The development from kinetic coefficients of a predictive model for the growth of Eichhomia crassipes in the field . I . Generating kinetic coefficients for the model in greenhouse culture

T h e kinetics o f Nand Plim ited growth o f Eichhornia crassipes (M art.) Solms w ere investigated in greenhouse culture w ith the object o f developing a m odel fo r p redicting population sizes, yields, growth ra tes and frequencies and am ounts o f harvest, under varying conditions o f nu trien t loading and clim ate, to contro l b o th nu trien t inputs and excessive growth in eutrophied aquatic system s. T he k inetic coefficients, maximum specific grow th ra te (U m ax), ha lf saturation coefficient (K s) and yield coefficient (Y c) w ere m easured u n d e r N and P lim itation in replicated batch culture experim ents. Um ax values and Ks concentra tions derived under N lim itation ranged from 5,37 to 8 ,86% d '1 and from 400 to 1 506 fjg N f 1 respectively. T hose derived under P lim itation ranged from 4,51 to 10,89% d 1 and from 41 to 162 fig P ( ' respectively. Yc values (fresh mass basis) determ ined ranged from 1 660 to 1 981 (87 to 98 dry mass basis) for N and from 16 431 to 18 671 (867 to 980 dry mass basis) fo r P . T h e reciprocals o f Yc values (dry mass basis), expressed as percentages, adequately estim ated the m inim um limiting concen tra­ tions o f N and P {% dry m ass) in the plant tissues. Kinetic coefficients determ ined are com pared w ith those re ­ po rted for algae. T he experim ental m ethod used and results ob tained are critically assessed.

Eutrophication. the enrichment of aquatic systems with inorganic nutrients (Stewart & Rohlich, 1967), is a world-wide water quality problem (Stumm. 1974).Eichhornia crassipes (M art.)Solms (w ater hyacinth), a free-floating, aquatic plant (Penfound & Earle, 1948;Bock, 1966), which has a high growth rate (Penfound, 1956;Yount & Crossman, 1970;Boyd, 1976) and produces a large standing crop per unit area (Knipling et al., 1970;Boyd & Scarsbrook, 1975), is the most promising floating, vascular aqua tic plant species for removing nutrients from eutro phied aquatic systems (Boyd, 1970).This specics ab sorbs large quantities of N and P, the nutrients gen erally associated with eutrophication (M ackenthun, 1964; 1965), from sewage effluents (Clock, 1968;Miner et al., 1971;Cornwell et al., 1977).In addi tion, it removes heavy metal and other chemical pol lutants from secondary waste-water effluents (Wolverton, 1975;Wolverton & McDonald, 1975a;1975b;1976;Wolverton & McKown, 1976) and re duces levels o f suspended solids, biochemical oxygen demand substances and other chemical factors in such effluents to levels below the standards set by some pollution control agencies (Wolverton & Mc Donald, 1975c;1975d).Its cultivation and removal may, therefore, constitute an effective m eans of withdrawing nutrients from effluents prior to their release into natural waters (Yount & Crossman, 1970).Similarly, the removal of water hyacinths growing in eutrophied aquatic systems may also assist in controlling excessive growth of plants by re ducing nutrient levels.
To achieve maximum nutrient removal efficiency by E. crassipes in a nutrient removal scheme, it is necessary to establish how much and how frequently to harvest the population.Clearly, if the population is continually over-harvested, the size of the popula tion and its effectiveness in removing nutrients will be progressively reduced.Alternatively, if the popu lation is under-harvested, nutrient removal may be ineffective and other adverse effects may arise.
Maintenance o f a high growth rate and nutrient removal capacity by E. crassipes is facilitated if the size of the population required to maintain desirable nutrient concentrations in the w ater, under varying conditions of nutrient loading and climate, can be predicted.Since harvesting is required to control the population size, amounts and frequencies of harvest must also be predicted.
From the kinetic standpoint, it is theoretically feasible to construct a mathematical model for E. crassipes from which population sizes, yields, growth rates and frequencies and am ounts o f harvest, under varying conditions o f nutrient loading and climate, can be predicted to control both nutrient inputs and excessive growth in eutrophied aquatic systems (Toerien, 1972;Musil & Breen, 1977).The follow ing relationships, however, require mathematical formulation: (i) The relationship between the yield of E. cras sipes, i.e. the mass of plant material produced and the mass of a specific lim itin g nutrient absorbed.
The following mathematical expression describes this relationship: Xt -Xo Yc = ----------So -St where Yc = yield coefficient; Xo = initial biomass; Xt = final biomass; So = initial concentration of •N utrient present a t concentrations below th a t req u ired for m axi m um plant grow th and hence restricting th e grow th rate.
limiting nutrient; St = final concentration o f limiting nutrient.
(ii) T he relationship between the specific growth rate of E. crassipes, i.e. the increase in mass of plants, per unit mass o f plant material, per unit time (Malek & Fencl, 1966;Radford, 1967) and the con centration of a specific limiting nutrient.Various models have been used to quantify this relationship in algae and bacteria (Shelef et al., 1968;Toerien et al., 1971;Goldman, 1972).The most important are Blackman's first order-zero order model, Teisser's exponential model and M onod's rectangular hyper bola model, the last defined as; U = Umax ---Ks + S where U = specific growth rate; Umax = maximum specific growth rate; S = concentration of limiting nutrient; Ks = half saturation coefficient = S when U = 0,5 Umax.
(iii) The relationship between the maximum speci fic growth rate o f E. crassipes and tem perature.Under a constant light intensity, the maximum speci fic growth rate (Um ax) may be described solely as a function o f tem perature, as shown by Goldman (1972) and Goldman & Carpenter (1974) for various species of marine and fresh water algae, by an Ar rhenius equation, defined as; Umax = A r E/RT where A -constant day-1; E = activation energy cal.mole-1; R = universal gas constant cal.mole 1 "K-1; T = tem perature on Kelvin scale °K.
Incorporating the Arrhenius equation into the Monod model, the following mathematical expres sion is obtained in which the specific growth rate (U) is related to both tem perature and the limiting nutri ent concentration: U = Ae-E'RT x -------Ks + S The predictive abilities of such models have been demonstrated in algae, for example, by Toerien & Huang (1973) where the P-limited growth rate of Selenastrum capricornutum in batch cultures was ac curately predicted from its kinetic coefficients and by Bhagat et al. (1972) where the algal concentration of a Vancouver Lake was adequately predicted by a water quality simulation model also using kinetic co efficients.
A number o f restrictions to the general use of the above equations, however, do exist.Firstly, for each plant species the Arrhenius equation is applicable only over a defined tem perature range as shown by Sorokin (1960) for various algal species.Secondly, there is evidence of a strong interaction between light intensity and tem perature.Sorokin (1960;1971) found that for a given tem perature the acti vation energy decreases with increasing light energy and Shelef (1968) has shown that the saturation light intensity is highly tem perature dependent.Thirdly, the half saturation coefficient for nutrient uptake is also sensitive to changes in tem perature (Shelef et al., 1970).A further potential complication is the possible tem perature dependency of the yield coeffi cient, since minor variations in the yield coefficient have been found with high and low tem perature strains of Chlorella grown under NO3-N limitation in continuous cultures (Shelef et al., 1970) and in the bacterium Aerobacter aerogenes (Topiwala & Sin clair, 1971).
No attem pts have, as yet, been made to model the effects of tem perature on the half saturation (Ks) and yield coefficients (Yc), although in Aerobacter aerogenes and Escherichia coli, Topiwala & Sinclair (1971) and Sawada et al. (1978) demonstrated that Ks changes with tem perature and that an Arrhenius plot of the change is linear.The difficult task of de termining tem perature dependent kinetic coeffi cients such as Ks and Yc in natural systems may re strict their application to well defined laboratory conditions.On a seasonal basis, however, it should be possible to assess the significance of these kinetic coefficients in modelling.
Numerous references exist in the literature on the nutrient uptake and growth characteristics o f E. crassipes.Despite this, the necessary mathematical relationships required for the proper evaluation and potential design of a predictive model have not been adequately formulated.In a preliminary study, Mu sil & Breen (1977) measured the kinetic coefficients, Umax, Ks and Yc for E. crassipes in one NO3-Nlimited batch culture experiment.They illustrated how these coefficients could be used in a predictive model, although its validity was not tested under field conditions.Since both N and P are the nutrients most frequently limiting for E. crassipes under natu ral conditions (Wahlquist, 1972), this investigation was designed to generate kinetic coefficients for E. crassipes growing under N and P limitation with the objective o f developing and validating a predictive model.

M A TERIALS A N D M ETHODS
The batch culture method or non steady-state ap proach (Toerien et al., 1971) was used to measure kinetic coefficients for E. crassipes growing under specific nutrient limitation, Batch culture experi ments were repeated, five times under N and three times under P limitation.
In each experiment, ca 120, vegetatively-propagated offsets (daughter plants) of uniform size (pos sessing two pseudolaminae with bulbous petioles and having a fresh mass ranging from ca 4 to 10 g) were sampled from a loosely crowded population in a sewage maturation pond.Plants were rinsed through three changes of deionised-distilled water, shaken to dislodge adhering water and their fresh masses recorded on an electric, top-loading balance.They were placed into 5 ( capacity, inert polyethy lene vessels (buckets) each containing 5€ of culture solution deficient in either N or P. O ne or two plants were used as an inoculum in each vessel (Table 1).
A modified culture solution based on that o f Hamner et al. (1942) was used (Table 2) in which the con centrations of either o f the anions, NO3 or PO4T could be varied independently with minimum influence on the concentrations o f cations and other anions.Reduced cation concentrations, resulting  28,10; 36,13; 45,16 18 from the lowering in concentration o f an anion in the culture solution, were restored by supplementing it with the appropriate additional cations.These were added predominantly as chlorides.The total salinity of the culture solution was 0,31°/<x>.This is well below the salinity of 16,6°/oo reported by Haller et al. (1974) to inhibit E. crassipes growth rate in cul ture.Ions were supplied to the culture solution in the inorganic form and in sufficient quantities not to be limiting for E. crassipes (Musil, 1982).Culture solutions were changed and adjusted to pH 7,0 weekly using 5 % H 2S 0 4 and 10% NaOH.Evapora tion loss from cultures was replaced daily with deionised-distilled water.
Experiments were conducted in an air-condi tioned greenhouse during summ er when light inten sities (radiant flux densities) and air temperatures were high.Maximum daytime air tem peratures in the greenhouse were maintained at ca 30°C required for maximum growth of plants (Knipling el al., 1970).Diurnal air tem perature and relative humidity fluctuations in the greenhouse, recorded on a ther mohydrograph, did not exceed the ranges 6 to 11°C Every two to four days, plants were removed from culture, allowed to drain for two minutes above the culture vessels, shaken to dislodge adhering water, their fresh masses recorded and returned to culture.Plants were grown in either N-or P-deficient cul tures until they showed a reduced growth rate, evi dent as a deviation from linearity in a plot o f their fresh mass against tim e, indicating a N or P defi ciency.They were then harvested from culture and necrotic or damaged leaves and roots removed.Cul ture solutions were changed, fresh masses o f plants redetermined and plants returned to culture.
In each experiment.N-or P-deficient cultures were spiked, at this stage, with six different levels of N or P to obtain six treatm ents (16 to 20 replicates per treatm ent) in which N concentrations in N-limited cultures ranged from 0 to 11,29 x I03 pg N ( 1 and P concentrations in P-limited cultures ranged from 0 to 2,09 x 103 pg P (Table 1).A rando mized block design was adopted (Rayner, 1967).
After spiking, mass recordings, which included both fresh as well as dead mass o f plants arising through necrosis of plant material during growth, continued every two to four days for all plants until no significant increase was recorded in the total fresh mass (fresh and dead mass) o f all plants grown at each level o f N or P supplied.
Culture solutions were not changed again.How ever, they were topped-up daily with deionised-distilled water and adjusted to pH 7,0 weekly, since the Ks may be influenced by pH (Goldman, 1972) and maximum growth of E. crassipes occurs at this pH in culture (Chadwick & Obeid, 1966).Concentrates of the culture solution deficient in either N o r P were added to the cultures at two weekly intervals to en sure an adequate supply of nutrients, other than the specific limiting nutrient, to the plants.In P-limited culture experiments, additional N at a concentration of 9,03 x ÍO-1 pg N €-' was also added to cultures in the intervening weeks to ensure that N concentra tions remained above those limiting for E. crassipes (Musil, 1982).The total nutrient additions after spiking, however, did not increase the salinity of cul tures above l , 6% o, i.e. 10 % of the inhibitory sali nity value of 16,6°/oo for E. crassipes (Haller et al., 1974).
When mass recordings were term inated, plants, including their offsets, were harvested from culture allowing the culture solution retained by plants to drain back into each vessel.Plants were shaken to dislodge adhering water and reweighed.They were then dried in a forced draft oven at 60°C to a constant weight and their dry masses determ ined.The dry plant tissues were ground in a mill, redried at 60°C in a forced draft oven to a constant weight, and stored in sealed glass bottles for later chemical analysis.
After plants had been harvested, the culture solu tions in three vessels taken at random from each treatment in each experiment were topped-up to the 5€ mark with deionised-distilled water and analysed for remaining N o r P using published methods (E n vironmental Protection Agency, 1974;American Public Health Ass.;Standard Methods, 1975).Loss o f the specific limiting nutrient (N or P) from cul tures, resulting from shaking of plants at each weigh ing interval, could not be accounted for, but was considered to be small.
The minimum concentration or subsistence quota (Rhee & Gotham , 1981) o f the specific limiting nu trient in harvested plants was analysed in three batches of dry, ground, harvested plant tissues cho sen at random from each treatm ent in each experi ment using published methods (Association of Offi cial Agricultural Chemists, 1975).
In each experiment, specific growth rates were calculated according to Malek & Fencl (1966) and Radford (1967) for each plant between each weigh ing interval for a period of ca 2 1 days after spiking.The highest specific growth rate attained by each plant in each treatm ent during this period was taken as its specific growth rate at that particular N or P concentration.The Umax value and Ks concentra tion were extrapolated for £. crassipes in each ex periment from the intercepts of a reciprocal plot of specific growth rates o f plants against limiting nutri ent concentrations (Lineweaver & Burk, 1934;Cur rie, 1982).The Yc value was derived in each experi ment from the slope of the line relating total fresh mass yields of plants to quantities of limiting nutrient absorbed.Simple linear regressions were used to ob tain the best straight lines through all points (Ray ner, 1967).All linear regressions were subjected to an analysis of variance (Rayner, 1967).

Growth in deficient culture
Plants with two pseudolaminae introduced into N-(Experiments 1 to 5) and P-(Experiments 6 to 8) d e ficient cultures showed an initial lag phase in growth lasting ca two to four days (Figs 1 & 2).Growth of plants in N-and P-deficient cultures then proceeded more o r less linearly until they showed a reduced growth rate, at which stage the growth rate of plants was assumed to be N-or P-limited.No significant differences (P^S-0,05) existed at this stage between the mean fresh masses of groups o f plants that were to comprise each treatm ent in each experiment (M u sil, 1982).In each experiment, a different growth period in deficient cultures was required to induce in plants a N-or P-limited state.This was attributed partly to different quantities of N and P stored in plants collected on different occasions from the field for each experiment.No correlation was evident be tween the duration of plant growth in deficient cul tures, required to induce N or P limitation, and en vironmental conditions recorded in the greenhouse (Musil, 1982).

Growth after spiking
In each experiment, the addition of the limiting nutrient caused an increase in growth rate with a short (three to four day) period of maximum growth rate which was proportional to the level o f N or P supplied.The periods of mean maximum growth rate of each group of plants for each treatm ent were evident from the maximum slopes of curves relating growth (fresh mass) and time (Figs 1 & 2B, C , D , E , F).Thereafter, the growth rates o f plants decreased, progressively until there was no measurable increase in the total fresh mass (fresh including dead mass produced during growth) o f plants.This required ca 75 to 95 days after the addition of N and ca 50 to 65 days after the addition o f P, in those treatm ents where these limiting nutrients were supplied a t the highest levels to cultures.In Experim ents 4 and 5, mass recordings were term inated prior to cessation of plant growth, i.e. about 2 1 days after spiking.
Nitrogen-and P-limited plants responded differ ently to the different levels o f limiting nutrient sup plied to cultures.In Treatm ents 3 to 6 ,. w here the limiting nutrients were supplied at levels above , where the limiting nutri ents were supplied at lower levels.This could not be reasonably explained by a restricted uptake o f N o r P in E. crassipes due to a limited nitrate reductase or alkaline phosphate activity in plants resulting from their growth in deficient cultures (Schwoerbel & Tillmans, 1974).O aks et al. (1972) in a study of the induction kinetics in the roots of Zea mays seedlings have shown that the induction o f nitrate reductase is very rapid with maximum levels of nitrate reductase being achieved four to six hours after transference of seedlings from a N O j-N-deficient medium to one containing N 0 3-N .Fitzgerald & Nelson (1966) and Fitzgerald (1969), on the other hand, have reported that alkaline phosphatase activity increases in algal cells and higher aquatic plants such as Ceratophyllum demersum L. with increasing P deficiency.It would appear, therefore, that in those treatm ents where plants were exposed to high levels o f N O j-N and P 0 4-P , these nutrients may have been accumu- lated in a pool and then reduced and incorporated into metabolism at a later stage, i.e. the assimilation of N and P by plants and their incorporation into new growth did not keep pace with their uptake in culture.Further research on the depletion of NO 3-N and PO4-P in the culture solution, levels and loca tion of nitrate reductase and alkaline phosphatase in the plant, however, will be required before any meaningful conclusions can be drawn from this prob lem.
Maximum specific growth rate (Umax) Lineweaver-Burk plots of the reciprocals o f speci fic growth rates (1/U), i.e. the highest specific growth rate attained by each plant after the addition of N o r P, against the reciprocals of limiting nutrient concentrations (Figs 3 & 4) showed that the relation ship between 1/U and 1/N o r 1/P was linear in each experiment with a high degree of correlation, signifi cant at Pss0,01 (Table 3).An analysis of variance of the regressions showed that the slopes and intercepts were significant at P^sf),05.The Umax value was ex trapolated for E. crassipes in each experiment from the intercept of the regression line on the y axis, cal culated from the regression equation.
The Umax values determined ranged from 0,0537 to 0,08X6 g fresh mass g-] d -1 (5,37 to 8,86% d-*) in N-limited experiments and from 0,0451 to 0,1089 g fresh mass g-1 d~> (4,51 to 10,89% d !) in P-limited experiments (Table 4).An exponential relationship was not evident between the Umax values derived under N and P limitation and the reciprocals of mean daily air tem peratures (expressed as °K) recorded in the greenhouse (Arrhenius plot), in addition, no correlation was evident between the Umax values determined and mean daily relative humidities re corded in the greenhouse.Significantly lower Umax values, however, were obtained in Experiments 2, 3, 7 and 8 where longer growth periods in deficient cul tures were required to induce N o r P limitation (Table 4).
The latter observation could not be explained in terms of non-competitive inhibition, i.e. by a re duced uptake rate o f the limiting nutrient by plants resulting from their longer growth periods in defi cient cultures.Investigations of the uptake kinetics of higher plants have shown that growth o f plants in starvation (deficient) media causes a subsequent in crease in their nutrient uptake rate with a corres ponding reduction in the half saturation coefficient (Km) for uptake.Glass (1978), for example, has shown that the uptake characteristics for K ' of bar ley plants grown initially with o r without K*are very different, the Km for K ' uptake being reduced in the starved plant from 0,1 to 0,03 mM.The same occurs for other ions, as for NO3 (Smith, 1973)   (ii) differences in the ratio of plant mass at spiking to levels of limiting nutrient supplied to culture, since a larger plant mass resulted at spiking in those experim ents where longer growth periods in defi cient cultures were required to induce N o r P limita tion; (iii) variations in light intensity in the greenhouse betw een experiments.

H a lf saturation coefficient (Ks)
The Ks was extrapolated for E. crassipes in each experim ent from the intercept o f the regression line o f 1/U against 1/N or !/P on the x axis, calculated from the regression equation (Figs 3 & 4).T he Ks concentrations determined ranged from 399,8 to 1 505.6 ug N £-■ in N-limited experiments and from 41,1 to 161,8 /íg P (~l in P-limited experiments (Table 4.) They showed no correlation with mean daily air tem peratures and relative humidities re corded in the greenhouse or with the duration of plant growth in deficient cultures required to induce N o r P limitation.The same reasons given for the different Umax values determ ined may also partly explain the different Ks concentrations measured for E. crassipes under N and P limitation.
The Ks concentrations derived for E. crassipes under N limitation are in the range of those reported for various species of algae, whereas those derived under P limitation are much higher (Table 5).This indicates that E. crassipes has a potential similar to algae to produce a high growth rate in N-limited waters, but a potential lower than algae to produce a high growth rate in P-limited waters.Since P is the nutrient most frequently limiting algal growth rate in relatively oligotrophic waters (Toerien et al., 1975), it w'ould appear that in such waters P may also be the nutrient limiting for E. crassipes.
The mean Ksn concentration o f 976 ^g N £-> d e term ined for E. crassipes from the five N-limited ex perim ents falls in the range 500 to 1 000 ^g N €-•, interpreted by Center & Spencer (1981) from the N/P uptake rates of E. crassipes o f 5 to 10 f ■ (Boyd, 1970;1976;Dunigan et al., 1975) as being the critical limiting N concentrations in the water for E. crassipes in the field, i.e. below which the growth rate o f this plant is significantly influenced by the N concentration in the water.The mean Ksp concen tration of 94,1 fxg P f 1 determ ined for E. crassipes from the three P-limited experiments compares fa vourably with 100 pg P reported by Haller et al. (1970) and Knipling etal. (1970) as being the critical limiting P concentration in the water for E. crassipes in the field.
The ratio of the mean Ksn/Ksp concentrations, derived for E. crassipes under N and P limitation, suggest an optimal N/P ratio in the water for E. cras sipes of ca 10, i.e. below which N and above which P concentrations in the water become growth rate limi ting for this plant.This value is well below the opti mal N/P ratio of 30 (cell and medium) reported by Rhee (1974Rhee ( , 1978) ) for algae.It should, however, be pointed out that, although the limiting nutrient can often be indicated from the N/P ratio in the water, in many instances the growth rate of phytoplankton is controlled by P even when the N/P ratio in the water is relatively low (Welch et al., 1978),

Yield coefficient (Yc)
With the exception of Experiments 4 and 5, where mass recordings were term inated prior to cessation of plant growth, the quantities of limiting nutrient remaining in three culture solution samples taken at random from each treatm ent, after plants had been harvested, were below 0 , 1 % o f that initially added (Musil. 1982).It was assumed, therefore, that in all culture solutions, with the exception of Experiments 4 and 5, the N o r P added had been absorbed by plants and incorporated into growth.
Plots o f the total fresh mass yields o f plants (fresh including dead mass produced during growth)   against the quantities of limiting nutrient added (Figs 5 & 6) showed that the relationship between these two factors, in each of the first three N-and Plimited experiments, was linear with a high degree of correlation, significant at P ^ 0,001 (Table 6).An analysis of variance of the regressions showed that the slopes and intercepts were significant at P*? 0,001, The Yc value (fresh mass basis) was derived for E. crassipes in each experiment from the slope of the regression line given by the regression equation.The Yc values (fresh mass basis) determined ranged from 1 659,6 to 1 981,1 in N-limited experiments and from 16 431,2 to 18 670,6 in P-limited experi ments (Table 7).
The mean water contents o f plants, harvested from each of the first three N-and P-limited experi ments, are given in Table 7. W ater contents ranged from 94,72 to 95,05% and showed no significant dif ferences (P=S 0,05) between experiments.They com pare favourably with the average water content of 94,75% derived from values reported by Penfound & Earle (1948), Westlake (1963) and Bock (1969), From the m ean water contents of plants, the Yc va- lues (fresh mass basis) were converted to a dry mass basis.
The Yc values (dry mass basis) determined ranged from 86,9 to 98,1 in N-limited experiments and from 867,1 to 980,2 in P-limited experiments (Table 7).Slightly higher Yc values (both fresh and dry mass basis) were obtained in Experiments 1 and 6 where plants were grown for the shortest spans in deficient cultures to induce N o r P limitation.
In all experiments, some growth (yield in plant material) was produced by E. crassipes grown in the absence o f N or P (Figs 5 & 6), This indicated that, although limiting N and P concentrations were exist ent in the plants, sufficient quantities were present to allow some growth.In fact, higher yields were produced by E. crassipes grown in the absence of the limiting nutrient in Experiments 1 and 6 , where  ---------------------------------<   plants were grown for the shortest periods in deficent cultures to induce N o r P limitation, than in other experim ents (Musil, 1982).This suggests that the limiting nutrients (N or P) were present at higher concentrations in plants at spiking in these two ex perim ents than in other experiments.In principle, however, higher limiting concentrations o f N and P present in plants at spiking in Experiments 1 and 6 respectively should not have had an influence on the Yc values determ ined, sincc these were derived from the slopes of regression lines relating total fresh mass yields o f plants to quantities o f limiting nutrient (N or P) supplied in culture.Consequently, the slightly higher Yc values m easured for N and P in Experi ments 1 and 6 respectively could not be readily ex plained.
The Yc values (dry mass basis) derived for E .cras sipes under P limitation are in the upper range of those reported for various species o f diatom s and other algae, whereas those derived under N limita tion are much higher (Table 8).This indicates that E. crassipes has the potential to produce a similar biomass per unit quantity o f P absorbed, but a much larger biomass per unit quantity o f N absorbed, than diatoms and other algae.Furtherm ore, the Yc val ues suggest that E. crassipes has the potential to re move similar quantities o f P , but sm aller quantities of N, per unit amount o f plant mass than diatoms and other algae.Maximum specific growth rates re ported for algae (Shelef et al., 1968;Zabat et al., 1970;Toerien et al., 1971;G oldm an, 1972), how ever, are considerably higher than those determined for E. crassipes.In eutrophic w aters, therefore, in which the limiting nutrient concentrations are high and specific growth rates of both algae and E. cras sipes approach their Umax values, E. crassipes would need to be present with a proportionately larger biomass than algae to compensate for its lower growth rate to ensure a potential similar to al gae for removing nutrients.E. crassipes lower poten tial than algae to produce a high growth rate in waters where P is limiting, as evident from a com parison o f its Ks concentrations for P with those of algae (Table 5), suggests that in relatively oligotrophic waters E. crassipes would also be less efficient in removing nutrients than algae, at least where both plants are present with the same biomass.
The minimum limiting concentrations of N and P (% dry mass) in plants harvested from each treat ment (means of 3 batches), in each of the first three N-and P-limited experiments, are shown in Table 9.The minimum limiting concentrations o f N and P (subsistence quotas) in the dry plant tissues ranged from 0.94 to 1,28% N in N-limited experiments and from 0,09 to 0,14% P in P-limited experiments.They

Y c (dry mass basis) Reference
Selenastm m capricomuturn  showed no significant differences ( P ^ 0.05) between experiments (Table 9).Toerien et al. (1971) andCoetzer et al. (1977) pointed out that the yield coefficient (dry mass basis) for a specific limiting nutrient, when expressed as a reciprocal and a percentage, should estimate the mi nimum concentration o f the limiting nutrient in the dry plant tissue.The Yc values (dry mass basis) de rived for E. crassipes under N and P limitation, when expressed as reciprocals and percentages (1/Yc x 100), adequately estimated the limiting concentrations of N and P in plants harvested from culture (Table 10).This suggests that the Yc values determined for E. crassipes are fairly reliable.The average minimum limiting concentrations of 1 , 10% N and (),!!% P. estimated in E. crassipes plant tis sues from the mean Yc values for N and P respec tively, also compare favourably with the minimum concentrations (% dry mass) of 1,33% N and 0,14% P reported by Boyd & Vickers (1971) in E. crassipes growing in the field, and with the minimum concen tration (% dry mass) of 0,098% P reported by Hatter & Sutton (1973) in E. crassipes growing in the ab sence of P in culture.Droop (1968) and Rhee (1973) showed that the minimum concentration of a specific limiting nutri ent in algal cells is equal to, or not significantly dif ferent from, the intracellular half saturation coeffi cient (Kq) for the limiting nutrient.Consequently, if it is assumed that a similar situation exists in E. cras sipes, then the ratio of the average minimum N/minimum P concentrations in E. crassipes.derived from the mean Yc values for these nutrients, give an opti mal N/P ratio in E. crassipes of ca 10.This value compares favourably with the optimal N/P ratio in the water for E. crassipes of ca 10, estimated from the ratio of the mean Ksn/Ksp concentrations d e rived under N and P limitation in culture.

CONCLUSIONS
Maximum specific growth rates (Umax) and half saturation coefficients (Ks) were not adequately de termined for E. crassipes growing in N-or P-limited batch cultures.In contrast, yield coefficients (Yc) were determined with sufficient accuracy.With bet ter facilities, it is possible that the batch culture method used for measuring kinetic coefficients for E. crassipes growing under specific nutrient limita tion in this investigation could be improved.For ex ample, if plants for culture were collected from populations grown under controlled environmental conditions in a standardized culture medium, it is possible that a uniform growth period required to induce in plants a N-or P-limited state could be ob tained.This might decrease the variability in Umax values and Ks concentrations determined.It is sug gested, however, that precise measurements of Umax and Ks may only be obtained for E. crassipes, under specific nutrient limitation in culture, by growing plants under constant environmental condi tions in some type of continuous flow culture system in which the limiting nutrient concentrations could be maintained at constant levels.In such a system, therefore, it would not be necessary to grow plants initially in deficient cultures to induce N or P limita tion, since the specific growth rate o f E. crassipes at T A B U 10.Although Umax values and Ks concentrations de rived for E. crassipes under N and P limitation va ried considerably, it should be possible to evaluate their potential in modelling by using the most reli able values determ ined in culture in the Monod mo del to assess its predictive ability.This, in turn, may serve as a basis for refinement of the model.In this investigation, the Umax values measured for E. crassipes were adversely influenced by the duration of plant growth in deficient cultures required to in duce N or P limitation.It is suggested, therefore, that, for purposes o f testing the model and as a basis for its refinem ent, the values determined in those ex perim ents where plants were grown for the shortest spans in N-and P-deficient cultures are possibly more reliable than those determined in other experi ments.The mean Ks concentrations derived for E. crassipes under N and P limitation, on the other hand, are possibly more reliable than the individual concentrations determ ined, since they compare fa vourably with the critical limiting N and P concentra tions in the water for E. crassipes in the field.

Minimum limiting concentrations o f N and I' in I: crassipcs estimated from yield coefficients (Y c). derived under N and I' limitation, compared with minimum limiting concentrations o f N and I' in plants harvested
T he Yc values derived for E. crassipes under N and P limitation showed little variation.They appear reliable, since their reciprocals (dry mass basis) ex pressed as percentages adequately estimated the mi nimum limiting concentrations of N and P in E. cras sipes harvested from culture, i.e. when no further significant increase in the total fresh mass of plants at each level of N o r P supplied was recorded.Since the minimum limiting concentrations of N and P in E. crassipes can be estimated from the respective Yc values for these nutrients, it should be feasible to predict the growth rate of E. crassipes in the field from the limiting N or P concentrations in plants us ing the D roop mode) (D roop, 1968;Rhee, 1973).

ACKNOW LEDGEM ENTS
W e wish to thank Mr A. Zakwe and Mrs J. Schaap for technical services rendered, Prof. D.F. Toerien and D rs P .J. Ashton and M .C. Rutherford for their valuable comments and criticisms and Mrs S.S. Brink for typing the manuscript.
2 260 Mg N e -1 and 260 fig P €-> (Figs 1 & 2C , D , E , F), plants generally attained a maximum growth rate m uch later after the addition of N and P than in T reatm ent 2 (Figs 1 & 2B) FIG. 4. -Experiment 8.A Lincweavcr-Burk plot o f specific growth rates o f E. crassipes (m eans o f 18 plants/ treatment) against levels o f P supplied in culture.Broken lines show 95% confidence limits on either side o f the regression line.Standard deviations o f means arc shown by bars.U = Umax.
FIG. 5. -Experiment 1.The relationship between total fresh mass yields o f E. crassipes (m eans o f 20 plants/treatment) and quantities o f N supplied in culture.Broken lines show 95% confidencc limits on cither side o f the regression line.Standard deviations o f means are shown by bars.
FIG, 6 .-Experim ent 8.The relationship betw een total fresh mass yields o f E. crassipes (m eans o f 18 plants/treatment) and quantities o f P supplied in culture.Broken lines show 95% confidence limits o n either side o f the regression line.Standard deviations o f m eans are shown by bars.
Standard methods fo r the examination o f water and waste-water.14th cdn.N ew York.ASSO CIATIO N O F OFFICIAL A G R IC U L T U R A L CH EM ISTS, 1975.Methods o f analysis.12th e d n ,957 pp.Washing ton, D .C .: A ssoc.Offic.Agric.Chem .B H A G A T , S. K ., FUNK, W . L .& JO H N ST O N E , D .L ., 1972.Correlated studies o f Vancouver Lake -Water quality pre diction study.O ffice o f Research and Monitoring.U .1966.A n ecological study o f Eichhornia crassipes with special emphasis on its reproductive biology.T W R IG H T , B ., 1972.The effect o f phosphate deficiency on the kinetics o f phosphate absorption by sterile excised barley roots, and som e factors affecting the iron uptake efficiency o f roots.Communs Soil Set.PI.Analys.Eichhornia crassipes (M art.)Solm s and Pistia stratiotes L. in water culture.J. Ecol.S4: 563-575.CLO CK , R. M ., 1968.Removal o f nitrogen and phosphorus from a secondary sewage treatment effluent. .J. Wat.Pollut.Control Fed.49: 57-65.C U R R IE , D .J ., 1982.Estimating M ichaelis M enten parameters: bias variance and experimental design.Biometrics 38: 907-919.D O D D E M A .H ..T E L E K A M P .G .P. & O T T E N , H ., 1979.U p take o f nitrate by mutants o f Arabidopsis thaliana, disturbed in uptake or reduction o f nitrate.Physiologia PL 45: 297-346.D R O O P .M .R ., 1968.Vitamin B-12 and marine ecology.4. The kinetics o f uptake, growth and inhibition in Monochrysis iutheri.J. mar.biol./4ss.U. K. 48: 689-733.D U N 1G A N , E .P ., SH A M SU D D IN .Z. H. & P H E L A N , R. A ., 1975.Water hyacinths tested for cleaning polluted water.La Agric.18: 12-13.EN V IR O N M EN TA L PROTECTION A G E N C Y , 1974.Manual o f methods fo r chemical analysis o f ivoter and wastes.The kinetics o f inorganic carbon limited growth o f green algae in continuous culture.Its relationship to eutrophication., W. T ., KNIPL1NG, E. B. & W EST, S. H ., 1970.Phosphorus absorption by and distribution in water hya cinths.Proc.Soil Crop Sci, Soc.Fla 30: 64-68.H A L L E R .W. T. & SU TTO N, D .L .. 1973.Effect o f pH and high phosphorus concentrations o n growth o f water hya cinth.Hyacinth Control J. 11: 59hyacinths.Proc Soil Crop Sci.Soc.Fla 30: 51-63.LIN EW EA V E R .H. & B U R K .D ., 1934.The determination o f enzyme dissociation constants.J.A m .chem.Soc.56: 658.M A C K EN TH U N , K. M ., 1964.Limnological aspects o f recrea tional lakes.Nitrogen and phosphorus in water : an annotated bibliography o f their biological effects.Washington D .C .: U .S .Government Printing Office.M ALEK .I. & F E N C L .Z ., 1966.Theoretical and methodological basis o f continuous culture o f micro-organisms.Prague: C ze choslovak Academy o f Sciences.M IDD ELBRO O K S, E. J , PO R C ELLA , D .B ., P E A R SO N .E. A ., M cG A U H E Y , P. H. & ROHL1CH.G .A ., 1971.B io stimulation and algal growth kinetics o f waste water.J. Wat.Pollut.Control Fed.43: 454-473.M INER, S., W O OTEN, J. W .& D O D D , J. D ., 1971.W ater hya cinths to further treat anaerobic lagoon effluent.In Live stock Waste Management and Pollution Abatement.The use o f growth kinetics in the develop ment o f a predictive model o f the growth o f Eichhornia cras sipes (Mart.)Solms in the field.Ph.D .thesis, reductase in corn roots.PI.Physiol.50: 649-654.P E N FO U N D , W. T ., 1956.Primary production o f vascular aqua tic plants.Limnoi.Oceanogr.1: 92-101.P E N F O U N D , W. T .& E A R L E , T. T ., 1948.The biology of water hyacinth.Ecol.Monogr.18: 448-472.R A D F O R D .P. J ., 1967, Growth analysis formulae -their use and abuse.Crop Sci.7: 171-175.R A Y N E R .A .A ., 1967.A first course in biometry for agriculture students.Pietermaritzburg: University o f Natal Press.R H E E , G -Y ., 1973.A continuous culture study o f phosphate up take, growth rate and polyphosphate in Scenedesmus sp.J. Phycol.9: 495-506.R H E E , G -Y ., 1974.Phosphate uptake under N limitation by Sce nedesmus sp. and its ecological implications.J. Phycol.Wasser und Nitratreductase-Aktivitat bei submersen Wasserpflanzen Fontinalis antipyretica L. Arch.Hydrobiol.Suppl.47: 282-294.SH ELEF, G .. 1968.Kinetics o f algal systems in waste-treatmenr.Light intensity and nitrogen concentration as growth-limiting factors.P h.D .thesis.University o f California.Berkeley.SH ELEF, G ., O SW A L D , W. J. & G O L U E K E , C. G ., 1968.Ki netics o f algal systems in waste treatment.Light intensity and nitrogen as growth limiting factors.Die eutrofikasiepeile van vier Transvaalse damme.M .Sc. verhandcling, Univcrsiteit van Pretoria.STUM M , W .. 1974.Man's acceleration o f hydrogeochemical cyc ling o f phosphorus-etttrophication o f inland and coastal waters.Paper presented at the IWPC Conference, & SC H ER FIG .J., 1971.Provisional algal assay proceduresfinal report.SERL Report No. in earthen ponds.Hyacinth Control J. 10: 9-11.W ELCH , E. B .. STU R T E V A N T , P. & PERK INS, M. A ., 1978.Dominance o f phosphorus over nitrogen as limiter to phyto plankton growth rate.Hydrobiologia 57,3: 209-215.W ESTLAKE. D .F., 1963.Comparisons o f plant productivity.Biol.Rev. 38: 385-425.W O LVERTO N, B. C ., 1975.Water hyacinths fo r removal o f cad mium and nickel from polluted waters.Water hyacinths and alligator weeds fo r removal of lead urtd m er cury from polluted waters.Water hyacinths and alligator weeds fo r rem oval o f silver, cobalt and strontium fro m polluted waters.Water hyacinths fo r upgrading sewage lagoons to meet advanced waste water treatment standards.Part I. Water hyacinths fo r upgrading sewage lagoons to meet advanced waste water treatment standards.Part II.Water hya cinths (Eichhornia crassipes) fo r removing chemical and pho tographic pollutants fro m laboratory waste waters.Kinetics o f algal systems in waste treatment.Phos phorus as a growth limiting factor.Report o f the Sanitary Engineering Research Laboratory, University o f California,

TABLE 1 .
-T reatm ent differences between experim ents designed to measure kinetic coefficients for E. crassipes growing in N-and P-limited cultures

TABLE 3 .-Statistical analysis o f regressions o f 1 /U against 1/lim iting nutrient concentration for E. crassipes grown in N-<Experiments 1 to 5 ) and P-(Experiments 6 t o 8) lim ited cultures Experi ment No.
and PO5'(Cartwright, 1972), and for other species.Doddema  et al. (1979), for example, have shown a reduction in Km from 111 to 40 mM NO} brought about by N starvation in Arabidopsis thaliana.It is suggested, therefore, that the different Umax values derived for

TABLE 5 , -Half saturation coefficien ts (K s) reported for various species o f algae compared w ith those determined for
E. crassipes

from culture
each limiting nutrient concentration could be estab lished over a much longer growth period in culture.This would eliminate any adverse effects on the growth rate of E. crassipes arising through growth of plants in N-o r P-deficient cultures.