
⎛Q⎞ ⎤
Q
⎜ ⎟ = ⎜ ⎟ ⋅ ⎢1 + K i ⋅ δ ⎜ ⎟ ⎥
⎝ B ⎠i ⎝ B ⎠i ⎣
⎝ B ⎠i ⎦
(7)
Diet fractions
Dij ′ = Dij + K ijD ⋅ δDij
(8)
Export
⎡ ⎛P⎞ ⎤
′
X i = X i + K iX ⋅ ⎢ Bi ⎜ ⎟ ⎥ ⋅ δX i
⎣ ⎝ B ⎠i ⎦
(9)
9
Note that the changes to the model parameters were applied relative to their starting values for B, P/B
and Q/B to account for the large range in magnitude of these values. The coefficients were applied to
actual changes in diet fractions, because these diet fractions are of similar magnitudes (between 0 and
1). KX is applied to changes in export as a fraction of the annual production of the group.
After adjustment in this way by SVD, the set of equality constraints will not be satisfied exactly
because the minimisation works on a linearised version of the constraints assuming small changes. We
hence iterate until the equality constraints are satisfied within a required error (3 iterations).
Finally, model parameters for three groups were further adjusted after the application of the SVD
method. First, because the biomass and energetic parameters for Antarctic bacteria are poorly known,
we nominally fix the consumption value and adjust the bacterial production and biomass parameters
for balance. Second, for the two primary producer groups (phytoplankton and epontic algae), we
return the biomass and productivity parameters to their original values and adjust their ecotrophic
efficiency parameters for model balance.
2.10 Trophic levels
We calculated trophic levels (Lindeman 1942; Odum & Heald 1975; Christensen & Pauly 1992) of
groups in the balanced model based on two rules: (1) primary producers, detritus and bacteria are
defined as having a trophic level of 1; (2) consumers trophic level is the sum of the trophic levels of
their prey items, weighted by diet fraction, plus one. Note that bacteria are defined as being at the
same trophic level as primary producers. It remains ambiguous to what extent detritivores consume
detritus itself rather than bacteria feeding on the detritus. Here, we assume that no consumers other
than bacteria consume detritus and that detritivores are solely bacteria-eaters.
3
3.1
RESULTS
Model balancing
Only 12 of our 134 initial estimates of diet fractions were found to lie outside our estimated feasible
ranges during stage 1 of the balancing procedure. We estimated that emperor penguins make up 7% of
the diet of leopard seals in the Ross Sea, but this has to be less than 3%. The other 11 changes
concerned the consumption of carcasses of apex predators (birds, cetaceans, seals) by benthic
scavenging organisms. Our initial estimates of the proportion of the diet of the scavengers made up of
the carcasses of apex predators were too high. We estimated these carcasses may constitute 1% of the
diet of benthic scavengers, but the maximum proportion is likely to be nearer 0.9%. The range of KD
values estimated by the method given above was 0.09–0.99.
Stage 2 of the balancing procedure applied Singular Value Decomposition to the linearised system,
with scaling (K) variables to account for different levels of uncertainty in the parameters. The model
had 149 variables and 55 constraints, implying a highly under-constrained system as expected. Three
iterations of SVD gave a steady solution with zero accumulations (residuals). The balanced model is
shown in Tables 2 and 3.
The balancing procedure changed the biomass and energetic parameters extensively. The biomasses of
seven groups were changed by more than 5% relative to the original estimate of the parameter. In
descending order of magnitude, the biomass changes were: bacteria (-74%), cephalopods (-45%),
microzooplankton (-22%), heterotrophic flagellates (+19%), macrozooplankton (+13%), meiobenthos
(-8%), mesozooplankton (+8%). The balancing process adjusted three values of P/B by more than 5%,
generally increasing productivities to find a balance point. The largest changes were: bacteria (+77%),
demersal fish (+15%), toothed whales (+9%). The balancing process did not adjust any consumption
values by more than 1%. Ecotrophic efficiencies of the two primary producers were lower than
anticipated: 0.526 (phytoplankton) and 0.691 (ice algae).
10
Twenty-nine diet fractions were changed by more than 0.05 in stage 2 of the balancing procedure. In
the balanced model, leopard seals consumed more krill/macrozooplankton (+0.06), pelagic fish
(+0.05), juvenile fish (+0.04), and cephalopods (+0.04), and less Adélie penguins (-0.10), emperor
penguins (-0.06) and crabeater seals (-0.05) than originally estimated.
The balancing suggested that pelagic fish consumed more cephalopods (+0.07) and mesozooplankton
(+0.04) but less macrozooplankton (-0.14) than originally estimated. Juvenile fish consumed more
mesozooplankton (+0.12) and less krill/macrozooplankton (-0.12) than originally predicted. The diet
of cephalopods was also changed substantially from our initial estimates, with more consumption of
other cephalopods (+0.08), macrobenthos (+0.08), mesozooplankton (+0.07), megabenthos (+0.04),
juvenile fish (+0.04) and less consumption of pelagic fish (-0.24) and krill/macrozooplankton (-0.07).
The diet of the krill/macrozooplankton component changed substantially during balancing, with more
consumption of ice algae (+0.28) and less consumption of other krill/macrozooplankton (-0.09),
phytoplankton (-0.08), hetrotrophic flagellates (-0.06) and mesozooplankton (-0.05). In contrast,
consumption of phytoplankton by heterotrophic flagellates and microzooplankton was increased in the
balanced model (by +0.12 and +0.11 respectively) compared to the initial parameter estimates.
Mesozooplankton consumed more heterotrophic microzooplankton (+0.19) and less hetrotrophic
flagellates (-0.14) in the balanced model than anticipated. The proportion of heterotrophic flagellates
in the diet of two other consumers also decreased during stage 2 balancing: flagellates themselves (0.07), and heterotrophic microzooplankton (-0.06). Meiobenthos consumed more meiobenthos than
originally estimated (+0.15) and less detritus (-0.15). Finally, the model suggested that bacteria are
0.06 less important to ice protozoa than predicted, the balance being made up by increased
consumption of other ice protozoa (+0.08).
3.2
Trophic levels
Trophic levels (TL) were calculated for the final model (Table 2) and allow a crude intercomparison
between trophic models of different areas by various studies. It is suggested that trophic levels of
particular organisms should be broadly similar between different ecosystems and this is generally
borne out by the current results. Our flying birds group at 4.4 compares well with 4.5 (Jarre-Teichman
et al. 1998) but less well with 3.8 (Arreguin-Sanchez et al. 2002). Pelagic fish at TL=4.1 is higher than
values for similar fish: 3.3 (Jarre-Teichman et al. 1998); 2.7–3.5 (Wolff 1994); and 3.2–3.9 (Mendoza
1993). Megabenthos and macrobenthos at TL=2.2–2.4 compares with values for crabs and predatory
invertebrates: 2.4 (Arreguin-Sanchez et al. 2002); 3.3–3.4 (Wolff 1994). Finally, heterotrophic
microplankton and mesozooplankton have trophic levels of 2.0 and 3.2 which bracket values for
“zooplankton” of 2.2–2.4 (Jarre-Teichman et al. 1997, 1998), 2.0 (Mendoza 1993), and 2.2 (ArreguinSanchez et al. 2002).
Antarctic toothfish in the model presented here have the highest trophic level of all groups of 5.2,
which is above the trophic level of other apex predators (in descending order); orca (5.1), Weddell
seals (5.1), sperm whales (5.0), Ross seals (5.0), toothed whales (4.9), emperor penguins (4.8). flying
birds (4.4), leopard seals (4.4), Adélie penguins (4.3), minke whales (4.1), baleen whales (3.7) and
crabeater seals (3.5). Antarctic toothfish are higher trophic level than orca because their diet is largely
(78%) demersal fish whereas orca in the model feed predominantly on pelagic fish (72%) and squid
(23%). Demersal fish in the model have a higher trophic level (4.3) than pelagic fish and cephalopods
(4.1 and 4.0 respectively).
Information on the stable isotopes of nitrogen in Antarctic seals (Zhao et al. 2004) suggests that
Weddell seals occupy the highest trophic level of pinnipeds, with leopard seals <0.1 TL lower
(changes per TL from Post 2002), Ross Seals 0.6 TL lower, and crabeater seals 1.2 TL lower than
Weddell seals. The balanced model hence may have leopard seals too low by 0.7 TL, Ross seals too
low by 0.5 TL, and crabeater seals too high by 0.4 TL.
11
4
DISCUSSION
The model presented has not been validated, and its results should be treated with caution at this stage
as there remain considerable uncertainties with regard to many model parameters.
Total primary production in the balanced model is estimated to be 88.1 gC m-2 y-1, the vast majority of
which is from phytoplankton in the water column (97%). Epontic algae produces about 3% of primary
production in the model. Only about half of all primary production in the model is directly consumed
(53%). The remainder enters the detrital pool and is decomposed by bacterial action in the water
column, benthos, or in sea-ice. Secondary production in the model is dominated numerically by the
lower trophic level groups of consumers in the water column. Bacteria are responsible for the majority
(49%) of total secondary production in the system. Hetrotrophic flagellates, microzooplankton and
mesozooplankton account for 24, 14 and 10% (respectively) of secondary production. Other
significant secondary producers in terms of absolute quantities of carbon transfer are
krill/macrozooplankton (0.8%), juvenile fish (0.7%), meiobenthos (0.5%), squid (0.2%) and pelagic
fish (0.2%). Other groups contribute less than 0.15% to secondary production.
As an illustrative example of how budget modelling can integrate information on various species, we
consider the first-order trophic links of toothfish in the model to assess the potential impact of the
toothfish fishery on the prey items. The three prey items of toothfish in the model are demersal fish
(78%), pelagic fish (6%), and squid (16%). These diet proportions are largely consistent with
measurements of stomach contents of toothfish from the Ross Sea (Fenaughty et al. 2003; Stevens
2004). In the model, the proportion of the annual production of each of these prey groups consumed
by toothfish is estimated to be 88% (demersal fish), 0.3% (pelagic fish), and 0.5% (squid). It is
emphasized that we have no reliable information on the abundances of these demersal fish in the Ross
Sea so these figures are highly uncertain. If the fishery significantly reduced the biomass of toothfish,
the model suggests that the largest impact amongst prey species would be on demersal fish. Key
demersal fish species in toothfish diet are Whitson’s grenadier (Macrourus whitsoni), icefish
(Chionobathyscus dewitti), blue antimora/deep-sea cod (Antimora rostrata), and moray (eel) cod
(Muraenolepididae microps). These species should hence be a high priority for further work.
Now we consider the first order trophic links between toothfish and its predators. The model
summarises information on a particular space and time scale: the Ross Sea shelf over a one year
period. On these scales, the balanced model suggests that Antarctic toothfish is likely to be a minor
component of the diets of apex predators. In the balanced model, toothfish make up 2.2% of the diet of
Weddell seals, 1.4% of the diet of orca, and 1.4% of the diet of sperm whales. We note that this result
may be invalidated by any of the following. (1) There may be fewer large predators present in the
study area, and/or their consumption is lower than we estimate. For example, the number of Weddell
seals in the model in summer (32 000: Ainley 1985) seems high given the much smaller number of
seals known to occur at breeding colonies in the south western Ross Sea (<5000: Testa & Siniff 1987;
Ross et al. 1982). (2) There are considerably more toothfish present than we estimate, and/or they are
more productive. The biomass of toothfish in the Ross Sea is one of the more reliable pieces of
information in the model so this is unlikely. (3) There may be important localised effects which are not
considered by the model. Consumption of toothfish in particular locations, at particular times of the
year, or by particular parts of the population may be especially important to predators, even though the
total consumption of toothfish by all individuals of a species is relatively low. For example, there is
some evidence of important trophic overlap between toothfish and Weddell seals in McMurdo Sound
between October and January (Pinkerton et al. 2008). These localised indirect effects are not
considered by the current version of the model.
Other possible indirect impacts of the fishery on the Ross Sea ecosystem include second order effects
(Brose et al. 2005), such as the “keystone” predator effect. Keystone predators maintain biodiversity
by preferentially consuming competitively dominant prey species. If keystone predators are removed
or their biomass reduced, abundance of some prey species can increase to levels where they start to
exclude subordinate competitors. Empirical studies show that the manifestation of the keystone
12
predator effect (and other second-order effects) is difficult to predict, though recent work suggests that
it may be possible to identify keystone species from mass balance ecosystem models (Libralato et al.
2006). Other potential indirect effects include trophic cascades, where links in an ecosystem are
changed by the removal of a species by fishing (e.g. McCann et al. 1998; Pinnegar et al. 2000; Frank
et al. 2005). The trophic modelling work will be used to investigate the potential for these second
order effects in the Ross Sea.
5
CONCLUSIONS
Knowledge of how species are interrelated through feeding is a vital step in identifying potential
indirect effects of the fishery for Antarctic toothfish on the ecosystem of the Ross Sea. Historically, a
huge amount of research has been conducted on the fauna of the Ross Sea. Within the project being
reported on here, significant progress has been made in sifting through this information to obtain an
initial set of parameters required for a Ross Sea trophic model, and adjusting these parameters taking
into account the relative uncertainties to obtain a balanced trophic model. Whereas we have obtained a
single balance point, in reality, there will be multiple feasible ecosystem states. We know that there is
large interannual variability in the abundance and distribution of biota the Ross Sea and it follows that
we should consider a corresponding range of balanced model states. In the future we aim to identify
multiple balance points for the Ross Sea ecosystem under the trophic modelling approach presented
here. Further work is needed to validate this model, develop a dynamic component, and consider
seasonal, spatial and interannual variations in ecosystem state. The aim of the modelling is to develop
a plausible, minimum-realistic model with which to investigate and manage the effects of the
Antarctic toothfish fishery on the Ross Sea ecosystem.
In addition to continuing to develop the trophic model, field research in the Ross Sea is required as
there are substantial gaps in the existing knowledge. The recent New Zealand IPY-CAML research
voyage to the Ross Sea January–March 2008 will provide valuable information to this end (Hanchet et
al. 2008). There is a need to establish appropriate monitoring in the Ross Sea to ascertain how species
are being affected by the removal of Antarctic toothfish. Such monitoring should begin as soon as
possible to establish a near unfished ecosystem baseline.
6
ACKNOWLEDGEMENTS
Funding for this work was provided by the New Zealand Foundation for Research, Science and
Technology (C01X0505) and New Zealand Ministry of Fisheries (ANT200405, ANT200603).
13
7
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8
TABLES
Table 1. Variation parameters for the Ross Sea trophic model as explained in the text.
B=Biomass, P=Production, Q=Consumption, X=Export, N/A=Not applicable.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Long name
Emperor penguins
Adelie penguins
Flying birds
Crabeater seals
Weddell seals
Leopard seals
Ross seals
Minke whale
Other baleen whales
Orca
Sperm whale
Other toothed whales
Antarctic toothfish
Demersal fish
Pelagic fish
Juvenile fish
Cephalopods
Krill/macrozooplankton
Mesozooplankton
Het. microplankton
Het. flagellates
Phytoplankton
Ice metazoa
Ice protozoa
Ice algae
Megabenthos
Macrobenthos
Meiobenthos
Bacteria
Detritus
Short name
Emperor
Adelie
Flying
Crabeater
Weddell
Leopard
Ross
Minke
Baleen
Orca
Sperm
Toothed
Toothfish
Demersal
Pelagic
Juvenile
Cephalopods
Macrozoo
Mesozoo
Microzoo
Flagellates
Phytoplankton
Ice_meta
Ice_proto
Ice_algae
Megabenthos
Macrobenthos
Meiobenthos
Bacteria
Detritus
18
KB
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
3
1
KP
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.5
0.2
0.2
0.5
0.2
0.2
0.2
1
0.1
KQ
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
N/A
0.2
0.2
N/A
0.2
0.2
0.2
1
0.1
KX
0.2
0.2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 2. Trophic group parameters for the balanced Ross Sea model. B=Biomass, P=Production, Q=Consumption, E=Ecotrophic efficiency, X=Export,
U=Unassimilated consumption, N/A=Not applicable, Det=Flow of organic matter to detritus (gC m-2 y-1)
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
GROUP
Emperor
Adelie
Flying
Crabeater
Weddell
Leopard
Ross
Minke
Baleen
Orca
Sperm
Toothed
Toothfish
Demersal
Pelagic
Juvenile
Cephalopods
Macrozoo
Mesozoo
Microzoo
Flagellates
Phytoplankton
Ice_meta
Ice_proto
Ice_algae
Megabenthos
Macrobenthos
Meiobenthos
Bacteria
Detritus
B (gC m-2)
4.91E-04
1.25E-03
1.35E-04
1.65E-03
1.69E-04
1.45E-04
2.86E-05
9.05E-04
4.68E-04
4.74E-04
3.63E-04
2.46E-05
7.39E-03
1.65E-02
9.15E-02
9.41E-02
2.75E-02
4.21E-01
1.01E+00
3.13E-01
2.96E-01
1.52E+00
3.25E-03
2.65E-03
2.85E-01
2.59E-01
2.26E-01
4.05E-02
4.46E-01
N/A
P/B (y-1)
0.103
0.361
0.545
0.142
0.154
0.108
0.159
0.0393
0.0270
0.0319
0.0288
0.0713
0.151
0.302
1.37
5.64
6.70
1.43
7.98
35.7
63.0
55.9
20.0
59.9
9.93
0.170
0.355
10.0
85.2
N/A
Q/B (y-1)
44.2
81.1
115.3
38.9
40.7
33.6
41.3
14.9
10.8
16.6
11.7
19.8
0.763
1.17
13.5
32.0
21.9
12.7
27.1
104
180
N/A
73.7
190
N/A
0.857
1.43
33.4
161
N/A
E
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.526
1
1
0.691
1
1
1
1
1
X/P
0.144
0.149
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
U
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.25
0.16
0.3
N/A
0.2
0.2
N/A
0.2
0.4
0.3
0.2
N/A
P/Q
0.00233
0.00445
0.00473
0.00364
0.00379
0.00322
0.00384
0.00264
0.00249
0.00192
0.00247
0.00361
0.198
0.258
0.101
0.176
0.306
0.113
0.294
0.345
0.349
N/A
0.272
0.315
N/A
0.199
0.248
0.299
0.530
N/A
19
R/B (y-1)
30.8
56.4
80.1
30.9
32.4
26.8
32.9
11.9
8.62
13.2
9.31
15.8
0.459
0.636
9.45
20.0
10.8
6.19
12.4
51.3
63.3
N/A
38.9
92.2
N/A
0.515
0.503
13.4
43.5
N/A
Det/P (y-1)
129
67.4
63.5
54.9
52.8
62.1
52.1
75.7
80.2
104
81.1
55.5
1.01
0.776
1.98
1.13
0.654
3.55
0.849
0.464
0.859
0.474
0.737
0.635
0.309
1.01
1.61
1.01
0.000
73.3
Trophic level
4.81
4.31
4.42
3.53
5.12
4.38
4.97
4.14
3.68
5.12
5.04
4.85
5.25
4.31
4.13
4.31
4.00
2.49
3.15
2.01
2.15
1
2.39
2.21
1
2.24
2.41
2.24
1
N/A
Table 3. Diet matrix for balanced trophic model of Ross Sea. Predators are shown on the x-axis and prey on the y-axis. Entries of “0.00” imply that the diet fraction
is >0 and <0.005.
#
GROUP
1
2
3
4
5
6
1
Emperor
0.01
2
Adelie
0.08
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
23
24
26
27
28
0.14
0.33
0.20
0.77
0.67
0.80
3
Flying
4
Crabeater
0.05
5
Weddell
0.01
6
Leopard
7
Ross
0.00
8
Minke
0.00
9
Baleen
0.00
0.00
0.00
0.00
10
Orca
0.00
11
Sperm
0.00
12
Toothed
0.00
13
Toothfish
0.02
14
Demersal
0.01
0.07
0.07
15
Pelagic
0.70
0.18
0.28
16
Juvenile
17
18
0.40
0.01
0.01
0.01
0.01
0.02
0.78
0.00
0.06
0.72
0.11
0.11
0.06
0.42
0.06
0.15
0.06
0.02
0.00
0.03
0.01
0.01
Cephalopods
0.07
0.08
0.11
0.08
0.09
0.57
0.03
0.23
0.86
0.75
Macrozoo
0.19
0.49
0.43
0.03
0.46
0.06
0.95
0.60
0.85
0.12
0.16
0.30
0.06
0.06
0.06
0.18
0.08
0.10
0.21
0.21
0.33
Mesozoo
Microzoo
0.06
0.40
21
Flagellates
0.04
0.41
0.01
0.13
22
Phytoplankton
0.39
0.07
0.89
0.22
23
Ice_meta
24
Ice_proto
25
Ice_algae
26
Megabenthos
0.13
0.07
27
Macrobenthos
0.13
0.11
28
Meiobenthos
Bacteria
0.62
0.03
0.86
0.06
20
Detritus
0.05
0.14
19
30
0.04
0.40
0.01
0.74
29
29
0.26
0.17
0.13
0.01
0.02
0.33
0.29
0.18
0.65
0.08
0.05
0.10
20
0.04
0.65
0.03
0.74
1
9
FIGURES
Figure 1. The coloured squares show the mean length (cm) of Antarctic toothfish in the fishery catch
from fishery observer data (after Phillips et al. 2005). The CCAMLR fishing areas (88.1 and 88.2),
and Small-Scale Research Unit areas are shown. The Ross Sea study area (pink) is bounded by the
3000 m depth contour, by 69°S, by the permanent ice shelf, land, and the 170°E and 160°W meridians.
21