Out of balance: implications of climate change for the ecological stoichiometry of harmful cyanobacteria van de Waal, D.B.

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1 UvADARE (Dgtal Academc Repostory) Out of balance: mplcatons of clmate change for the ecologcal stochometry of harmful cyanobactera van de Waal, D.B. Lnk to publcaton Ctaton for publshed verson (AA): van de Waal, D. B. (010). Out of balance: mplcatons of clmate change for the ecologcal stochometry of harmful cyanobactera General rghts It s not permtted to download or to forward/dstrbute the text or part of t wthout the consent of the author(s) and/or copyrght holder(s), other than for strctly personal, ndvdual use, unless the work s under an open content lcense (lke Creatve Commons). Dsclamer/Complants regulatons If you beleve that dgtal publcaton of certan materal nfrnges any of your rghts or (prvacy) nterests, please let the Lbrary know, statng your reasons. In case of a legtmate complant, the Lbrary wll make the materal naccessble and/or remove t from the webste. lease Ask the Lbrary: or a letter to: Lbrary of the Unversty of Amsterdam, Secretarat, Sngel 5, 101 W Amsterdam, The Netherlands. You wll be contacted as soon as possble. UvADARE s a servce provded by the lbrary of the Unversty of Amsterdam ( Download date: 17 Jan 019

2 Appendx 1 Lake data We measured Mcrocysts bomass, mcrocystn composton and seston N:C ratos n 1 Mcrocystsdomnated lakes n The Netherlands. Samples were taken from the open water (at 1 m depth) and, f present, from surface blooms (at 5 cm depth), resultng n a total of 19 lake samples. The data are presented n Table A1 below. In addton to the relatonshps reported n Fg. of the man text, we note here that the bomass, mcrocystn concentraton and seston N:C rato were hgher n surface blooms than n the open water. Table A1. Mcrocysts bomass, mcrocystn composton and seston N:C ratos measured n the lake samples. Lake sample Lake Sample poston* Mcrocysts bomass (mm L 1 ) Total MC (µg L 1 ) MCLR (µg L 1 ) MCRR (µg L 1 ) MCYR (µg L 1 ) Seston N:C rato (molar) 1 Braassemermeer W Braassemermeer S Eemmeer W Eemmeer S GoomeerAlmere 1 W Goomeer Almere 1 S GoomeerAlmere W GoomeerAlmere S GoomeerHuzen W Njkerkernauw S Noord Aa W Noord Aa S t Joppe W t Joppe S Vletlanden W Vletlanden S Westenderplassen W Wjde Aa W Zegerplas W *W = sample from open water; S = sample from surface bloom. 10

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4 Appendx Full descrpton of the model We develop a model that consders several phytoplankton speces competng for norganc carbon n a wellmxed water column. The populaton dynamcs of the phytoplankton speces depend on the assmlaton of carbon doxde and bcarbonate. Uptake of carbon doxde nduces dynamc changes n ph. These changes n ph, n turn, affect the avalablty of the dfferent carbon speces, whch feeds back on phytoplankton growth. In addton, the growng phytoplankton populatons cast more shade and thereby reduce lght avalablty for photosynthess. Here, we descrbe the full structure of the model. opulaton dynamcs We assume that the specfc growth rates of the competng speces depend on ther ntracellular carbon content, also known as carbon quota (Droop 197; Grover 1991). Let n denote the number of phytoplankton speces, let X denote the populaton densty of phytoplankton speces, and let Q denote ts carbon quota. The populaton dynamcs of the competng speces, and the dynamc changes of ther carbon quota, can be summarzed by two sets of dfferental equatons: dx = µ X DX (A1) dt dq = u u CO, r µ Q HCO, (A) dt where =1,,n. The frst set of equatons descrbes the populaton denstes of the competng speces, where µ s the specfc growth rate of speces and D s the dluton rate (.e., the turnover rate) of the system. The second set of equatons descrbes the carbon quota of the speces, whch ncrease through uptake of carbon doxde (u CO, ) and bcarbonate (u HCO, ), and decrease through respraton (r ) and through dluton of the carbon quota by growth. The model assumes that the cellular carbon assmlated by phytoplankton conssts of structural bomass and a transent carbon pool. The relatve sze of the transent carbon pool, S, s defned as: Q Q MIN, S = (A) Q Q MAX, MIN, where Q MIN, s the mnmum amount of cellular carbon ncorporated nto the structural bomass of speces, and Q MAX, s ts maxmum amount of cellular carbon. The transent carbon pool can be nvested to make new structural bomass, whch contrbutes to further 105

5 Appendx phytoplankton growth. More precsely, we assume that the specfc growth rate of a speces s determned by ts transent carbon pool: Q Q MIN, µ = µ S = µ MAX MAX (A),, QMAX Q, MIN, where µ MAX, s the maxmum specfc growth rate of speces. Our model formulaton resembles Droop s (197) classc growth model. However, we assume that the cellular carbon quota are constraned between Q MIN, and Q MAX,, as there are physcal lmts to the amount of carbon that can be stored nsde a cell. Hence, the specfc growth rate equals zero f the transent carbon pool s exhausted (.e., µ = 0 f Q = Q MIN, ), and reaches ts maxmum f cells are satated wth carbon (.e., µ = µ MAX, f Q = Q MAX, ). Dssolved norganc carbon Carbon doxde readly dssolves n water, but only a small fracton of the dssolved carbon doxde reacts wth water formng carbonc acd (H CO ). Carbonc acd may subsequently dssocate nto bcarbonate and a proton. The reacton from dssolved carbon doxde to bcarbonate, and vce versa, depends on ph and s relatvely slow (Stumm and Morgan 1996). Bcarbonate can dssocate further nto carbonate and a proton. Ths s a much faster process, such that the dssocaton of bcarbonate nto carbonate and ts reverse reacton are essentally n equlbrum wth alkalnty and ph (Stumm and Morgan 1996). The chemcal reactons of norganc carbon are summarzed n Table A. In addton to these chemcal processes, carbon doxde and bcarbonate are consumed for phytoplankton photosynthess, and carbon doxde s released by respraton. Dssolved carbon doxde and carbonc acd cannot be dstngushed expermentally. Therefore, let [CO ] denote the total concentraton of dssolved carbon doxde and carbonc acd. In addton, let [CARB] denote the total concentraton of bcarbonate and carbonate. Changes n dssolved norganc carbon can then be descrbed by (ortelje and Ljklema 1995; Stumm and Morgan 1996): n n d[ CO ] = D( [ CO ] [ CO ]) gco c r X CO uco X (A5) IN, dt = 1 = 1 n d[ CARB] = D( [ CARB] IN [ CARB] ) c CO u X (A6) HCO, dt = 1 The frst equaton descrbes changes n the concentraton of dssolved carbon doxde through the nflux ([CO ] IN ) and efflux of water contanng dssolved CO, through gas exchange wth atmospherc CO (g CO ), and through the chemcal reactons from dssolved CO to bcarbonate and vce versa (c CO ). In addton, the concentraton of dssolved carbon doxde ncreases through respraton (r ) and decreases through uptake of CO (u CO, ) by the phytoplankton speces. The second equaton descrbes changes n the summed concentraton of bcarbonate and carbonate through n and efflux of water contanng these 106

6 Appendx norganc carbon speces, through the chemcal reactons from bcarbonate to dssolved CO and vce versa (c CO ), and through uptake of bcarbonate (u HCO, ) by the phytoplankton speces. The concentratons of bcarbonate and carbonate are calculated from [CARB] assumng equlbrum wth alkalnty and ph (ortelje and Ljklema 1995; Stumm and Morgan 1996). The chemostat s contnuously aerated wth a defned concentraton of CO. The CO from ths gas mxture dssolves n water. We assume that the CO gas nflux (g CO ) s proportonal to the aeraton rate (a), and to the concentraton dfference between dssolved CO n equlbrum wth the gas pressure ([CO * ]) and the actual dssolved CO (Segenthaler and Sarmento 199): CO * ( CO ] [CO ]) g = γ a (A7) [ where γ s a constant of proportonalty. The value of [CO * ] s calculated from the partal pressure of CO n the gas nflow (pco ) and the solublty of CO gas n water (Table A). Dssolved CO reacts wth water and subsequently dssocates nto HCO and H. Ths process occurs at a rate k CO (Table A). Dssolved CO can also react wth OH formng HCO, whch occurs at a rate k OH. Conversely, HCO and H assocate to dssolved CO and water at a rate k H, whle HCO can also react to dssolved CO and OH at a rate k HCO. The overall change n dssolved CO through these chemcal reactons (c CO ) can then be descrbed as follows (Johnson 198): c k k OH CO k H HCO (A8) ( [ ])[ ] ( [ ] )[ ] = k CO CO OH H HCO Alkalnty and ph Concentratons of bcarbonate and carbonate depend on ph and alkalnty, where alkalnty s defned as the acdneutralzng capacty of the water. In our experments, alkalnty s largely determned by dssolved norganc carbon and norganc phosphates. Contrbutons of ntrate and sulfate are neglgble as they do not functon as proton donor or acceptor n the ph range observed n our experments (ph = 711). Hence, the alkalnty n our expermental system can be defned as (WolfGladrow et al. 007): ALK = HCO CO HO O OH [ ] [ ] [ ] [ ] [ ] [ O ] [ H ] H (A9) We note from ths equaton that bologcal uptake or release of carbon doxde does not change alkalnty. Furthermore, uptake of bcarbonate for phytoplankton photosynthess s accompaned by the release of a hydroxde on or uptake of a proton to mantan charge balance, and therefore does not change alkalnty ether. Hence, carbon assmlaton by phytoplankton does not affect alkalnty. Ntrate, phosphate and sulfate assmlaton, however, are accompaned by proton consumpton n order to mantan charge balance. Therefore, assmlaton of these nutrents ncreases alkalnty (Brewer and Goldman 1976; WolfGladrow et al. 007). More specfcally, both ntrate and phosphate uptake ncrease alkalnty by 1 mole equvalent, whereas sulfate uptake ncreases alkalnty by mole 107

7 Appendx equvalents (WolfGladrow et al. 007). Accordngly, changes n alkalnty can be descrbed as: dalk = D dt n ( ALK ALK ) ( ) IN u u u X N,, S, = 1 (A10) Ths equaton states that changes n alkalnty depend on n and efflux of water wth a gven alkalnty, and on the uptake rates of ntrate (u N, ), phosphate (u, ), and sulfate (u S, ) by the phytoplankton speces. The ph s calculated teratvely at each tme step from alkalnty usng the summed concentratons of bcarbonate and carbonate (CARB) and the summed concentratons of dssolved norganc phosphates (R ) (ortelje and Ljklema 1995; Stumm and Morgan 1996). Intal values of bcarbonate, carbonate, phosphorc acd (H O ), dhydrogen phosphate (H O ), hydrogen phosphate (HO ), and phosphate (O ) are estmated usng the proton concentraton (H ) calculated from the ph at the prevous tme step (ph t1 ): [ HCO ] [ CO ] [ H ] [ ] [ CARB] H = (A11) K K = (A1) K [ ] [ CARB] H [ H ] [ H O ] [ H O ] [ HO ] = R (A1) α K [ H ] 1 = R (A1) α K K α [ H ] 1 = R (A15) K K K 1 [ O ] R = (A16) α where K s the equlbrum constant of bcarbonate and carbonate, K 1, K and K are the equlbrum constants of the norganc phosphates, andα s calculated as: [ H ] K [ H ] K K [ H ] K K K α = (A17) Alkalnty can be calculated from these ntal estmates usng equaton A9. From the dscrepancy, dalk, between ths newly calculated alkalnty and the actual alkalnty predcted by equaton A10, a new ph estmate s made: ph t = ph t1 dph (A18) Where dph s calculated accordng to (Stumm and Morgan 1996): dalk d ph = (A19) [ H ] [ OH ] α α [ CARB] α α [ ] HCO CO [ ] [ ]. α α α α

8 Appendx where α HCO = [H ]/([H ] K ), α CO = K /([H ] K ), α 01 = [H ]/([H ] K 1 ), α 10 = K 1 /([H ] K 1 ), α 1 = [H ]/([H ] K ), α 1 = K /([H ] K ), α = [H ]/([H ] K ), α = K /([H ] K ), [ 01 ] = [H O ] [H O ], [ 1 ] = [H O ] [HO ], and [ ] = [HO ] [O ]. Ths new ph s then used to calculate new values for bcarbonate, carbonate, the norganc phosphates and alkalnty usng equatons A11A17, and so on. Ths teratve procedure s contnued untl ph and alkalnty have both reached a stable value. Carbon assmlaton We assume that uptake rates of carbon doxde and bcarbonate are ncreasng but saturatng functons f CO, and f HCO, of the avalablty of carbon doxde and bcarbonate, respectvely, as n MchaelsMenten knetcs: [CO ] f = CO, u MAX, CO, H [CO ] CO, (A0) [HCO ] f = u HCO, MAX, HCO, H [HCO ] HCO, (A1) where u MAX,CO, and u MAX,HCO, are the maxmum uptake rates of carbon doxde and bcarbonate, respectvely, H CO, and H HCO, are the halfsaturaton constants. In addton, we assume that carbon uptake rates are suppressed when cells become satated wth carbon (Morel 1987; Ducobu et al. 1998), and depend on the photosynthetc actvtes of the speces. The uptake rates of carbon doxde and bcarbonate by a phytoplankton speces can then be descrbed by: u = f (1 S ) (A) CO, CO, = f HCO, HCO, u (1 S ) (A) where S s the relatve sze of the transent carbon pool as defned by equaton A, and s a measure of photosynthetc actvty (wth 0 < < 1). We assume that the respraton rate s proportonal to the sze of the transent carbon pool: r = rmax S (A), where r MAX, s the maxmum respraton rate when cells are fully satated wth carbon. Nutrent assmlaton In our experments, uptake of ntrate, phosphate and sulfate by phytoplankton speces affects alkalnty. The model therefore keeps track of dynamc changes n the concentratons of ntrate (R N ), phosphate (R ), and sulfate (R S ): n dr j = D( R R ) IN j j u X j = N,,S (A5), j, dt = 1 Ths equaton states that changes n these nutrent concentratons depend on the n and efflux of water contanng these nutrents, and on the nutrent uptake rates (u j, ) of the 109

9 Appendx phytoplankton speces. For smplcty, we assume that phytoplankton speces have a constant C:N::S stochometry. That s, uptake rates of ntrate, phosphate and sulfate are proportonal to the net uptake rate of carbon: u ( u u r ) j = y j, CO, HCO, j = N,,S (A6), where y N,, y, and y S, are the cellular N:C, :C and S:C ratos of phytoplankton speces. Lghtdependence of carbon assmlaton Lght avalablty determnes the photosynthetc rate, and thereby the amount of energy avalable for carbon assmlaton. Accordng to LambertBeer s law, the underwater lght ntensty vares wth depth (Husman and Wessng 199; Husman et al. 1999): n I( z) = I exp K z n bg k X z (A7) = 1 Ths equaton states that the lght ntensty transmtted through the water column ncreases wth the ncdent lght ntensty (I n ), but decreases wth the depth of the water column (z), the background turbdty of the water tself (K bg ), the specfc lght attenuaton coeffcents of the phytoplankton speces (k ), and the populaton denstes of the phytoplankton speces (X ). The photosynthetc actvty of the phytoplankton speces can be calculated as the ntegral of ther photosynthetc rate over the depth of the water column: 1 = z M z M 0 p ( I( z)) dz (A8) where z M s the total depth of the water column, and the notaton p (I(z)) ndcates that the photosynthetc rate of speces s a functon p of lght ntensty I, whch n turn s a functon of depth z. Our model assumes that the lght dependence of the photosynthetc rate of phytoplankton speces can be descrbed by a Monod functon: pmax, I p ( I ) = (A9) H I I, where p max, s the maxmum photosynthetc rate of speces, and H I, s ts halfsaturaton constant for lght. The maxmum carbon uptake rate s already specfed n equatons A0 and A1. Therefore, we set p max, = 1, whch constrans to 0 < < 1 (as requred n equatons A and A). The depth ntegral n equaton A8 can now be solved (Husman and Wessng 199), whch yelds: 1 H I ( ) I, n = ln ln I / n I out H I I, out where I out s the lght ntensty at the bottom of the water column (.e., I out = I(z M )). (A0) 110

10 Appendx Table A. Reactons and equlbrum constants of dssolved norganc carbon and dssolved norganc phosphates n water. Equlbrum constants and rates values assume a temperature of 1.5 o C and a pressure of 1 atm. Reactons Equlbrum constants Descrpton Value (1) Unts [ H O] [ H ] [ OH ] [ ][ ] H OH = K W * pco [ HO] [ CO] [ CO ] = K0 pco CO H [ H ][ HCO ] = K [ ] [ ] [ ] HCO [ HCO ] [ H ] [ CO ] [ HO] [ CO] [ HCO] [ H ] [ OH ] [ CO] [ HCO] [ HCO] [ H ] [ HO] [ CO] [ HCO ] [ OH ] [ ] Equlbrum constant of water 1 [ CO ] [ ][ ] H CO = K [ HCO ] k CO Solublty of CO gas n water Dssocaton constant of CO mol L 1 atm Dssocaton constant of HCO Reacton rate of H O and CO s 1 Reacton rate of OH k OH s 1 and CO k HCO Reacton rate of HCO and H s 1 Reacton rate of the k H s 1 dssocaton of HCO CO [ H O ] [ H ] [ H ] [ ][ ] H H O O [ H O ] [ H ] [ ] HO = K 1 [ H O ] [ H ][ HO ] = K [ HO] H [ H ][ O ] = [ ] K HO [ HO ] [ ] [ ] Dssocaton constant of H O Dssocaton constant of H O Dssocaton constant O of HO (1) The solublty of CO n water and the dssocaton constants are based on Stumm and Morgan (1996); the reacton rates are based on Welch et al. (1969). 111

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12 Appendx arameter values Ths Appendx provdes the parameter values used n the model smulatons. The speces parameters are provded n Table A, and the system parameters n Table A. Table A. arameter values estmated for the toxc stran Mcrocysts CYA10 and the nontoxc stran Mcrocysts CYA. arameter Descrpton CYA CYA10 Unts µ MAX Maxmum growth rate d 1 k Specfc lght attenuaton coeffcent m mm H I Halfsaturaton constant for lght 11 1 µmol photons m s 1 u MAX,CO Maxmum uptake rate of CO µmol mm d 1 H CO Halfsaturaton constant for CO µmol L 1 r MAX Maxmum respraton rate µmol mm d 1 u MAX,HCO Maxmum uptake rate of HCO H HCO Halfsaturaton constant for HCO µmol mm d µmol L 1 Q MIN Mnmum carbon content 1 10 µmol mm Q MAX Maxmum carbon content µmol mm y N Cellular N:C rato molar y Cellular :C rato molar y S Cellular S:C rato molar V Cell volume mm cell 1 11

13 Appendx Table A. System parameters used n the chemostat experments. arameter Descrpton Carbonlmted chemostat Lghtlmted chemostat Unts D Dluton rate h 1 I IN Incdent rradance 50 5 µmol photons m s 1 z M Mxng depth m K bg Background turbdty* m 1 T Temperature ο C a Gas flow rate 5 5 L h 1 γ pco [CO ] IN [CARB] IN Constant of proportonalty for gas nflux* artal pressure of CO n gas nflow Concentraton of dssolved CO at nflux Summed concentraton of bcarbonate and carbonate at nflux L ,00 ppm 8 9 µmol L 1 500,000 µmol L 1 ALK IN Alkalnty at nflux meq L 1 R IN,N Concentraton of ntrate at nflux 1,000 6,000 µmol L 1 R IN, Concentraton of phosphate at nflux µmol L 1 R IN,S Concentraton of sulfate at nflux µmol L 1 *The background turbdty and constant of proportonalty for the gas nflux had dfferent values for dfferent chemostat vessels. 11

14 Appendx Drawng the zero soclnes Resource competton theory has developed a graphcal approach usng zero soclnes to assess the compettve abltes of speces competng for two resources (Tlman 198). The zero soclnes are plotted n a resource plane, wth CO concentratons on the xaxs and bcarbonate concentratons on the yaxs (Fg. 6.). From our model, we can derve an explct expresson to calculate the zero soclnes. At steady state, the cellular carbon quota wll not change (.e., dq /dt = 0). Applyng ths to equaton 6., wth equaton 6. and equatons AA, we obtan: * ( f )(1 S = µ S Q r S (A1) f CO, ) HCO, MAX, MAX, where the superscrpt * ndcates that the cellular carbon quota are evaluated at steady state, S s defned by equaton 6., and s defned by equaton A0. Ths can be wrtten as: f S 1 µ (A) * f CO, = ( MAX, Q rmax, ) HCO, 1 S Furthermore, at steady state, net populaton growth s zero (.e., dx /dt = 0). Ths mples that the specfc growth rate equals the dluton rate (.e., µ MAX, S = D). Accordng to equaton 6., the cellular carbon quota wll then be: Q * MAX, D = QMIN, ( QMAX, QMIN, ) (A) µ Insertng ths equaton nto equaton A, we obtan: f = where we defned: f CO A, HCO, (A) 1 D = D µ µ MAX, ( Q ( D) Q D r ) A MIN, MAX, MAX, MAX, (A5) The zero soclne s mplctly gven by equaton A. Insertng equaton A1 nto A, the bcarbonate concentraton can be wrtten as a functon of the CO concentraton: H ( A f ) HCO, CO, [HCO ] = (A6) u A f MAX, HCO, CO, where f CO, depends on the CO concentraton accordng to equaton A0. The zero soclnes can now be plotted from equaton A6, usng the defntons of A and f CO, n equatons A5 and A0. 115