impacts of nutrient competition on microalgae biomass production

Impacts of nutrient competition on microalgaebiomass productionLauren H. White, David W. Martin, Khendl K. Witt and Frank Vogt*

Marine microalgae cells are key environmental players as they transform inorganic nutrients dissolved in oceans intobiomass. Most prominent among these inorganic compounds is bicarbonate, which originates in considerablequantities from atmospheric CO2, a potent greenhouse gas. Because microalgae cells act as a sink of anthropogenicCO2, understanding phytoplankton’s carbon sequestration is a crucial link between environmental chemistryand ecology.The impact of ambient chemical and physical parameters onto phytoplankton and their chemical compositionhave been investigated in some detail. However, species↔species interactions, namely their nutrient competi-tion, require in-depth investigations of the impact of competing species on the dynamics of biomass produc-tion as well as the amount of biomass produced. Experimental studies presented here have been based ontwo marine microalgae species, that is, Nannochloropsis oculata and Dunaliella parva. For investigating dy-namic aspects of biomass production, the species growth rates have been measured, under otherwise identicalconditions, in single-species cultures as well as in competition situations. Depending on the species and nutri-ent type the cells compete for, growth rates in species mixtures were found to change from 50% to 200% ofthe corresponding single-species cultures. Competition impacts regarding the maximum cell concentration in aculture were even more drastic as the cell production was reduced, in some cases, down to 11% of the corre-sponding single-cell culture’s growth rate. Furthermore, a slight but significant shift in cell size distributionstoward smaller cell sizes was found in competition situations. This study demonstrates that biomass produc-tion is also driven by the cells’ biological environment. Copyright © 2013 John Wiley & Sons, Ltd.

Keywords: modeling environmental shifts; microalgae growth dynamics; biomass production; nutrient competition

1. INTRODUCTION

Increasing industrialization strongly impacts the global environ-ment through the release of CO2 [1], a major greenhouse gas.This has become a serious environmental concern [2,3]. On theother hand, it has been estimated that about half of the globalprimary carbon production is based on CO2 sequestering byalgal photosynthesis [4–10]. Hence, phytoplankton counterbal-ance anthropogenic CO2 production, and therefore, they carrya considerable ecological importance. The amount and chemicalcomposition of the produced microalgal biomass have also beenlinked to the availability of inorganic nutrients such as carbon,nitrogen, phosphorus, iron, and sulfur [11–15]. Furthermore, ithas been observed that microalgae cultures develop biomassof different chemical composition when grown among otheralgae species [16]. This can possibly be credited to competitionfor common nutrients. Based on these latter findings, it has beenhypothesized for this study that the amount of producedphytoplankton biomass and the production kinetics are alsoinfluenced by nutrient competition among microalgae species.For an accurate assessment and prediction of microalgae-basedtransformation of CO2 and other inorganic compounds intobiomass, a more detailed understanding of these processes isessential. This is especially relevant as there are first indicationsthat the carbon storage capacities of the oceans are starting todiminish [17].

The objective of this project is to investigate the relevance ofmicroalgal nutrient competition for the amount and kinetics ofphytoplankton biomass production. This then expands the

understanding of phytoplankton’s role as sink of atmosphericCO2. The present study has two main goals: (i) determinewhether a species’ growth rate, that is, the kinetics of biomassproduction, is impacted by the presence of nutrient competitorsand (ii) determine whether the amount of produced biomass isimpacted by the presence of nutrient competitors. Because thetotal biomass is the product of the number of cells and their size,topic (ii) is divided into two aspects: (ii-a) number of cells perspecies and (ii-b) cell size distributions of each species. Excludedfrom this study are investigations determining the relationbetween nutrient concentrations and amounts of producedmicroalgal biomass as well as growth rates. While this is a relatedtopic, it is beyond the scope of this manuscript, which focuses oncompetition impacts.In the given application, three well-defined biological parame-

ters need to be determined, that is, a culture’s growth rate, max-imum cell concentration, and cell size. Because chemometricmodels must derive exactly these pre-determined characteristicsof a cell culture, empirical data models are not suitable althoughthey may be capable of describing unknown data sets. There-fore, goal of section 3 is to derive ab initio models, which then

* Correspondence to: F. Vogt, Department of Chemistry, University of Tennessee,552 Buehler Hall, Knoxville, TN 37996–1600, USA.E-mail: [email protected]

L. H. White, D. W. Martin, K. K. Witt, F. VogtDepartment of Chemistry, University of Tennessee, 552 Buehler Hall, Knoxville,TN, 37996-1600, USA

Special Issue Article

Received: 10 May 2013, Revised: 6 August 2013, Accepted: 12 August 2013, Published online in Wiley Online Library: 10 September 2013

(wileyonlinelibrary.com) DOI: 10.1002/cem.2534

J. Chemometrics 2014; 28: 448–461 Copyright © 2013 John Wiley & Sons, Ltd.

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facilitate a straightforward biological interpretation of differ-ences between single-species versus mixed-species culturesand thus impacts of nutrient competition.

2. EXPERIMENTAL

Two seawater microalgae species, that is, Dunaliella parva (cellsize ~10μm) and Nannochloropsis oculata (size ~2μm), suppliedby The Culture Collection of Algae at the University of Texas atAustin, have been selected for studying nutrient competition.Both species were cultured individually and in mixture under

series of different nutrient concentrations. These cultures’growth rates, number of produced cells, and their size distribu-tions can be measured either by means of flow cytometry orbased on image analyses (cp. top row of Figure 1) the authorshave developed in a recent project [14,15]. While bothexperimental techniques facilitate in situ contact free analysesof large numbers of cells with a minimum of sample handling/disturbance, imaging has been chosen as it requires less equip-ment and is thus more widely applicable.

Cell culturing has been performed in batch mode [18] individ-ually and in binary mixtures as outlined in [13,14]. Identicalconditions, both species were grown individually as well as in

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Figure 1. (top row) Microscope images of Nannochloropsis oculata (top left) and Dunaliella parva (top right) captured on day 10 of the culturing pro-cess under [HCO3

�] = 2071μM and [NO3�] = 549μM; (middle row) measured growth curves and their fits (1) – the steepness of the curves is determined

by the growth rate s, and the plateau the function approaches is ymax; (bottom left) size distribution of N. oculata, D. parva, and mixed-species cells;(bottom right) decomposition of the size histograms’ Poisson-shaped model function (3) into its M=20 contributors.

Impacts of nutrient competition on microalgae

J. Chemometrics 2014; 28: 448–461 Copyright © 2013 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/cem

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binary species mixtures. Competition impacts regarding growthrates, cell concentrations, and cell size distributions were thenassessed by comparing single and multispecies cultures grownunder identical nutrient conditions. The nutrient concentrationsthemselves were anticipated to be influential as well. Hence,six different carbon concentrations (1110, 2071, 3630, 5180,6720, and 8260μM) were provided to the cultures via sodiumbicarbonate dissolved into the culture media. Furthermore, fivenitrogen concentrations (350, 549, 873, 1280, and 1470μM) wereprovided via ammonium chloride and sodium nitrate, respec-tively; two different nitrogen sources were considered in thisstudy to test whether the pathway of nitrogen has an impact.To take the naturally occurring variability in biological materialsinto account, five replicate cultures were grown per nutrientcondition. In order to ensure high reproducibility among thereplicate cell cultures, all ambient parameters other thanintentionally varied nutrient concentrations were kept asconstant as experimentally feasible. Because microalgae needboth carbon and nitrogen, only one of these nutrients was variedwith the other set to “standard conditions” [18], that is, 2071μMbicarbonate and 549μM nitrate, respectively.

Growth curves were obtained via counting cells on a hemocy-tometer (Cole-Palmer, IL, USA) whose wells had a known volume.In preparation for these counts, 20μL of Lugol’s solution and200μL of algae culture were pipetted into a small, sterile glasstest tube. A 10-μL aliquot thereof was placed in the hemocytom-eter cavity followed by cell counting using a 10� microscopeobjective. Cell counts of five replicate flasks have been deter-mined. Furthermore, the counts were performed at the sametime of the day in order to minimize fluctuations introduced bydifferent growth times. Cell counting for binary species mixtureshas been performed via visual species discrimination, which wasfeasible for the chosen microalgae species (Figure 1, top row). Todetermine cell size distributions, microliter amounts of the samecell-containing mixture of culturing medium and Lugol’s solutionwere deposited onto a calcium fluoride (CaF2) microscope slide.Five images for each of the five replicate cultures were captured.

3. THEORY

Novel algorithms have been developed and applied to theanalyses of time series of microscope images (cp. Figure 1, toprow) to determine the growth dynamics (section 3.1), cellconcentration, and cell size distributions (section 3.2) with andwithout nutrient competitors present. All software required forthis study has been written in C and utilizes the GNU ScientificLibrary [19] as well as the NLopt library version 2.3 [20] forconstrained minimizing sum-of-squared-errors functions basedon an augmented Lagrange algorithm [21,22].

3.1. Growth dynamics

Studying the extent to which the dynamics of biomass pro-duction is related to nutrient availability and/or nutrientcompetition among species has been based on the cultures’time-dependent cell concentrations. So-called growth curves(1) represent the cell concentration y(t) at time t in a culturethat had been started by inoculating y0 cells per milliliter intothe culturing medium at t = t0; such growth curves are of sig-moidal shape. A culture’s growth dynamics is described by itsgrowth rate s, which is inversely proportional to the timespan τ within which the cell concentration doubles.

Furthermore, the maximum cell concentration that can besupported in a closed culture is indicated in equation (1) asymax. A derivation of the growth curve’s equation (1) is givenin the Appendix A.

y tð Þ ¼ ymax�1

1þ exp � ymaxymax�y0

�s� t � t0ð Þn o

� ymaxy0

� 1� � (1)

Figure 1 (middle row) depicts two microalgal growth curves y(t) with s and ymax being clearly species dependent. In order tomeasure s (along with ymax and y0), cell counts y(t) havebeen obtained on multiple days t to which equation (1)has been fitted. The following constraints have been builtinto nonlinear least squares: y0, ymax, s ≥ 0 and ymax ≥ y0.While ymax is not related to growth dynamics, it representsinformation needed to assess the amount of biomass pro-duced by a culture (section 3.2). Thus, fit parameters derivedfrom equation (1) are key for the aforementioned researchgoals (i) and (ii-a).From single-species cultures of N. oculata (N.o.) and D. parva

(D.p.), sN. o. (single) and sD. p. (single) have been determined for allnutrient situations listed in section 2. These growth rates werethen compared to their counterparts derived from binary-speciescultures, that is, sN. o. (mix) and sD. p. (mix). Comparing sN. o. (single)to sN. o. (mix) as well as sD. p. (single) to sD. p. (mix) as obtained fromotherwise identical culturing conditions reveals impacts ofnutrient competition onto phytoplankton growth dynamics.

3.2. Amounts of produced biomass

Investigating whether species competition for nutrients has animpact on the amount of produced biomass requires investigatingtwo aspects: Firstly, comparing (1) ymaxN. o. (single) to ymaxN. o. (mix) aswell as ymaxD. p. (single) to ymaxD. p. (mix) will indicate competitionimpacts on themaximum cell concentration a culture can produce.Secondly, it can be determined via cell size distributions howmuchbiomass each cell contributes. While ymax is derived along withthe cultures’ growth rates s, cell size distributions need to beestablished by a different method.Hence, goal (ii-b) of this project investigated whether cell size

distributions are impacted by nutrient competition. Acquiringdistributions of cell sizes,1 S, in single-species and binary-speciescultures has been realized by means of the image analysismethod presented in references [14,15]. These image analysesare based on fitting an upside-down 2D Gaussian to the shadoweach cell casts (dark dot in Figure 1, top row) in 3D representa-tions of light intensity (z-axis) across an x–y plane. From thewidths of such a 2D Gaussian, that is, σx and σy, the cells ellipticcross section can be calculated as π � σx � σy.Because of the biological nature of the cells and random

measurement errors, a distribution of cell sizes has to beexpected in a given culture as opposed to a single, well-definedcell size. After assigning a sufficiently large number of cells intothe discrete bins of a histogram, Poisson-shaped distributionshave been observed (Figure 1, bottom left). These distributions

1Note: A capital S denotes the size of a cell, whereas a lower case s denotes aculture’s growth rate.

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peaked at the species-dependent, average cell size Sλ, which iscomprised in the bin number λ.While a Poisson distribution p(k) describes the probability

for a certain cell to fall into the kth bin, λ and thus Sλ areunknown in this application. However, determining λ is ofcentral interest here as competition induced changes in thecell sizes are reflected in λ. Thus, λ is derived by fitting a“Poisson-shaped” function

S kð Þ ¼ A� λk

k!�exp �λf g (2)

to experimentally obtained cell size histograms. As opposedto “Poisson distribution”, the term “Poisson-shaped function”is used here to indicate that for fitting purposes, λ is handledas a continuous fit parameter rather than the integer binnumber. Furthermore, an additional fit parameter, A, hasbeen introduced in equation (2) to describe the specific max-imum height of a data set. Once λ has been derived, the truemean cell size Sλ can be deduced utilizing the number ofbins and the bin width.If M species are present in a culture, equation (2) needs to be

modified to reflect that a cell size distribution is the superposi-tion of M Poisson-shaped functions:

S kð Þ ¼ ∑M

m¼1Am� λ

km

k!�exp �λmf g (3)

Additionally, two experimental artifacts influence the sizedistributions. The first being the culturing medium from whichimages are captured has a certain thickness. Hence, as can beseen in the two pictures shown in Figure 1 (top), some cellsare out of focus and thus appear larger than they truly are.The other being the fact that the cells are of non-sphericalshape [14] and thus their orientation in the culturing mediumwith respect to the camera also widens their size distribution.These effects both add randomness and have been incorpo-rated into equation (3) by empirically choosing M= 20 for theresults shown later. Figure 1 (bottom right) depicts the decom-position of the corresponding N. oculata histogram (Figure 1,bottom left) into such Poisson-shaped functions. It was foundthat for the given data sets, most histograms fitted toequation (3) resulted in correlation coefficients of ≥0.99. Fit con-straints that can be implemented here are max{S(k)}≥Am≥ 0and #bins≥ λm≥ 0.When keeping nutrient sources and concentrations identi-

cal, competition impacts are manifested in deviations of thebinary-species size histogram SN. o. &D. p.(k) from a linearcombination of the two single-species histograms SN. o.(k)and SD. p.(k). Hence, testing whether the rank of a three-col-umn matrix containing SN. o., SD. p., and SN. o. &D. p. has ranktwo or three would demonstrate absence or presence ofcompetition impacts on the cell size distribution. However,this approach faces two challenges, that is, the difficulty toreliably discriminate between rank two and three and the in-capability to determine how the size distribution has shifted.Comparing the three sets of fit parameters (3) {AN. o.m=1,…,M, λN. o.m=1,…,M}, {AD.p.m, λD.p.m}, and {AN. o. &D.p.m, λN. o. &D.p.m} theoreticallycould derive insights about a shift’s nature. However, there isstrong tendency to be misled in that nonlinear least squarescannot guarantee finding the optimum solution and the fitparameters are inherently ambiguous. Furthermore, noise in

the histograms required a statistical assessment of shifts in sizedistributions. To overcome the aforementioned limitations andfacilitate the needed analyses, a linear least-squares fittingapproach solving (see equation (2))

SN:o: 1ð Þ SD:p: 1ð Þ⋮ ⋮

SN:o: Kð Þ SD:p: Kð Þ

0B@

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� �

¼SN:o:&D:p: 1ð Þ

⋮

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0B@

1CAþ δ K�1ð Þ

(4)

for the two weight factors, wN. o. and wD. p., has been chosen.Equation (4) expresses the mixed-species size distribution as acombination of the individual species size distributions. Thereconstructed mixed-species size distribution, that is,

SN:o: 1ð Þ SD:p: 1ð Þ⋮ ⋮

SN:o: Kð Þ SD:p: Kð Þ

0B@

1CA� wN:o:

wD:p:

� �, then describes how much of

the measured size distribution

SN:o:&D:p: 1ð Þ⋮

SN:o:&D:p: Kð Þ

0B@

1CAcan be explained

in terms of the single-species distributions. Any differences be-tween measured and reconstructed are then assigned to com-petition impacts. Implementing regression constraints,wN. o. ≥ 0 and wD. p. ≥ 0, prevents this multivariate least-squaresfit from determining an unreasonable linear combination. Fur-thermore, this approach has been effective, in part, becausethe mixed-species distributions are very similar to the single-species’ distributions.

As the measured histograms were determined from repli-cate cultures, error bars were available for each histogrambin.2 Performing bin-wise t-tests of the mean-measured his-tograms versus their reconstructed counterparts revealswhether these two histograms’ bins contain significantly dif-ferent counts. Based on such t-test results, the nature ofcompetition-induced shifts in cell size distributions can bedetermined. Instead of using histograms decomposed intoPoisson-shaped functions (4), the originally measured histo-grams could be used in an identical approach. However,the considerable noise level in the histograms would oblit-erate clear trends among size changes.

4. RESULTS AND DISCUSSION

4.1. Competition impacts on growth dynamics

Detecting and assessing impacts of nutrient competition on thegrowth dynamics of microalgae cells have been based on spe-cies-dependent growth rates s (1). Values for s (and for ymax) havebeen derived from nonlinear least-squares fits, which can onlyguarantee finding a local minimum of the sum-of-squared errors.The local minimum found depends on the iteration’s startingpoint. In order for the minimum to become less dependent on

2However, histograms derived from different images comprise different num-bers of cells and thus require normalization in order to be comparable. Here,the histogram vector S has been normalized to length one.



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a specific starting point, the fits have been repeated 1000 timesfrom slightly varying starting points. Initial values for s (and ymax)have been determined as outlined in the Appendix A (cp. equa-tion (A3)). Prior to using these values in the nonlinear regression,they were multiplied with a normal distributed random numberwith mean 1 and an empirically chosen standard deviation of0.05; in other words, the fit initialization for the growth rate, s(init)

β with β ∈N(1, 0.05), was used. From each set of 1000 values fors (and ymax), the mean and standard deviation have beenderived. This procedure has been carried out for all culturesand all nutrient situations (six carbon, five ammonium, and fivenitrate concentrations). Figure 2 depicts mean growth ratesand their standard deviations as derived from mixed-species

cultures versus the single-species cultures’ values. A 45° line(gray dashed) has been included to indicate where s(single) = s(mix). If a data point falls below this 45° line, s(single)> s(mix)

indicating that the growth rate is reduced in species mix-tures compared to the single-species culture containingthe same nutrient situation. On the other hand, if a datapoint is above the 45° line, the growth rate is enhanced inthese mixtures. The green lines in the panels of Figure 2are regression lines of s(mix) versus s(single) under the con-straints that the regression function passes through the ori-gin. The stated slopes then measure by what factor thegrowth rates of the mixture and the single-cell culturesdeviate.

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Figure 2. Comparing the growth rates s (1) of species grown in binary-species cultures versus singly grown cultures; deviations from the 45° lines (graydashed) indicate impacts from species competition for nutrients; the outlying data points encircled in red belong to the same pair of growth curves([NO3

�] = 873μM); see section 4.1 for discussion of the error bars and the green lines.

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The panels in Figure 2’s left column display growths rates for N.oculata exposed to different concentrations of (top to bottom)carbon, ammonium, and nitrate; the right column depicts equiva-lent results for D.parva. It was found that competition for carbonclearly reduces the growth rate for D.parva by a factor ofapproximately two and to a lesser extent (by ~15%) for N.oculata.Competing for ammonium clearly increases s for N.oculataconsiderably (>2�) but slows down the growth rate of D.parvato less than half the single-species growth rate. The competitionfor nitrate has the least apparent impact: Disregarding the[NO3

�] = 873 μM data point, N. oculata’s s is increased by roughly40% because of competition; however, this increase corre-sponds to another outlying point, and without it, no change in swould result. The data points for D.parva are the least apparentones, and after excluding the 873μM data point, the growth rateremains approximately unchanged or may increase slightly.

4.2. Competition impacts on the amount ofproduced biomass

A comparison of the maximum cell concentration ymax (1) hasbeen performed in an equivalent manner to the one for thegrowth rate s. The panels in Figure 3 show ymax(mix) versus ymax

(single) together with gray, dashed 45° lines and green regressionlines constrained to pass through the graphs’ origins. The grayline shows where ymax(mix) = ymax(single), and the green line indi-cates by what factor ymax(mix) and ymax(single) deviate because ofcompetition for a given nutrient. While competition for carbondoes not strongly impact the maximum N. oculata concentration(slope≈ 0.96), it reduces ymax for D. parva considerably by a factorof ~7. For ammonium, a similar but less striking behavior of ymax

was found; with exception of one outlier, removed data point([NH4

+] = 1470μM), the maximum concentration of N. oculata

60 1x106 2x106 3x10 4x106 5x106

slope = 0.1108

NO-

3

slope =0.1356

carbon

5.0x106 1.0x107 1.5x107 2.0x107 2.5x107 0.0 2.0x106 4.0x106 6.0x106 8.0x106

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slope = 0.9619

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slope = 0.8188

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NH+

4

1470µM1470µM

Figure 3. Comparing the maximum cell concentration ymax (1) of species grown in binary-species cultures versus singly grown cultures; deviationsfrom the 45° lines (gray dashed) indicate impacts from species competition for nutrients; the outlying data points encircled in red belong to the samepair of growth curves ([NH4

+] = 1470μM); see section 4.1 for discussion of the error bars and the green lines.



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remains essentially unaffected by competition. However,D. parva’s ymax is reduced by 30%. Again, if the somewhat outly-ing data point is disregarded, species competition for nitrateleaves the N. oculata maximum concentration in species mixtureunchanged compared to single-species cultures under the samenutrient concentrations. Competition clearly reduces the maxi-mum concentration of D. parva by a factor of ~9. Consideringall three nutrients, ymax for N. oculata has been found to belargely unaffected by competition, whereas D. parva’s ymax isconsiderably reduced. Thus, N. oculata seems to outcompeteD. parva.

Next, the impacts of competition on the cell size distributions(Figure 1, bottom left) were studied. In conjunction with the cor-responding ymax, these distributions then define the amount of aspecies’ biomass produced in a certain nutrient and competitionsituation. In a preliminary step, it was found that the shape of the

size distributions obtained from the same culture on differentdays did not change significantly. Hence, after normalization2

for increasing cell numbers, average size histograms and theirbin-by-bin error bars were calculated for further analyses.Figures 4–6 display experimental and reconstructed cell sizedistributions (4) for binary species mixtures after beingexpressed as a superposition of M=20 Poisson-shaped functions(Figure 1, bottom row). The reconstructed distributions shown inred also possess associated error bars that have been computedfrom 10 repetitions of the constrained linear fit3; however,these error bars were so small that they have been omittedfrom the graphs.

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Figure 4. Detecting competition impacts via t-testing experimental size distributions of species mixtures and those reconstructed from single-speciessize distributions; cultures grown under different bicarbonate concentrations.

3Note: The constraints are the source of minute fluctuations in the fitparameters.

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It is noticeable that the mixed-species histograms resemblethose of N. oculata rather than featuring two distinct peaks.This is not surprising after observing (Figure 3) that competi-tion suppresses the number of D. parva cells or, moreprecisely, the maximum cell concentration ymax D. p.(mix). Com-petition impacts were searched for by means of t-testing(95% confidence) each individual bin of an experimentalversus the corresponding bin in the reconstructed histogram.Outcomes of these t-tests are shown in Figures 4–6 as bluegraphs (“t-histogram”). A negative value in a t-histogramindicates that for that specific cell size, significantly fewer cellshad been found than were expected, if the mixed culture wasa linear combination of the single species (= reconstruction). Apositive value of a t-histogram indicates that significantlymore cells in that specific size range were found thanexpected because of the single species. In other words, a

negative t-histogram value indicates that fewer cells wereproduced in mixture than in the single-species cultures; apositive value in a t-histogram indicates larger productionof a certain cell size in mixture compared to the individualcultures. A zero value in a t-histogram reflects that there isno significant difference in numbers between single-speciesand mixed-species cultures for that cell size.

Detecting competition-induced shifts in the size distributionsfocused on bin # ’ s≲ 40 as this size region contains most cells.The t-histograms shown in Figures 4–6 are non-zero in vastareas. This is a clear indication that for all nutrient types andnutrient concentrations, the measured distributions are signifi-cantly different from the ones expected based on single-speciescultures. For bicarbonate concentrations, however, no clearconcentration-dependent trend in this size distributions’ shift isapparent. On the other hand, one consistent observation is that

Figure 5. Detecting competition impacts via t-testing experimental size distributions of species mixtures and those reconstructed from single-speciessize distributions; cultures grown under different ammonium concentrations.



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near the distributions’ maxima (bin #10), the measured numbersof cells are higher than expected based on the reconstruction.For different ammonium and nitrate concentrations, with theexception of [NH4

+] = 549μM and [NO3�] = 350μM, respectively,

a systematic shift in the size distribution is detectable; the peaknear bin #10 is shifted toward smaller cell sizes as indicated bythe t-histogram featuring a positive number to the peak’s left(more cells than expected) and a negative number to themaximum’s right (fewer cells than expected). Thus, nutrientcompetition, in particular for ammonium and nitrate, hassmall but measureable impacts on the cell size distributions.When grown in mixed-species cultures, the cells’ competi-tion for their N source renders them to be smaller thanexpected because of the size distributions derived from single-species cultures.

For the purpose of completeness, Appendix B containsequivalent analyses utilizing the originally measured cell sizedistributions without expressing them as a sum of Poisson-shaped functions. As a consistent observation in these figures,the noise level in the experimental data makes it much harderto recognize shifts in the size distributions.

5. CONCLUSIONS

This study focuses on species↔species interactions in particulartheir competition for nutrients and resulting implications ofphytoplankton carbon sequestration. For acquiring experimentaldata, two marine microalgae species have been selected,N. oculata and D. parva. Cell cultures have been exposed to six

0.0

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0 10 20 30 40 50 60 70 80

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0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80

experimental histogram reconstruction

t -histogram


t -histogram


t -histogram



t -histogram

t -histogram

Figure 6. Detecting competition impacts via t-testing experimental size distributions of species mixtures and those reconstructed from single-speciessize distributions; cultures grown under different nitrate concentrations.

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different bicarbonate concentrations as well as five differentconcentrations of two separate nitrogen sources, that is,ammonium and nitrate. Both species have been cultured individ-ually as well as in binary species mixtures and investigatedregarding cell growth rates, maximum cell concentrations, andcell size distributions. When keeping all ambient parametersthe same, in particular the nutrient concentrations, mixed-speciescultures can be compared to the corresponding single-speciescultures for assessment of competition impacts.Growth dynamics: Cell cultures were grown in “batch mode”

for up to 14 days, and on several of those days, cell concentra-tions were measured from which growth curves and thus growthrates were obtained. It was evident from comparing the growthrates of single species to species mixtures that competitioninduced changes in the culture’s growth dynamics; thus, nutrientconsumption over time could be indirectly determined. It wasfound that N. oculata’s growth rates slightly decreased whencompeting with D. parva for bicarbonate but considerablyincreased when competing for ammonium (2.1�) and nitrate(1.4�). D. parva’s growth rates were cut in half when competingfor bicarbonate and ammonium and remained essentiallyunchanged when competing for nitrate.Amount of produced biomass: Two aspects have been covered

in regard to production of biomass, that is, cell concentrations pro-duced by a culture and cell size distributions; both pieces of infor-mation are required to determine how much biomass had beenproduced. The microalgae species were considered separatelyand in mixture for both aspects allowing for the analyses of com-petition impacts. For N. oculata, it was found that the maximumcell concentrations a culture can produce are not impacted bycompetition with D.parva. However, cell production for D.parvawas reduced to 11–70% of the non-competing, mono-speciescultures depending on the nutrient type the microalgae werecompeting for. The distribution of the cell sizes was also influencedby nutrient competition. While contests for bicarbonate did notreveal a [HCO3

�]-dependent trend, cell size distributions are shiftedtoward smaller cell sizes; these shifts were determined to be smallbut significant at 95% confidence.

Acknowledgements

This work was supported by the National Science Foundationunder CHE-1058695 and CHE-1112269. In addition, L. W.acknowledges a graduate student stipend from the Chancellorof the University of Tennessee. We also appreciate valuablediscussions with Mario Giordano, Università Politecnica delleMarche, Ancona, Italy.

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Rapid growth in CO2 emissions after the 2008–2009 global financialcrisis. Nat. Clim. Change 2012; 2: 2–4.

2. Eby M, Zickfeld K, Montenero A, Archer D, Meissner K, Weaver A. Life-time of anthropogenic climate change: millennial time scales ofpotential CO2 and surface temperature perturbations. J. Climate2009; 22: 2501–2511.

3. Blunden J, Arndt D, Baringer M. (Eds.) State of the climate in 2010.Bull. Am. Meteorol. Soc. 2011; 92: S1–S266.

4. Field C, Behrenfeld M, Randerson J, Falkowski P. Primary productionof the biosphere: integrating terrestrial and oceanic components.Science 1998; 281: 237–240.

5. Behrenfeld M, O’Malley R, Siegel D, McClain C, Sarmiento J, FeldmanG, Milligan A, Falkowski P, Letelier R, Boss E. Climate-driven trends incontemporary ocean productivity. Nature 2006; 444: 752–755.

6. Martinez E, Antoine D, D’Ortenzio F, Gentili B. Climate-driven basin-scale decadal oscillations of oceanic phytoplankton. Science 2009;326: 1253–1256.

7. Raven J, Giordano M, Beardall J, Maberly S. Review: algal and aquaticplant carbon concentrating mechanisms in relation to environmen-tal change. Photosynthesis Res. 2011: 109: 281–296.

8. Giordano M, Beardall J, Raven J. CO2 Concentrating mechanisms inalgae: mechanisms, environmental modulation, and evolution. Ann.Rev. of Plant Bio. 2005; 56: 99–131.

9. Halsey K, Milligan A, Behrenfeld M. Linking time-dependent carbon-fixation efficiencies in dunaliella tertiolecta (chlorophyceae) tounderlying metabolic pathways. J. Phycol. 2011; 47: 66–76.

10. Raven J, Giordano M, Beardall J, Maberly S. Review: algal evolution inrelation to atmospheric CO2: carboxylases, carbon-concentratingmechanisms and carbon oxidation cycles. Phil. Trans. R. Soc. B 2012:367: 493–507.

11. Behrenfeld M, Halsey K, Milligan A. Review: evolved physiologicalresponses of phytoplankton to their integrated growth environment.Phil. Trans. Royal Soc. B 2008; 363(1504): 2687–2703.

12. Bilanovic D, Andargatchew A, Kroeger T, Shelef G. Freshwater andmarine microalgae sequestering of CO2 at different C and N concen-trations – response surface ethodology analysis. Energ. Convers.Manag. 2009; 50: 262–267.

13. Horton R, McConico M, Landry C, Tran T, Vogt F. Introducingnonlinear, multivariate ‘predictor surfaces’ for quantitative modelingof chemical systems with higher-order, coupled predictor variables.Anal. Chim. Acta 2012; 746: 1–14.

14. McConico M, Horton R, Witt K, Vogt F. Monitoring chemical impacts oncell cultures by means of image analyses. J. Chemom. 2012; 26: 585–597.

15. McConico M, Vogt F. Modeling Nutrient Impacts on Microalgae Cellsvia Image Analyses. J. Chemom. 2013; DOI: 10.1002/cem.2510.

16. McConico M, Vogt F. Assessing impacts of nutrient competitionamong microalgae species on their chemical composition. Anal. Lett.2013; DOI:10.1080/00032719.2013.811682.

17. Quéré C, Rödenbeck C, Buitenhuis ET, Conway TJ, Langenfelds R,Gomez A, Labuschagne C, Ramonet M, Nakazawa T, Metzl N,Gillett N, Heimann M. Saturation of the southern ocean CO2 sinkdue to recent climate change. Science 2007; 316: 1735–1738.

18. Andersen R. Algae Culturing Techniques. Elsevier Academic Press:Burlington, 2005.

19. Galassi M, Davies J, Theiler J, Gough B, Jungman G, Alken P, Booth M,Rossi F. GNU Scientific Library Reference Manual (3rd ed., software V1.12). Network Theory Ltd, 2009.

20. http://ab-initio.mit.edu/nlopt [6 August 2013].21. Conn A, Gould N, Toint P. A globally convergent augmented

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http://ab-initio.mit.edu/nlopt

APPENDIX A: DERIVATION OF EQUATION (1)

For deriving an equation for a growth curve y(t) (1), it is assumed that at time t = t0, y0 cells per milliliter are inoculated intothe culturing medium. From t0 on, the number of cells duplicates within a timespan τ. Hence, in the absence of inhibitors,

the cell concentration at t ≥ t0 is given by y tð Þ ¼ y0�2t�t0τ . Utilizing ab = exp{ln(ab)} = exp{b � ln(a)}, an exponential function is

derived: y tð Þ ¼ y0y0�2t�t0τ ¼ y0�exp t � t0ð Þ� ln 2ð Þ

τ

n o¼ y0�exp s� t � t0ð Þf g with ln 2ð Þ

τ ¼ s being the culture’s growth rate. However,

from a biological perspective, an unrestrained exponential growth is not possible as, for example, the nutrients consumedby the cells are limited. Thus, we assume that there is a currently unknown maximum cell concentration ymax that can beproduced in a given, closed culturing system. In order to derive a biologically feasible growth curve y(t), we considertwo time windows:

• For t→ t0, the cell concentration is realistically described by the aforementioned exponential function because the limitations haveno impact yet and thus y(t)→ y0.

• For very long times, that is, for t→∞, y(t)→ ymax, and thus, the exponential growth has to go over into saturation asymptoticallyreaching ymax.For constructing a more realistic equation y(t), which describes the growth of a culture under these two constraints,additional information is available and utilized: For t→∞, dy tð Þ

dt →0 as y(t)→ ymax = const, and for t→ t0,dy tð Þdt →s�y0�exp s� t � t0ð Þf g ¼

s�y tð Þ. To incorporate a transition from exponential growth to saturation, a function g(t) is proposed, which modifies the aforemen-tioned exponential growth, and thus, the differential equation just stated:

dy tð Þdt

¼ s�y tð Þ� 1� g tð Þð Þ (A1)

To satisfy the aforementioned two “biological” constraints, this modification function g(t)→ 0 as t→ t0 and g(t)→ 1 for t→∞.Defining g tð Þ ¼ y tð Þ�y0

ymax�y0fulfills all the requirements, and thus, differential equation (A1) becomes

dy tð Þdt

¼ s�y tð Þ� 1� y tð Þ � y0ymax � y0

� �¼ s�y tð Þ� ymax � y tð Þ

ymax � y0

� �(A2)

After rearranging equation (A2) into ymax�y0ð Þy� ymax�yð Þ �dy ¼ s�dt (“separation of variables” [23]), this differential equation is solved via

integration [24] and results in

ymax � y0ð Þ� 1ymax

�ln �2�y�2�y þ 2�ymax

�� ¼ ymax � y0

ymax�ln y

y � ymax

�� ¼ s�t þ const

The absolute value inside the logarithm is resolved by taking into account that y< ymax as well as y> 0, and thus,ymax�y0ymax

�ln yymax�y

� �¼ s�t þ const . From the last equation, a solution for equation (A2) is derived as y tð Þ ¼

ymax� 1

1þexp � ymaxymax�y0

� s�tþconstð Þn o . In the last step, the integration constant, const, has to be determined from the initial

condition, that is, y(t0) = y0. This leads to the final solution (1) for the growth curve, which is of a sigmoidal shape.Nonlinear least-squares regressing (1) to measured cell concentrations requires an initial solutions for the fit parame-ters s, ymax, y0, and t0. These were derived via a linearization of (1) followed by fitting a straight line:

lny initð Þmax

y tð Þ � 1

!|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

¼f tð Þ

¼ � y initð Þmax

y initð Þmax � y initð Þ

0

�s initð Þ

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}¼m

�t þ y initð Þmax

y initð Þmax � y0

�s initð Þ�t initð Þ0 þ ln

y initð Þmax

y initð Þ0

� 1

!|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

¼b

(A3)

Approximating y0≈yinitð Þ0 ¼ min ymeasuredð Þ and ymax≈y

initð Þmax ¼ max ymeasuredð Þ followed by solving m for s(init) and then b for

t initð Þ0 completes the initialization of the nonlinear fitting.

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Figure 7. Same as Figure 4 but based on raw data, that is, without decomposing histograms into Poisson-shaped functions (3); cultures grown underdifferent bicarbonate concentrations.

The histograms shown in Figures 4–6 had been pre-processed by means of expressing them as M= 20 Poisson-shaped functions (3).This pre-processing had been performed in order to reduce the noise level and to better extract the underlying cell size distributionsand shifts thereof induced by nutrient competition. Figures 7–9 display the same results as Figures 4–6 but have been derived fromthe raw histograms. The advantage of the pre-processing step concerning the enhancement of the differences between measuredfrom mixed cultures and reconstruction based on single-species histograms is obvious.

APPENDIX B: COMPETITION IMPACTS ON THE AMOUNT OF PRODUCED BIOMASS – RAW DATA



459

Figure 8. Same as Figure 5 but based on raw data, that is, without decomposing histograms into Poisson-shaped functions (3); cultures grown underdifferent ammonium concentrations.

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Figure 9. Same as Figure 6 but based on raw data, that is, without decomposing histograms into Poisson-shaped functions (3); cultures grown underdifferent nitrate concentrations.



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impacts of nutrient competition on microalgae biomass production

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