Complex Dynamics of Adaptation in a Nonaxenic Microcystis Culture

Ecotoxicology and Environmental Safety 48, 241}254 (2001) Environmental Research, Section B doi:10.1006/eesa.2000.2023, available online at http://www.idealibrary.com on

Complex Dynamics of Adaptation in a Nonaxenic Microcystis Culture 2. Computer Simulation of Dinitrophenol Effects Clay L. Montague, Renata Behra, Tom N. P. Bosma, Giulio P. Genoni, and Herbert GuK ttinger Swiss Federal Institute for Environmental Science and Technology (EAWAG), CH-8600 Duebendorf, Switzerland Received March 11, 1999

A hypothesis was modeled to account for complex 20-day dynamics in a culture of blue-green algae Microcystis and heterotrophic bacteria exposed to 2,4-dinitrophenol (DNP). In trials with little or no added DNP, a limiting factor (light or CO2) may cause algal density to 6uctuate after 14 days of increase. Such factors may be unimportant at levels of DNP that restrict photosynthesis. Bacterial growth may be limited by organic substrate, and bacteria may be more resistant to DNP than blue-green algae. Hence, at intermediate levels of DNP, substrate provided by increased algal death stimulates bacterial growth more than DNP retards it, causing a bacterial peak. Sorption of DNP to cells may cause the DNP decline. Greater growth and slower DNP decline in experiments with preexposed organisms indicate lower DNP sorption a7nity in preexposed cells. Bacterial assimilation of DNP-containing substrate may cause the reappearance of DNP. The model reproduced the 6uctuation in algal density after growth was limited and better growth and lower DNP decline with preexposed organisms. Reappearance of DNP occurred, but was not obvious. Bacterial dynamics were least well reproduced. Changes in bacterial constants most a4ected output. Despite model inadequacies, probable aspects of toxicant action in nature have been revealed. Ecological relationships among populations of di4erent species and genetic di4erences among individuals may have led to lower than expected toxicity, adaptation, and even growth stimulation. Responses of single species tested in isolation may be inadequate to predict toxicant impact.  2001 Academic Press Key Words: Microcystis; 2,4-dinitrophenol; simulation; microcosm; ecotoxicology.

INTRODUCTION

A computer simulation model can be used to evaluate hypotheses that account for complex ecosystem dynamics. To whom correspondence should be addressed at present address: Department of Environmental Engineering Sciences, P.O. Box 116450, University of Florida, Gainesville, FL 32611. E-mail: [email protected]#.edu.  Present address: TNO Institute of Environmental Sciences, Energy Research and Process Innovation, P.O. Box 342, NL-7300 AH Apeldoorn, The Netherlands.  Present address: Ch. Ruisselet 15, CH-1009 Pully, Switzerland.

Such dynamics arise from the simultaneous operation of multiple feedback loops. Hence, many in#uences believed to occur between living and nonliving variables in the ecosystem must be linked into a set of plausible loops. It is, however, di$cult to imagine correctly the dynamics produced from such a complex hypothesis. By representing the set of simultaneous in#uences in a computer simulation model, the dynamics produced by the overall hypothesis can be evaluated and faulty parts of the hypothesis can be discovered and corrected. In a study of the adaptation of interacting species populations to exposure to a toxicant (Genoni et al., 2001), a laboratory culture was used that consisted of the blue-green alga Microcystis aeruginosa and various unidenti"ed species of associated heterotrophic bacteria. A 19-day exposure of up to 120 lM 2,4-dinitrophenol (DNP) reduced the growth of algae and the net ecosystem production in proportion to the concentration of exposure. Preexposure (20 lM) to the toxicant led to better tolerance of further exposure by the entire community of microbes. Pollution-induced communitylevel tolerance has been predicted and found in other studies as well and may be a general phenomenon (Molander et al., 1990). Mechanisms for such tolerance may be revealed through an examination of the dynamics of response patterns. Though the Microcystis culture was simple, the dynamics of bacterial and algal populations and of DNP concentration were complex (Genoni et al., 2001). To account for these dynamics a set of hypotheses was developed about the dynamic interactions among algae, bacteria, DNP, and the culture's environment. First, at all concentrations, DNP declined during most of the experiment, yet reappeared near the end. Moreover, in trials with preexposed algae and bacteria, algal growth and net ecosystem production were higher, and dissolved DNP declined more slowly. Both of these dynamics could be at least partially explained if reduced DNP sorption accounts for the greater DNP tolerance of preexposed microorganisms. Preexposure to a low level of DNP causes natural selection of cells with a lower sorption a$nity for DNP.

241 0147-6513/01 $35.00 Copyright  2001 by Academic Press All rights of reproduction in any form reserved.

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Dissolved DNP declines as a consequence of sorption to living cells and only to a lesser extent by biodegradation. The subsequent reappearance of dissolved DNP may be caused by release of DNP from nonliving organic matter during mineralization by bacteria. A marked #uctuation in algal density occurred near the end of trials with little or no added DNP, but not at higher exposures. Although algal population growth is limited during DNP exposure, in the absence of DNP it may be limited by lack of inorganic carbon and light. The pH often exceeded 10 during the "rst week, which is indicative of low levels of inorganic carbon. In contrast to the algal pattern, bacteria peaked before the "fth day in trials with high levels of DNP. This early peak in bacterial growth at intermediate concentrations of DNP may result from bacterial assimilation of rapidly accumulating organic matter from stressed and dying algae. Heterotrophic bacteria may be more tolerant than bluegreen algae of intermediate DNP levels. More rapid selection of tolerant bacterial cells may occur owing to their greater number and potential for growth. An optimal level of DNP may exist for maximum bacterial production early in the experiment. Bacterial growth may be limited by the availability of nonliving organic substrate. Initial sources of organic matter include material transferred from stock cultures with live cells, ethanol used as the solvent for DNP, and a small contribution from the DNP itself. Later sources of nonliving organic matter included accumulated exudate and dead cells from algae and bacteria. Linking these hypotheses together in a dynamic simulation model displays their combined consequences (Mon-

tague et al., 1982; Forrester, 1961). All can be linked through the carbon cycle, whose rates are coupled to DNP and the external environment. Dinitrophenol not only in#uences rates of carbon #ow*it can also cycle into and out of microbial cells through sorption/uptake and lysis. Moreover, it seemed to reappear in the dissolved form late in the experiment. A simple sorption mechanism for DNP and only two phenotypes of DNP tolerance are su$cient to represent the hypotheses. High- and low-tolerance types di!er only in their DNP sorption a$nity constant. By initializing the model with di!erent concentrations of each phenotype, cultures inoculated from either preexposed cultures (mostly high-tolerance forms) or non-preexposed cultures (mostly low-tolerance forms) can be simulated. By changing the initial value of dissolved DNP, the various experimental conditions can be simulated and the output compared to experimental data. MATERIALS AND METHODS

Model Overview Cycles of carbon and DNP form the basic structure of the simulation model. The carbon cycle illustrated in Fig. 1 consists of seven compartments: dissolved organic carbon (DIC), low- and high-tolerance forms of M. aeruginosa and of heterotrophic bacteria, and pools of fresh and aged dead organic matter, the substrate for bacteria (particulate and dissolved forms combined). Each storage of C in Fig. 1 has a corresponding storage of DNP in Fig. 2: dissolved, sorbed onto the two forms of algae and bacteria, and contained in fresh and aged dead organic matter. The #ow networks di!er, however. Carbon can enter the system by di!usion

FIG. 1. Diagram of the carbon cycle for the Microcystis}bacteria}DNP model. Rectangles represent storages, arrows represent #ows, and valve symbols represent controls on #ows. Stippled symbols represent DNP-tolerant organisms.

SIMULATION MODEL OF DNP IN A Microcystis CULTURE

243

FIG. 2. Diagram of the dinitrophenol cycle for the Microcystis}bacteria}DNP model. Pathways di!er, but symbols are similar to those of the carbon cycle in Fig. 1.

from air, but DNP is assumed not to. Organic C is remineralized to DIC via algal and bacterial respiration, but regeneration of dissolved DNP occurs only through bacterial assimilation of DNP-containing organic matter. Biodegradation of DNP by bacteria, and to a far lesser extent algae, causes loss of DNP from the cycle (Shea et al., 1983; Hess et al., 1990). Model Equations The C and DNP cycles illustrated in Figs. 1 and 2 are represented by the equations and constants given in Tables 1 and 2. Increases in available light and DIC increase photosynthesis up to a maximum per algal cell through standard saturation equations [Eqs. (11) and (13)]. The equation for light [Eq. (11)] is derived by integrating the Beer}Lambert function over culture depth. Other factors (e.g., temperature, nutrients) are not explicitly modeled. Temperature is constant and nutrients are assumed in excess. Algal biomass absorbs light and takes up DIC [Eqs. (12) and (8), respectively], thereby reducing each, creating negative feedback on photosynthesis that limits algal biomass in the absence of DNP. Increased DNP sorbed to algal cells reduces photosynthesis [Eq. (14)], increases algal respiration up to a maximum per algal cell [Eq. (18)], and increases algal death and exudation rates also up to a saturation limit [Eq. (24)]. In addition, algal death and exudation rates are increased through delayed reactions to algal population density and

stress caused by poor growth conditions. This negative feedback is accomplished with a complex function [Eqs. (20)}(23)]. The delayed negative e!ect of population density is exponentially greater under shortages of light or DIC or when DNP is present [Eq. (23)]. The delays represent the time required for e!ects to accumulate or the time over which stressful conditions must occur before an e!ect on algae occurs. After simpler functions failed, this higher order function was included to produce a marked up to down}up pattern like that found in experiments with no or low DNP. The rate of assimilation of organic substrate by bacteria increases with organic matter concentration up to a maximum per bacterial cell [Eq. (26)]. Dinitrophenol sorbed to bacterial cells reduces assimilation [Eq. (27)], and, as for algae, increases bacterial respiration, exudation, and death up to a maximum per cell [Eqs. (31) and (34)]. Unlike algae, bacterial death and exudation are not a!ected by cell density or other environmental conditions. Without DNP, cellspeci"c rates of respiration, exudation, and death are constant. The equations and constants in the bacteria sector of the model are not as well supported by literature as those for the sector representing M. aeruginosa. Several unidenti"ed species were present. Estimates from the general literature on assemblages of heterotrophic bacteria in nature were used to guide the model development. The model allows organic matter to age before being consumed by bacteria. Aging is assumed to occur within

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TABLE 1 Equations of the Microcystis+Bacteria+DNP Model for Algae and Bacteria of Low DNP Tolerance No.

1 2 3 4 5 6 7

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Equation

Description

Carbon-cycle accumulations X1"X1#dt*(R21#R31#R41#R51#R01!R12 Total dissolved inorganic carbon !R13) X2"X2#dt*(R12!R21!R26) Algae with normal tolerance of DNP X3"X3#dt*(R13!R31!R36) Algae with greater tolerance of DNP X4"X4#dt*(R74!R41!R46) Bacteria with normal tolerance of DNP X5"X5#dt*(R75!R51!R56) Bacteria with greater tolerance of DNP X6"X6#dt*(R26#R36#R46#R56!R67) Particulate and dissolved organic matter X7"X7#dt*(R67!R74!R75) Aged organic matter Carbon-Cycle tranfer rates (replace all 2s with 3s for tolerant algae equations) R12"s12*X2 Gross primary production of algae s12"s12max*s12I*s12C*s12D Biomass-speci"c rate of photosynthesis s12I"Ipar/(s12Ik#Ipar) Light e!ect on photosynthesis Ipar"(Io/(c*z))*(1!exp(!c*z)) Depth-averaged light within the culture c"cm#cprime*(X2#X3) Light attenuation coe$cient s12C"X1/(s12Ck#X1) Inorganic carbon e!ect on photosynthesis s12D"s12Dk/(s12Dk#Ds2) E!ect of DNP on photosynthesis Ds2"D2/X2 Sorbed DNP per gram of algae carbon R21"s21*X2 Respiration rate of algae s21"s21n#s21D Total biomass-speci"c rate of algal respiration s21D"s21Dmax*Ds2/(s21Dk#Ds2) Biomass-speci"c rate of algal respiration caused by DNP R26"s2*X2 Rate of exudation and death of algae s26"s26n#s26k1*DelAlgD ) (s26k2*Dels26S)#s26D Biomass-speci"c rate of algal exudation and death DelAlg"DelAlg#dt*((X2#X3)-DelAlg)/AlgDelTm Delayed population density e!ect on algal exudation and death Dels26S"Dels26S#dt*(s26S!Dels26S)/s26SDelTm Delayed stress e!ect on algal exudation and death s26S"s26Sk/(s26Sk#s12I*s12C*s12D) Index of algal stress s26D"s26Dmax*Ds2/(s26Dk#Ds2) DNP e!ect on biomass-speci"c algal exudation and death R74"s74*X4 Rate of assimilation of aged organics by bacteria s74"s74D*s74max*X7/(s74k#X7) Biomass-speci"c assimilation of aged organic matter by bacteria s74D"s74Dk/(s74Dk#Ds4) DNP e!ect on biomass-speci"c bacterial assimilation rate Ds4"D4/X4 Sorbed DNP per gram of bacteria carbon R41"s41*X4 Respiration rate of bacteria s41"s41n#s41D Biomass-speci"c rate of bacterial respiration s41D"s41Dmax*Ds4/(s41Dk#Ds4) Biomass-speci"c rate of bacterial respiration caused by DNP R46"s46*X4 Rate of exudation and death of bacteria s46"s46n#s46D Biomass-speci"c rate of bacterial exudation and death s46D"s46Dmax*Ds4/(s46Dk#Ds4) DNP e!ect on biomass-speci"c bacterial exudation and death R67"X6/R67t Rate of aging of organic matter (particulate and dissolved) R01"(R01max/Ceq)*(Ceq!X1) Rate of out#ow of carbon dioxide by di!usion

38 39 40 41 42 43

DNP-cycle accumulations D1"D1#dt*(RD714#RD715!RD12!RD13 Dissolved DNP !RD14!RD15) D2"D2#dt*(RD12!RD20!RD26) DNP sorbed to normal algae D3"D3#dt*(RD13!RD30!RD36) DNP sorbed to tolerant algae D4"D4#dt*(RD14!RD40!RD46) DNP sorbed to normal bacteria D5"D5#dt*(RD15!RD50!RD56) DNP sorbed to tolerant bacteria D6"D6#dt*(RD26#RD36#RD46#RD56!RD67) DNP in particulate and dissolved organic matter D7"D7#dt*(RD67!RD714!RD715) DNP in aged organic matter

44 45

DNP-cycle transfer rates (replace all 4s with 5s for tolerant bacteria equations) RD12"sD12*(RD12k*D1*X2!D2) Rate of DNP sorption by algae RD20"sD20*D2 Rate of biodegradation of DNP by algae

37

Units

g C ) L\ g C ) L\ g C ) L\ g C ) L\ g C ) L\ g C ) L\ g C ) L\

g C ) L\ day\ day\ Unitless fraction E ) m\ ) s\ cm\ Unitless fraction Unitless fraction mol DNP ) g C\ g C ) L\ ) day\ day\ day\ g C ) L\ ) day\ day\ g C ) L\ Unitless fraction Unitless fraction day\ g C ) L\ ) day\ day\ Unitless fraction mol DNP ) g C\ g C ) L\ ) day\ day\ day\ g C ) L\ ) day\ day\ day\ g C ) L\ ) day\ g C ) L\ ) day\

M DNP M M M M M M

DNP DNP DNP DNP DNP DNP

M DNP ) day\ M DNP ) day\

245

SIMULATION MODEL OF DNP IN A Microcystis CULTURE

TABLE 1=Continued No.

Equation

46 47 48 49

RD14"sD14*(RD14k*D1*X4!D4) RD40"sD40*D4 RD26"s26*D2 RD46"s46*D4

50 51

RD67"D6/R67t RD714"R74*(D7/X7)

Description Rate of DNP sorption by bacteria Rate of biodegradation of DNP by bacteria DNP transfer to organics upon algal exudation and death DNP transfer to organics upon bacterial exudation and death DNP transfer to aged organics after aging DNP release from aged organics upon bacterial assimilation

Units M DNP ) day\ M DNP ) day\ M DNP ) day\ M DNP ) day\ M DNP ) day\ M DNP ) day\

Note. Equations for DNP tolerant algae and bacteria are identical. Constant coe$cient values are given in Table 2.

a day, enough time for cell membranes to hydrolyze and for cell contents to become available to bacteria. The delay slows the carbon cycle and reduces the likelihood of an unrealistically rapid increase in bacteria in response to a sudden increase in freshly dead cells. Dissolved inorganic carbon exchanges with overlying air in proportion to the di!erence between its concentration and the equilibrium concentration in fresh water of the same temperature and alkalinity [Eq. (36)]. The equation is based on Fick's "rst law of di!usion. The ratio of the maximum possible di!usion rate (into DIC-free growth medium) to the equilibrium concentration represents the fraction of the di!erence between a given DIC concentration and the equilibrium concentration that can be reduced per day by di!usion. Dinitrophenol moves around the cycle through sorption and release from cells [Eqs. (44) and (46)] and through transfers from living to nonliving organic matter upon exudation and death of algae and bacteria [Eqs. (48) and (49)]. The DNP sorbed to algae and bacteria is transferred to nonliving organic matter by applying the respective speci"c rates of exudation and death to the DNP in each organism. For both algae and bacteria, the rate of DNP sorption declines with the di!erence between the cells' capacity for sorption (a$nity for DNP) and the amount already sorbed. The DNP a$nity constant for each type of cell is the ratio of the amount sorbed per cell at equilibrium to the molar concentration of dissolved DNP. High-tolerance algae and bacteria are hypothesized to have low a$nity for DNP. In the model, both algae and bacteria biodegrade in proportion to the amount sorbed, though the fraction biodegraded is small [Eqs. (45) and (47)]. Dinitrophenol is transferred from the fresh nonliving compartment to the aged compartment after the aging time used in the C cycle [Eq. (50)]. Dissolved DNP is released as organic matter is assimilated by bacteria [Eq. (51)]. Most simulations were 20 days long and used the Euler method of integration with a time step of 0.0004 days. A smaller time step was necessary in some runs. The model was programmed in QuickBasic 4.5 and run on a Pentium

166 microcomputer in the MS DOS mode of the Windows 95 operating system. Constant Model Coezcients The constant values given in Table 2 were measured where possible or were estimated from published studies and general principles of environmental biology and chemistry under similar experimental conditions (30 lE ) m\ ) s\, 223C, BG-11 medium). For some values, however, no published information could be found (e.g., constants in all DNP functions). In these cases, values were set by model calibration, in which the model was repeatedly run with di!erent values of one or several of the unknown coe$cients to bring the scale and pattern of the output into a plausible range. For DNP-related constants, calibration was done at 40 lM DNP. Constraints on constant values included plausibility, that DNP a$nity constants were higher for low-tolerance organisms, and that bacteria were an order of magnitude more e!ective than algae at biodegradation. Fit was judged by inspection, not according to an optimization or error minimization scheme. The goal of model calibration was to "nd a single set of constant values that could be used under any of the given conditions and give reasonable dynamics for all response variables (algae, bacteria, and DNP). A more restrictive calibration was used when uncertainty in an estimate arose from con#icting reports in the literature, convoluted derivations, and unit conversions. For example, after conversion of units and accounting for temperature di!erences (assuming a Q10 of 2), estimates for the maximum biomass-speci"c rate of assimilation of organic C by bacteria range over two orders of magnitude, from 0.5 to 50 day\, depending in part on substrate (Jensen, 1985; Wright and Hobbie, 1966; Bell, 1980). The lowest estimates were derived from M. aeruginosa exudate (Jensen, 1985), so lower values seemed more reasonable. Reported values for half-saturation of uptake by organic substrate range from 1 to 4000 g ) L\ of C (Jensen, 1985; Bell, 1980; Jannasch, 1967), a range that left a wide latitude in setting a model value.

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TABLE 2 Constant Coe7cient Values Used in the Microcystis+Bacteria+DNP Model Variable

Value units

Eq. No.

AlgDelTm

5 days

(21)

Ceq

0.0147 g ) L\

(36)

cm CpCellA

0.0188 cm\ 1.12;10\ mg)cell\

(12) (IV)

CpCellB

5.4;10\ mg ) cell\

(IV)

Cprime

3.3 cm\ ) (g ) L\)\

(12)

Io R01max

30 E ) m\ ) s\ 0.175 (g ) L\) ) day\

(11) (36)

R67t

1 day

(35)

RD12k

7500 L ) g\

(44)

RD13k

400 L ) g\

(44)

RD14k

1.5;10 L ) g\

(46)

RD15k

5000 L g\

(46)

s12Ck

6;10\ g ) L\

(13)

s12Dk

500 mol ) g\

(14)

s12Ik

2 E ) m\ ) s\

(10)

s12max

1 day\

(9)

s21Dk

250 mol ) g\

(18)

s21Dmax s21n s26Dk

5 day\ 0.15 day\ 250 mol ) g\

(18) (17) (24)

s26Dmax

8 day\

(24)

s26k1

0.01 day\ ) (g ) L\)\

(20)

s26k2

100 (unitless)

(20)

s26n

0.0275 day\

(20)

s26SDelTm

5 days

(22)

s26Sk

0.1 (unitless)

(23)

s41Dk

1;10 mol ) L\

(31)

s41Dmax s41n

1 day\ 1.43 day\

(31) (30)

s46Dk

1;10 mol ) g\

(34)

s46Dmax

1 day\

(34)

Meaning Time lag for population density to a!ect algal growth Equilibrium level of dissolved inorganic carbon in culture medium Light (PAR) attenuation by blank culture medium Organic carbon content per algal cell (conversion of cells to carbon) Organic carbon content per bacterial cell (conversion of cells to carbon) Light (PAR) attenuation per unit algae (assuming no gas vacuoles) Incident light (PAR) Hypothetical CO di!usion rate when inorganic  carbon in culture medium is 0 Time required for nonliving organics to age (and become usable by bacteria) DNP a$nity, DNP sorption per unit algal biomass (normal algae) DNP a$nity, DNP sorption per unit algal biomass (tolerant algae) DNP a$nity, DNP sorption per unit bacterial biomass (normal bacteria) DNP a$nity, DNP sorption per unit bacterial biomass (tolerant bacteria) Half-saturation coe$cient for algal production as a function of inorganic C Half-saturation coe$cient for algal production as a function of DNP Half-saturation coe$cient for algal production as a function of light (PAR) Maximum biomass-speci"c rate of photosynthesis by algae Half-saturation coe$cient for algal respiration as a function of DNP Maximum e!ect of DNP on algal respiration Normal biomass-speci"c rate of algal respiration Half-saturation coe$cient for algal exudation and death as a function of DNP Maximum e!ect of DNP on algal exudation and death Biomass-speci"c multiplier of algal exudation and death Multiplier for algal susceptibility to exudation and death when under stress Normal biomass-speci"c rate of algal exudation and death Lag time for stress to create enhanced algal exudation and death Half-saturation coe$cient for algal stress as indicated by low productivity. Half-saturation coe$cient for bacterial respiration as a function of DNP Maximum e!ect of DNP on bacterial respiration Normal biomass-speci"c rate of bacterial respiration Half-saturation coe$cient for bacterial exudation and death as a function of DNP Maximum e!ect of DNP on algal exudation and death

Source references Model calibration De!eyes (1965) Measured Olesen and Ganf (1986); Reynolds et al. (1981); Takamura et al. (1985) Wright and Hobbie (1966) and estimate from measured size. Kappers (1984); Aiba et al. (1983); Ganf et al. (1989); Zohary and Madeira (1990) Measured Extrapolation from Broecker and Peng (1974) and back-calculation from biomass produced in culture Model calibration Model calibration Model calibration Model calibration Model calibration Estimate from data of Paerl (1983) and van der Westhuizen and Elo! (1983) Model calibration Kappers (1984); van der Westhuizen and Elo! (1983); Whitelam and Codd (1983) Kappers (1984); van der Westhuizen and Elo! (1983); Oh and Rhee (1991) Model calibration

Jensen (1985); Oh and Rhee (1991) Model calibration Model calibration Model calibration Model calibration Estimate based on Jensen (1985) and Oh and Rhee (1991) Model calibration Model calibration Model calibration Model calibration Jensen (1985) Model calibration Model calibration

247

SIMULATION MODEL OF DNP IN A Microcystis CULTURE

TABLE 2=Continued Variable

Value units

Eq. No.

s46n

0.001 day\

(33)

s74Dk

1;10 mol ) g\

(27)

s74k

8;10\ g ) L\

(26)

s74max

1.65 day\

(26)

sD12 sD14

5;10\ day\ 6;10\ day\

(44) (46)

sD20 sD40

0.001 day\ 0.01 day\

(45) (47)

z

1.94 cm

(11)

Meaning

Source references

Normal biomass-speci"c rate of bacterial exudation and death Half-saturation coe$cient for bacterial assimilation as a function of DNP Half-saturation coe$cient for bacterial assimilation as a function of organics Maximum biomass-speci"c rate of bacterial assimilation of organics Di!erence-speci"c rate of DNP sorption by algae Equilibrium di!erence-speci"c rate of DNP sorption by bacteria Biomass speci"c rate of DNP biodegration by algae Biomass speci"c rate of DNP biodegration by bacteria Culture depth

Estimate based on low expected value Model calibration Jensen (1985); Bell (1980); Jannasch (1967) Jensen (1985); Wright and Hobbie (1966); Bell (1980) Model calibration Model calibration Model calibration Model calibration Measured

Note. Referenced equations are in Table 1. Values are given in the units required for dimensional consistency: carbon concentration in g ) L\; DNP in M; and time in days. IV, initial value equation. DNP-tolerant algae and bacteria di!er from low-tolerance forms only in their DNP a$nity constants.

Other constants were based on literature values that agreed more closely or were directly measured. The C contents of algae and bacteria were used to convert from cells (the experimental measure) to units of organic C (the modeled units). Published estimates for M. aeruginosa range from 6.6 to 13.8 pg ) cell\ (Olesen and Ganf, 1986; Reynolds et al., 1981; Takamura et al., 1985). Estimates of maximum photosynthesis and half-saturation with light for M. aeruginosa grown under conditions similar to those in our study range from 0.7 to 2.4 day\ and from 1.6 to 23.5 lE ) m\ ) s\, respectively (Kappers, 1984; Aiba et al., 1983; Oh and Rhee, 1991; van der Westhuizen and Elo!, 1983; Whitelam and Codd, 1983). For DIC, the chosen half-saturation coe$cient was based on studies of the e!ects of pH (van der Westhuizen and Elo!, 1983; Paerl, 1983), since no direct studies of this could be found. Literature estimates for light attenuation by M. aeruginosa vary widely and are higher with more gas vacuoles. Unit C estimates under subdued light vary from 6.9 to 31.1 cm\(g ) L\)\ with some variation from original estimates given per unit chlorophyll and some coming from converting chlorophyll to equivalent units for algal carbon (Ganf et al., 1989; Zohary and Madeira, 1990). Gas vacuoles were not known to have been present in the experiment, so a lower value was used. Equilibrium DIC concentration in growth medium was taken from De!eyes (1965), assuming a pH of 7 and an alkalinity of 0.01 mEq ) L\. The hypothetical maximum CO di!usion rate (which occurs when the medium has no  DIC) was determined by considering the inorganic carbon necessary to support the growth that occurs in trials without DNP, the equilibrium DIC concentration, the 24.6-cm surface area of the microcosm, and by assuming CO di!us ivity of 1.86 ) 10\ cm ) s\ (Broecker and Peng, 1974;

Stumm and Morgan, 1981; Emerson, 1975). The resulting value, when inserted into the stagnant boundary layer model of di!usion (Broecker and Peng, 1974) indicated a stagnant boundary layer thickness of 664 lm, a value for mildly agitated water of high surface tension such as might occur in a dense culture. Initial Concentrations Initial concentrations approximated conditions in the experiment. Dissolved DNP was set to an experimental concentration (0 to 120 lM). All other forms of DNP were set to zero. Algal and bacterial carbon concentrations were set to the organic C equivalent of the quantities inoculated in the cultures (2,000,000 and 20,000,000 cells/ml, respectively). To simulate experiments with the preexposed culture, 99.9% of the algal and bacterial C concentrations was assigned to the high-tolerance category (X3 and X5, respectively), with the remainder assigned to the low-tolerance forms (X2 and X4). For non-preexposed simulations, 0.0001% was assigned to high-tolerance forms. The initial concentration of nonliving organic C was set at a base amount of 1.7 mg ) L\ plus 750 g/mol DNP times the initial DNP concentration. Two-thirds was assigned to the fresh category (X6) and 1/3 to the aged category (X7). The base amount was that amount reasonably expected to be transferred to the experimental #asks from the stock cultures. The DNP-dependent amount was based on the ethanol used to dissolve DNP (19.2 mg ethanol per mole of DNP). Most (90%) of the ethanol was assumed to have volatilized. Although DNP itself is organic matter that could be utilized as a substrate by certain bacteria, each mole adds only 72 g C.

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The initial concentration of dissolved inorganic C was set to equilibrium with the atmosphere. For delayed algae [Eq. (21)], the initial values of the low- and high-tolerance algae populations were summed. For the stress index [Eq. (22)], initial values were arbitrarily set to 0.1. Since these delays have little impact initially, the choices were unimportant.

when a constant is doubled minus that when halved, divided by the baseline value for the output characteristic when no constants are altered. A negative index indicates an inverse in#uence of a constant change on the response of an output characteristic. RESULTS

Sensitivity Analysis The 70 model constants were each halved and doubled on 140 model reruns for each of three combinations of initial DNP and DNP-tolerant algae and bacteria (no DNP with 0.0001% tolerant cells; 40 lM DNP with 0.0001% tolerant cells, and 40 lM DNP with 99.9% tolerant cells). For each of the three output variables (algae, bacteria, and DNP), analogs of amplitude and frequency were measured. The four output characteristics included: (a) the di!erence between the overall minimum and maximum (Range 1); (b) the time elapsed between these extremes (Interval 1); (c) the di!erence between the maximum and a subsequent minimum, if one occurred (Range 2); and (d) the time elapsed between these postmaximum points (Interval 2). If the overall minimum occurs after the overall maximum, the two ranges and intervals are the same. In this case, only Range 1 and Interval 1 are reported. An index of model sensitivity to constant changes was computed as follows: the value of an output characteristic

The model's output (Fig. 3) captures the features of the experimental data to varying degrees of success. Simulations initialized with 0.0001% high-tolerance microorganisms are given in Figs. 3a to 3c. Those with 99.9% high-tolerance forms are in Figs. 3d to 3f. As in the experimental data, greater concentrations of dissolved DNP resulted in lower net production, but stimulated production of bacteria. Also, non-preexposed cultures were far more sensitive to DNP than preexposed cultures, and DNP concentrations declined more rapidly. Dinitrophenol reappeared almost imperceptibly after 15 days in the non-preexposed simulations (Fig. 3c). Algae In the absence of DNP, algal growth was limited by DIC and light, though at peak algal density the computed growth factor for DIC was lower than that for light, which indicates a greater limitation by DIC. The #uctuation after

FIG. 3. Model generated dynamics for algae, bacteria, and DNP when initial DNP is 0, 20, 40, 80, and 120 M. a, b, and c indicate output from simulations initialized with 0.0001% DNP-tolerant organisms; d, e, and f indicate results after initializing with 99.9% DNP-tolerant organisms.

SIMULATION MODEL OF DNP IN A Microcystis CULTURE

the peak was similar to that of the experimental data. The pattern continued as a dampened oscillation in simulation runs longer than 20 days. In the presence of DNP, algal growth was progressively lower with increasing DNP concentration. In simulated trials with preexposed microorganisms, the negative e!ect of DNP was lower (Figs. 3a and 3d). With increasing additions of DNP, the peak in algal biomass was progressively delayed. This was veri"ed for the non-preexposed cultures in runs longer than 20 days (not shown). In trials with preexposed cells, the delay in algal growth peak with increasing DNP concentration is considerably reduced and the subsequent oscillation is dampened. A transition from low-tolerance to high-tolerance forms occurs in non-preexposed cultures exposed to high levels of DNP. This helps account for the growth improvement toward the end of the simulations. The transition is far more rapid at higher DNP concentrations. In 40 lM DNP, hightolerance algae increase from the initial 0.0001% to 3% by day 20. In 80 lM DNP, high-tolerance algae account for more than 99.9% of the population after only 5 days. The transition for bacteria is similar. Bacteria Bacterial dynamics are least well represented by the model, although the mechanisms believed to account for the experimental dynamics are evident. Although simple exponential growth of bacteria without added DNP occurs, bacterial density at the end of the simulation is only about one-tenth that in the experiments. Moreover, the more complex dynamics are not reproduced by the model. For example, the early peak in bacteria that occurs when preexposed cultures are exposed to intermediate levels of DNP did not occur. As in the experiments, however, bacterial growth was stimulated at intermediate exposure to DNP. The very large growth of bacteria in simulations of non-preexposed organisms in 20 lM DNP, though not characteristic of the experimental results, does illustrate the possibility of an optimal level of toxicant for maximum bacterial production. At higher exposures, bacteria in simulations of non-preexposed cultures decline, but later and more suddenly than in experimental data. As DNP is sorbed and high-tolerance organisms become more prevalent, bacterial populations deplete the substrate and then decline after day 15 (Fig. 3b). A slightly higher peak occurs in 40 lM DNP than in 80 lM DNP, which is reminiscent of the greater densities at intermediate DNP levels in the experiments (Fig. 3b). However, at 120 lM DNP, even more bacteria are produced than in 80 lM DNP. At high levels of DNP, assimilation and respiration are retarded unequally in the model. The e!ect is a slow growth at higher production e$ciency as DNPtolerant bacteria grow on the limited organic substrate.

249

Overall, instead of an optimal level of DNP for maximum bacterial production, an optimal level for minimum production is evident. This e!ect was not predicted at the beginning, and the explanation was developed only after the model output was viewed. In preexposed simulations, growth continually improves with greater DNP (Fig. 3e). This is not unlike the experimental data (Genoni et al., 2001). When these cultures are exposed to higher DNP concentrations, increased speci"c rates of exudation and death continually provide substrate that stimulates bacterial growth. The di!erence is that the algae do not die completely, but continue to produce organic substrate. At higher levels of DNP, bacterial production e$ciency is again higher. However, the e!ect diminishes, as shown by the similarity in the output for exposures above 40 lM DNP (Fig. 3e). Dinitrophenol The equations for DNP sorption account for the decline in dissolved DNP in the model. The equations for biodegradation make little di!erence, and when completely removed from the model, no changes are detectable. Since sorption a$nity was set lower in high-tolerance cells, DNP declines more rapidly in the simulated non-preexposed cultures. Dissolved DNP can reappear in the model when DNP containing nonliving organic matter is assimilated by bacteria, but only if the reappearance rate exceeds the sorption rate. This occurs in the simulated non-preexposed cultures, but not to the degree seen in the experiments (Fig. 3c). Reappearance is imperceptible in the simulated preexposed cultures. Sensitivity Analysis Results Values of the index of model sensitivity for the "ve most in#uential model constants are given for the four output characteristics in Tables 3, 4, and 5 for algae, bacteria, and DNP, respectively. Results for the various combinations of DNP and DNP tolerance are shown in separate sections of each table. If a constant is not among the top "ve for any of the three combinations of DNP and DNP tolerance, it is not reported. Without DNP, algal dynamics are in#uenced most by constants that control CO di!usion and the algal sector  constants representing productivity, carbon content, and the lag in the population stress function (Table 3). The exponent of the term for stress-induced exudation and death [s26k2 in Eq. (20)] was the single most e!ective constant for changing the postmaximum interval (Interval 2). Higher values produced a shorter interval because of a more rapid decline. When the model is initialized with 40 lM DNP and only 0.0001% DNP-tolerant algae and bacteria, however, none of the constants mentioned above are among the top

250

MONTAGUE ET AL.

TABLE 3 Sensitivity Index Values for the Top Five Model Constants That In6uence Simulated Algal Dynamics 40 lM DNP; 0.0001% tolerant

No DNP; 0.0001% tolerant

Constant AlgDelTm Ceq CpCellA CpCellB R10max RD12k RD13k RD14k s12Ck s12max s13max s21n s26k2 s26n s26Sk s36Dk s36Dmax s41n s51n s74max s75max SD12 SD13 SD14

40 lM DNP; 99.9% tolerant

Baseline: 146.7 14.0 72.9 2.7 45.9 10.7 45.9 10.7 112.1 19.0 1.3 1.0 Eq. No. Range 1 Interval 1 Range 2 Interval 2 Range 1 Interval 1 Range 2 Interval 2 Range 1 Interval 1 Range 2 Interval 2 21 36

0.40

0.37

1.08

!0.24 !2.00

!1.52

0.14

!1.50

!1.57 3.30

36 44 46 13 9

0.55

0.65

1.74

!2.51

3.29

!2.07

0.78

0.82

!2.51 1.97 0.21

0.59

1.11

3.08

61.8

!0.12

!3.52

0.24

3.62

0.71 0.46 !1.06

!0.16

!0.24 !2.07 1.97 0.80 17 20 20 23

0.42

!3.09

!2.73

!0.35 !0.77 3.63 !3.62

30

!3.31

26

3.33

44

!3.09

2.25

!3.29

!0.46

0.46

!53.8 !32.3 0.27 45.7 34.6 !3.52

46

!2.51

3.08

!2.07

Note. Baseline range units are million algal cells per millileter. Interval units are days. Range and Interval 1 refer to the di!erence between the overall maximum and the overall minimum in the model output. Range and Interval 2 refer to the di!erence between the overall maximum and a postmaximum minimum if one occurs.

"ve in#uences on algal dynamics. Instead, dominant constants are from the low-tolerance bacterial sector: cell carbon content, respiration, and DNP sorption. With 40 lM DNP and 99.9% DNP-tolerant algae and bacteria, the important constants are again those involved with CO  di!usion, algal productivity, and carbon content. As expected from the level of DNP, productivity of DNP-tolerant algae (s13max) is the most in#uential constant. Constants from the bacteria sector are also in#uential, especially on Range 2. In the model, when assimilation of organic matter increases or respiration decreases, a shortage of inorganic carbon causes the postmaximum decline in algae to be greater. The overall range of bacterial concentration (Range 1) greatly increases, and the time elapsed between the overall maximum and minimum (Interval 1) decreases when cell respiration is reduced or substrate assimilation is increased (Table 4). Range 1 is particularly sensitive to respiration. Even though no DNP is present and tolerant cells account for only 0.0001% of the initial bacteria cells, substrate assimilation by DNP-tolerant bacteria a!ects bacteria dynamics as e!ectively as that of low-tolerance cells. When

their assimilation is doubled, they quickly become the predominant form. This does not occur when the model is initialized with 40 lM DNP and 0.0001% DNP-tolerant cells (Table 4). Instead, changes in rates of assimilation and respiration by low-tolerance bacteria are more in#uential on bacterial dynamics. For low-tolerance cells, high maximum assimilation and low respiration constants compensate for the e!ect of DNP in the model. Productivity of low-tolerance algal cells also increases bacterial range and decreases interval. The same constants for high-tolerance algae, however, are not among the top "ve. As for the bacteria, an increase in the maximum algal productivity compensates for the greater e!ect of DNP on low-tolerance cells. The e!ect of this compensation is less for high-tolerance cells for two reasons: they initially account for a small fraction of cells and the di!erence in algal production by tolerant forms is smaller in the absence of DNP, so high-tolerance forms respond less to an increase in productivity. When the model is initialized with 40 lM DNP and 99.9% tolerant algae and bacteria, rates of assimilation and respiration by both low- and high-tolerance bacteria

251

SIMULATION MODEL OF DNP IN A Microcystis CULTURE

TABLE 4 Sensitivity Index Values for the Top Five Model Constants That In6uence Simulated Bacterial Dynamics 40 lM DNP; 0.0001% tolerant

No DNP; 0.0001% tolerant Constant

Baseline: Eq. No.

CpCellB RD12k s12max s13max s21Dk s21Dmax s26n s41n s51n s74k s74max s75max sD12

0.13 Range 1

16.5 Interval 1

0.21 Range 1

!0.18

!3.64 4.56

14.6 Interval 1

0.20 Range 2

40 lM DNP; 99.9% tolerant 4.22 Interval 2

1.13 Range 1

20.0 Interval 1

!1.31 44 9

!1.98

!2.13 !1.00

18 18 20 30 26 26

!1.91 1.93 !0.10 !108.54 !1.69 !1.62 59.70 61.02

1.87

!32.27

!2.27 0.23

38.27

!1.97

!3.64

1.91

44

0.65

!0.07

!1.90 1.95 !31.46

4.23

!11.97 !11.87

!0.08 1.26

38.23 2.85

!5.53

6.07 7.14

0.18 !1.43

Note. Baseline range units are billion bacterial cells per milliliter. Interval units are days. Range and interval de"nitions are the same as in Table 3.

in#uence Range 1 and Interval 1 (Table 4). In this case, changes in assimilation and respiration by high-tolerance bacteria are similar in e!ect as for low-tolerance bacteria, owing to the initially large proportion of high-tolerance forms. The overall range of DNP dynamics increases when respiration of low-tolerance bacterial cells decreases and substrate assimilation increases (Table 5). Model sensitivity to these changes occurs whether the model starts with 0.0001 TABLE 5 Sensitivity Index Values for the Top Five Model Constants That In6uence Simulated DNP Dynamics 40 lM DNP; 0.0001% tolerant

Constant RD12k RD14k s12max s13max s21Dk s21Dmax s41n s51n s74max s75max sD12 sD14

Baseline: Eq. No.

39.4 Range 1

16.2 Interval 1

44 46 9

!0.04 0.07 0.06

!0.40

18 18 30

0.04 !0.04 !0.90

0.40 !0.41

26

0.84 !0.11 !0.04 0.07

40 lM DNP; 99.9% tolerant 12.5 Range 1

0.44 0.81

44 46

!0.33 !0.40

!2.23 !1.34 2.23 0.82

Note. Baseline range units are lM. Interval units are days. Range and Interval de"nitions are the same as in Table 3.

or 99.9% tolerant algal and bacterial cells. With 99.9% high-tolerance cells, the model is sensitive to changes in rates of respiration and assimilation by high-tolerance cells, but less so by low-tolerance cells. A shorter Interval 1 for DNP occurs when the model is initialized with 0.0001% DNP-tolerant cells (in 40 lM DNP runs). Moreover, only constants for low-tolerance algae are e!ective. Reductions in algal productivity (s12max) and increases in the e!ect of DNP on algal respiration (s21Dmax) cause the interval to become shorter. Increases in the sorption of DNP by lowtolerance cells and the e!ect of DNP on algal respiration decrease the interval between the maximum and the minimum DNP. DISCUSSION

Inorganic carbon rather than light limits model photosynthesis, bacteria are more in#uential than algae on model dynamics, and constants for low-tolerance algae and bacteria elicit greater e!ects on model output than those for high-tolerance forms. The sensitivity of the model to CO  di!usion rather than light indicates DIC as the primary limiting factor for algal growth in the model. If this is the case for the real cultures, enrichment with CO should  stimulate greater growth than brighter lighting of the same relative increase. Nevertheless, the sensitivity of the model to bacterial constants suggests a fundamental function of bacteria in the culture. In the model, remineralization of carbon by bacteria is the limiting step in the carbon cycle. Of less importance are the constants involved with the production of organic substrate by algae. Those constants a!ected algal dynamics, but a concomitant inverse e!ect of

252

MONTAGUE ET AL.

similar magnitude did not occur in bacterial dynamics. This would be expected if production of organic matter was as limiting to bacterial production as inorganic carbon was to algal production. Instead, responses by bacteria to increased production of organic substrate were diminutive. Adaptation to DNP occurs in the model. It remains to be determined whether DNP adaptation in the experimental cultures is the result of genotypic di!erences in the di!erent phenotypes. Nevertheless, when DNP is present, high-tolerance algae and bacteria have an advantage. In non-preexposed cultures, low-tolerance forms dominate at 40 lM because most of the DNP becomes sequestered in organic matter. Dinitrophenol sequestering in the model signi"cantly limits the rate of adaptation at low levels of DNP. Sequestering may also limit adaptation in the cultures. The model, itself a hypothesis, was able to reproduce the general features of the experimental dynamics using plausible equations and coe$cients. Yet the distinctions between the two cell phenotypes and the two culture types were very simple (DNP sorption a$nity and initial proportion of high-tolerance cells). The ability to represent so many of the experimental dynamics without changing coe$cient values other than the initial proportion of high-tolerance cells is encouraging support for the model and the four linked hypotheses on which it is based. The model did not reproduce every aspect of the experimental data well, but this may simply be a matter of degree. The overall mechanisms represented in the model should produce a better match to experimental data if they employed speci"c functions and coe$cients developed through direct experimentation with the cultures instead of those developed purely by examining the literature. Algae In the absence of DNP, DIC limits algal growth more than light. Di!usion of DIC, however, could be greater if either the boundary layer thickness was less than 664 lm or the equilibrium DIC was greater than assumed. Broecker and Peng (1974) gave a boundary layer thickness of mildly agitated fresh water of 233 lm, but our dense cultures probably have greater surface tension, and may not have been agitated as much, so the boundary layer thickness is likely to be higher. The equilibrium concentration of DIC, however, would have been smaller if the alkalinity estimate was too high. A more appropriate estimate for Ceq may be 0.005 g ) L\ (Beat MuK ller, EAWAG, personal communication). Ironically, if a boundary layer of 233 lm and an equilibrium DIC of 0.005 g ) L\ are used, the speci"c rate of di!usion (R01max) is unchanged. Limitation by nutrients not included in the model is also possible in the absence of DNP, though the model assumes excess nutrients other than C. BG-11 growth medium contains 17.6 mM N and 0.23 mM P, among other nutrients.

The peak total organic C for algae and bacteria together is perhaps 1.7 or 1.8 g ) L\ in the cultures, but estimates of C content vary over a factor of 2. Nevertheless, if the demand for nutrients is stoichiometric and the C:N:P atom ratio is 122:20:1 (average for M. aeruginosa grown in various levels of light; Kappers, 1984), then about "ve times more P is needed than is supplied by BG-11 medium. This indicates a severe P limitation in cultures without DNP. In tests done to develop a growth medium for M. aeruginosa, the demand for N exceeded that for P by as much as 75 times (Gerlo! et al., 1952). If true for our cultures, then the observed growth would require six times the N, roughly the same de"cit computed for P. Direct experimentation should reveal the extent to which light, DIC, N, and P limit growth in cultures without DNP. A biomass increase upon addition of any item after Day 15 will identify the degree to which it is limiting. If N or P is the primary limiting factor, inclusion of cycles of these elements may improve the model and may obviate the complex stress function used to create the #uctuation in algal concentration. In any case, the dynamics that occur after these additions can be predicted by the model. A comparison of the actual outcome would test the validity of the model as a predictive tool. Bacteria The lack of an early peak in simulated preexposed bacteria around day 5 at intermediate concentrations of DNP is perhaps the greatest problem in the model. We hypothesized that an optimal concentration of DNP might exist for bacteria, at which the cellular products from DNP-a!ected algae would stimulate bacterial production early, after which the bacteria would decline until conditions improved for algae (as DNP became sequestered in nonliving organic matter). All of these mechanisms are in the model, yet the early peak did not occur. None of the constant changes performed in the sensitivity analysis produced a peak in bacteria anywhere in the runs initialized with 99.9% tolerant cells and 40 lM DNP. Only in runs starting with 0.0001% tolerant cells was a bacterial peak created, yet in the experimental data, a peak was more characteristic of trials with preexposed organisms. A more detailed understanding of the uptake of the various organics that become available during the detritus aging process may be needed to account for bacterial dynamics in the experiment. Jensen (1985) found that a multisubstrate uptake model can produce more accurate predictions of bacterial growth than a model in which all types of organic matter are aggregated. Perhaps the early peak in the experiments was stimulated by the ethanol added with the DNP. For the model, we assumed that 90% of this was volatilized. However, runs in which the full amount of ethanol was assumed to be present

SIMULATION MODEL OF DNP IN A Microcystis CULTURE

(not shown) resulted in a bacterial increase of less than 10% and no early peak. Experimentation with ethanol as a single additive to the cultures is necessary to clarify its in#uence on the bacterial dynamics. The bacteria sector may be too simple to produce an early peak in bacteria. Bacteria in the mucus sheath of M. aeruginosa cells, for example, were not counted in the experiment and were not speci"cally included in the model. The species of bacteria that were counted have not been identi"ed. Species-speci"c information on bacterial ecology and interaction with M. aeruginosa may improve the representation of bacterial dynamics. Results from experimental additions of di!erent types of organic substrate, including M. aeruginosa exudate and ethanol, can be compared to model predictions. This would provide a validation check for the model, indicate the importance of considering separate pools of organic substrate, and allow isolation of the e!ect of ethanol on bacteria. If the model is currently too simple to allow an accurate prediction of bacterial dynamics, then a more complex model should show improvement. A hypothetical model could be created by splitting the pool of organic substrate into several pools of di!erent lability and also separating the bacteria into various types with di!erent a$nities for the di!erent pools of organic matter. Labile substrate may be available immediately upon the death of other cells. Both labile cellular-derived substrate and ethanol were available early in the experiments with DNP. In the model, bacteria with the highest a$nity for labile organics may peak early, while other types grow better later. Functional di!erences among species within the microbial community when interacting with a variety of substrates may account for repeatable features of the microbial population dynamics seen in the experiments that cannot be produced by simpler models. The concept of an optimal DNP for maximum bacterial production and regeneration of DNP in ecological communities suggests the possibility that toxic e!ects may di!er considerably from what is expected from exposing a species separately to DNP. In single-species experiments, e!ects from exposure to a toxicant usually increase with concentration. In nature, however, this is unlikely to be the norm because usually when some species decline at low concentrations, other more tolerant species can replace them and may #ourish on the newly regenerated resources left in the decomposition products of the more sensitive organisms. Only at higher levels of toxicants are uniformly negative results for an ecological community likely. Dinitrophenol The general agreement in DNP decline between the model output and the experimental data is encouraging, but not surprising. All constants in the DNP sector were set by model calibration. Although DNP is a well-studied toxi-

253

cant, the details necessary for the model were not available in the literature. No values for DNP uptake, e!ects, or release at the cellular level could be found. This leaves open an enormous range of possible alternative values and little justi"cation for those chosen other than a reasonable "t to the data. Nevertheless, the model could still have been rejected if no suitable values had been found. Of greater concern is the lack of an obvious increase in DNP near the end of the simulations. The relative insensitivity of the model to changes in constants that a!ect DNP sorption could result if rates are so large that the sorption process is essentially complete within a few seconds of simulated time even if the rate is halved. Very rapid rates of sorption in the model do not allow dissolved DNP to accumulate in the water after it is released by bacteria. Instead, DNP in the model is immediately resorbed onto other cells, which prevents an increase in DNP near the end of the simulations. Sorption rates of DNP by cells in the experiments may not have been as fast as represented. Alternatively, the seeming reappearance of DNP near the end of the experiment could be an artifact of the spectrophotometric method used to detect DNP in the experimental study. For example, cellular degradation products with good light absorption in the range absorbed by DNP may have appeared (Genoni et al., 2001). In any case, better knowledge of DNP sorption and of the e!ects of DNP on carbon allocation processes in microorganisms is needed to allow more reasonable calibration of models that incorporate basic ecological mechanisms operating at the level of individual cells and populations. The scale of mechanistic studies of toxicant action is usually molecular, while toxic e!ects are usually determined empirically. Between the two is a paucity of physiological and ecological studies that can provide a mechanistic understanding of the ecosystem impact of toxicants. Conclusion Hypothesis testing with a simulation model helps in the exploration and elucidation of complex relationships, especially when interpretation of experimental results alone yields few insights. Ecosystem complexity includes multiple causality and indirect e!ects that can overshadow simple causality and direct e!ects (Patten, 1990). In the present system, for example, the interaction of organisms in a toxic environment can be complex and can lead to surprising consequences. These may include lower than expected toxicity, adaptation to toxicants over a long period of time, and stimulation of production of the more tolerant heterotrophs by the windfall of organic matter. Remineralization of limiting nutrients by these heterotrophs may also stimulate high-tolerance autotrophs. Toxicity in the environment involves not only species, but also species interactions with one another and with their physicochemical environment.

254

MONTAGUE ET AL.

The study of the toxic response at the single-species level only is inadequate for predicting toxicant impact on ecosystem function and community composition. The simulation model represents a hypothesis that may account for at least some of the complex dynamics observed in the cultures. What is learned from repeated testing and modi"cation of this hypothesis can eventually be transferred to issues of toxicants in the environment. Parts of the hypothesis in this study have been supported by the reasonable match of model output to experimental data. The challenge now is to replace refuted portions with new hypotheses. The natural alteration of toxicity in the environment must be taken into account when establishing a basis for limiting toxicant discharge from wastewater e%uents. Working with cultures and their model provide one approach to understanding complex ecotoxicological responses that expose the reciprocal feedback between toxicants and ecological function in the environment. In the hypothesis represented in our model, not only do toxicants a!ect the organization and functioning of an ecosystem, but interactions among the organisms within the ecosystem a!ect the toxicity of the substance in the environment. The interaction between model output and experimental data allows complex interactions in ecosystems to be considered. Such interactions can unexpectedly alter the toxicity of substances after their release into the environment. ACKNOWLEDGMENTS The authors thank Rita Ternay-Aegerter for her patient review of all laboratory techniques from the experimental study that had bearing on the simulation model. Beat MuK ller computed possible DIC concentrations for the growth medium. The authors also thank other colleagues at EAWAG for helpful discussions throughout the modeling process. EAWAG and the University of Florida provided the computer facilities and literature searches required for model development, analysis, and manuscript preparation.

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