bacterial competition in activated sludge

Bacterial Competition in Activated Sludge: Theoretical Analysis ofVarying Solids Retention Times on Diversity

P.E. Saikaly and D.B. Oerther

Department of Civil and Environmental Engineering, University of Cincinnati, Box 210071, Cincinnati, OH 45221-0071, USA

Received: 19 February 2003 / Accepted: 19 June 2003 / Online publication: 3 May 2004

Abstract

A mechanistic model for activated sludge sewage treat-ment was developed to predict exploitative competitionof six aerobic heterotrophic bacterial species competingfor three essential resources. The central hypothesis of themodel is that in a multispecies/limiting resource systemthe number of coexisting bacterial species, N, exceeds thenumber of limiting resources, K, available for them. Theexplanation for this is that for certain species combina-tions, the dynamics of the competition process generateoscillations in the abundances of species, and theseoscillations allow the coexistence of greater number ofspecies than the number of limiting resources (N > K).This result is a direct contradiction of an existing acti-vated sludge steady state competition theory, the prin-ciple of competitive exclusion, which states that thecompetition process proceeds to equilibrium, allowingonly N K species to coexist. The model was used toinvestigate the effect of varying solids retention times onthe diversity of species using the conventional, com-pletely mixed activated sludge configuration. The resultsof model simulations showed that for a certain range ofsolids retention times (2.285.66 days) the competitionof six species for three essential resources producesoscillations within the structure of the bacterial com-munity allowing for the sustained growth of more thanthree species on three resources.

Introduction

Several mathematical models have been developed todescribe the effect of exploitative competition on thecoexistence of different species and thus, on speciesdiversity in natural ecosystems and chemostat-typebioreactors. Exploitative competition is when species

compete by lowering the shared pool of limited re-sources, as opposed to interference competition wherespecies compete by harming their rivals and by seques-tering some of the resources for their exclusive use. Mostof these models were based on the classical ecologicalprinciple of competitive exclusion. This principle,which was pioneered by Lotka and Volterra [26, 48] andfirst described mathematically by Voltera [49] and latersupported by several authors [1, 11, 28, 29, 36, 37], statesthat the number of coexisting competing species, N, cannot exceed the number of growth-limiting resourcesavailable to them (N K). This principle is the outcomeof competitive equilibrium or steady-state competition(dX/dt = 0,where X is species abundance), where com-petition is allowed to proceed to equilibrium. It presumesthat increased competition for common resources causesfewer numbers of species to coexist, leading to a pre-dictable outcome where species that are strong compet-itors dominate. Many authors adopting this principleshowed theoretically and experimentally that the out-come of competition between two or more speciessharing a single limiting resource could be predictedbased on knowledge of Monod growth kinetics (halfsaturation constant, Ks, of the growth-limiting resourcesand maximum specific growth rate, rmax) and the speciesdeath rate, b [5, 12, 23, 38]. Their results showed thatonly one species is competitively dominant and theremaining species are excluded. Similar results were ob-tained for several species competing for two resourceswhere eventually only two species can stably coexist [43,44].

Experimental and theoretical studies challenging thecompetitive exclusion principle exist in the literature [2,25, 39, 41, 45]. These studies rely upon nonequilibriumconditions to promote species diversity by preventingcompetitive equilibrium. An example of a process thatprevents competitive equilibrium from occurring is thevariability in resource supply ratios. Sommer [41] studiedthe diversity of natural phytoplankton species in che-Correspondence to: D.B. Oerther; E-mail: [email protected]

274 DOI: 10.1007/s00248-003-1027-6 d Volume 48, 274284 (2004) d Springer Science+Business Media, Inc. 2004

mostat-type bioreactors receiving continuous vs pulsednutrients. The results obtained with continuous nutrientaddition showed that the community reached stableequilibrium (dX/dt = 0), and the number of species wasequal to the number of limiting resources. However,when nutrients were provided in pulses, the number ofcoexisting species increased. Furthermore, the pulsenutrient condition corresponded to regular oscillations insome species.

Recently, Huisman and Weissing [1719] developeda series of models describing the competition of phyto-plankton species for growth-limiting resources in aquaticecosystems. Their model was based upon a chemostat-type system where growth was modeled using the Mo-nod equation, and the loss of biomass was assumed tofollow first-order decay and washout due to dilution.Their work showed that competition could generateoscillations in the abundance of species. These oscilla-tions prevented competitive equilibrium from occurringand allowed the coexistence of a greater number of spe-cies than the number of growth-limiting resources.

Although the studies described above show theimportance of competition in predicting species diversity,most of the models were developed to predict behavior innatural ecosystems or chemostat-type bioreactors.Therefore, these models have not examined the impact ofselective solids retention upon the competition process.

Activated sludge sewage treatment systems are engi-neered bioreactors used to remove organic substancesand nutrients (nitrogen and phosphorus) from municipalwastewater. A consortium of bacterial species is requiredto achieve the desired biological conversions, and theperformance of these reactors largely depends on thebacterial community structure and their competition fordifferent growth-limiting resources. Therefore, under-standing the dynamic behavior of different speciescompeting for a variety of growth-limiting resources isexpected to provide information useful for optimizingactivated sludge systems. None of todays state-of-the-artactivated-sludge models (e.g., Activated Sludge ModelNumber 1 [ASM1], ASM2, and ASM3) [9, 13, 14] de-scribe processes occurring at the species level. The ASMmodels describe microorganisms in activated sludgeaccording to the average composition of three functionalgroups, namely heterotrophs, autotrophs, and phospho-rus-accumulating organisms (PAO). In the ASM models,species of bacteria are lumped into one of these threefunctional groups.

In the current study, a mechanistic model for acti-vated sludge systems describing the competition of het-erotrophic bacterial species for essential resources wasdeveloped. Essential resources fulfill metabolically inde-pendent requirements for growth. For example, ammoniaand orthophosphate are examples of essential resourcesbecause they meet the requirement for nitrogen and

phosphorus. Essential resources obey Liebigs law of theminimum where the concentration of the growth-limit-ing essential resource controls the overall growth of theorganism. Environmental engineers often use the termcomplementary nutrient in place of essential resource. Forclarity, we have adopted the term essential resourcethroughout this manuscript.

The central hypothesis of our model is that in acomplex system, with multiple species and multiplelimiting resources, competition under certain operatingconditions is expected to enhance species diversity. Spe-cifically, we hypothesize that the number of coexistingspecies, N, would exceed the number of growth-limitingresources, K, available to them (N > K). The model wasused to study the impact of the solids retention time(SRT) on the competition of heterotrophic bacteria foressential resources.

Methods

Model Development. The model developed in thisstudy is based on mass balance equations for a conven-tional, completely mixed activated sludge system (Fig. 1).Dashed lines designate the control volume used to gen-erate the mass balance equations for essential resourcesand heterotrophic species. In activated sludge systems,biomass is separated from the treated effluent through abiomass separator (e.g., clarifier). The purpose of theclarifier is to selectively separate the retention of thebiomass from the retention of the liquid. From theclarifier, a fraction of the biomass is intentionally re-moved from the system through the process of wast-ing, and the remaining biomass is recycled from theclarifier to the reactor. The process of wasting controlsthe solids retention time, or SRT, which is the averagetime that biomass is retained in the reactor. Ranges ofSRT for municipal activated sludge systems can varyfrom 1 day to 30 days with typical values for conventionalsystems of 2 to 5 days. For the purpose of our simula-tions, we studied a broad range of SRT (0 to 30 days).

The rationale for modeling heterotrophic bacteria isthat this functional type of organism is responsible forthe removal of soluble, readily biodegradable organicpollutants typical of municipal sewage. Therefore, the

Figure 1. Schematic of a completely mixed activated sludge sys-tem.

P.E. SAIKALY, D.B. OERTHER: IMPACT OF SRT ON DIVERSITY 275

selection of heterotrophic bacteria is consistent with theecosystem of interest, namely activated sludge sewagetreatment.

In developing the model the following assumptionswere made: (i) readily biodegradable substrates (i.e.,sources of carbon and energy) are present in excess; (ii)oxygen is present in excess; (iii) the limiting resources areconsumed by all of the different heterotrophic bacteria;(iv) competition is exploitative; (v) the hydraulic reten-tion time (HRT) is kept constant at 0.6 days (i.e., adilution rate of 1.66 d)1); and (vi) the clarifier is ideal;with assumed zero volume.

The model was developed to describe the competi-tion of six groups of heterotrophic bacteria (e.g., spe-cies) competing on three growth-limiting resources.Although a thorough discussion of an appropriate defi-nition of species is beyond the scope of the current work,we feel that it is important to provide the species con-cept used throughout this manuscript. In our model,species are defined as groups of like individuals that sharea common set of kinetic and stoichiometric characteris-tics as defined in Table 1. This may or may not corre-spond to species as defined by 16S ribosomal DNAsequence comparisons [21, 32] nor species as defined byoperational taxonomic units (OTU) based on molecularfingerprinting assays [4, 15, 31, 34].

The general forms of the differential mass balanceequations for N heterotrophic species competing for Klimiting resources are

dSj

dt

V QinSjoQeSj

XNi1

riS1; :::SKXiVYji

for j 1; :::K 1

dXidt

V riS1; :::SKVXi QwXi biXiV

for i 1; :::N 2where K is the number of different essential resources, Nis the number of different heterotrophic species, j rep-resents different limiting resources, i represents different

species, Sjo is the influent concentration of resource j, Sj isthe effluent concentration of resource j, Qin is the influ-ent flow rate, Qe is the effluent flow rate, Qw is the wasteflow rate (see Fig, 1), Yji is the yield coefficient of species ifor resource j, V is the volume of the completely mixedreactor, ri is the specific growth rate of species i, Xi is theconcentration of species i, and bi is the first-order decayrate for species i.

We assumed that the specific growth rate on anyessential resource is described by the Monod equation.Furthermore, we assumed that growth on essential re-sources obeys Liebigs law of the minimum. The use ofLiebigs law of the minimum is well established [3, 17, 19,24] and leads to a form of the overall growth equationwhere the specific growth rate is limited by one resourceat a time (i.e., growth is described by a switching functionwhere the identity of the growth-limiting resource mightchange as environmental conditions (S1...SK) change).Therefore, ri will be equal to the lowest value in Eq. (3):

riS1; :::SK min rmaxi S1K1i S1 ; :::

rmaxi SKKKi SK

for i 1; :::K 3where rmaxi is the maximum specific growth rate forspecies i, K1i is the half-saturation constant of species i onresource 1, and KKi is the half-saturation constant ofspecies i on resource K.

To understand this equation, consider an example oftwo essential resources. Dual limitation by both resourcesis possible only under conditions where the growth ratesare equal (r(S1) = r(S2)). The relationship between S1and S2 where this equation is satisfied is called aswitching curve because the identity of the growth-limiting resource switches when the environmental con-ditions (S1, S2) change [3]. Next, assume that the maxi-mum specific growth rate for both resources is the same,rmax1 = rmax2 = 1 d

)1, K1 = 1, and K2 = 0.9. In this casethe equation of the switching curve becomes S2 = (K2/K1)S1, and the switching curve is a straight line passingthrough the origin with slope 0.9. S1 is the growth-lim-iting resource for (S1, S2) above and to the left of theswitching curve, whereas S2 is the growth-limiting re-

Table 1. Model parameters

Half saturation constant, Ks, mg/L Yield coefficient, Y

Species Resource 1 Resource 2 Resource 3 Resource 1 Resource 2 Resource 3

1 1.00 3.20 0.30 0.96 0.90 2.88 0.42 0.36 0.21 0.18 0.12 0.102 0.90 2.88 1.00 3.20 0.30 0.96 0.24 0.20 0.21 0.18 0.17 0.143 0.30 0.96 0.90 2.88 1.00 3.20 0.42 0.36 0.17 0.14 0.17 0.144 1.04 3.33 0.71 2.27 0.46 1.47 0.17 0.14 0.17 0.14 0.10 0.085 0.34 1.10 1.02 3.26 0.34 1.08 0.55 0.48 0.33 0.28 0.30 0.246 0.77 2.46 0.76 2.43 1.07 3.42 0.83 0.71 0.10 0.08 0.12 0.10

276 P.E. SAIKALY, D.B. OERTHER: IMPACT OF SRT ON DIVERSITY

source for (S1, S2) below and to the right of the switchingcurve.

All simulations were done using Berkeley MadonnaVersion 8.0.1 [27] employing a fourth-order RungeKutta numerical approximation with a fixed time step of0.0625 d. Our model differs from the model described byHuismen and Weissing [17, 19], in that it does not allowfor continuity of Xi. Instead the model sets Xi to be equalto zero when the mass of bacteria is

Oscillatory behavior was observed for a wide range ofSRT values (species 1, 2, and 3, SRT = 2.226 d; species1, 2 and 6, SRT = 2.04.0 d; species 1, 3 and 5,SRT = 2.33.6 d). These oscillations occur because thespecies displace each other in a round-robin fashion[17, 18, 47]. For example, consider the competition ofspecies 1, 2, and 3 (Fig. 2A) Species 1 is the best com-petitor (lowest Ks = 0.3 mg/L) for resource 2 but canbecome limited by resource 1 or resource 3. Species 2 isthe best competitor (lowest Ks = 0.3 mg/L) for resource 3but becomes limited by resources 1 and 2. Species 3 is thebest competitor (lowest Ks = 0.3 mg/L) for resource 1but becomes limited by resources 2 and 3. These limitingconditions lead to transient conditions where each spe-cies is dominant. This pattern of transient dominancerepeats in an oscillatory fashion. Similar observations canbe made for species combinations 1, 2, and 6 (Fig. 2B)and 1, 3, and 5 (Fig. 2C), respectively. When the numberof essential resources was reduced from three to two, thispattern of transient dominance and oscillations did notoccur. Therefore, we suggest that for oscillations to existcompetition should be for at least three or more growth-limiting resources [17].

Two things can be deduced from these results, (i)Oscillations are the result of nonequilibrium conditionsthat are generated by the competition process itself (i.e.,no external disturbance is necessary to generate oscilla-tions). Previous competition theories, based on equilib-rium arguments, eventually lead to stable speciescomposition where each species is competitively domi-nant on its growth-limiting resource, monopolizes thegrowth-limiting resource, and eventually excludes allother competing species that are limited by the sameresource, (ii) No species is competitively dominant (i.e.,no species is capable of monopolizing the limiting re-

source) for its limiting resource as each species switchesthe identity of its limiting resource through the course ofcompetition. This is important because it is possibleunder these conditions to have coexistence of severalspecies competing for the same resources.

Oscillatory Coexistence of Six Species on Three

Growth-Limiting Resources. The central hypothesis ofour work is that oscillations in the abundance of speciesallow the coexistence of more species than growth-lim-iting resources. To examine this phenomena, consider thecompetition shown in Fig. 2A. Species 1, 2, and 3 wereadded to the system at t = 0 days. Species 1, 2, and 3establish a pattern of repeated oscillations due to com-petition. At later times, additional species are added (i.e.,species 4, 5, and 6 were added to the system at t = 1000,2000, and 5000 days, respectively). Species 4, 5, and 6were able to coexist in the system because of the patternof repeated oscillations created by the competition ofspecies 1, 2, and 3 for essential resources (Fig. 3A). Thecycle time for the oscillations in Fig. 3A for species withkinetic parameters shown in Table 1 and SRT = 2.73 d is90 days.

Three things can be deduced from the result, (i) It isalready recognized in the literature that nonequilibriumconditions and oscillations allow the coexistence of morespecies than there are limiting resources [1719, 25, 41].Therefore, the oscillations that are caused by nonequi-librium conditions imposed by SRT create an opportu-nity to increase species diversity. It should be noted thatadding all six species at t = 0 (results not shown) alsoresulted in the oscillatory coexistence of six species onthree limiting resources. This result suggests that theamplitude of the oscillations generated by species 1, 2,and 3 were large enough to create an opportunity for

Figure 3. (A) Oscillatory coexistence of six species on three essential resources at SRT = 2.73 d and dilution rate of 1.66 d)1. (B)Oscillatory resource concentrations.


other species to coexist even at t = 0 days, (ii) Thedynamics in the structure of the bacterial communityimpact the functional performance of the system as re-flected by the oscillatory behavior in the concentrationsof the essential resources (Fig. 3B). This observation isimportant because it highlights a critical difference be-tween our model and the ASM models. In the ASMmodels, functional performance is based on steady-stateconditions where the concentration of the essential re-sources are stable. Figure 3B presents the effluent re-source concentrations. For completely mixed activatedsludge systems, the effluent resource concentration isequal to the concentration inside the reactor, (iii) Sincethese oscillations and coexistence are the result of non-steady-state conditions, then one would predict thatimposing non-steady-state conditions would result inoscillations of essential resources permitting a greaterdiversity of species to coexist on fewer limiting resources(Fig. 3B). This phenomenon is similar to the resource-ratio theory [39, 41] where variability in resource ratioscreates non-steady-state conditions, which promotes thecoexistence of more species.

Imposing non-steady-state conditions in activatedsludge systems was shown theoretically and experimentallyin a recent study using a completely stirred tank reactor(CSTR) with sludge recycle [16]. The coexistence of nit-rifiers, denitrifiers, and aerobic heterotrophs, competingfor the limiting resource dissolved oxygen (DO), waspossible because the activated sludge reactor was exposedto sinusoidal oscillations of influent DO concentrations,resulting in dynamic population composition and coex-istence of the three functional group of organisms. Incontrast, our model maintained a constant concentrationof resources in the influent, and the only parameter thatwas varied was the SRT. From an engineering standpoint,the next step is to determine the operating conditions thattrigger these oscillations and cause increased speciesdiversity in activated sludge systems.

Effect of SRT on Species Diversity. The results ofmodel simulations at SRT = 2, 3, and 6 days are shownin Fig. 4. The results show steady state coexistence ofthree species on three growth-limiting resources (Fig. 4Aand C) at SRT values of 2 and 6 days, whereas, at SRTvalue of 3 days, we have oscillatory coexistence of sixspecies on three growth-limiting resources (Fig. 4B). Thecycle time for the oscillations in Fig. 4B is 70 dayscompared to 90 days in Fig. 3A, which means thatincreasing the SRT results in a concurrent decrease ofcycle time. The model was run for a period of 20,000days, and it produced the same pattern of cyclesthroughout (results not shown). The competitive exclu-sion principle dominates for some values of SRT and isrelaxed for other values of SRT. To characterize thisobservation more thoroughly, the impact of SRT on

species diversity was evaluated using SRT values withinthe range of 0 and 30 days with an increment of 0.01 d. Atotal of 3000 runs were conducted with 20,000 dayssimulation time with a fixed time step of 0.0625 d. Spe-

Figure 4. Time course of competition of six species on three re-sources. (A) Steady-state coexistence of three species at SRT = 2 d.(B) Oscillatory coexistence of six species at SRT = 3 d. (C) Steadystate coexistence of three species at SRT = 6 d.


cies 1, 2, and 3 were added at time zero, whereas species4, 5, and 6 were added at times 1000, 2000, and 5000days, respectively.

Table 2 is a summary of the simulation outputshowing coexistence (+) and washout ()) of six hetero-trophic species competing for three growth-limiting re-sources at various SRT values. At SRT values between 0and 1.49 d, we observed washout of all species becausethe maximum net specific growth rate is exceeded by thewashout rate.

Environmental engineers design activated sludgesystems based on SRTmin (Eq. 4) [8].

SRTmin Ks SioSiormaxi bi Ksbi

4

where SRTmin is the minimum solids retention time andSio is the influent resource concentration.

For operation at any SRT value that is lower thanSRTmin, species are removed from the system because ofwashout. Table 3 presents the SRTmin of the six specieswhen each exists alone and is limited by only one re-source. Values of Ks were obtained from Table 1. From themodel simulations in the SRT range from 0 to 1.49 d,species 1, 2, 4, and 6 are limited by S1, whereas species 3and 5 are limited by S2, and the corresponding SRTmin areshown in bold (Table 3). Comparing the results of modelsimulation with Table 3, we can see that SRT values in therange 0 to 1.49 d are lower than the SRTmin for eachspecies (bold numbers), and hence they all wash out.

From these results, traditional engineering theorywould argue that an SRT value that is greater thanSRTmin calculated by Eq. (4) would not cause washout ofthe species from the system. However, this is not the casein a multispecies system. A possible explanation for suchbehavior is that the SRTmin required for the organisms togrow in a multi-species/resource system is greater thanthat predicted by Eq. (4), because Sio available for eachspecies is lowered by the presence of other species com-peting for the same resource. For example, at SRT valuesbetween 1.5 and 1.72 d, model results show that species 1and 2 are limited by S1, and their corresponding SRTminas determined by Eq. (4) are 1.647 and 1.614 d, respec-tively (Table 2). Therefore, any value of SRT that isgreater than 1.647 will allow species 1 to grow. Similarly,any value of SRT that is greater than 1.614 d will allowspecies 2 to grow. However, since both species share thesame resource (S1), their SRTmin for growth should begreater than that predicted by Eq. (4), and hence theyboth wash out.

At SRT values in the ranges 1.732.27 and 5.6730 dthe competitive exclusion principle dominates, andonly N K species coexist where K in our case is 3(Table 2). This result is due to equilibrium conditions.For example, if Eq. (1) and Eq. (2) are solved simulta-neously for equilibrium (dSj/dt = 0 and dXi/dt = 0), thenthe number of species that can coexist cannot exceed thenumber of limiting resources available to them. In otherwords, since we have K limiting resources, then thenumber of equilibrium solutions that satisfy Eq. (2) withXi > 0 cannot exceed three. For every SRT value exam-ined in the range 1.731.94 d, the model results show thatwe have only one steady-state value of resource concen-tration that satisfies Eq. (2) at equilibrium with Xi > 0.Therefore, only one species can stably coexist, and in thiscase it is species 6 (Table 2). Similar arguments apply toother SRT ranges where competitive exclusion domi-nates.

Another deduction from Table 2 is that the identityof the competitively dominant species in SRT ranges1.952.2 and 5.6730 d changes even though competitive

Table 2. Coexistence and washout of six species competing for three essential resources at various SRT

SRT values (d) Species 1 Species 2 Species 3 Species 4 Species 5 Species 6

01.49 ) ) ) ) ) )1.51.72 ) ) + ) ) )1.731.94 ) ) ) ) ) +1.952.2 + ) + ) ) +2.21 + ) + ) ) )2.22 ) ) ) ) ) +2.23 ) ) + ) ) )2.242.27 ) ) ) ) ) +2.282.5 + ) + ) + +2.514.33 + + + + + +4.345.66 + + + + ) +5.6730 + + + ) ) )

Table 3. SRTmin of different species for different limiting re-sources

SRTmin (d)

Species S1 (mg/L) S2 (mg/L) S3 (mg/L)

1 1.647 1.387 1.4502 1.614 1.517 1.3723 1.424 1.498 1.4634 1.660 1.521 1.3925 1.436 1.521 1.3776 1.572 1.472 1.473


exclusion dominates in both ranges. This is attributed tothe fact that the steady-state resource concentrationvaries according to the SRT value (Eq. 7). This equationis derived by solving Eq. (2) at steady state (Eq. 5).

When Eq. (3) is solved for equilibrium, we get:

O riVXi QwXi biXiV for i 1; :::N 5Substituting V/SRT for Qw and solving Eq. (5) for r yieldsEq. (6):

ri 1SRT

bi 6

Substituting Eq. (7) in Eq. (1) and rearranging gives:

S Ks1=SRT birmaxi 1=SRT bi

7

To better understand this point, consider SRT values of 2and 6 days. Table 4 presents steady-state resource con-centrations for the six species at SRT = 2 and 6 daysusing Eq. (7). The bold numbers in Table 4 correspond tothe steady-state resource concentrations satisfying Eq. (2)at equilibrium with Xi > 0. The three steady-state valuesat SRT = 2 days correspond to species 1, 3, and 6,whereas, for SRT = 6 days, the three steady-state valuescorrespond to species 1, 2,and 3, respectively (Table 4).

Simulations at SRT values between 2.285.66 dshowed that the competition of six heterotrophic speciesfor three growth-limiting resources produced oscillationswithin the structure of the bacterial community allowingfor the coexistence of more than three species on threeresources (Table 2). This result is a direct contradictionof the competitive exclusion principle.

We ran a variety of simulations using different valuesof rmax (2 d

)1), Ks, and Y (Table 1, values in the secondcolumn of each resource), and the results show similartrends (Fig. 5). This implies that the impact of SRT onspecies diversity is a general phenomenon and not simplylimited to the values of the kinetic parameters (Table 1)selected for these simulations. The cycle time for theoscillations in Fig. 5B is 30 days. The cycle time has de-creased to 30 days because of the higher values of rmaxand Ks. This observation may have important implica-tions for real-world situations. For example, if the

structure of the bacterial community in activated sludgesystems is dynamic in nature and operates according tothe conditions described in our model, then reactorsshould be operated for a period greater than 30 days toexperimentally observe oscillations.

Discussion

Our work had two overlapping goals. The first goal wasto derive a mechanistic model that could describe com-petition of heterotrophic species for growth-limiting re-sources in activated sludge systems. The second goal wasto use this model to study the effect of operatingparameters, in particular the effect of SRT, on the com-petition process and species diversity.

The results of the model simulations suggest that thecompetitive exclusion principle, which states that Nspecies must be equal to or less than K growth-limitingresources, is not the only mechanism dictating the out-come of species competition for limited resources inactivated sludge systems. Instead, model simulationsshowed that N could be greater than K in some casesbecause of nonequilibrium conditions and oscillations inspecies concentration.

The recent work of Huisman and Weissing [1719] isrelevant to the present study. They showed that non-equilibrium conditions and oscillations in the structureof microbial communities allow the coexistence of morespecies than there are limiting resources. Taken together,the results of these studies are significant because theydirectly contract a long-held notion of microbial diversityin activated sludge systems. As described by Sykes, manyenvironmental engineers approach activated sludge sys-tems with the following belief [42]: The number ofcoexisting species in an activated sludge process equalsthe number of limiting resources available to them and ifall that is required is the solution of an N by N matrix(species by substrate), then a nearly complete ecosystemmodel of the activated sludge process is computationallyfeasible. However, the hypothesis proposed by Sykes isbased on equilibrium arguments and the notion ofcompetitive exclusion.

Two other interesting results are obtained from themodel simulations. First, we showed that under certain

Table 4. Steady-state resource concentration at SRT = 2 and 6 days

SRT 2 days SRT 6 daysSpecies S1 (mg/L) S2 (mg/L) S3 (mg/L) S1 (mg/L) S2 (mg/L) S3 (mg/L)

1 3.00 0.90 2.70 0.71 0.21 0.642 2.70 3.00 0.90 0.64 0.71 0.213 0.90 2.70 3.00 0.21 0.64 0.714 3.12 3.06 1.38 0.74 0.73 0.335 1.02 3.06 1.02 0.24 0.73 0.246 2.31 2.28 3.21 0.55 0.54 0.76


operating conditions competition for growth-limitingresources in activated sludge results in oscillations in theabundances of species. Second, we showed that theseoscillations allow the coexistence of more species andhence can increase species diversity. The controllingfactor for the absolute level of species diversity was the

SRT. These two observations have significant applicationsin design and modeling of activated sludge systems.

The first significant application is that the modelcould be used as a design tool to predict which engi-neering control strategies (i.e., SRT, HRT, or hydraulicconfiguration of the aeration tank) can be used to en-hance species diversity. This is important because bothlaboratory and field studies showed that diversity (speciesrichness) is positively related to ecosystem stability [35,46]. Stability can refer to resistance to disturbance,resilience (rate of recovery after disturbance), andsameness of the identity of community biomass overtemporal scales [46]. If the diversitystability hypothesisdeveloped in these studies of macroecological systemsapplies to activated sludge systems, then we expect sys-tems with higher diversity to better maintain perfor-mance when exposed to environmental perturbations(e.g., toxic shock loads). The importance of speciesdiversity was shown in a recent study examining toxicloads of mercury in bioreactors [6]. The results of thestudy showed that diverse biofilm communities demon-strated enhanced resistance to mercury toxicity as com-pared to monoculture biofilms. Thus, an increase inspecies diversity may increase the chance of obtainingspecies with different complementary physiological traitsthat are better adapted to handle specific environmentalperturbations.

Another significant application of the model is thatfor the first time we showed theoretically that the bac-terial community structure in activated sludge system isdynamic. Furthermore, we showed that this dynamicnature arises from the natural process of competition foressential resources. Our result is novel for activatedsludge models because traditional models do not includecompetition within functional groups, nor do they relatecompetition to the diversity of the microbial communityin activated sludge. Our results predict that there aresituations where dynamic microbial communities are thenorm and steady-state conditions do not exist. Thistheoretical observation is supported by several recentstudies, which show experimentally that the microbialcommunity composition is dynamic. One example is thestudy done by Kaewplpat and Grady [20] where theyexamined the structure of the bacterial in a laboratory-scale sequencing batch reactor operated using denaturinggradient gel electrophoresis (DGGE) targeting 16S ribo-somal RNA. The DGGE data showed that the bacterialcommunity was highly dynamic, and this dynamicbehavior was observed within the initial 17 days ofreactor operation and continued throughout the experi-ment.

Studies using anaerobic reactors have also shownthat the structure of bacterial communities is dynamic.Fernandez et al. [7] studied the community dynamics in afunctionally stable methanogenic reactor over a period of

Figure 5. Time course of competition of six species on three re-sources. (A) Steady-state coexistence of three species at SRT = 1.5d. (B) Oscillatory coexistence of six species at SRT = 3 d. (C)Steady-state coexistence of three species at SRT = 6 d.


605 days. The results of their study showed that thebacterial community structure was dynamic and followeda chaotic behavior, even though the reactor was operatedunder stable conditions. In a similar study, Zumstein etal. [50] showed that the bacterial community structure inan anaerobic digester operated under constant environ-mental conditions (feeding, temperature, and pH) over a2-year period was dynamic.

The theoretical results of the current model and theresults of the experimental studies discussed above sug-gest that microbial communities in aerobic and anaerobicbioreactors are dynamic. We speculate that this dynamicbehavior could be caused, in part, by the process ofcompetition for essential resources as described in ourmodel. Furthermore, we suggest that specific operatingparameters for bioreactors affect microbial diversity byaffecting the nature of competition for essential re-sources. The results of our work suggests that the currentactivated sludge models (e.g., ASM1, 2, and 3), may needto be modified to include non-steady-state conditions aswell as competition and the dynamic behavior of themicrobial community.

Although the model provides a testable hypothesisfor the impact of SRT on bacterial diversity in activatedsludge systems, a number of limitations should be dis-cussed. First, the model was developed to study thecompetition of species within one functional group ofmicroorganism, namely the aerobic heterotrophs.However, activated sludge systems are designed to re-move nutrients as well as organics. Therefore, a morecomplete model should include multiple functionalgroups of organisms including aerobic and denitrifyingheterotrophs, nitrifying autotrophs, and phosphorus-accumulating organisms. In addition, this study focusedon the effects of competition within a single trophic level(bacteria). Effects of competition in the presence ofhigher trophic levels, ciliates (predators) and carnivores(top predators), should also be considered. The currentmodel assumes that the influent wastewater is composedof essential resources with bacterial species competing forthese resources. However, influent wastewater at a realwastewater treatment plant contains a variety of re-sources including essential and substitutable resources(e.g., amino acids and ammonia are substitutable re-sources because they are both used as a source of nitrogenby aerobic heterotrophs). The model was only used totest the impact of a single operational parameter, namelythe SRT. There are other design and operationalparameters that can be modified, including reactor con-figuration (plug flow versus complete mixed) andhydraulic retention time (HRT). Future model testingshould be used to develop a rank order of the effec-tiveness of different operational parameters for affectingthe diversity of the bacterial community in activatedsludge systems. Finally, the model assumes a constant

decay rate for all species. The reason we made thisassumption is that most models of activated sludgewastewater treatment use a constant value for the decayrate of all heterotrophic organisms [9, 13, 14]. However,in a recent study [22] it was shown that cells that undergoa starvation response during substrate pulse leading toperiods of substrate limitation and hence low growth ratehave a reduced death rate compared to cells that do notundergo a transition from active to dormant state. Thisreduced death rate allows these cells to be at a competi-tive advantage compared to cells with higher death rate.Therefore, a competition model that takes into consid-eration the difference in death rate between differentbacteria (those with adaptive starvation response andthose with no adaptive mechanism) could better describethe impact of decay rate on competition.

In conclusion, the mechanistic model that wedeveloped to predict exploitative competition of sixaerobic heterotrophic bacterial species competing forthree growth-limiting resources showed that the com-petitive exclusion principle is not the only outcome ofcompetition in activated sludge wastewater treatmentsystems. We also showed that SRT is a key parameter incontrolling competition and hence diversity in activatedsludge systems. The results of the model simulationshowed that for an SRT range of 2.285.66 d, diversity isenhanced.

Acknowledgments

The authors gratefully acknowledge financial supportfrom the National Science Foundation (BES 0116912)and the University of Cincinnati, Department of Civiland Environmental Engineering. We are also grateful forthe helpful comments of two anonymous reviewers.

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