. -- Arch.Hydrobiol. 167 1-4 467-487 Stuttgart. September 2006 Stoichiometry and growth kinetics in the "smallest zooplankton" - phagotrophic flagellates James P. Grover1 * and Thomas H. Chrzanowski1 University of Texas at Arlington With 5 figures and 1 table , Abstract: A stoichiometric approachis applied to model nutrient element content and population growth kinetics in phagotrophic flagell~tes. Available evidence is limited, but suggests that the nutrient composition of flagellates is not strictly homeostatic,but instead varies with the nutrient element composition of their food resources. A mathe- matical model is constructed that couples the C, N, and P contents of flagellates to their population growth rate and the nutrient fluxes assimilated from food resources. Variants of the model are explored to examine the effects of saturatingingestion, main- tenance respiration, and selective feeding from food mixtures. In agreement with observations, the models predict non-homeostatic variation in the nutrient content of flagellates. Population growth rate is predicted to vary with both food quantity and quality (in terms of nutrient element content). It is proposed that lack of homeostasis and selective feeding on prey with high nutrient content enhance fitness of pha- gotrophic flagellates under someconditions. Key words: ecological stoichiometry, homeostasis, heterotrophic nanoflagellates, phagotrophy, cell quota, Droop model. Introduction The rates at which organismsconsumeresources and use them for growth and reproduction are fundamental to many of the questions that have fascinated WINFRIED LAMPERT (e. g. LAMPERT 1977a, b, ROTHHAUPT & LAMPERT 1992, KESSLER & LAMPERT 2004). For individuals, the energy and nutrient budgets summarized by these rates predict fitness in some environments and constrain it in others. For populations, rates of resource processing can determine com- 1 Authors' address: Department of Biology, University of Texas at Arlington, Box 19498, Arlington, TX 76019, USA. * Correspondingauthor; E-mail: [email protected]001: 10.1127/0003-9136/2006/0167-0467 0003-9136/06/0167-0467$ 5.25 @ 2006 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart
Transcript
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Arch. Hydrobiol. 167 1-4 467-487 Stuttgart. September 2006
Stoichiometry and growth kinetics in the "smallestzooplankton" - phagotrophic flagellates
James P. Grover1 * and Thomas H. Chrzanowski1
University of Texas at Arlington
With 5 figures and 1 table
,Abstract: A stoichiometric approach is applied to model nutrient element content andpopulation growth kinetics in phagotrophic flagell~tes. Available evidence is limited,but suggests that the nutrient composition of flagellates is not strictly homeostatic, butinstead varies with the nutrient element composition of their food resources. A mathe-matical model is constructed that couples the C, N, and P contents of flagellates totheir population growth rate and the nutrient fluxes assimilated from food resources.Variants of the model are explored to examine the effects of saturating ingestion, main-tenance respiration, and selective feeding from food mixtures. In agreement withobservations, the models predict non-homeostatic variation in the nutrient content offlagellates. Population growth rate is predicted to vary with both food quantity andquality (in terms of nutrient element content). It is proposed that lack of homeostasisand selective feeding on prey with high nutrient content enhance fitness of pha-gotrophic flagellates under some conditions.
The rates at which organisms consume resources and use them for growth andreproduction are fundamental to many of the questions that have fascinatedWINFRIED LAMPERT (e. g. LAMPERT 1977 a, b, ROTHHAUPT & LAMPERT 1992,KESSLER & LAMPERT 2004). For individuals, the energy and nutrient budgetssummarized by these rates predict fitness in some environments and constrainit in others. For populations, rates of resource processing can determine com-
1 Authors' address: Department of Biology, University of Texas at Arlington, Box
petitive ability and many other aspects of a species' niche. Finally, when re-sources are partitioned among multiple species, the processing of resourcesbecomes intimately tied to ecosystem dynamics and species diversity. Thus
many levels of the biological hierarchy are linked through basic ecophysiolog-ical rates.
For many heterotrophs, theoretical representations of resource processingcan often be simplified through assumptions of homeostasis. The approach of
"ecological stoichiometry" has emphasized a strong version of homeostasis, inwhich the element composition of a consumer is strictly regulated (STERNER& ELSER 2002). The rate at which consumers produce new biomass through
growth and reproduction is then simply related to their rate of resource con-sumption, and a comparison of the element composition of consumers versusresources permits budgeting of assimilated and recycled nutrient t'1uxes.
Strong homeostasis applies, as a good first approximation, to some zooplank-ton (STERNER 1990, HESSEN 1990, ANDERSEN & HESSEN 1991) and underpinsan extensive body of theory representing zooplankton-phytoplankton-nutrient
interactions (ANDERSEN 1997, HESSEN & BJERKING 1997, ELSER & URABE1999, GROVER 2002, HALL 2004, LOLADZE et al. 2004).
On the other hand, it is well appreciated that the assumption of strong ho-meostasis applies poorly to many autotrophs, which can typically accumulatehigh levels of nutrient elements (STERNER & ELSER 2002). Variations in storednutrients, in terms of both identity and quantity, and their subsequent use ingrowth are important determinants of phytoplankton competitive fitness (TuR-PIN 1988, GROVER 1991), and of their quality as food for zooplankton (MIT-CHELL et al. 1992, STERNER 1993, STERNER et al. 1993, URABE et al. 1997, DE-MOTT et al. 1998).
The smallest zooplankton - phagotrophic flagellates - consume particulate
matter like the larger zooplankton, though their foods are small compared tothat consumed by metazoans. The ecophysiology of resource consumption andnutrient processing in phagotrophic flagellates has received less attention thanhave the same processes in other zooplankton. As yet, it is unclear whether the
assumption of homeostasis is reasonable for phagotrophic flagellates. We sus-pect it is not since most clades of phagotrophic flagellates are phylogeneticallyrelated to certain of the algae, and some "algae" that retain plastids are predo-
minantly phagotrophic.This paper briefly summarizes observations suggesting that phagotrophic
flagellates are not strictly homeostatic and proposes theoretical models to de-scribe variable nutrient composition. Predictions of these models are presentedfor relationships between growth rates and food quantity and quality, and forthe nutrient element composition of flagellates. The theory developed here for
heterotrophic flagellates might also apply to mixotrophs under some condi-tions. The theory suggests hypotheses for further research on these organisms,
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Stoichiometry of phagotrophic flagellates 469
while contributing to an understanding of consumer-resource dynamics when
strict homeostasis does not apply.
The nutrient composition of phagotrophic flagellates
There is little experimental data on the nutrient composition of phagotrophic flagella-tes. This is, perhaps, not surprising given the technical difficulties of separating flagel-
lates from their bacterial prey and ensuring that undigested and unassimilated prey
items within food vacuoles do not contribute significantly to the element composition
attributed to the flagellate itself. Some phagotrophic flagellates are mixotrophs that can
be grown autotrophic ally, and during such growth they can display variations in cellu-lar nutrient content similar to those documented in strictly autotrophic algae. The P
content of Dinobryon cylindricum varies up to tenfold (SANDGREN 1988), whil~ that of
Prymnesium patelliferum varies a more modest twofold (LEGRAND et al. 2001). These
observations suggest that mixotrophs share the relative lack of homeostasis character-
istic of autotrophic algae, and point to a possible lack of strict homeostasis for pha-
gotrophic flagellates in general.STERNER & ELSER (2002) suggested examining homeostasis of nutrient competi-
tion with log-log plots of consumer versus resource nutrient ratios. A simple linear
relationship having a slope approaching unity suggests a lack of homeostasis; the ele-ment composition of the predator varies linearly with the element composition of the
prey. A slope of zero suggests strict homeostasis; predator element stoichiometry re-
mains constant in the face of shifting element composition of prey items. A slope be-
tween one and zero implies weak physiological regulation in the direction of homeo-
stasis; the element composition of the predator varies less than a strict one-to-one pro-
portion with the element composition of the prey.The most extensive data addressing the element composition of phagotrophic flag-
ellates are those of GOLDMAN et al. (1987) and NAKANO (1994). GOLDMAN et al. (1987)
fed the flagellate Paraphysomonas imperforata two species of algae (Phaeodactylumtricornutum and Dunaliella tertiolecta) of varying C : N: P stoichiometry. NAKANO
(1984) fed an unidentified heterotrophic flagellate (thought to be Paraphysomonas or
Spumella) four types of bacteria with varying C : N: P stoichiometry.We have used these data to develop stoichiometric homeostasis plots for various
nutrient ratios for phagotrophic flagellates and their prey (Fig. 1), which suggest that
phagotrophic flagellates may not be strictly homeostatic. C : N ratios in phagotrophicflagellates, like that of bacteria (CHRZANOWSKI & KYLE 1996), seem to be less varia-
ble than N : P or C : P ratios. The phagotrophic flagellate C : N ratio (panel A) also ap-
pears to be more highly correlated with prey element stoichiometry than does either
phagotrophic flagellate N: P (panel B) or C : P (panel C) suggesting greater flexibilityin regulation of P accumulation. Flexibility in P accumulation is consistent with mod-
els suggesting that P content (or Q, see below) must increase as a function of growthrate (ELSER et al. 1996). Interestingly, the slopes of these relationships are similar in
magnitude to those found for a wood-decaying fungus (STERNER & ELSER 2002), sug-gesting a similar degree of weak homeostasis in another group of heterotrophic euka-
ryotic microbes.
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470 James P. Grover and Thomas H. Chrzanowski
A.10
8
6Z 5
U 4
2-~ 3Q) AOJ ,Aroi.: 2
Y = 2.26 XO.47
12 3 4 5 6 7 8 9 10 20
Prey C:N ,B.
50 .40
A30 A
a- A A
Z 20Q)
~ .."Q5OJroi.: 10 " .
8 ". Y=3.31 XO.587 .6 .5
7 8 910 20 30 40 50 60
Prey N:P
C.300
.. .200 .
a-U 100 .Q)~ 80 . ."Q5OJ 60 .~ 50 .
40 A
30 . Y=15.4XO.37
2030 40 50 60 7060 100 300 400 500
Prey C:P
Fig. I. Stoichiometric homeostasis plots for phagotrophic flagellates fed prey items ofvarying element stoichiometry. Dotted line is the 1: 1 line. Circles - data from GOLD-
MAN et al. (1987); triangles - data from NAKANO (1994). All regression lines are statis-
tically significant, P <0.01.
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Stoichiometry of phagotrophic flagellates 471
Theoretical models of flagellate growth and nutrient composition
GROVER (2003, 2004) represented the population growth rate (,u) of phagotrophic flag-ellates in relation to nutrient element composition with the equation
,u=,u~[I-'"t"{~}) forj=C,N,P .. (I).
Here, Qj are the cell quotas of nutrient elements (C, N, or P), i. e. the nutrient mass percell (see Table I for notation). The parameter Qjin is the minimal quota for nutrientj,at which the growth rate goes to zero. The parameter J.Lmax is the apparent maximalgrowth rate that would occur if quotas of all nutrients were infinite. Realized maximalgrowth rates are lower, due to physiological limitations described below. According toequation (I), the growth rate is limited by the nutrient whose quota is lowest inuelationto its minimal value. If quotas of any two elements are sufficiently high, then thegrowth rate is an increasing and saturating function of the third element's quota. Sinceits introduction by DROOP (1974), equation (I) has been widely used to model algalgrowth, and it has also been applied to bacterial growth (THINGSTAD 1987).
Equation (I) for growth rate presumes complementary equations governing quotadynamics. Phagotrophic t:Iagellates acquire nutrients through ingestion of bacterialprey. Let the ingestion rate (prey cells ingested per unit time) be denoted t(X), where Xis prey density. Then the nutrient flux made available through ingestion is the productof the ingestion rate and the quota of nutrient j in prey cells, qj- Typically, only a frac-tion of this ingested nutrient flux is assimilated, while the remainder is released at arate Rj- An additional nutrient flux is related to population growth: the partitioning ofquota into new cells produced at a rate,u decreases quota at the instantaneous rate ,uQj-These assumptions lead to the differential equations
dQ.--L =t(X)q. - ,uQ -R. (2).dt ) ) )
GROVER (2003, 2004) used a simple linear function of prey density for the ingestionrate:
t(X)=aX (3),
where a is the attack rate, and also the clearance rate, representing the volume of watercleared of food by ingestion per unit time.
In previous work, the nutrient release rate followed the expression
[ ( QID8X -Q. )~Rj =t(X)qj l-Ej Q~-=~; ~ (4),
where ~ is the physiological upper limit to cell quota and Ej is the dimensionless,maximal assimilation efficiency of nutrientj. Equation (4) for nutrient release is equi-valent to assuming that the net assimilation rate (Ap is
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472 James P. Grover and Thomas H. Chrzanowski
( Q~-Q )A =tX £ J jj ()qj j Q~ -Q;in (5),
which shows that assimilation efficiency is maximal when quota approaches its mini-mal value, and is reduced to zero as quota approaches its maximal value. Equation (4)
Table 1. Notation, dimensions and parameter values.
Symbol Definition Units Value
VariablesJl Population growth rate d-1Qc Cell quota for carbon fmol C cell-1QN Cell quota for nitrogen fmol N cell-1Qp Cell quota for phosphorus fmol P cell-1 ,Flagellate Parameters~max Maximal growth rate occurring if cell .. d-1 3.2
quotas are infiniteQ'l!in Minimal cell quota for carbon fmol C cell-1 148~n Minimal cell quota for nitrogen fmol N cell-1 51QFin Minimal cell quota for phosphorus fmolPcell-1 1.6Q~ax Maximal cell quota for carbon fmol C cell-1 108Q!:i'ax Maximal cell quota for nitrogen fmol N cell-1 231QWax Maximal cell quota for phosphorus fmol P cell-1 9.1EC Maximal assimilation efficiency for carbon none 0.65EN Maximal assimilation efficiency for nitrogen none IEp Maximal assimilation efficiency for phosphorus none IPc Fixed release rate for carbon, representing fmol C cell-1 d-1 80
maintenance respirationPN Fixed release rate for nitrogen fmol N cell-1 d-1 0pp Fixed release rate for phosphorus fmol P cell-1 d-1 0a Attack rate rnlcell-Id-1 8.1 X 10-5or Handling time d 0.00125Xo Threshold prey density at which flexible cells rnl-1 1 x 107
preferences occurPrey ParametersX Prey density cells rnl-1 0-1 x 108qc Prey cell quota for carbon fmolCcell-1 1.06-2.12qN Prey cell quota for nitrogen fmol N cell-1 0.16-0.32qp Prey cell quota for phosphorus fmol P cell-1 0.01-0.06Other symbolsj Index for nutrients C, N or Pk Index for a non-limiting nutrientI Index for a limiting nutrientn Index for non-preferred prey type in a mixturep Index for a preferred prey type in a mixtureRj Release rate of nutrientj fmol celI-1 d-1Aj Assimilation rate ofnutrientj fmol cell-I d-1
/"
I Stoichiometry of PhagotroP~;C flagellates 473
I predicts that nutrient releas~ rates ~o to z~ro when prey ~e~sity, and hence ingestionrate, approach zero. For the morganIc nutrients N and P thIS IS perhaps reasonable, butfor C the release rate specified by equation (4) includes respiration. Thus maintenancerespiration that occurs during starvation is neglected.
In this paper, the previous model (GROVER 2003, 2004) is extended by includingmore realistic assumptions of saturating ingestion and maintenance respiration. Satur-ating ingestion is described by the function
aXI(X) = (6),
l+arX
where T is the handling time per prey cell and a is the attack rate. This latter rate alsorepresents the maximal clearance rate exhibited under low prey density. Equation (6)corresponds to an ingestion function with a maximal ingestion rate of lmax, = T-I,reached asymptotically at high prey density, and half-saturation prey density of K, =lmax/a. Incorporating maintenance respiration, or other losses under starvation condi-tions, is accomplished by including a constant release rate Pj into equation (4):
[ ( Qmax -Q. 11Rj =1(X)qj l~Ej Q~-=~; )J+Pj (7).
Additional extensions of previous work permit a preliminary exploration of preymixtures, which could represent nutritionally different bacterial species or strains.These are applied only with the most realistic assumptions detailed above, entailingsaturating ingestion rates and maintenance respiration. Only mixtures of two prey ty-pes are considered here, with ingestion rates following an extension of equation (6):
a.X.I(Xj) = J J (8),
1+a1T1X1 +a2"r2X2
where subscript i indicates prey type 1 or 2. Equation (1) is unchanged for prey mixtu-res, but the first term equation (2) must be replaced by "the flux of nutrientj obtainedfrom ingesting both prey types: I(XJqlj + I(X2)q2j- Preferences for ingesting differentprey types could follow many scenarios, but two are examined here: fixed preferencesquantified as differences in attack rate constants ah and flexible preferences exhibitedonly when total prey density is high (BOENIGK et al. 2002). For the latter, the attackrate on the less-preferred prey type was a decreasing function of total prey densityabove a threshold, but equal to the attack rate on the preferred prey type below thethreshold. A simple function with these properties is
- . { Xo }an -mm ap,ap (9),
X1+X2
where subscripts n and p indicate less preferred and preferred prey types, respectively,and Xo is the threshold prey density at which ingestion becomes selective.
[ ';~£~
."'~~
474 James P. Grover and Thomas H. Chrzanowski,,, u..,"~~.. ~ . .._~-
Numerical analysesThese theories are explored to develop numerical predictions of flagellate growth ratesand nutrient composition in relation to prey density and food quality as nutrient com-position. The relationship between growth rate and prey density is commonly studiedin laboratory cultures (e. g. FENCHEL 1982). Although nutrient composition of flagella-tes is technically more difficult to study, predictions are presented for comparison to
the few data available (Fig. 1).The model with linear ingestion and no maintenance respiration was previously pa-
rameterized (GRovER 2003) based on a number of laboratory studies of the flagellategenus Paraphysomonas (CARON et al. 1985, 1986, GOLDMAN & CARON 1985, GOLD-MAN et al. 1985, 1987, ANDERSEN et al. 1986, NAKANO 1994, EcCLESTON-PARRY &
LEADBEATER 1995). The same parameters are adopted here. For Paraphysomonaspreying on bacteria, GoLDMAN & DENNETT (1992) found a maximal ingestton rate ofabout 800 prey cells d-1, implying a handling time of 0.00125 d. Respiration rates of
starving flagellates are typically about 2-4 % of,respiration rates during exponentialgrowth (FENCHEL 1982). CARON et al. (1986) observed respiration rates of about2000 fmol C cell-l d-1 for exponentially-growing Paraphysomonas, so a value Pc =
80 fmol C cell-l d-1 is adopted here. Release of N and P under starvation is assumednot to occur, so PN = pp = O. The ranges of prey quotas (~) considered here representbacteria that vary two-fold in C and N content (THINGSTAD 1987), but six-fold in
P-content (VADSTEIN 2000).Three versions of models parameterized with values from Table 1 were examined
for a single type of prey: (I) the original model with linear ingestion and no mainte-nance respiration (GROVER 2003); (II) a model with saturating ingestion but no mainte-nance respiration; and (III) a model with both saturating ingestion and maintenance re-spiration. For each version, steady state flagellate quotas for C, N and P are calculatedacross a range of prey densities X and nutrient contents qj' from setting equations (2) tozero. Only one nutrient (denoted l) limits growth rate and its steady state quota is
Q* - t(X)E,q,Q,max + (,u~Qlmin - PI ) (Q,max _Q,min), - . " ( max min) (10). t(X)E,q,+,umax Q, -Q,
This equation must be evaluated for all three nutrients, and the one producing thelowest growth rate according to equation (1) is identified as the limiting nutrient. Thesteady state quotas of the other, non-limiting nutrients (denoted k) then depend on the
growth rate calculated from the limiting nutrient, according to
Note that in equations (10) and (11), the terms PI and Pk are zero, except for the case of
carbon (Pc) in model III with maintenance respiration.For each of the three models, steady state growth rates in relation to density X of a
single prey type were calculated from zero to 1 x 108 cells ml-cl, for all combinations of
Stoichiometry of phagotrophic flagellates 475
the highest and lowest nutrient quotas considered for bacterial prey in Table 1. Only se-lected examples are presented below to illustrate the effects of food quality (as nutrientcomposition) on growth rate. To explore food quality further, stoichiometric plots fol-lowing Fig. 1 were constructed with varying nutrient composition of prey. Bacterial Cquota qc was set to 1.6fmol C cell-I, and N quota was increased over the range indi-cated in Table 1, while P quota was decreased. Steady state nutrient composition offlagellates was then calculated according to equations (10) and (11) at a low prey den-sity of 3 x 106 cells ml-l, and a high prey density of 1 x 108 cells mi-i. The higher preydensity saturates growth under all conditions examined, while the lower prey densitysupports positive growth under all conditions examined. Model III with maintenancerespiration predicts negative growth rates at very low prey densities, under which con-ditions equation (11) can predict negative cell quotas, and such computations areavoided here.
For prey mixtures, only model III with both saturating ingestion and maintenancerespiration was considered. For simplicity, handling times for both prey types in equa-tion (8) were set equal to the value used for single prey scenarios. There is only scantjustification for assuming equal handling times of prey types. SHANNON (2006) foundthat digestion kinetics were invariant for a strain of Ochromonas fed prey of differingnutrient element composition, suggesting that some of the processes related to handl-ing time might also be inv~ant for different prey types (but see BOENIGK et al. 2001 a,b). For the fixed preference scenario, the attack rate on the less preferred prey type wasset to 4.0 x 105 m1 flagellate-I d-l, about half the attack rate on the preferred prey type(8.1 x 105 m1 flagellate-I d-I). For the flexible preference scenario, the attack rate onthe preferred prey type was again set to this value, and the preference threshold Xo wasset to 1 x 107 cells ml-l, roughly the prey density above which BOENIGK et al. (2002)observed selective ingestion in three flagellate species. Several combinations of prefer-ences and nutrient contents for various mixtures of prey types were examined numeri-cally, and only some selected results are presented to illustrate potential effects of preymixtures on flagellate growth rates and nutrient composition.
Results
Growth on a single prey type
Although the simplest model examined here assumes that ingestion rate is alinear function of prey density, growth rate is a saturating function for thismodel (Fig. 2 A). The saturated growth rate is always less than the parameterlJmax and the half-saturating prey density depends on both prey nutrient contentand the parameters describing flagellate physiology. The identity of the nutri-ent that limits growth depends primarily on prey nutrient content, rather thanprey density. In one of the cases illustrated, with prey nutrient quotas at thelowest values in Table 1, N limits flagellate growth at all prey densities, whileC limits in the other cases shown.
Fig. 2. Growth rate in relation prey density, for parameterized models of flagellatesgrowing on bacteria of differing nutrient content: solid line - bacterial quotas of allnutrients set to low values of ranges in Table 1; dashed line - bacterial quotas of allnutrients set to high values of ranges in Table 1; dotted line - bacterial quota for C set
to low value and quotas for N and P set to high values of these ranges. A. Model I withlinear ingestion and no maintenance respiration. B. Model II with saturating ingestionand no maintenance respiration; C. Model III with saturating ingestion and mainte-nance respiration.
Fig. 3. Stoichiometric homeostasis plots for phagotrophic flagellates fed prey of vary-ing element stoichiometry predicted from parameterized models. Dotted line is the I : Iline. Solid line - low food density; dashed line - high food density. A-C. Model Iwith linear ingestion and no maintenance respiration. D-F. Modelll with saturatingingestion and no maintenance respiration. G-I. Model III with saturating ingestionand maintenance respiration.
~_. ~
:-~ ,478 James P. Grover and Thomas H. Chrzanowski !
When saturating ingestion is incorporated in model II, growth rate is againa saturating function of prey density (Fig. 2B). The saturated growth rate is re-duced compared to model I, because saturating ingestion constrains the nutri-ent fluxes made available for growth. The saturated growth rate also stronglydepends on prey nutrient content. The half-saturating prey density for inges-tion is 9.9 x 106 cells ml-l, but the half-saturating prey density for growthranges about 30-50 % of this value, depending on prey nutrient content. Theidentity of the nutrient that limits growth depends primarily on prey nutrientcontent, rather than prey density. In one of the cases illustrated, with prey Cquotas at the lowest value in Table I and prey N and P quotas at the highestvalues, C limits flagellate growth at all prey densities, while N limits in theother cases shown.
When both saturating ingestion and maintenance respiration are irlcorpo-rated in model III, growth rate is a saturating function of prey density with athreshold required for positive growth (Fig. 2 C). These thresholds range fromabout 8 x 105 cells ml-1 for prey with high C content to 2 x 106 cells ml-1 forprey with low C content. Saturated growth rates are not changed much by add-ing maintenance respiration to the model, and such respiration has a muchstronger effect on growth at low prey density. The half-saturating prey densityfor growth ranges about 30-70 % of the density that is half-saturating for in-gestion, depending on prey nutrient content. Growth is always limited by C atlow prey density, due to the C requirement for maintenance respiration. Forprey with high C content, the nutrient that limits growth switches from C to Nas prey density increases, usually at a prey density supporting growth at 50-70 % of the saturated rate.
The models examined here usually predict that flagellate nutrient contentdisplays weak homeostasis (Fig. 3), qualitatively similar to observations(Fig. 1). That is, the slopes of stoichiometric plots are similar for predictions(Fig. 3) and observations (Fig. 1). For model I, homeostasis is more closely ap-proached at high prey density than at low prey density (Figs 3 A-C). Whensaturating ingestion is incorporated in model II, the approach to homeostasis athigh prey density disappears, and flagellate nutrient composition respondsstrongly to prey composition at all prey densities (Figs 3 D-F). When bothsaturating ingestion and maintenance respiration are incorporated in model III,weak homeostasis at all prey densities is preserved (Figs 3 G-I). However,low prey density strongly reduces the relative amount of C in flagellates, due
: - to the C requirements of maintenance respiration.!
Growth on prey mixtures
When flagellates feed on a mixture of two prey types with fixed preferences,growth rate is predicted to be a saturating function of total prey density with a
Fig. 4. Growth rate in relation prey density, for parameterized models of flagellatesgrowing on mixtures of two prey types, one with high N and P and low C content, andthe other with low Nand P and high C content. Upper dotted line - growth on high NPprey alone; lower dotted line - growth on low NP prey alone; dashed line - growth ona mixture of two prey types with non-preferential feeding; solid line - growth on amixture of two prey types with preferential feeding on the high NP prey. A. Fixedfeeding preferences, mixtures with 30 % prey of the high NP type. B. Flexible feedingpreferences, mixtures with 20 % prey of the high NP type.
threshold for growth (Fig. 4 A). The exact relationship depends on prey nutri-ent contents, flagellate preferences, and the proportion of each prey type in themixture. For purposes of illustration, one prey type is assigned the lowest C
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~ James P. Grover and Thomas H. Chrzanowski-
quota from the range in Table 1, and the highest quotas for Nand P, while theother type is assigned the higher C quota and the lowest quotas for N and P.Thus one prey type is rich in the inorganic nutrients N and P relative to or-
ganic C, while the other has opposite characteristics.The upper dotted line in Fig. 4 A shows growth in relation to prey deQsity
when the flagellate feeds on only the high NP prey, and the lower dotted lineshows growth when feeding only on the low NP prey. The solid line showsgrowth when feeding on a mixture with 30 % prey of the high NP type, as-sumed to be the preferred type (with a higher attack rate parameter in equation8). For comparison, the dashed line in Fig. 4 A shows growth for the samemixture, but with no feeding preferences and both prey types assigned thesame, high value for the attack rate. Thus, preference is modeled as a reducedrate of ingestion for the high C, low NP prey type. This preference is costly atlow prey densities for which C limits flagellate growth, but is beneficial at
high prey density, permitting more rapid growth than would non-preferentialfeeding. For mixtures with other proportions of prey types (not shown), prefer-ential feeding on the low C, high NP prey type is always beneficial at suffi-ciently high prey densities, but costly at lower prey densities. Preferentialfeeding on the high C, low NP prey type is never predicted to be beneficial
compared to non-preferential feeding.The costs of preferential feeding on prey with low C content, but high NPcontent at low prey densities are ameliorated to some extent when feedingpreferences are flexible, rather than fixed (Fig. 4 B). At the lowest prey densi-ties, feeding is non-preferential, and the predicted growth rate with feedingpreferences (solid line in Fig.4B) is identical to that for non-preferential feed-ing (dashed line in Fig. 4 B). For intermediate prey densities, preferential feed-ing on the high NP prey type is costly, reducing growth below that achievedfrom non-preferential feeding. For sufficiently high prey densities, preferentialfeeding on the high NP prey type is beneficial, elevating growth above thatachieved from non-preferential feeding. These results are illustrated in Fig.4Bfor a mixture with 20 % prey of the high NP type, but are qualitatively similarfor various other mixtures fed upon with flexible preferences. For all mixturesexamined, flexible, preferential feeding on the high C, low NP prey type is
never beneficial compared to non-preferential feeding.Preferential feeding on mixtures of prey types with different nutrient com-
position could have complex effects on flagellate nutrient composition(Fig. 5). With fixed preferences (Figs 5 A-C), stoichiometric plots for C: Nand C : P ratios display weak homeostasis, in agreement with results for asingle prey type. However, something close to homeostasis is predicted for theflagellate N : P ratio under the conditions examined: mixtures with 0-100 %prey of the low C, high NP type, at two total prey densities (3 x 106 and 1 x108 cells ml-!). Flexible preferences produce similar results at the low total
Fig. 5. Stoichiometric homeostasis plots for phagotrophic flagellates feeding on mixtu-
res of two prey types, one with high N and P and low C content, and the other with
low N and P and high C content. Average prey stoichiometry is shown on the horizon-
tal axes, based on the proportion of two types in the mixture, varying from 0-100 %.
Dotted line is the 1: 1 line, Solid line - low food density; dashed line - high food den-sity, A-C. Fixed preference for the prey type with high NP content is assumed. D-F.
A flexible preference for the prey type with high NP content is assumed.
prey density (Fig. 5 D-F), but at high total prey density, flagellates are pre-, dicted to be close to homeostatic for C: Nand C: P.
1:~
~ James P. Grover and Thomas H. Chrzanowski-
Discussion
Based on admittedly limited data (Fig. 1), we have proposed that the nutrientcomposition of phagotrophic flagellates is weakly, but not strictly homeosta-tic. The theory presented here predicts weak homeostasis and permits exp~ora-tion of its implications. Even if departures from strict homeostasis are rela-tively weak, compared to autotrophs for example, there are two reasons to ex-plore their implications. Departures from homeostasis influence the competi-tive fitness of consumers, and they influence the biogeochemical impacts of
consumer-resource interactions.The fitness implications of weak homeostasis are related to the decoupling
that causes the growth rate to saturate at a lower prey density than the inges-tion rate. DROOP'S equation (1) implies that as a consumer's growth rate be-comes nutrient limited and is reduced from m~imal, the quota for the limitingnutrient falls from the high level required for maximal growth. This in turn re-duces the nutrient flux required for growth, while maintaining growth rate ashigh as possible, ultimately reducing the ingestion rate and prey density re-quired to meet demands for growth. This permits the consumer to achieve alower "R *" (sensu TILMAN 1982, pp. 43 -45) in terms of prey density. Otherthings being equal, the species with weaker homeostasis would thus have bet-
ter competitive fitness in a constant environment.It seems likely that weak homeostasis could also contribute to competitive
fitness in non-constant environments. When DROOP'S equation is applied to
the theory of competition among algae for dissolved nutrients, increasing Qrnax
and thus weakening homeostasis permits nutrient storage that is competitivelyadvantageous when nutrient supply varies and long periods of starvation occur
(GRovER 1991). Therefore, in addition to proposing that phagotrophic flagella-tes display weak homeostasis in nutrient composition, we also propose that
they are under selective pressure against strict homeostasis.Weak homeostasis also affects the biogeochemical implications of consum-
er-resource interactions, which can be partly understood from plots such asthose in Fig. 1. The intersection of the regression line with the 1: 1 line esti-mates a resource stoichiometry that is "optimal" in that it matches consumerstoichiometry. Under such conditions the need for consumers to dispose of ex-cess nutrients by excreting or otherwise releasing them is minimized. Owingto less than perfect assimilation of resources, consumers will likely still re-lease nutrients in a ratio matching that of the resources. If the resource popula-tion relies on these released nutrients, as the bacterial and algal prey of flagel-lates often do, then stoichiometric matching of consumer and resource trophiclevels implies an ecosystem "optimality", wherein trophic efficiency and nu-trient retention are maximized. If resource stoichiometry does not match con-sumer stoichiometry, then the strength of homeostasis - related to the slopes
-
Stoichiometry of phagotrophic flagellates 483
of the regression lines in Fig. 1 - determines how much excess nutrient is re-
leased by consumers. As the slope of such a line reduces to zero, strict ho-meostasis is approached and the release of excess nutrients is maximized. Re-leased nutrients are often dissolved and at risk of transport from the ecosys-tem. Rotating the regression lines in Fig. 1 counter-clockwise weakens ho-meostasis, and implies that consumers retain a greater proportion of excess nu-trients, potentially holding them within the ecosystem.
Despite qualitative agreement, the elevations of the observed stoichiomet-ric plots (Fig. 1) differ consistently from the predictions developed here(Figs 3 and 5). The mathematical models portray flagellates with higher Ncontents than the observations, despite assigning parameters for the genus Pa-raphysomonas using data from some of the same studies. In part, this discre-pancy might arise from simulating bacterial prey in the models, while,the ex-perimental observations involved a broader range of prey including small al-gae. The discrepancy could also arise from oilier simplifications made in con-structing the models. With the assigned parameters, these models predict thatflagellate growth is usually C- or N-limited under the conditions explored, andrarely P-limited. If flagellates were parameterized with relatively lowerN con-tents and higher P contents, then P-limitation would be more often predicted.As yet, too little is known about the nutrient requirements for growth of heter-otrophic flagellates to determine their relative susceptibility to limitation bydifferent nutrient elements. The necessary information on the nutrient elementcomposition of flagellates is difficult to obtain, as it requires careful separationfrom nutrient composition of their prey.
The most realistic parameterized model analyzed here included a saturatingingestion rate and maintenance respiration under starvation conditions. Thislatter property predicts that a threshold prey density is required for positivepopulation growth. Although this is a realistic prediction (ROTHHAUPT 1996),we caution against applying our model to very low or negative growth rates.Modifications are needed to describe nutrient composition at negative growthrates, for which equation (11) can present negative solutions. Moreover, canni-balism or transformation to resting cysts or other special cell types occurswhen some species are forced to low growth rates (FENCHEL 1982, 1986). Norhas this body of theory been explored much under non-steady state conditions(but see GROVER 2003, 2004). Coupling between ingestion and growth ratescould be especially weak under such conditions, leading to large variations incell composition.
Much more work is also needed to address feeding on mixtures of preyspecies and selective ingestion. There are long-standing observations of size-selective feeding flagellates (CHRZANOWSKI & SIMEK 1990, GONZALEZ et al.1990), and more recent observations of selectivity based on nutrient composi-tion (JOHN & DAVIDSON 2001). Here, only a few of the conceivable patterns of
~
484 James P. Grover and Thomas H. Chrzanowski
selectivity were examined. The results suggest that flagellates might someti-
mes exhibit a closer approach to homeostatic composition by selectively feed-ing on prey of different nutrient composition. This is but one issue to explorein future theoretical and experimental work.
If it is true that phagotrophic flagellates often display weak homeostasis asproposed here, it is possible that they could be useful model organisms for stu-
dying the implications of weak homeostasis in consumer-resource interactions,much as the cladoceran Daphnia has become a model for studying the im-plications of strict homeostasis. WINFRIED LAMPERT contributed much to thestudy of Daphnia biology, for example by developing continuous flow sys-tems permitting steady state growth studies (LAMPERT 1975, 1976). Many ofthe references cited in this paper are written by people affiliated in some waywith WIN FRIED LAMPERT. We do not think this is a biased selection of the rele-vant literature, but rather a genuine outcome of his contributions to aquaticsciences. .,
References
ANDERSEN, O. K., GOLDMAN, J. C., CARON, D. A. & DENNETT, M. R. (1986): Nutrientcycling in a microflagellate food chain: III. Phosphorus dynamics. - Mar. Eco1.
Prog. Ser. 31: 47-55.ANDERSEN, T. (1997): Pelagic Nutrient Cycles: Herbivores as Sources and Sinks. -
Springer, Berlin, pp.1-280.ANDERSEN, T. & HESSEN, D. O. (1991): Carbon, nitrogen, and phosphorus content of
BOENIGK, J., MATZ, C., JURGENS, K. & ARNDT, H. (2001 a): The influence of pre cul-lure conditions and food quality on the ingestion and digestion process of threespecies of heterotrophic nanoflagellates. - Microb. Ecol. 42: 168 -176.
- - - - (2001 b): Confusing selective feeding with differential digestion in bacte-rivorous nanoflagellates. - J. Eukaryot. Microbiol. 48: 425 -432.
CARON, D. A., GOLDMAN, J.C., ANDERSEN, O. K. & DENNETT, M. R. (1985): Nutrientcycling in a microflagellate food chain. II. Population dynamics and carbon cy-cling. - Mar. £Col. Prog. Ser. 24: 243-254.
CARON, D. A., GOLDMAN, J. C. & DENNETT, M. R. (1986): Effect of temperature ongrowth, respiration, and nutrient regeneration by an omnivorous microflagellate. -
Appl. Env. Microbiol. 52: 1340-1347.
CHRZANOWSKI, T. H. & KYLE, M. (1996): Ratios of carbon, nitrogen, and phosphorusin Pseudomonas fluorescens as a model for bacterial element ratios and nutrientregeneration. -Aquat. Microb. Ecol.l0: 115-122.
CHRZANOWSKI, T. H. & SIMEK, K. (1990): Prey size selection by freshwater flagellatedprotozoa. - Limnol. Oceanogr. 35: 1429-1436.
Stoichiometry of phagotrophic flagellates 485
DEMoTT, W. R., GULATI, R. D. & SIEWERTSEN, K. (1998): Effects of phosphorus-deficient diets on the carbon and phosphorus of Daphnia magna. - Limno1. Ocea-
nogr. 43: 1147-1161.DROOP, M. R. (1974): The nutrient status of algal cells in continuous culture. - J. Mar.
BioI. Assoc. UK 54: 825-855.EcCLESTON-PARRY, J. D. & LEADBEATER, B. S. C. (1995): Regeneration of phosphorus
and nitrogen by four species of heterotrophic nanoflage11ates feeding on three nu-tritional states of a single bacterial strain. - App1. Env. Microbio1. 61: 1033 -1038.
ELSER, J. J., DOBBERFUHL, D. R., MACKAY, N. A. & SCHAMPEL, J. H. (1996): Orga-nism size, life history, and N:P stoichiometry. - BioScience 46: 674-684.
ELSER, J. J. & URABE, J. (1999): The stoichiometry of consumer-driven nutrient recy-cling: theory, observations, and consequences. - Ecology 80: 735-751.
FENCHEL, T. (1982): Ecology of heterotrophic microflage1lates. II. Bioenergetics andgrowth. - Mar. Eco1. Prog. Ser. 8: 225-231.
- (1986): The ecology of heterotrophic microflage11ates. - Adv. Microb. &01. 9:
57-97.GOLDMAN, J. C. & CARON, D. A. (1985): Experimental studies on an omnivorous
microflagellate: implications for grazing and nutrient regeneration in the marinemicrobial food chain. - Deep-Sea Res. 32: 899-915.
GOLDMAN, J. C., CARON, D. A., ANDERSEN, O. K. & DENNETT, M. R. (1985): Nutrientcycling in a microflagellate food chain: I. Nitrogen dynamics. - Mar. Ecol. Prog.
Ser. 24: 231-242.GOLDMAN, J. C., CARON, D. A. & DENNETT, M. R. (1987): Nutrient cycling in a
microflagellate food chain: IV. Phytoplankton - microflagellate interactions. -
Mar. Ecol. Prog. Ser. 38: 75-87.GOLDMAN, J. C. & DENNETT, M. R. (1992): Phagotrophy and N~ + regeneration in a
three-member microbial food loop. - J. Plankton Res. 14: 649-663.GONZALEZ, J. M., SHERR, E. B. & SHERR, B. F. (1990): Size-selective grazing on bac-
teria by natural assemblages of estuarine flagellates and ciliates. - Appl. Env.
Microbiol. 56: 583-589.GROVER, J. P. (1991): Resource competition in a variable environment: phytoplankton
growing according to the variable-internal-stores model.. - Amer. Nat. 138: 811-
835.- (2002): Stoichiometry, herbivory and competition for nutrients: Simple models
based on planktonic ecosystems. - J. Theor. Bioi. 214: 599-618.- (2003): The impact of variable stoichiometry on predator-prey interactions: A
multinutrient approach. -Amer. Nat. 162: 29-43.- (2004): Predation, competition and nutrient recycling: a stoichiometric approach
with multiple nutrients. - J. Theor. Bioi. 229: 31-:43.HALL, S. R. (2004): Stoichiometrically explicit competition between grazers: Species
replacement, coexistence, and priority effects along resource supply gradients. -
Amer. Nat. 164: 157-172.HESSEN, D. O. (1990): Carbon, nitrogen, and phosphorus in Daphnia at varying food
conditions. - J. Plankton Res. 12: 1239-1249.HESSEN, D. O. & BJERKING, B. (1997): A model approach to planktonic stoichiometry
and consumer-resource stability. - Freshwat. Bioi. 38: 447-471.
486 James P. Grover and Thomas H. Chrzanowski
JOHN, E. H. & DAVIDSON, K. (2001): Prey selectivity and the influence of prey car-bon:nitrogen ratio an microflagellate grazing. - J. Exp. Mar. Bioi. Ecol. 260: 92-
III.
KESSLER, K. & LAMPERT, W. (2004): Fitness optimization of Daphnia in a trade-offbetween food and temperature. - Oecologia 140: 381-387.
LAMPERT, W. (1975): A laboratory system for the cultivation of large numb~rs ofDaphniae under controlled conditions. - Arch. Hydrobiol. Suppl. 48: 138-140.
- (1976): A directly-coupled, artificial two-step food chain for long-term experi-
ments with filter-feeders at constant food concentrations. - Mar. Bioi. 37: 349-355.
- (1977 a): Studies on the carbon balance of Daphnia pulex De Geer as related to en-
vironmental conditions. II. The dependence of carbon assimilation on animal size,temperature, food concentration and diet species. - Arch. Hydrobiol. Suppl. 48:
310-335. ,- (1977b): Studies on the carbon balance of Daphnia pulex De Geer as related to en-
vironmental conditions. II. Production and pro~uction efficiency. - Arch. Hydro-bioi. Suppl. 48: 336-360.
LEGRAND, C., JOHANSSON, N., JOHNSEN, G., BORSHEIM, K. Y. & GRANELI, E. (2001):Phagotrophy and toxicity variation in the mixotrophic Prymnesium patelliferum(Haptophyceae). - Lirnnol. Oceanogr. 46: 1208-1214.
LOLADZE, I., KUANG, Y., ELSER, J. J. & FAGAN, W. (2004): Coexistence of two pred-ators on one prey mediated by stoichiometry. - Theor. Populo Bioi. 65: 1-15.
MITCHELL, S. F., TRAINOR, F. R., RICH, P. H. & GOULDEN, C. E. (1992): Growth ofDaphnia magna in the laboratory in relation to the nutritional state of its food spe-cies, Chlamydomonas reinhardtii. - Lirnnol. Oceanogr. 14: 379-391.
NAKANO, S. (1994): Carbon:nitrogen:phosphorus ratios and nutrient regeneration of aheterotrophic flagellate fed on bacteria with different elemental ratios. - Arch. Hy-
drobiol. 129: 257-271.
ROTHHAUPT, K. O. (1996): Utilization of substitutable carbon and phosphorus sourcesby the mixotrophic chrysophyte Ochromonas sp. - Ecology 77: 706-715.
ROTHHAUPT, K. O. & LAMPERT, W. (1992): Growth-rate dependent feeding rates in
Daphnia pulicaria and Brachionus rubens: adaptation to intermediate time-scalevariations in food abundance. - J. Plankton Res. 14: 737-751.
SANDGREN, C. D. (1988): The ecology of chrysophyte flagellates: Their growth andperennation strategies as freshwater phytoplankton. - In: SANDGREN, C. D. (ed.):
Growth and Reproductive Strategies of Freshwater Phytoplankton. - CambridgeUniversity Press, Cambridge, pp.9-104.
SHANNON, S. P. (2006): Comparison of the ingestion and digestion rates of Ochromo-nas danica grazing on Pseudomonas fluorescens of varying food quality. - Ph. D.Dissertation, University of Texas at Arlington, Arlington, Texas, USA.
STERNER, R. W. (1990): The ratio of nitrogen to phosphorus resupplied by herbivores:Zooplankton and the algal competitive arena. -Amer. Nat. 136: 209-229.
- (1993): Daphnia growth on varying quality of Scenedesmus: mineral limitation ofzooplankton. - Ecology 74: 2351-2360.
STERNER, R. W. & ELSER, J. J. (2002): Ecological Stoichiometry. - Princeton Univer-
sity Press, Princeton, pp.1-439.
-
Stoichiometry of phagotrophic flagellates 487
STERNER, R. W., HAGEMEIER, D. D., SMITH, W. L. & SMITH, R. F. (1993): Phytoplank-ton nutrient limitation and food quality for Daphnia. - Lirnnol. Oceanogr. 38:
857-871.THINGSTAD, T. F. (1987): Utilization ofN, P, and organic C by heterotrophic bacteria. I.
Outline of a chemostat theory with a consistent concept of 'maintenance' metabo-lism. - Mar. Bcol. Prog. Ser. 35: 99-109.
TILMAN, D. (1982): Resource Competition and Community Structure. - Princeton Uni-
versity Press, Princeton, pp.1-296.TuRPIN, D. H. (1988): Physiological mechanisms in phytoplankton resource competi-
tion. - In: SANDGREN, C. D. (ed.): Growth and Reproductive Strategies of Fresh-" water Phytoplankton. - Cambridge University Press, Cambridge, pp. 316-368.
:;,] URABE, J., CLASEN, J. & STERNER, R. W. (1997): Phosphorus limitation of Daphnia'li growth: Is it real? - Lirnnol. Oceanogr. 42: 1436-1443.;~ VADSTEIN, O. (2000): Heterotrophic, planktonic bacteria and cycling of phosphorus:
Phosphorus requirements, competitive ability, and food web interactions..- Adv.Microb. Bcol. 16: 115-167.
Submitted: 12 January 2006; accepted: 8 April 2006.
