Functional response of carbon absorption efficiency in the pelagic calanoid copepod

Acartia tonsa Dana

Peter Thor* and Ida Wendt

University of Gothenburg, Department of Marine Ecology, Kristineberg, Sweden

Abstract

We constructed a general relationship between prey concentration and absorption efficiency (AE; previouslytermed assimilation efficiency) in the cosmopolitan calanoid copepod Acartia tonsa. The relationships betweenobserved AEs and prey concentrations developed differently on different prey species. While AEs decreasedasymptotically with prey concentration on the cryptophyte Rhodomonas baltica, the chlorophyte Dunaliellatertiolecta generated a v-shaped response, whereas AEs remained constant on the diatom Thalassiosira weissflogii.We used these observations to develop a mechanistic gut model in which gut carbon concentrations depend oningestion rate and either egestion rate or absorption rate. To investigate which rate was more important for AE,two different model modes were run: absorption was set to vary according to absorptive enzyme kinetics andegestion set to relate linearly to gut carbon concentration, or the contrary, egestion was set to vary according toenzyme kinetics and absorption set to relate linearly to gut concentration. This approach revealed that copepodcarbon AE is controlled primarily by egestion rate kinetics and is independent of absorptive enzyme kinetics.Accordingly, we suggest a simplified regression model for the functional response of AE in pelagic copepodsbased solely on rates of ingestion and egestion.

Transport of elements through food webs is constrainednot only by predator–prey interactions such as the successof predation or escape of prey, but also by the physiologicalprocessing of ingested elements in the predator organism.Processes that allocate elements to biosynthesis governincreased trophic transport, whereas processes that act inthe catabolic loss of elements (e.g., respiration) governdecreased trophic transport (Thor et al. 2002). However, inpelagic copepods, as in all gut carrying metazoans,elements must be absorbed through the gut epitheliumbefore they become available for any processes within theorganism. Elemental absorption efficiency (AE, fraction ofingested element absorbed) therefore constrains the supplyof elements to biosynthesis and metabolism. Thus, anyphenomenon restraining elemental AE may seriouslydiminish biosynthesis and growth and thereby also thetransport of the element up through the food web.Previously, we have seen that variations in AEs, due tochanging nutritional quality of the prey, for instance,induce differences in growth rate and growth efficiency incopepods (Jones et al. 2002; Thor et al. 2007). Accordingly,weight-based individual models predict that variations inAE between 0.6 and 0.8, a range of AEs commonly foundin herbivorous copepods (Carlotti et al. 2000), change thedevelopmental rate of copepodite larvae by more than 40%(Gentleman et al. 2008). Ultimately, such changes also haveserious implications for population development, not onlyin terms of maximum growth rate, but also in the temporaldevelopment of population peaks (Mitra et al. 2003). Whenkey ecosystem species are involved, this has implications forthe entire food web structure.

Calanoid copepods comprise the most abundant groupof metazoan pelagic grazers and, as such, constitute a keygroup in the lower trophic levels of the plankton ecosystem.

Most organic matter of phytoplankton origin is at somepoint in the food web ingested and processed by thesecrustaceans, and the trophic transport of elements in thepelagic environment therefore depends greatly on itsabsorption into copepod biomass. Since elements aretransferred through food chains in an exponentiallydecreasing manner with loss at every level, due torespiration of carbon, for instance, the total ecologicaleffect of changing trophic efficiencies in particular preda-tors will increase toward lower trophic levels. ElementalAEs in lower trophic level grazers such as calanoidcopepods are therefore paramount, not only to theimmediate vicinity of the food web, but to the entireecosystem function.

Very little is known about the kinetics of foodabsorption in calanoid copepods, and, at present, nopublished studies have employed direct measurements ofthe relationships between prey abundance or species andcopepod AE. Only one study, employing indirect calcula-tions of AE from rates of ingestion and fecal pelletformation, exists (Besiktepe and Dam 2002). We aretherefore left with insufficient and tentative fixed AEswhen modeling the role of copepods in pelagic ecosystemfunction (Carlotti et al. 2000; Mitra and Flynn 2007). In thestudy presented here, we established a general relationshipbetween carbon AE and prey concentration in thecosmopolitan calanoid copepod Acartia tonsa based onthe hypothesis that AE is exclusively dependent on rates ofingestion and egestion.

The term assimilation is widely, and inaccurately, usedto describe the uptake of elements in the gut (e.g., inBamstedt et al. 2000). In the present paper, we use the termabsorption for gut uptake. Assimilation encompasses gutabsorption, as well as transport across cell membranes,transformation of biomolecules, and the resulting energeticexpenses. Thus, assimilation equals ingestion minus eges-* Corresponding author: peter.thor@marecol.gu.se

Limnol. Oceanogr., 55(4), 2010, 1779–1789

E 2010, by the American Society of Limnology and Oceanography, Inc.doi:10.4319/lo.2010.55.4.1779

1779

tion minus unused elements removed by excretion, whereasabsorption equals ingestion minus egestion. For thefraction of ingested carbon (I) absorbed (R), we use theterm absorption efficiency (AE), which can be convenientlycalculated by comparing rates of ingestion and egestion (E):

AE~R

I~1{

E

I

If not noted in the text, we compare only with previousstudies measuring absorption efficiency and not assimila-tion efficiency, regardless of what term may have been usedin these studies.

Methods

To establish a functional response of carbon AE, wemeasured AEs on a range of prey concentrations of threedifferent phytoplankton species. We then compared theempirical results with a simple mechanistic model of gutdynamics. This comparison allowed us to investigatewhether the changes in AE with increasing prey concen-trations were induced primarily by changing absorptionrates or changing egestion rates. Ultimately, we used thisinformation to construct a simple regression equation forthe functional response.

We chose three prey species based on earlier observa-tions of their nutritional quality in terms of efficiency ofconversion of ingested food. The cryptophyte Rhodomonasbaltica represents a high-quality flagellate diet, whereas thechlorophyte Dunaliella tertiolecta represents a low-qualityflagellate diet. Thalassiosira weissflogii represents a diet ofdiatoms, which are generally regarded as important preyfor herbivorous copepods.

A. tonsa were reared in culture at 18uC in 0.3-mm filteredseawater under indirect natural light conditions. Thecopepods were sustained on a diet consisting of a mixtureof R. baltica and T. weissflogii. R. baltica, D. tertiolecta, andT. weissflogii were cultured in f/2 algal growth medium atexponential growth. The growth medium was prepared from34% 0.3-mm filtered and pasteurized seawater. Cultures weremaintained at 18uC at a light : dark cycle of 14 h : 10 h. Priorto all experiments, copepods were acclimated to the diets atthe corresponding experimental concentrations in 2400-mLglass bottles placed on a rotating plankton wheel (0.5revolutions per minute [rpm]) for 48 h. Water and algae wererenewed after 24 h. One batch of these copepods was usedfor measurements of clearance and ingestion rates. A secondbatch was used for measurements of AE.

Clearance and ingestion rates—For each diet, fivedifferent food concentrations were prepared from algalstock cultures by dilution with 0.3-mm filtered f/2 medium.Four replicate 20-mL samples were taken for measure-ments of initial algal cell concentrations at each concen-tration. Four replicates of each concentration wereprepared in 620-mL glass bottles, and nine A. tonsa femaleswere added. Likewise, four replicate controls withoutcopepods were prepared. All bottles were incubated for20–30 h in dim light conditions (dark during night) on arotating plankton wheel (0.5 rpm) at 18uC. After the

incubation, 20-mL samples were taken for measurements offinal algal cell concentrations.

Algal cell concentrations were measured using an Elzone5380 electronic particle counter and converted to carbonconcentrations using carbon : volume ratios given byMontagnes et al. (1994). Clearance rates were measuredfrom the disappearance of particles in the bottles contain-ing copepods compared with control bottles (Frost 1972).Weight-specific ingestion rates were calculated using acarbon weight of A. tonsa females of 4.6 mg C ind21 (Thoret al. 2007) by multiplying clearance rates with averagephytoplankton carbon concentrations, assuming ingestionof all cleared particles (Frost 1972).

Functional responses of ingestion rates were constructedaccording to Real (1977). The Hollings disc equationdescribes the functional response of predators based on preyencounter rate, attack success, and prey handling time(Holling 1966). This model behaves according to first-orderMichaelis–Menten kinetics (Holling type II response).However, functional responses of copepods fall into twocategories (Carlotti et al. 2000). While the type II responseshows a hyperbolic increase in ingestion rates with preyconcentration, the type III response shows a sigmoid increase.Fortunately, both types can be integrated into the samemathematical framework, and the type II response may beviewed as a special case of the type III response by employingthe Hill equation to model ingestion rate (i) (Real 1977):

i~imaxCh

p

KhmzCh

p

ð1Þ

Here, imax is maximum ingestion rate, Cp is prey concentra-tion, Km is the prey concentration at which i 5 imax/2. The hexponent introduces the possibility for adaptation by thepredator. The value of h scales to the number of preyencounters a predator must have before the predator ismaximally efficient at feeding. The lowered feeding rates atprey concentrations below the inflexion point of the sigmoidresponse may be explained either by a switch in feedingmodes (e.g., from filtering to ambush feeding) or byinsufficient stimulation to inflict feeding responses at lowprey concentrations. The equation gives a hyperbolic type IIfunctional response when h 5 1. At h . 1, the functionalresponse becomes sigmoidal (type III). We fitted theequation to the relationships between ingestion rates andprey concentrations on all three diets by least squareregression to calculate best values of imax, Km, and h.

Absorption efficiencies—AEs were measured using adual-tracer technique with 14C as the absorbable tracerand 51Cr as the inert tracer (Lopez 2001). Batches of R.baltica, D. tertiolecta, and T. weissflogii from the phyto-plankton cultures were incubated with f/2 growth mediumto which 500 mCi NaH14CO3 L21 was added and grownexponentially at dilution rates identical to those in thebatches used for ingestion rate experiments. To ensureuniform labeling, the algae were grown for a minimum offive cell divisions prior to the experiments, and 100 mCi51CrCl3 L21 was added 1 d before the experiments. The51CrCl3 stock solution was kept dissolved in 0.5 mol L21

1780 Thor and Wendt

HCl before use. When introduced into the phytoplanktoncultures at pH , 8.5, the 51Cr3+ adsorbs to surfaces,thereby labeling the phytoplankton cells. The labeled cellswere rinsed by centrifugation and resuspension in 0.3-mmfiltered f/2 medium. Centrifugal forces were chosen so thatcells were alive and the flagellates motile after the process:1810 3 g for 5 min for R. baltica and T. weissflogii and1100 3 g for 5 min for D. tertiolecta.

Labeled and rinsed phytoplankton were diluted to theexperimental concentrations in 0.3-mm filtered f/2 medium,five replicate 10-mL samples from each concentration werefiltered onto Whatmann GF/F filters (pore size 0.7 mm),and the isotopic activities of 14C and 51Cr were measuredby liquid scintillation counting (Beckman LS5000TD).Tests showed no difference in isotopic activities when usinglarger pore size GF/D filters (pore size 2.7 mm) forelimination of potential contributions from labeled bacte-ria. Auger electrons (4.5 keV) and X-rays (5 keV) from 51Crwere counted from channel 0 to 270, and b electrons from14C (156 keV) from channel 270 to 1000 on the liquidscintillation counter (Sheppard and Marlow 1971), bothcorrected for counting efficiencies and quenching. Blankswere subtracted for each isotope. For each diet, fourreplicates of each prey concentration were prepared in1200-mL glass bottles, 30 copepods were added, and thebottles were incubated for 6 h in dim light conditions on theplankton wheel (0.5 rpm). Shorter incubation periodswould reduce potential ingestion of fecal pellets, butprevious tests showed no difference in results between a2 h and a 6 h incubation period. After incubations, fecalpellets were filtered onto a 30-mm mesh, washed with 0.3-mm filtered seawater three times, and rinsed into Petridishes. All intact fecal pellets were carefully mouth pipettedunder a dissecting microscope at 40 times magnificationinto scintillation vials using drawn glass Pasteur pipettes.Isotopic activities of fecal pellets were measured as above.AEs were calculated as AE 5 (1 2 Wfeces/Wprey) where Wfeces

and Wprey are the ratios of the isotopic activities of 14C and51Cr in fecal pellets and algal prey (Lopez 2001).

AE model—Several different models on animal gutperformance have been formulated by Penry and Jumars(1987). These are based on chemical reactor theory ofwhich the continuous-flow stirred tank reactor model(CSTR) is the mathematically most simple. For the purposeof the present study, we wanted to create a model thatcould be easily implemented into the larger context ofecosystem models rather than specific complex physiolog-ical models of gut function. Therefore, we chose the CSTRmodel by adherence to the principle of parsimony that thebest explanation of any phenomenon includes as fewassumptions as possible. Moreover, the morphology andfunction of the copepod gut bear resemblance to acontinuously stirred vessel with a relatively large diame-ter-to-length ratio as opposed to the longer and moreslender gut found in other marine invertebrates. We discussthe suitability of the CSTR to model copepod guts in moredetail in the discussion section of this paper.

In our CSTR model, AE depends on the concentrationof food in the gut (Cg), which in turn varies with prey

ingestion rate (Ip), egestion rate (Eg), and absorption rateitself (Rg), so that

dCg

dt~Ip{Rg{Eg ð2Þ

and

AE~Rg

Ipð3Þ

We fixed Ip to relate to prey concentration by the calculatedfunctional responses of ingestion on the three diets (Ip 5 iin Eq. 1), and Rg and Eg were set to vary with Cg (hence thesuffixes p for prey and g for gut).

Digestion and transport across the gut epithelium ofsingle biomolecules are facilitated by enzymatic reactionsand follow Michaelis–Menten kinetics. However, higherorder kinetics may apply when reactions proceed in parallelwith several different substrates. Carbon is most likelyextracted from several different biochemical substrates(carbohydrates, lipids, protein, etc.) in the gut, and wetherefore applied the more general Hill equation to estimateabsorption rate (r) (Dade et al. 1990; Jumars 2000):

r~rmaxChr

g

KhrmrzChr

g

ð4Þ

where rmax is maximum potential uptake rate, Kmr is thehalf-saturation concentration, and hr is the Hill exponent.This equation is mathematically similar to the type IIIfunctional response model of i (Eq. 1). When hr 5 1, Eq. 4equals the classic Michaelis–Menten equation. Exponents, 1 may result from reaction rates vs. substrate concen-tration being more linear due to passive absorption ofingested elements (Dade et al. 1990), or may occur when thereaction is rate limited by elements other than thosemeasured. Exponents . 1 may result from parallelabsorption where the measured element (in the presentstudy carbon) is contained in a range of differentsubstrates. Dade et al. (1990) modeled gut uptake byseparate kinetics of digestion and absorption (assuminghigher order kinetics of both), but like Penry and Jumars(1987), we chose a more simple model using only a singleequation to express the ultimate absorption rate (r).

Egestion is primarily controlled by the concentration ofmaterial in the gut. However, the construction and egestionof fecal pellets is governed by biochemical processes as wellas mechanical processes. These are limited by maximumrates of formation of the chitin in the peritrophicmembrane surrounding pellets and the nervous inductionof peristaltic gut movement. Egestion rates therefore showsaturation kinetics in copepods (Besiktepe and Dam 2002).Moreover, just as the biochemical processes controllingabsorption, the biochemical processes involved in egestionmay also proceed in parallel, and we therefore convenientlyalso applied the Hill equation to model egestion rates (e):

e~emaxChe

g

KhemezChe

g

ð5Þ

Pelagic copepod absorption efficiency 1781

Here, emax is the maximum egestion rate, Kme is the half-saturation Cg, and he is the Hill coefficient.

We created the CSTR model in the modeling softwareStella 8.0 (High Performance Systems). For each diet, themodel was run at the five prey concentrations to be able togain functional responses of AE. For each prey concentra-tion, run time was chosen so that rates (Rg and Eg) hadsufficient time to reach steady state before calculation ofAE, and time steps were chosen sufficiently small to avoidoscillations in Cg due to equation stiffness. To investigatethe importance of variations in Rg and Eg on AEs, we usedtwo different modes of the model: (1) the dR mode: Rg was

set to vary kinetically with Cg according to Eq. 4 (Rg 5 r),while Eg was set to relate linearly to Cg (Eg 5 Cg), and (2)the dE mode: Rg 5 Cg and Eg 5 e (Eq. 5).

We fitted AEs predicted by the model to observed AEsby least squares regression. Input parameter values (for dRmode: rmax, Kmr, and hr; and for dE mode: emax, Kme, andhe) were varied in a factorial grid by inputting arrays of allthree parameters into the model. Values of rmax, emax, Kmr,and Kme were limited by imax so that they varied between1023 and imax on the diet in question. Limits for hr and hewere set at 1 and 2.8. Optimal parameter sets were selectedwhen minimum values of the unexplained sum of squares(SSpred-obs),

P(AEpred{AEobs)

2, were reached. HereAEpred are values predicted by the model, and AEobs areaverage observed values at each prey concentration.

Finally, we tested a regression approximation of themodel to enable a simplified formulation of a functionalresponse of AE, where ‘‘functional response’’ may bedirectly interpreted as a variable’s (in this case AE)response to varying prey concentrations. To accomplishthis, we substituted Cg with Cp in Eq. 5 so that E becamedirectly dependent on prey concentration. At equilibrium,dCg/dt 5 0 and

Rp~Ip{Ep ð6Þ

where Rp and Ep represent rates of absorption and egestiondependent on prey concentration. Dividing by Ip yields

AEp~1{Ep

Ipð7Þ

where AEp is the prey concentration dependent AE. We setIp 5 i and Ep 5 ep, where ep is from the modified Eq. 5, andfitted Eq. 7 to observed values of AE by computing valuesof maximum rate, Km, and h of ep by least squaresregression.

Results

Clearance and ingestion rates—Clearance rates decreasedasymptotically with increasing prey concentration on allthree diets (Fig. 1). Moreover, there was a clear lowerthreshold of clearance rates on the flagellate diets (R.baltica and D. tertiolecta) below which clearance ratesdecreased abruptly. On the contrary, clearance ratescontinued to increase toward low concentrations on theT. weissflogii diet. Ingestion rates increased significantlywith increasing algal concentrations on all three diets (one-factor ANOVAs among concentrations on each diet, p ,0.01) (Fig. 2).

The Hill functional response model fitted ingestion rateswith significantly increasing i on all three diets (leastsquares nonlinear regression, p , 0.01) (lines in Fig. 2).Maximum ingestion rate, imax, differed significantly amongdiets (one-factor ANOVA, F2,57 5 6.05, p 5 0.004) and wassignificantly higher for copepods feeding on R. balticacompared with those feeding on D. tertiolecta and T.weissflogii (Student–Newman–Keuls post hoc tests, p ,0.05). Moreover, the functional responses differed signifi-cantly in shape among diets (Km, one-factor ANOVA, F2,57

Fig. 1. Clearance rates on the three phytoplankton prey R.baltica, D. tertiolecta, and T. weissflogii. Lines depict clearancerates derived from the Hill regressions on ingestion rates(clearance rate equals ingestion rate divided by prey concentra-tion).

1782 Thor and Wendt

5 4.722, p 5 0.013) so that i increased significantly sloweron the D. tertiolecta diet (Km, Student–Newman–Keulspost hoc tests, p , 0.05). While the two flagellate diets (R.baltica and D. tertiolecta) induced type III functionalresponses (h . 1), the T. weissflogii diet induced a type IIresponse (h 5 1).

Absorption efficiencies—Observed AEs varied signifi-cantly with phytoplankton concentrations on all three diets(one-factor ANOVAs among concentrations on each diet, p, 0.001) (Fig. 3). While AEs decreased asymptotically with

increasing phytoplankton concentration on the R. balticadiet, there was a more complex response with the D.tertiolecta diet. Here AEs decreased to a minimum at 116 mgC L21 and again increased significantly toward higherconcentrations (one-factor ANOVA, F4,18 5 7.95, p 50.001, Student–Newman–Keuls post hoc test, p , 0.05). Onthe T. weissflogii diet, the AEs were fairly constantthroughout the full range of concentrations tested butnevertheless significantly different among concentrations,due to very low variations within groups (one-factorANOVA, F4,18 5 9.27, p 5 0.001).

AE model—Best fits of the model with the two modes(dR and dE) of the CSTR are shown in Fig. 3. Therewere clear single general minima of the unexplained sumof squares of the fit of predicted AEs on observed AEs(SSpred-obs) for each prey species and model mode (Fig. 4;for the purpose of clarity we plotted the negative log ofSSpred-obs so that SSpred-obs minima are revealed as maximaof 2log SSpred-obs). This enabled coherent selection ofvalues for rmax, Kmr, and hr and emax, Kme, and he. Wecalculated model sensitivities using a sensitivity index of SI5 (AEmax 2 AEmin)/AEmax (Bauer and Hamby 1991),where AEmax and AEmin are maximum and minimumvalues of output AE at maximum and minimum values ofthe input parameters. SI ranges from zero to 1 with a valueof 1 representing highest sensitivity, and judging fromTable 1, the model was sensitive to variations in all threeinput parameters in both the dR and dE modes (Table 1).

We also tested the models reliability using Leggett andWilliams’ reliability index (k, Leggett and Williams 1981),which is interpreted so that 68% of values predicted by themodel lie within 1/k and k of observed values. Thus, k attainsvalues . 1, and the lower the value the more precise themodel. In general, both model modes showed goodreliability on all three prey species (Table 2), except for thedR mode on the D. tertiolecta diet. Here, the model couldnot predict the increase in AE at higher concentrations whenonly Rg varied kinetically (solid line in Fig. 3, middle panel).

Since multiple measurements of AE were available foreach prey concentration, a lack-of-fit test could be appliedto test the model’s ability to explain observed data (Riceand Cochran 1984; Smith and Rose 1995). Contrary togoodness-of-fit tests, this test enables a more detailedinvestigation of the origin of statistical error of the fit toobserved data. In general, we found best fits with the dEmode (Table 2), and the model gained no lack-of-fit withall three prey species except for dE with R. baltica (p 50.049). However, both bias (intercept of a regressionbetween observed and predicted values) and consistency(slope of this regression) were good for dE with R. baltica(bias, p 5 0.174, consistency, p 5 0.198). Coefficients ofdetermination (r2) were generally highest with the dE mode.Correlation was lower with the T. weissflogii prey in thismode, probably due to the high variability of observedvalues of AE at high prey concentrations.

In brief, the dE mode showed best fits to observedvalues, and we based the simple regression for thefunctional response model (AEp) on Ep rather than on Rp

(Eq. 7). This regression model was able to fit observed AEs

Fig. 2. Ingestion rates on the three phytoplankton prey R.baltica, D. tertiolecta, and T. weissflogii. Lines depict regressionsof the Hill equation. R. baltica, imax 5 1.033 6 0.102 (mean 6SE), Km 5 98.4 6 20.3, h 5 1.83 6 0.61, r2 5 0.81, and p , 0.001.D. tertiolecta, imax 5 0.513 6 0.140, Km 5 128 6 60, h 5 1.89 61.25, r2 5 0.57, and p 5 0.002. T. weissflogii, imax 5 0.673 6 0.069,Km 5 93.0 6 25.2, h 5 1, r2 5 0.81, and p , 0.001.

Pelagic copepod absorption efficiency 1783

well with p values less than 0.05 on all three diets (Table 3).Using this approach, predicted egestion rates (Ep) fittedwell to measured egestion rates from two previous studieson A. tonsa feeding on D. tertiolecta (Besiktepe and Dam2002) and T. weissflogii (Butler and Dam 1994) (Fig. 5).Unfortunately, no literature data on egestion rates on R.baltica were available.

Discussion

In the present study, we found significant prey-specificdifferences in the relationship between AE and phyto-plankton prey concentration in A. tonsa. While AEsdecreased asymptotically with prey concentration on the

cryptophyte prey, R. baltica, the chlorophyte D. tertiolectagenerated a v-shaped response, whereas AEs remainedmore or less constant on the diatom T. weissflogii.Nevertheless, by decoupling rates of egestion and ingestion,we were able to explain the different AE responses with theCSTR model entirely on the basis of rates of ingestion andegestion while keeping absorption rate linearly related togut carbon concentration. It seems that models assumingAEs as fixed functions of ingestion rates, such as thosesuggested for benthic animals (Kofoed et al. 1989; Willows1992), but also for copepods (Slagstad and Tande 1981),are not applicable to pelagic calanoid copepods in general.

While several previous studies support our observedaverage values of carbon AE (Conover 1966a,b; Tang andDam 1999), only one study included calculations of AEwith varying prey concentrations (Besiktepe and Dam2002). Two previous studies have shown nearly constantAEs regardless of phytoplankton concentration (AbouDebs 1984; Wang et al. 1996), which led Xu and Wang toconclude that carbon AEs are invariable and nonlimitingfor physiological processes in copepods (Xu and Wang2003). The present study confirmed this for the diatom prey(T. weissflogii), but showed that AEs, in general, arecontrolled by rather more complex gut dynamics. AEs willbe constrained, for instance, with increasing concentrationsof high-quality cryptophytes like R. baltica or when feedingon low-quality chlorophytes like D. tertiolecta at interme-diate concentrations.

Previously proposed gut dynamics models were based onthe assumption that AEs are controlled exclusively by gutpassage time (GPT), and AEs should accordingly increaseasymptotically with increasing GPT (Slagstad and Tande1981; Kofoed et al. 1989; Willows 1992). These models wereall mathematically founded on the CSTR principle, butrestrictions had been imposed on the freedom of thebehavior of AE. Absorption rates were assumed to relatelinearly to GPT, whereas ingestion rates were assumed tobe regulated to fit gut throughput so that they became theinverse of GPT. As a result, AE would become a fixedfunction of ingestion rate and should, as observed in severalbenthic suspension feeders (Widdows 1978; Ren et al.2006), decrease asymptotically with prey concentration.But evolution tends to produce efficient systems, andassuming linear gut absorption kinetics may be a seriousoversimplification. One such efficient system is activemembrane uptake, and one would expect uptake processes(Rg) adhering to Michaelis–Menten kinetics. Nevertheless,the model successfully traced the observed changes in AE inthe dE mode where Rg was set to relate linearly to Cg. Moreso than with the dR mode where Rg was set to relatekinetically to Cg. The logical conclusion is that changes inAE with prey concentration are imposed primarily bychanging egestion rates, Eg, in A. tonsa.

One important difference between our model and modelson benthic suspension feeders is that Eg is held independentof ingestion rate, Ip, and GPT. Assuming that AE shouldconstitute a fixed function of ingestion rate would violate afundamental property of our model. Only by decoupling Eg

and Ip could we reasonably well explain the observedvariation in AEs on all three prey species. Although strict

Fig. 3. Absorption efficiencies (AE) on the three phyto-plankton prey R. baltica, D. tertiolecta, and T. weissflogii. Linesdepict fits of the two modes of the CSTR model.

1784 Thor and Wendt

linear relations between egestion and ingestion has beenobserved in some copepod species (Gaudy 1974), decou-pling of egestion and ingestion is not unusual, andnonlinear relationships have been observed in severalspecies with a range of different prey species (Dagg andWalser 1986; Pagano and Gaudy 1986; Tirelli andMayzaud 2005). Thus, egestion rate may well show alinear relation to ingestion rate at low ingestion rates, but itis often stagnating toward higher ingestion rates (Besiktepeand Dam 2002).

A physiological explanation for nonlinear relationsbetween egestion and ingestion can easily be incorporatedinto the rationale for our model. Eg is controlled by Cg,which in turn would increase with any compacting offoodstuff in the gut. Such compacting is in fact takingplace—fecal pellets are denser than most copepod prey—

and the degree of compacting may be highly variable.Accordingly, fecal pellet densities vary with both prey typeand concentration (Butler and Dam 1994; Urban-Rich etal. 1998). This compacting causes egestion to becomesaturated at lower prey concentrations than ingestion(lower Km). Hence, Km was 77 mg C L21 for Ep and128 mg C L21 for Ip on the D. tertiolecta diet. This results inincreased carbon concentration gradients across the gutepithelium, leading to increased AEs at high preyconcentrations. In brief, two forces will be acting antago-nistically on AE when prey concentration increases.Decreasing GPT will lower AE, whereas increasingcompacting of gut material will increase AE. The AEfunctional response curve is thereby shaped by the ratiobetween the rates of these two processes with increasingprey concentration, potentially leading to the observedbehavior of AE on the D. tertiolecta diet. Howeverunexpected it may be, this behavior was also observed byBesiktepe and Dam (2002) on the D. tertiolecta diet.Moreover, our own earlier observations have also shownperpetually low AEs around 100 mg C L21 on D. tertiolecta,which corresponds to the local minimum concentration ofour model on this prey species (Thor et al. 2007).Physiologically, compacting of gut material may beexplained by reduced maximum rates of fecal pelletformation in the hind gut. Processes leading to pellet

Fig. 4. An example of the variations in unexplained sums of squares (SSpred-obs) of the fit ofpredicted AEs on observed AEs with the CSTR model. This example shows results for the modelrun in dE mode with copepods preying on D. tertiolecta. (A) Kme 5 0.1, (B) Kme 5 0.2, (C) Kme

5 0.3, and (D) Kme 5 0.4. For clarity, we plotted the negative log of SSpred-obs.

Table 1. Sensitivity of the model output to variations in inputparameters. Values depict the magnitude of the sensitivity index(SI), which attains a value of 1 at maximum sensitivity. Values ofSI are shown for rmax, Kmr, and hr (in dR mode) and emax, Kme,and he (in dE mode).

Model mode Maximum rate Km h

dR 0.995 0.820 0.304dE 0.437 0.985 0.160

Pelagic copepod absorption efficiency 1785

formation, such as degradation of epithelium cells,synthesis of the peritrophic membrane, etc., may be unableto follow the increase in ingestion rates. The flow of matterthrough the gut may therefore be restricted in thenonabsorbing hind gut. This would increase the carbonconcentration in the absorbing midgut and hence increaseAE.

Besiktepe and Dam also studied absorption of T.weissflogii. While T. weissflogii were absorbed at AEsaround 0.6 at all prey concentrations in our study, theyfound AEs decreasing from 0.4 to less than 0.2 withincreasing concentration. Although feeding on similar preyspecies, gut dynamics apparently were different between thetwo studies. However, ingestion rates were much higher intheir study, and while clearance rates followed a Hollingtype II response in our study, they found a clear type IIIresponse. Perhaps some property of the offered diatomsdiffered between the two studies. There is evidence thatcopepods probe the chemical signature of the prey prior toattack (Schultz and Kiørboe 2009), and different preyquality may elicit different clearance rates, especially at lowprey concentrations. On the other hand, the calculations ofegestion rates of Besiktepe and Dam were quite sensitive tovariations in conversion factors used for fecal pellet dryweight and carbon mass. If we recalculate AEs from theirstudy using pellet carbon mass to volume ratios fromUrban-Rich et al. (1998), which are based on exactmeasurements of pellet carbon mass by high temperaturecombustion, their values become 0.6 to 0.4.

Morphologically, the region of the copepod gut involvedin absorption is quite well described as a single tank with arelatively large diameter vs. length, much like the CSTR(Penry and Jumars 1987; Hassett and Blades-Eckelbarger1995). The copepod gut consists of three regions, theforegut, midgut, and hindgut, and digestion and absorptiontakes place primarily in the midgut (Arnaud et al. 1978).There are no narrow passages, and communication among

these three regions is relatively unhindered. Using a one-compartment CSTR model, we thus assumed that ingestedmatter is easily shifted between the foregut and midgutregions during digestion and absorption, whereas matterreaching the hindgut is removed from the CSTR andbecomes unavailable for absorption. Dade et al. (1990)concluded that a plug flow reactor model (PFR), in whichmatter is digested and absorbed as it moves through anonstirred elongate tube, would be suitable to model gutcharacteristics in marine invertebrate predators. The PFRmodel may well be appropriate for, e.g., benthic depositfeeders that ingest large amounts of inorganic compoundswhile feeding. In these predators, both substrate anddigestive enzymes are diluted in a complex inorganic matrixin the gut and may move unstirred along the tubular gutcontained in this matrix. We argue that feeding byplanktonic animals is not similarly hampered by largeamounts of indigestible inorganic matter so that foodsubstrates are highly concentrated, easily mixed withdigestive enzymes, and readily available for absorption.Penry and Frost suggested a system of a CSTR and a PFR inseries to model the copepod gut (Penry and Frost 1990).Their suggestion fits well with the general morphology of thecopepod gut; a relatively wide foregut and midgut followedby a long and slender hindgut. However, active absorptionhad to be assumed in foregut, midgut, and hindgutcompartments when applying a CSTR-PFR series model.Based on gut epithelium cell composition, we assumed activeabsorption only in the midgut region (Arnaud et al. 1978),and were fully able to explain variations in AE using thesimpler CSTR single compartment model.

When assuming linear absorption kinetics of Rg in thedE model mode, we inherently simplified absorption to aone-step process incorporating both digestion andresorption. But absorption is in fact a two-step process.In copepods, ingested matter is digested in the largevacuolated ‘‘blister-like cells’’ (B-cells) in the midgut.

Table 2. Lack-of-fit test of the model for the two different modes, dR and dE. k is the reliability index for the model. The bias andconsistency columns show the statistics of the regression of observed vs. predicted AEs. Bias is the intercept and consistency is the slope ofthis regression. The tests gain significant results (p , 0.05) when the model is unable to fit the observed values of AE. Degrees of freedomare shown as suffixes to F and t. R2 depicts the coefficients of determination of regressions of the observed vs. predicted AEs.

Mode Prey species k

Lack-of-fit Bias Consistency

R2F3,15 p t5 p F1,18 p

dR R. baltica 1.054 2.45 0.104 0.74 0.467 0.8 0.384 0.815D. tertiolecta 2.880 8.21 0.002 6.02 ,0.001 27.01 ,0.001 0.042T. weissflogii 1.044 3.91 0.030 3.07 0.007 9.74 0.006 0.180

dE R. baltica 1.058 3.31 0.049 1.42 0.174 1.79 0.198 0.794D. tertiolecta 1.081 0.27 0.845 20.28 0.781 0.1 0.758 0.700T. weissflogii 1.031 1.37 0.291 0.69 0.497 0.44 0.514 0.414

Table 3. Output of maximum rate, half-saturation concentration (Km), and Hill exponent (h) of Ep with the AEp regression model.Means 6 standard errors. r2 and p are statistics of the regression.

Prey species Maximum rate (mg C mg C21 d21) Km (mg C L21) h r2 p

R. baltica 0.49760.021 12969.0 1.8960.11 0.82 ,0.001D. tertiolecta 0.11460.008 7765.5 3.2660.31 0.69 ,0.001T. weissflogii 0.23460.015 7369.4 1.2060.09 0.38 0.017

1786 Thor and Wendt

The products are then expelled into the gut lumen to beresorbed into so-called resorption or R cells (Arnaud etal. 1978; Nott et al. 1985; Hassett and Blades-Eck-elbarger 1995). Thus, Dade et al. proposed an evolved

model incorporating separate kinetics of digestion andabsorption (Dade et al. 1990). We chose the one-stepmodel due to its mathematical simplicity. By doing sowe implicitly assumed either that prey is ingested in aform that can be absorbed directly or, what wouldprobably be the more realistic alternative, that digestionis never rate limiting. This is probably not far from thetruth, since digestion rates may be perpetually higherthan absorption rates due to high enzymatic affinity(low Km) to the food source in acclimated copepods.Accordingly, both B-cell volume (a proxy of digestiveactivity) and activity of digestive enzymes are relativelyinvariable during the diel feeding cycle in pelagiccopepods (Mayzaud et al. 1992; Hassett and Blades-Eckelbarger 1995; Mayzaud et al. 1998), and manipula-tions of prey species or concentration have showed littleor no effect on enzymatic activity in pelagic copepods(Hassett and Landry 1983; Hassett and Landry 1990;Mayzaud et al. 1998).

The simplified model fitted egestion rate data fromprevious studies well and is as such robust. It constitutes apurposeful substitution of the differential model to describethe functional response of AE in copepods. However,substituting Cg for Cp to calculate Ep requires considerablesimplifications in terms of gut dynamics. The differentialmodel runs allowed inspection of all variables during theruns, and it was clear that Cg was by no means linearlyrelated to Cp. However, the applicability of the modelprobably warrants such a simplification. Copepod gutconcentrations are difficult to measure and may changerapidly, and the couplings between gut dynamics andgeneral growth dynamics are therefore exceptionallyelusive. The simplified model, which does not involveexplicit gut dynamics, explained the variations in AEequally well. It offers estimates of AE based on easilymeasured prey concentrations, and it allows direct com-parison with copepod growth dynamics at timescales morerelevant to growth and development.

According to our model AEs vary between 0.55 and 0.75at moderate to high prey concentrations, depending on thedominating prey species. Toward extremely low concen-trations AEs converge on 1.0 due to very long GPTs. ButAEs are between 0.63 and 0.81 already at a phytoplanktonconcentration of 30 mg C L21, which often occurs duringthe copepod summer peak abundance in temperate neriticwaters. Considering the developmental models mentionedin the introduction (Gentleman et al. 2008), the implica-tions for copepod production and larval development maybe substantial when AEs vary in these ranges. We believethat the present study presents a much needed opportunityto include empirically verified information on AE variabil-ity in the formulation of more precise models on growth,population development, and ecosystem effects of pelagiccopepods.

AcknowledgmentsWe thank Charlie Miller and Peter Jumars for helpful

suggestions on the modeling of the copepod gut and Eric Smithfor help with the statistical analysis. We also thank two anonymousreviewers for suggestions that improved of the manuscript. The

Fig. 5. Ingestion rates (Ip) and egestion rates (Ep), absorp-tion efficiencies (AEp), and absorption rates (Rp) calculated withthe simple regression model (Eq. 7). Measured egestion rates(open circles) were recalculated from Butler and Dam (1994) forT. weissflogii and Besiktepe and Dam (2002) for D. tertiolectausing fecal pellet densities and conversion to carbon mass fromButler and Dam (1994). Prey carbon concentrations wererecalculated from these two studies to fit concentrations in thepresent study using their prey cell abundances and our cellvolume : carbon weight ratios.

Pelagic copepod absorption efficiency 1787

study was financially supported by grants number 2004-0200 and2004-2484 from the Swedish Research Council for Environment,Agricultural sciences, and Spatial Planning to P.T.

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Associate editor: Michael R. Landry

Received: 16 September 2009Accepted: 15 March 2010

Amended: 30 April 2010

Pelagic copepod absorption efficiency 1789