ICES Journal of
Marine Science
ICES Journal of Marine Science (2016), 73(6), 1651– 1655. doi:10.1093/icesjms/fsv211
Contribution to the Themed Section: ‘Balanced harvest and the ecosystem approach to
fisheries’
Comment
Assumptions behind size-based ecosystem models are realistic
Ken H. Andersen 1 *, Julia L. Blanchard 2, Elizabeth A. Fulton 3, Henrik Gislason 1, Nis Sand Jacobsen 1,
and Tobias van Kooten 4
1
Centre for Ocean Life, National Institute of Aquatic Science, Technical University of Denmark, Jægersborg Allé 1, DK-2920 Charlottenlund, Denmark
Institute of Marine and Antarctic Studies, University of Tasmania, 20 Castray Esplanade, Battery Point, TAS 7004, Australia
3
CSIRO Oceans & Atmosphere, GPO Box 1538, Hobart, TAS 7001, Australia
4
Institute for Marine Research and Ecosystem Studies (IMARES), PO Box 68, 1970 AB Ijmuiden, The Netherlands
2
*Corresponding author: tel: +45 35 88 33 99; e-mail: [email protected]
Andersen, K. H., Blanchard, J. L., Fulton, E. A., Gislason, H., Jacobsen, N. S., and van Kooten, T. Assumptions behind size-based
ecosystem models are realistic. – ICES Journal of Marine Science, 73: 1651– 1655.
Received 22 September 2015; revised 18 October 2015; accepted 21 October 2015.
A recent publication about balanced harvesting (Froese et al., ICES Journal of Marine Science; 73: 1640–1650) contains several erroneous
statements about size-spectrum models. We refute the statements by showing that the assumptions pertaining to size-spectrum models discussed by Froese et al. are realistic and consistent. We further show that the assumption about density-dependence being described by a stock
recruitment relationship is responsible for determining whether a peak in the cohort biomass of a population occurs late or early in life. Finally,
we argue that there is indeed a constructive role for a wide suite of ecosystem models to evaluate fishing strategies in an ecosystem context.
Keywords: balanced harvesting, cohort biomass, size-spectrum model.
Introduction
The concept of “Balanced Harvesting” (BH) was recently exposed to
a comprehensive critique (Froese et al., 2016). We agree with many
of the overarching conclusions: that BH in its current pure form is technically difficult to implement in industrial fisheries; is unlikely to offset
fisheries induced evolution; is economically unviable for many countries and cultures; and that BH is can be viewed as cultivated forage
fishing (Burgess et al., 2015). We also agree with the premise that exploitation should be guided by “moderate harvesting of resilient
species . . . with the least impact on stocks and ecosystems”.
We are, however, concerned that Froese et al. describe sizespectrum models en bloc as “highly unrealistic” and based on
“unrealistic and even contradictory assumptions”. These are strong
sweeping statements that dismiss a large body of work, built on
.40 years of empirical and theoretical work (much more than can
be cited here): observations of biomass size spectra (Sheldon and
Prakash, 1972; Boudreau and Dickie, 1992) and size-based predator–prey relationship (e.g. Ursin 1973; Barnes et al., 2010, Jennings
et al., 2001) over steady-state models (e.g. Sheldon et al., 1977;
Kerr and Dickie, 2001; Andersen and Beyer, 2006) with application
to fisheries (e.g. Hall et al., 2006; Pope et al., 2006), developed into
dynamic physiologically structured models (de Roos and Persson,
# International
2013) with detailed applications to real systems [e.g. Blanchard
et al., 2014; reviewed in Andersen et al. (2015)].
Although these models differ from the single species models traditionally used in fisheries management, they are, together with other
foodweb models that have been used to explore BH (e.g. Ecopath with
Ecosim and Atlantis), part of a complementary set of tools being
developed to address questions about the wider ecosystem consequences of fisheries management strategies. These are questions
that cannot be fully addressed by single species models. Such tools
should not be sacrificed as collateral damage in a debate about BH.
Setting the facts straight about size-spectrum
models
Froese et al. make several erroneous statements about size-spectrum
models, which we correct and explain in detail below:
(i) Contrary to the claim in Froese et al., Jacobsen et al. (2014) did
not use a model to “support BH”. In Jacobsen et al. (2014),
a size-based community model was used to make an impact assessment of various fishing strategies. The paper neither supports nor opposes BH, but instead examines the concept and
discusses its definition. Such clarification is needed because,
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K. H. Andersen et al.
unlike Froese et al., we do not find it obvious that “ecosystem
models in general . . . cannot, support the proposition that BH
across sizes and trophic levels will somehow result in less disruption of ecosystem structure . . .” without a formal modelbased assessment. The original modelling work by Garcia
et al. (2012) was done mainly with models that were unstructured (the two Atlantis models used contained size/age/stage
structure, but the 34 Ecopath with Ecosim did not), and therefore primarily focused on species as the main type of selectivity.
Two subsequent size-spectrum model studies focused on the
consequences of targeting individual sizes (ignoring species;
Law et al., 2012, 2013). Jacobsen et al. (2014) set out to
clarify some of the confusion surrounding the idea of BH,
which could be interpreted as either targeting a wider range
of species vs. targeting a wider range of individual sizes in proportion to their natural productivity. When balanced fishing
was defined as a fishery, where all species and sizes are fished
in accordance with their productivity, the overall conclusion
was the same as reached by Froese et al.: BH “. . . is effectively
a fishery predominantly targeting small forage fish” and “its
practical implementation and ecological and socio-economic
consequences need to be further studied before it can be
used as a general principle to guide the rational exploitation
of fish communities in the context of ecosystem-based
management”.
(ii) Froese et al. write that Jacobsen et al. (2014) used a model to
“predict higher yield from individual species”. Jacobsen et al.
did not report yield from individual species, but only reported
the yield and size composition of the yield from the entire community. If they had reported yield from individual species, the
study would have confirmed the prediction from “basic population dynamics” (see point iii).
(iii) Froese et al. argue that size-spectrum models are unrealistic
because they do not produce “lumpy” or “dome-shaped”
biomass distributions. However, the models (usually) do
produce “dome-shaped” biomass distributions, e.g. Jacobsen
et al. (2014) or Engelhard et al. (2014). Moreover, Froese
et al.’s statement that size-spectrum models see “a peak in
cohort biomass at the smallest body size” demonstrates a
basic misunderstanding about the relation between a
biomass density distribution and the biomass of a cohort.
The biomass density distribution is essentially what empiricists often call the “normalized biomass size spectrum” sensu
Platt and Denman (1978). It is determined from data by dividing the biomass by the width of the weight class, leading to
a “density” (units of biomass per body weight) (Figure 1a).
The ‘cohort biomass’ is the biomass of a cohort as a function
of size. It is proportional to biomass density multiplied by
somatic growth rate (Figure 1b). Proof of this is provided in
Law et al. (2014), appendix E. Size-spectrum models most
often produce biomass density distributions of single species
that decrease with size, but cohort biomasses that increase
with size up to some point, typically around size at maturation,
and then decline. In some cases, cohort biomass peaks early or
have an early local maximum (e.g. Law et al., 2012, 2013)—we
discuss that later.
(iv) Froese et al. state that the models are unrealistic because they
do not allocate a proportion of biomass to reproduction.
Size-spectrum models do not assume that reproduction is
Figure 1. Output from the trait-based size-spectrum model used in
Jacobsen et al. (2014) in an unfished situation. Thin lines show 10
asymptotic size groups and the thick lines show the total community
spectra. Thin dashed line is the resource spectrum representing
non-fish food. (a) Biomass density distribution and (b) cohort
biomasses scaled with initial cohort biomass.
proportional to body mass (vis-à-vis a fecundity – weight relationship). Instead, they assume that an individual partitions its
available energy between growth and reproduction (Hartvig
et al., 2011; Andersen and Beyer, 2015) in accordance with
physiological theory (Kooijman, 2000). Under typical conditions, this results in reproductive output roughly proportional
to body mass (corresponding to a constant gonado-somatic
index; Figure 2). Furthermore, this assumption leads to a correlation between food availability and reproductive output, in
accordance with observations (Mcbride et al., 2013). These
two properties are the reason why this assumption is used in
many types of ecosystem models, e.g. Atlantis (Fulton et al.,
2011) and APECOSM (Maury, 2010). Had the models
assumed that reproduction was a fixed fraction of body
mass, the individual would decrease in weight to prioritize
and maintain reproductive output under low food conditions,
and the models would be unable to reproduce the observed
correlation between food availability and reproductive
output. The assumptions about how energy is allocated to reproduction are therefore realistic.
(v) Size-spectrum models are claimed to “assume strong replacement of natural mortality . . . by fishing”. Size-spectrum
models do not contain any assumptions about how predation
mortality and fishing mortality interact. Replacement of one
by the other is an emerging result, not an assumption. The
core of the models is mass balancing that connects predator
growth and reproduction to a corresponding predation mortality on prey, and thereby represent the inevitable “thermodynamic losses during trophic transfer” explicitly as losses
due to assimilation and metabolism.
Size-based ecosystem models are realistic
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Besides these general assumptions, each implementation has its
own special assumptions. While the validity of some of these may
be questioned, such as the high senescence mortality and the fixed
resource used by Law et al. (2012), we will show that there is a specific
assumption that is important for two of the issues discussed in
Froese et al. related to models: (i) which mechanism leads to a
peak in cohort biomass before maturation in a single species? and
(ii) what are the ecosystem responses to fishing?
Peak in cohort biomass and maximization of yield from
a single species
Figure 2. Individual reproductive output divided by body weight for all
the asymptotic size groups in Figure 1, shown on an axis relative to size
at maturation (vertical dotted line). This measure is proportional to the
gonado-somatic index. Line width denotes asymptotic size. The specific
reproductive output declines with asymptotic body size, but turns
out to be constant within each asymptotic size group, once all
individuals have matured. Note that larger species have smaller specific
reproductive output, in accordance with observations (Gunderson,
1997; Charnov et al., 2001).
(vi) Froese et al. correctly pointed out that the senescence mortality
was unrealistically high in Law et al. (2012). This was acknowledged in a later work and adjusted (Law et al., 2014), showing
the results were insensitive to this assumption. Other sizebased models have used similar assumptions in an attempt
to prevent the unrealistic build-up of large fish that otherwise
can occur and in some cases prevents coexistence (Hall et al.,
2006). This is again not an issue restricted to size-spectra
models. It has been used in single species (Quinn and Collie,
2005) models and for some groups in some Atlantis implementations (Fulton et al., 2007) and reflects a shortage of
ecological understanding around what constrains the abundance of larger bodied marine animals (Freedman and
Noakes, 2002; Andersen et al., 2008). Consequently, senescence mortality is a convenient model mechanic. Other
models do not use senescence mortality, but a constant background mortality (Jacobsen et al., 2014), so senescence may
not really be needed. More importantly, although there is actually high uncertainty about how senescence mortality
works, it is not the driving force behind the predictions of an
early cohort peak found in some of the models (see later).
In summary, the specific assumptions mentioned by Froese et al. are
realistic and internally consistent. In fact, realism and consistency
are major strengths of the size-spectrum modelling approach, and
are a reason to value its contribution to the scientific discourse.
What else do size-spectrum models assume?
All models are based on assumptions and it is always beneficial to
check their veracity. There are many different types of size-spectrum
models and it is not possible to go through all of them in detail here.
The assumptions common to all of them are that predator and prey
body size largely determine prey encounter of individuals and that
physiology of individuals is largely determined by body size and possibly other life history traits (size at maturation in particular).
The “basic population dynamics” (Beverton and Holt, 1957) predicts that yield is maximized when large individuals are fished.
The same applies to single-species size-spectrum models (Andersen
and Beyer, 2015) and most multispecies size-spectrum models
where cohort biomass increases with size until around maturation
(Figure 1b). An exception is the single-species model of Law et al.
(2012), which produces a peak in cohort biomass at a small size,
and consequently maximizes yield when small fish are targeted, e.g.
by a “balanced” selection pattern. Why do different types of sizespectrum models lead to seemingly different results?
The key difference between the two classes of models mentioned
above is how density-dependence operates. The basic population
model assumes that all density-dependence acts early in life,
before fishing starts and before maturation. This is embodied in
the stock– recruitment relationship. The shape of the stock– recruitment relationship is not important; what matters is that all densitydependent processes act early. Law et al. (2012, 2013) do not employ
a stock –recruitment relationship. Instead, the entire reproductive
output becomes recruitment and density-dependence emerges
from the model’s dynamics. Density-dependent regulation early
in life cannot occur in the models by Law et al., (2012, 2013)
because the resource is constant, so juveniles do not compete for
food. Density-dependence instead emerges late in life through a reliance of large individuals on cannibalism and the ensuing competition for feeding on juveniles. It is this competition-induced
density-dependence between adults that leads to an early peak in
cohort biomass.
We illustrate the importance of density-dependence with the
size-spectrum model used in Jacobsen et al. (2014). In this model,
density-dependence is a combination of the imposed stock –
recruitment relationship and additional food-dependent growth
and cannibalism. This way of modelling density-dependence is
similar to other size-spectrum models (e.g. Hall et al., 2006;
Engelhard et al., 2014; Jacobsen et al., 2014) or ecosystem models
such as Atlantis or OSMOSE (Shin and Cury, 2004). In this case,
the cohort biomass is increasing with size as seen in Figure 1b. We
then select a population in the middle of the spectrum and
remove the stock – recruitment relationship for this population,
such that all produced eggs are converted to recruits (Figure 3).
With this change, the cohort biomass develops a local maximum
at smaller sizes. This result is similar to Law et al. (2012, 2013)
(though the secondary peak is less pronounced) and demonstrates
the importance of imposed early density-dependence for determining how cohort biomass depends on size. It also demonstrates
that Law et al.’s result will emerge even without senescent mortality
and when the resource is dynamic and juveniles can compete
for food. Law et al.’s results are therefore not driven by senescence
mortality or a constant resource (though these may accentuate
the early cohort peak), but by their predictions about late densitydependence.
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Figure 3. Cohort biomasses from simulations with stock–recruitment
relation (solid) and without stock – recruitment relation (dashed) for a
species with asymptotic size 850 g. The simulations are made with the
full size-spectrum model shown in Figure 1. The simulation with stock –
recruitment relation is the same as in Figure 1b. For the dashed line, the
stock – recruitment relationship is removed for just that one species
such that all density-dependence emerges from changes in growth and
cannibalism.
Such explorations should provoke future work to determine
when (at which size/age) and how density-dependent regulation actually occurs in marine fish populations. Does it occur exclusively
early as in “standard population dynamics”, does it occur throughout life, or does it under certain circumstances occur late and lead to
a local maximum in cohort biomass? We do not know, but we find
explorations of the type in Law et al. (2013), an important example
of how theoretical models can shed new light on long-standing, yet
unresolved research questions. The results from such explorations
do, however, need stronger empirical backing before they can
form the basis for general statements about fisheries management
measures. Nevertheless, they are relevant and exciting questions
that reach beyond the issues of BH.
Ecosystem responses to fishing
Froese et al. base many of their arguments on the premise that the
models used to explore BH do not conform to “basic population
dynamics”. However, the goal and interesting aspect of BH, even
just as a concept, is as an ecosystem harvesting strategy maintaining
the trophic and functional structure of the ecosystem being fished.
Models relying on basic single-species population dynamics,
where growth and natural mortality are assumed to be constant,
cannot properly assess this aspect. To evaluate how the trophic
and functional structure of an ecosystem will change in response
to fishing requires the use of multispecies models where species
interactions are explicitly described. A multitude of such models
is available ranging from highly complex ecosystem models such
as Atlantis, foodweb models such as and Ecopath with Ecosim,
over size-spectrum models and Osmose, to models of intermediate
complexity such as Gadget, SMS, and MSM where statistical tools
can be used to estimate the parameters from data within the
model and where uncertainty therefore can be accounted for
(Plagányi, 2007; Collie et al., 2014; Plagányi et al., 2014). While
the complex models can be used to confirm the robustness of the
results from the simpler models, or point to important processes
that need additional consideration, they do so at the cost of added
uncertainty (Fulton et al., 2011). These models are therefore
best-suited for providing strategic advice, while models of intermediate complexity are more appropriate when tactical advice is
K. H. Andersen et al.
needed, because they provide estimates of the uncertainty of their
predictions (Collie et al., 2014; Plagányi et al., 2014). Because BH
is likely to require management interventions of both tactical and
strategic nature, the whole range of species interaction models
should ideally be used to evaluate its implications. However, it
must be emphasized that all fisheries models, whether singlespecies, multispecies, or ecosystem-based, contain assumptions
that can be considered as less solidly supported. Discussing the
implications of these assumptions for the predictions produced by
the models seems the best way forward towards understanding
whether BH or other ecosystem harvesting strategies are likely to
lead to their intended outcomes.
Objective evaluation of strengths and weaknesses of complex ecosystem models and better communication of assumptions would
help to prevent misconceptions in the future. Comparing different
ecosystem models of the same system through the lens of their underlying assumptions (Jacobsen et al., 2015; Woodworth-Jefcoats et al.,
2015) is a necessary step towards deeper understanding of the potential range of ecosystem responses to harvesting. However, we acknowledge that this can be challenging and that misconceptions
about model assumptions and results will arise from the inability
of a reader to access, understand, and evaluate the technical details
of models. The onus is therefore on the modelling community to
better communicate model assumptions, results, and limitations.
Where models differ or contradict intuition, this can be harnessed
as an opportunity to learn more about the system and improve the
models. Empirical tests of assumptions and predictions should be
used not only to assess model skill, but also to continually develop,
re-evaluate, and advance models. Ultimately, conclusions can only
be reached by judgment of model results in light of the limitations
of each model, careful consideration of different model hypotheses,
and better integration with observations of ecosystems.
Conclusions and the way forward
In conclusion, we urge both sides of this debate to use ecosystem
models for what they are: caricatures of the natural system. They
can be used to make qualitative and quantitative hypotheses about
the nature of marine ecosystem, but those statements should
always be interpreted though the lens of the model’s underlying
assumptions. BH is unlikely to be a useful guiding principle for
ecosystem-based fisheries management for many reasons, one of
them being the unclear definition of what BH actually is (Jacobsen
et al., 2014; Burgess et al., 2015). Nevertheless, BH should be acknowledged as an attempt among others (Murawski, 2000; Link, 2005) to
formulate an overarching strategy for ecosystem-based fisheries
management (how to achieve “moderate harvesting of resilient
species . . . with least possible impact on stocks and ecosystems”),
however flawed it might be. The flaws should provoke betterformulated suggestions for ecosystem-based fisheries management
strategies that acknowledge the two-way trophic interactions in the
ecosystem, and objective interpretation of data and model results.
Acknowledgements
We thank Tim Essington, Keith Farnsworth, Simon Jennings, Keith
Sainsbury, and André de Roos for comments on a draft of this
manuscript.
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Handling editor: Howard Browman