MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 491: 1–14, 2013doi: 10.3354/meps10484

Published October 2

INTRODUCTION

How closely linked to net primary production is theproduction of upper-trophic-level consumers? Classi-cal food chain theory suggests that a constant frac-tion of production (approximately 10%) is transferredfrom each trophic level to the next (Pauly & Chris-tensen 1995, May & McLean 2007), and a variety ofregional studies have shown positive linear trendsbetween common indicators of primary production(such as chlorophyll a) and fisheries yields (Ware etal. 2005, Frank et al. 2006, Chassot et al. 2007). How-ever, in their analysis of bottom-up predictor vari-ables versus fisheries yields, Friedland et al. (2012)

© Inter-Research 2013 · www.int-res.com*Email: kkearney@rsmas.miami.edu

FEATURE ARTICLE

Amplification and attenuation of increased primaryproduction in a marine food web

Kelly A. Kearney1,4,*, Charles Stock2, Jorge L. Sarmiento3

1Department of Geosciences, Princeton University, Princeton, New Jersey 08544, USA 2Geophysical Fluid Dynamics Laboratory (GFDL), National Oceanic and Atmospheric Administration (NOAA),

201 Forrestal Road, Princeton, New Jersey 08540, USA3Program in Atmospheric and Ocean Sciences, Princeton University, Princeton, New Jersey 08544, USA

4Present address: Marine Biology and Fisheries, University of Miami Rosenstiel School of Marine and Atmospheric Sciences, 4600 Rickenbacker Causeway, Miami, Florida 33149, USA

ABSTRACT: We used an end-to-end ecosystemmodel that incorporates physics, biogeochemistry,and predator−prey dynamics for the Eastern Subarc-tic Pacific ecosystem to investigate the factors con-trolling propagation of changes in primary produc-tion to higher trophic levels. We found that lowertrophic levels respond to increased primary produc-tion in unexpected ways due to complex predatoryinteractions, with small phytoplankton increasingmore than large phytoplankton due to relief frompredation by microzooplankton, which are kept incheck by the more abundant mesozooplankton. Wealso found that the propagation of production toupper trophic levels depends critically on how non-predatory mortality is structured in the model, withmuch greater propagation occurring with linear mor-tality and much less with quadratic mortality, both ofwhich functional forms are in common use in eco -system models. We used an ensemble simulationapproach to examine how uncertainties in modelparameters affect these results. When consideringthe full range of potential responses to enhanced pro-ductivity, the effect of uncertainties related to thefunctional form of non-predatory mortality was oftenmasked by uncertainties in the food-web parameter-ization. The predicted responses of several commer-cially important species, however, were significantlyaltered by non-predatory mortality assumptions.

KEY WORDS: End-to-end model · Trophic efficiency· Primary production · Food web · Subarctic PacificOcean · Ecosystem model

Resale or republication not permitted without written consent of the publisher

Realistic, complex marine food webs (left) complicate thesimple paradigm of linear production and energy transferacross trophic levels (right).

Image: Eileen Kearney

FREEREE ACCESSCCESS

Mar Ecol Prog Ser 491: 1–14, 2013

found that phytoplankton production itself was avery poor predictor of fisheries yields over globallydistributed systems. Across ecosystems, they foundthat metrics that accounted for variations in trophictransfer efficiency and the size structure of the plank-tonic food web, such as the particle export ratio or themesozooplankton to primary production ratio, weremore highly correlated with fisheries yields than pri-mary production. The variation in the relationshipbetween primary production and fisheries produc-tion across different ocean environments is in keep-ing with classical studies, which estimated very different transfer efficiencies in marine food websunder varying environmental conditions (coastal versus open ocean versus upwelling areas) (Ryther1969). Improved understanding of fisheries yieldsand fisheries capacity requires refinements beyondan estimated 10% transfer efficiency betweentrophic levels (e.g. Pauly & Christensen 1995).

A nearly universal characteristic of marine eco -system models is the inclusion of ‘non-predatory lossterms’. These terms are used to represent the neteffect of a diversity of loss processes, including natu-ral mortality (i.e. death due to old age), loss to diseaseand viruses, unresolved intra-group mortality (suchas egg cannibalism and predation on juveniles ofsimilar species), aggregation and sinking out of themodeled system (primarily of large phytoplankton),and respiration. As these terms channel energy awayfrom higher predators, choices concerning the sizeand functional form of these terms also have thepotential to influence the flow of energy to highertrophic levels. Historically, fisheries ecosystem mod-els, such as Ecopath with Ecosim, tend to assume alinear relationship between biomass of a functionalgroup and loss due to non-predatory processes(Christensen & Walters 2004). However, planktonmodels tend to use quadratic mortality closures toachieve stability and match observed seasonal cycles(Steele & Henderson 1992, Edwards & Yool 2000).Both functional forms can be appropriate for differ-ent contributing processes of the non-predatory loss;viral loss (Brussaard 2004), intra-group predationmortality (Ohman & Hirche 2001), and aggregation(Thornton 2002) are often observed to be density-dependent processes, and may be better modeled bya quadratic form, whereas basal metabolic rate isgenerally assumed to be constant per unit biomassand thus would be better modeled with a linear for-mula (Flynn 2005).

The structural uncertainties presented by uncertainprocess formulations, such as that of non-predatorymortality, are further complicated by the already

high parameter uncertainty that exists in complexecosystem models. Population-scale variables, suchas standing stock biomass, are challenging to com-pile for an entire ecosystem. The large range in spatial scales covered by these ecosystems makes itvery difficult to thoroughly survey the population ofeven a single target fish species, for which there maybe regular scientific sampling programs as well asplentiful fisheries-based observations. Non-targetspecies, such as myctophids or other forage fish, playequally key roles in ecosystem dynamics as fisheries-targeted species, but there is far less data availableregarding the populations of these species. Seabirdsare often counted only at their roosting spots, but for-age over a much larger swath of ocean, while whalesmay migrate thousands of miles to forage. Gelatinouszooplankton may play important roles in mesozoo-plankton communities, but are inadequately sampledby traditional net tows; therefore there is far less dataon them than their crustacean counterparts. The lackof plentiful observations at all levels of the food webcan lead to wide error bars on the input parametersused in ecosystem models, and this uncertainty ispropagated to the output of any simulations.

In this study, we attempted to quantify and under-stand the factors controlling the response of the end-to-end ecosystem model to a bottom-up perturbation,namely an increase in net primary production due toalleviation of micronutrient limitation. The impact ofnon-predatory mortality on the energy flow throughthe system was quantified and drivers of the amplifi-cation of primary productivity perturbations werediagnosed. We also assessed the contribution of un -certainties in non-predatory loss structure to theoverall uncertainty of the upper-trophic-level pro-ductivity response to primary production changes.

METHODS

Description of the ecosystem model

We used an end-to-end ecosystem model that fullycouples physics, biogeochemistry, and predator−prey dynamics for the Eastern Subarctic Pacific eco-system (Kearney et al. 2012). The physical portionof this model simulated the seasonal evolution of aone-dimensional water column, resolved verticallyand forced at the surface by winds, radiation, andtemperature. The biogeochemical and food-web por-tion of the model was coupled to the physical model,and tracked state variables that encompass the nutri-ent cycles of nitrogen, silicon, and iron, as well as the

2

Kearney et al.: Transfer efficiency of modeled primary production 3

primary production and predator−prey interactionsbetween 2 phytoplankton (P) functional groups, 5zooplankton (Z) functional groups, and 16 ‘nekton’(i.e. non-planktonic organisms, including fish, squid,mammals, and birds) (K) functional groups (Figs. 1 &2, Table 1). The distinction between plankton andnekton indicates how each group is coupled to thephysical model; planktonic groups are resolved verti-cally, subject to physical mixing, and feed only onprey within the same grid cell, whereas nektonicgroups are not vertically resolved and view preyfields as the integrated sum over the water column.

All components of the model, including physical interactions, biogeochemical cycling, and predator−prey dynamics, were calculated in a fully coupledmanner at each time step, with 2-way feedbackthroughout the entire food web. For a completedescription of the model, including both physical andbiological components, as well as description of allparameters used for this study, see the Supplement atwww.int-res.com/articles/suppl/ m491p001_ supp. pdf.

The food-web portion of the model represents theEastern Subarctic Gyre of the North Pacific, which

is an important foraging ground for a variety ofepipelagic species (Brodeur et al. 1999), and a rear-ing and growth area for commercially importantPacific salmon (Aydin et al. 2005). Although themodel was parameterized for this specific region, theprocesses included are generic across open oceanecosystems, and the analysis in this paper isintended as a more general exploration applicable toall models of similar type. This sensitivity studylooked specifically at the changes that arise throughdirect propagation of net primary productivitythrough the food web, isolating this from any directeffects of climate on upper-trophic-level groups.

The Eastern Subarctic Pacific Gyre region is ahigh-nutrient, low-chlorophyll region, with ironplaying the role of limiting nutrient (Martin & Fitz -water 1988, Martin et al. 1989). Therefore, the easi-est way to systematically augment primary produc-tion in this model was to alleviate the ironlimitation through increased surface deposition ofiron. Note that in designing this experiment, wewere not attempting to replicate a short-term iron-fertilization experiment, but rather to look at the

1

2

3

4

5

6

Trop

hic

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l

Fig. 1. The food web used forthis study incorporates 23 living functional groups. Thepredator−prey interactions be-tween these groups are shownhere, with arrows pointingfrom prey to predator. Theaxis to the left indicates thetrophic level of each group,following the Ecopath defini-tion where trophic level of aconsumer is equal to 1 plus thediet-fraction-weighted averageof its prey’s trophic levels. SeeTable 1 for identification anddescription of each functional

group

Mar Ecol Prog Ser 491: 1–14, 2013

response of the entire ecosystem to a long-termchange in productivity, such as those due to per-sistent shifts in iron dust sources or atmospherictransport (Luo et al. 2008, Mahowald et al. 2009) orother projected effects of climate change (Stein -acher et al. 2010)

As iron plays a central role in this set of simula-tions, we implemented an improved representationof iron dynamics following Stock et al. (in press).Rather than the relaxation scheme used in Kearneyet al. (2012), we explicitly resolved 2 forms of iron:dissolved iron and particulate iron (Fig. 2). The ironmodel uses a single ligand to bind free iron (Johnsonet al. 1997), with free iron scavenged onto sinkingdetritus at a constant linear rate. Iron binding be -comes less effective in well-lit areas due to photo-chemical effects (Fan 2008). While this representa-tion of iron-scavenging dynamics is simple relative tothe full scope of iron chemistry and particle interac-

tions (Boyd & Ellwood 2010), we emphasize that theprimary objective of this contribution was to under-stand the response of an end-to-end model to per -turbations in primary productivity. Climatologicalsurface iron deposition was derived from the Geo-physical Fluid Dynamics Laboratory Global Chemi-cal Transport model’s soluble iron flux, extracted atthe location of Ocean Station Papa (50° N, 145° W)(Moxim et al. 2011).

Simulation setup

To quantify the propagation of in creased primaryproduction to higher trophic levels in the context ofmodel uncertainty, we ran several sets of simulations,varying the strength of the perturbation, the func-tional form of non-predatory mortality loss, and themodel parameterization.

4

Si(OH)4 Opal Fe POFe

Phytoplankton Zooplankton Nekton

NO3 NH4 DON PON

Morta

lity

Res

pir

atio

n

Ext

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r ex

cret

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Consumption

Decomposition

Adsorption

Decomposition

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mar

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rod

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Resp

iration

Respiration

Mortality

Consumption

Mo

rtality

Eg

estion

Decomposition Decomposition Decomposition

ConsumptionConsumption

Decomposition

Primary production

Extracellular excretion

Excre

tion

ExcretionEgestion

Egestion

Mortality

MortalityEg

estio

n

Primary production

Prim

ary pro

ductio

n

Fig. 2. Water column ecosystem model processes and state variables. The phytoplankton, zooplankton, and nekton boxesrepresent classes of variables; Fig. 1 diagrams the connections between each of the individual functional groups state vari-ables represented by these classes. Wavy arrows indicate state variables that sink in the model. Fe: dissolved iron; POFe:

particulate iron; DON: dissolved organic nitrogen; PON: particulate organic nitrogen

Kearney et al.: Transfer efficiency of modeled primary production 5

Each simulation consisted of a 10 yrclimatological spin-up period, followedby a 10 yr increased iron-depositionperiod. We systematically raised thesurface deposition flux of iron from itsclimatological annually averaged valueof 2.83 pmol Fe m−2 s−1 to values 1.25,1.5, 2.0, 3.0, and 5.0 times higher thanthat. The 1.25× perturbation capturesthe approximate magnitude of interan-nual variability in dust deposition inthe subarctic gyre, while the highervalues represent levels that might beexpected more rarely, such as in re -sponse to volcanic activity in thenearby Aleutian Islands (Duggen et al.2007), or perhaps from a long-termincrease in combustion-related sources(Luo et al. 2008). For our quantitativeanalysis, we used values from the finalyear of each simulation. While notevery functional group had reached acompletely new steady state by the 10and 20 yr marks, all groups showedless than 1.5% change in yearly aver-aged biomass per year at the end ofthe climatological period and eventhe slowest-growing groups showedless than a 5% change 10 yr after thestrongest perturbations; therefore, wefelt this spin-up time was sufficient forour analyses.

The biogeochemical and food-webportion of the model incorporates ob -servational uncertainty into the para -meters constraining predator− preyfunctional response, non-predatorymor tality, and initial biomass throughthe use of an intramodel ensemble.The ensemble is derived though theuse of Ecopath models (Christensen &Pauly 1992); the biomass, production/biomass, consumption/biomass, anddiet com position variables assigned toeach functional group are associatedwith an uncertainty range based onthe quality of data from which theyare derived, and parameter sets arethen chosen from log-normal distribu-tions defined by these parameters, fil-tered such that all parameter setsused meet the mass-balance criteria ofthe Ecopath algorithm (Aydin et al.

Index Name Type Symbol Consolidated groups

1 Albatross K

Albatross

2 Mammals and sharks K Northern elephant seals,northern fur seals, spermwhales, Dall’s porpoises, Pacificwhite sided dolphins, northernright whale dolphins, sharks

3 Neon flying squid K

Neon flying squid

4 Orcas K Toothed whales

5 Boreal clubhook squid K Boreal clubhook squid

6 Seabirds 1 K

Skuas, jaegars, fulmars

7 Pomfret K Pomfret

8 Seabirds 2 K

Shearwaters, storm petrels, kittiwakes, puffins

8 Large gonatid squid K

Large gonatid squid

10 Salmon K Coho salmon, pink salmon, sockeye salmon, chum salmon,

Chinook salmon, steelhead

11 Baleen whales K

Fin whales, sei whales

12 Micronektonic squid K

Micronektonic squid

13 Mesopelagic fish K Mesopelagic fish

14 Pelagic forage fish K Pelagic forage fish

15 Saury K Saury

16 Large jellyfish K

Jellyfish

17 Predatory zooplankton Z

Sergestid shrimp, chaetognaths, miscellaneous predatory

zooplankton

18 Large zooplankton Z Euphausiids, amphipods,pteropods

19 Gelatinous zooplankton Z Salps, ctenophores

20 Copepods Z

Copepods

21 Microzooplankton Z

Microzooplankton

22 Small phytoplankton P

Small phytoplankton

23 Large phytoplankton P

Large phytoplankton

Table 1. The simplified food-web model includes 23 functional groups, listed belowalong with the picture used to identify each in the food-web diagram (Fig. 1). Thetype column indicates whether each group is classified as phytoplankton (P), zoo-plankton (Z), or nekton (K) in the fully coupled model. See the Supplement (www.int-res.com/articles/suppl/m491p001_supp.pdf) for a more complete description

of each group

Mar Ecol Prog Ser 491: 1–14, 2013

2007, Kearney 2012). The same set of 50 ensemblemembers was run for each combination of surfaceiron flux and mortality formulation. See the Supple-ment for the para meter values associated with theensemble members. To assess the impact of theassumed form of non-predatory mortality, all con-sumer groups were run with non-predatory mortal-ity functions of the form:

M0 = aBc (1)

where M0 is the total loss due to non-predatorymortality (mol N m−3 s−1 for plankton, mol N m−2

s−1 for nekton), B is the biomass of the group (molN m−3 for plankton, mol N m–2 for nekton), and cwas set to either 1.0, 1.5, or 2.0, representinglinear, mixed, and quadratic mortality, respectively.The coefficient a was constrained through the Ecopath-derived values for biomass (B *, the mass-balanced biomass of a functional group) and M0*(the mass-balanced value for all group productionnot passed to higher trophic levels) such that a =M0*/(B *c ). The quadratic structure captures theend case where density-dependent processes arethe primary contributors to non-predatory loss,whereas the linear structure represents the otherend case where density-independent processespredominate. Note that producer groups used aquadratic non-predatory mortality term in all sce-narios; this form was necessary to maintain properseasonal dynamics in primary production, as dis-cussed in Kearney et al. (2012). We encounteredsome issues when attempting to analyze theresults of the purely linear mor tality case. Whilewe wanted to include this formulation as a criticalend case representing non-density dependent pro-cesses, the linear case is mathematically less stablethan higher-order functions (Armstrong 1999).Coupled with the high temporal resolution of thephysical forcings included in this model, the insta-bility manifests itself by causing some ensemblemembers to drift away from observed values, evenunder climatological conditions. To ensure consis-tent comparisons across all 3 mortality re gimes, forour final analysis we considered only those ensem-ble members whose yearly averaged biomass val-ues remained within the initial uncertainty rangesdefined by the Ecopath model over all 3 mortalityregimes, for a total of 39 ensemble members. Insummary, 750 model simulations were run: 5 nutri-ent scenarios, 3 mortality scenarios, and 50 para-meterization ensemble members; 585 (5 nutrient, 3mor tality, 39 ensemble) of these were used in thefinal analysis.

Simulation analysis

We calculated a variety of metrics to quantify thepropagation of primary production through the eco-system as a whole.

Total net primary production (NPP) was calculatedas the sum of net primary production across bothphytoplankton groups. We also calculated net sec-ondary production (NSP) for each of the 21 consumergroups in the ecosystem.

To quantify the different patterns of propagationthroughout the food web (and across the many ordersof magnitude spanned by production rates from pro-ducers to top consumers), we defined a metric torelate relative change in net primary productivity(NPPrel) to relative change in consumer productivity(NSPrel), which we termed amplification. The amplifi-cation values were calculated by fitting a line to rela-tive net total primary production versus relative netsecondary production across all iron regimes, whererelative values were defined as follows:

(2)

(3)

The slope of the fitted line across the 6 iron regimes(5 high-iron periods (hiFe) plus the climatological(clim) period) is defined as the amplification value,with one amplification value calculated per ensem-ble member, mortality regime, and functional group(i). While the trend across iron regimes was notalways perfectly linear, 98% of the ensemble−mor-tality−group sets showed a significant fit to the linearregression (p < 0.05), and less than 5% of the fits hadR2 values of less than 0.9. An amplification value(NSPrel�NPPrel) of 1 indicates that a functional group’sproduction remained the same proportional to therelative change in net primary production. A valuegreater than 1 indicates an amplification of the pri-mary production signal, while a value less than 1indicates an attenuation (the choice to refer to themetric as amplification rather than attenuation in thetext of this paper was arbitrary).

We performed several regression analyses to elu-cidate the factors contributing to the differences inamplification between mortality regimes for a givenensemble member. The ratio of quadratic:linear am -plification metric was regressed against trophiclevel and ecotrophic efficiency (i.e. fraction of mass-balanced loss attributed to predatory loss ratherthan non-predatory loss). We also performed a

NPP =NPP

NPPrelhiFe

clim

NSP =NSP

NSPrel,hiFe,

clim,i

i

i

6

Kearney et al.: Transfer efficiency of modeled primary production

multiple linear regression (with interaction terms)against the 2 predictors. Finally, we assessed theimportance of assumptions concerning the func-tional form of non-predatory mortality relative touncertainties in the food-web parameterization indetermining the range of simulated responses to theprimary production increase. To do this, we testedwhether the differences between mortality regimesremained important when the ensemble memberswere treated as independent observations. For thiscomparison, we performed a Mann-Whitney U-test(α = 0.05) to test whether the sample medians weresignificantly different between the linear and quad-ratic mortality regimes. We applied the test to bothbiomass and net secondary production for eachfunctional group.

RESULTS

Primary productivity under enhanced iron deposition

Increased iron deposition led to an increase in totalnet primary productivity, although there was consid-erable variability in the magnitude of this increaseacross ensemble members, particularly at very highiron levels (Fig. 3). The increase in surface iron con-centrations was approximately linear as surface dep-osition increased. In response, annually averaged netproductivity increased until surface dissolved ironlevels reached ~0.2 nM Fe, which occurs in the 3.0deposition regime; beyond this level, macronutrientsbecame limiting once more and primary productionleveled off.

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Apr19 Jul19 Oct190

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.450

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250Total annually−averaged

Surface Fe (nM)

1.001.251.502.003.005.00

Surface iron fluxrelative to

climatological

a

b

c

d

Fig. 3. Net primary productivity undervarying surface iron deposition. Netproductivity versus time over a singleyear of each iron regime for (a) small(PS), (b) large (PL), and (c) total phyto-plankton. Bold lines indicate the en-semble average and the shaded area indicates the 25th to 75th percentilesacross ensemble members (the 1.25,2.0, and 3.0× surface iron flux lines arenot shown to avoid clutter in the graph;they show a similar seasonal pattern asthe simulations shown). (d) Yearly aver-aged total net production versus yearlyaveraged surface iron concentration foreach ensemble member (points); greycircle: ensemble average for each iron

regime

Mar Ecol Prog Ser 491: 1–14, 2013

The increased primary productivity manifested it -self primarily through increases in the small phyto-plankton group. Large phytoplankton exhibitedhigher production in the spring, but decreased pro-duction in the fall under high iron deposition, whichled to the annually averaged production values forthis group remaining more or less constant across all5 iron regimes. These responses were due to a com-bination of both bottom-up and top-down controls onthe population growth of the larger size class.Enhanced iron deposition increased production byboth size classes in the spring, when macronutrientsare plentiful (Fig. 4). However, the enhanced bloomand high iron deposition early in the summer led to adepletion of macro nutrients and an enhanced meso-zooplankton com munity in late summer and earlyfall, both of which strongly limit the production of thelarge phytoplankton population. The newly strength-ened mesozooplankton community maintained astrong top-down control on the microzooplanktongroup, which is the primary predator of small phyto-plankton, allowing small phytoplankton biomass andproduction to expand. Although observations of theNorth Pacific phytoplankton community response toa long-term change like the one we simulated are notavailable to either confirm or refute our results, theincreased net primary production levels under thehigher surface iron flux conditions allowed us toclosely analyze the propagation of production to

higher trophic levels. We will revisit the simulatedresponse to iron enrichment in the ‘Discussion’ sec-tion.

Propagation of productivity to higher trophic levels

In our simulation results, increased net primaryproduction led to increased consumer net secondaryproduction for all functional groups included in thismodel (Fig. 5). However, the sensitivity of consumerproduction to changes in net primary production var-ied widely across both ensemble members and mor-tality structures. We saw smaller absolute changes inconsumer production at higher trophic levels, but thiswas primarily a reflection of the overall decline inenergy flows as one moves to higher trophic levels.

Analysis of relative changes in production throughthe amplification metric (Eqs. 2 & 3) revealed differ-ences in the response of the food web under the 3 dif-ferent mortality structures (Fig. 6). At the lowesttrophic levels, the microzooplankton and copepodgroups showed no significant difference in amplifi -cation between the linear and quadratic mortalityschemes. For all 3 sets of simulations, the change inmicrozooplankton production was amplified relativeto primary production, while the change in copepodproduction was attenuated, indicating a shift in thefood web towards the smaller size class. This was

consistent with the simulated redistributionof primary production (Fig. 3). Whilestronger top-down control restricted thebiomass of small zooplankton, the subse-quent enhancement of small phytoplanktonproduction increased the overall energyflow through small zooplankton.

The remaining functional groups did seea significant difference in the amplificationmetric across mortality schemes. Under thequadratic scheme, all groups except themicrozooplankton showed median valuesless than 1, indicating that a higher fractionof ecosystem production was being lost tonon-predatory loss terms under high-pro-duction conditions than under low-produc-tion conditions. On the other hand, underthe linear mortality scheme, the majority ofthe groups had median amplification valuesgreater than 1, indicating that more produc-tion is staying within the food web andbeing passed to higher trophic levels, ratherthan being lost to non-predatory sources.Our regression analysis revealed that both

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Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

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Surface iron fluxrelative to

climatological

Fig. 4. Realized growth rates (i.e. light- and nutrient-limited growthrates) for large and small phytoplankton under climatological (1.0×) and5.0× surface iron deposition levels. The realized growth rates for bothfunctional groups increase under the high-iron conditions. Shaded areas represent the 25 to 75% ensemble range and the solid lines indicate the

ensemble median

Kearney et al.: Transfer efficiency of modeled primary production

trophic level and ecotrophic efficiency showed statis-tically significant relationships with the relativeamplification between the linear and quadraticregimes (Table 2).

Higher trophic levels tended to show larger differ-ence between the 2 mortality regimes, as did func-tional groups with larger mass-balanced non-preda-tory loss fractions (i.e. lower ecotrophic efficiencies).

However, together these 2 factors only explained amodest amount of the overall variability, illustratingthe complex dependence of individual functionalgroup responses on food-web interactions, includingthe responses of preferred prey, competitors, and primary predators.

Across the entire ensemble of projected responses,differences in the simulated response to enhanced

9

Relative surface iron

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Albatross

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4e−07 Seabirds 2

0

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Pomfret

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1 235 1 235 1 235

Pelagic forage fish

0

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1 235 1 235 1 235

Microzooplankton

0

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Fig. 5. Net consumer secondary production across all simulations. The x-axis coordinates indicate the simulated surface irondeposition relative to climatological levels, for linear (blue), mixed (green), and quadratic (red) mortality schemes, and the

y-axis indicates the annually averaged net consumer production

Mar Ecol Prog Ser 491: 1–14, 201310

primary production arising from uncertainties inthe functional form of non-predatory mortality wereoften obscured by other uncertainties in the food-web parameterization. We tested both the distribu-tions of biomass and net production of each con-sumer to see whether they were significantly higheror lower under the linear mortality structure thanwith the quadratic structure. Even following thestrongest perturbation, the majority of variables didnot display any statistically significant differences(Mann-Whitney U-test, α = 0.05) in their distributions.The exceptions to this fell into 2 groups. First, as withthe relative metric discussed in the previous para-graph, functional groups with a high non-predatorymortality rate, including jellyfish, salmon, mammals,orcas, and gelatinous zooplankton, showed signifi-cantly higher biomass and production values underthe linear mortality structure than the quadratic one.At the other end of the trophic spectrum, microzoo-plankton, copepod, and large zooplankton biomasswere all lower under the linear scheme than thequadratic one (Fig. 7). This difference at the bottomof the food chain stems from changing predationpressure as a result of the amplified response of theprimary predators of these organisms, particularly ofthe jellyfish group.

DISCUSSION

This analysis revealed a complex response to aseemingly straightforward perturbation, and alsodemonstrated the interplay of structural and parame-ter uncertainty in determining the range of simulatedresponses. First, this set of model simulations demon-strated that the interacting effects of light limitation,temperature dependence, and nutrient limitation oneach individual phytoplankton group, as well as theirindirect effects on each other through top-down ef-fects of changing grazing pressure, can lead to unex-pected changes in primary production even with a

0

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Jelly

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fora

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opela

gic fis

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id squid

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squid

Orcas

Neon

flying

squid

Mam

mals

, sha

rks

Albatro

ss

Am

plif

icat

ion

Fig. 6. Amplification metric across all simulations. The amplification metric quantifies the strengthening or weakening of achange in production across trophic levels. These boxplots show the spread of values for each consumer; boxes indicate 25th to75th percentiles across ensemble members, with a central mark at the median, whiskers extend to the maximum and mini-mum non-outlier values, and outliers are marked as points. Two medians are significantly different (at the 5% level) if theirnotch ranges (i.e. region from bottom narrowing point to top narrowing point) do not overlap. As in Fig. 5, blue, green, and red

boxes correspond to linear, 1.5, and quadratic mortality schemes, respectively

Predictor Coefficient of Fdetermination (R2)

Trophic level 0.114 55.67Ecotrophic efficiency 0.147 73.12Both (no interaction) 0.183 63.74Both (with interaction) 0.185 35.48

Table 2. Regression analysis of the relative amplificationmetric between quadratic and linear regimes revealed sig-nificant (all at p < 0.001) but low correlations with trophiclevel and eco trophic efficiency. Regressions included 1050

observations (1 per consumer−ensemble pair)

Kearney et al.: Transfer efficiency of modeled primary production 11

0

0.2

0.4

Albatross5.9e-07 4.2e-06

B3.5e-08 3.5e-07

NSP

0

0.2

0.4

Mammals,sharks0.00063 0.011

B0.00017 0.002

NSP

0

0.2

0.4

Neon flying squid0.0049 0.045

B0.01 0.27

NSP

0

0.2

0.4

Orcas4.6e-07 1.8e-06

B7.8e-09 1.6e-07

NSP

0

0.2

0.4

Boreal clubhook squid

Frac

tion

of e

nsem

ble

mem

ber

s

0.00014 0.0014B

0.00034 0.0051NSP

0

0.2

0.4

Seabirds 13.2e-06 1.6e-05

B1.8e-07 2.1e-06

NSP

0

0.2

0.4

*

Pomfret0.0033 0.033

B

*

0.002 0.044NSP

Seabirds 28.5e-06 4.7e-05

B8.5e-07 6.3e-06

NSP

Gonatid squid0.00037 0.0041

B0.00075 0.011

NSP

Salmon0.0021 0.031

B0.004 0.067

NSP

Baleen whales0.00054 0.0024

B8.3e-06 6.7e-05

NSP

**

Micronektonic squid0.006 0.13

B0.04 0.38

NSP

Mesopelagic fish0.029 0.52

B0.013 0.78

NSP

Pelagic forage fish0.0049 0.13

B

*

0.012 0.31NSP

Saury0.0068 0.043

B

*

0.0093 0.13NSP

Jellyfish0.036 0.67

B0.074 2.8

NSP

Predatory zooplankton0.099 1.1

B0.081 8.1

NSP

Large zooplankton0.18 1.3

B1.2 14

NSP

Gelatinous zooplankton0.048 0.36

B0.074 6.5

NSP

Copepods0.37 0.8B 12 28NSP

Microzooplankton0.4 0.84

B19 51

NSP

Fig. 7. Distributions of biomass (B, g C m−2) and net secondary production (NSP, g C m−2 yr−1) for each consumer in the foodweb under the linear (blue) and quadratic (red) mortality structures, at the end of the 5.0× surface iron flux perturbation. Themedian values of each dataset are indicated by the dotted stem lines. The shaded panels indicate variables where the medianvalue is significantly higher or lower under the linear regime than the quadratic regime. All axes share the same verticalrange, which indicates the fraction of ensemble members falling in a given range. Horizontal axis limits are labeled in the

upper corners of each axis

Mar Ecol Prog Ser 491: 1–14, 2013

relatively simple forcing factor. While both phyto-plankton groups benefit directly—through an in-creased growth rate—from the increased iron deposi-tion levels, increased annual net primary productionwas isolated to only one of these functional groups.Before running the simulations, we hypothesized thatthe large phytoplankton would be more likely to ben-efit from the increased iron levels, since the commonassumption in plankton models is that small phyto-plankton are more tightly regulated by the quick-responding microzooplankton (Armstrong 1999,Dunne et al. 2005). Although the small phytoplanktonpopulation was initially prevented from expandingdue to microzooplantkon grazing, over time the mi-crozooplankton population was reduced by a growingmesozooplankton community that also fed on largephytoplankton, releasing small phytoplankton fromboth predatory and competitive pressure.

Although our simulations, with their long-termchanges in surface iron flux, cannot be directly com-pared with short-term iron fertilization experiments,it is interesting to note that iron addition experimentsin the subarctic Pacific region have demonstratedmixed responses by the phytoplankton community.Since the iron hypothesis was first proposed as amechanism for incomplete nutrient use in thisregion (Martin & Fitzwater 1988, Martin et al. 1989),3 mesoscale iron fertilization experiments have beencarried out in the Eastern Subarctic gyre: the Subarc-tic iron Enrichment for Ecosystem Dynamics Study(SEEDS) in 2001, Sub-arctic Ecosystem Response toIron Enrichment Study (SERIES) in 2002, and SEEDSII in 2006. All 3 experiments were conducted duringlate summer, which is the approximate mid-pointof the phytoplankton growing season in this region.The phytoplankton communities were very similarbefore fertilization for all 3 experiments, with thesmall phytoplankton (primarily prymnesiophytes andchlorophytes) dominating, and similar chlorophylllevels were measured each time (Suzuki et al. 2009).Over the 13 d post-fertilization observation period,SEEDS saw an increase of 2 to 5 times in the nano-plankton, but the response was dominated by a 45-fold increase in the diatom community, with a shifttowards centric diatoms (Takeda & Tsuda 2005). TheSERIES experiment observed increases in all sizeclasses over the first 10 d of observations, followed bya bloom of diatoms, this time primarily the smallerpennate diatoms, over the final 8 d of observation(Marchetti et al. 2006). Contrary to these 2 studies,the SEEDS II fertilization observed no bloom ofdiatoms, with the picophytoplankton instead domi-nating the increase in biomass and productivity seen

over the 26 d study (Uematsu et al. 2009). The diver-sity of responses may indicate that higher predationclosures are more dynamic than we consider them,and that they may induce structural changes in theplanktonic food web.

In our study, the upper-trophic-level consumersshowed fairly regular increases in production as aresult of the increased primary production. Despitethe complex network of pathways connecting thevarious functional groups to each other, there wereno clear ‘winners’ or ‘losers’ resulting from this par-ticular ecosystem perturbation. Instead, all consumergroups tended to experience an increase in both netproduction and biomass following 10 yr of increasedprimary production.

We found that when looking at an individual setof model parameters (i.e. one ensemble member),the structural form of non-predatory mortality couldaffect whether the increased production was ampli-fied as it moved up the food chain. Linear mortalityfunctions, which do not increase in prominence as asystem becomes more productive, tend to pass largefractions of the increased production to the top of thefood web, benefiting top predators more so thanlower-trophic-level consumers. In contrast, quadraticmortality functions lead to damping of this response,as more of the increased production is recycledthrough the non-predatory loss terms rather thanbeing passed to higher-trophic-level predators. Thedifference between these 2 structural regimes shouldbe considered when constructing complex ecosystemmodels, particularly when not explicitly accountingfor the uncertainty in input parameters. Often, eco-system studies look only at the relative change inpopulation variables, rather than the absolute change,recognizing that input uncertainty may render theabsolute change less useful than the relative change.However, this study demonstrates that the relativechange in ecosystem variables can be strongly influ-enced by structural uncertainties, more so than theabsolute values of these variables.

However, whether choices regarding the func-tional form of non-predatory mortality significantlyaltered the range of predicted productivity of a singlegroup varied based on other sources of uncertainty.When considering the full range of parameter uncer-tainty, we found that the differences in the responsespredicted by the 3 non-predatory mortality structurescould only be seen for a few variables, related to toppredators with low predatory mortality. The salmongroup (representing the most commercially impor-tant species in this food web), though, was one of thefunctional groups that did show different responses

12

Kearney et al.: Transfer efficiency of modeled primary production

under different mortality structures. Because we didnot explicitly model fishing mortality, loss to fishingpressure was considered part of this functional group’snon-predatory mor tality. This perturbation experi-ment supports the importance of understanding thecorrect structural form of fishing loss and other non-predatory losses when modeling fisheries targetgroups.

In this context, our coupling of biogeochemistry to afood web has not completely eliminated closureterms, but rather pushed them higher in the foodchain, towards the level of commercially targeted spe-cies and the fisheries that ‘prey’ on them. The likelyrole of fishing in these closure terms makes it essentialto further push the end-to-end concept towards thelinks connecting the diverse social and economic fac-tors that control dynamic fishing responses.

Acknowledgements. This work was partially supported bythe NOAA Dr. Nancy Foster Scholarship Program, the NF-UBC Nereus Program, and BP and Ford Motor Companythrough the Carbon Mitigation Initiative at Princeton Uni-versity. Artwork for the food-web diagram was created byEileen Kearney.

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Editorial responsibility: Kenneth Sherman, Narragansett, Rhode Island, USA

Submitted: April 22, 2013; Accepted: July 1, 2013Proofs received from author(s): August 30, 2013