Modelling temporal decoupling between biomass and numbers during the transient nitrogen-limited growth of a marine phytoflagellate

A mathematical model of single-nutrient-limited algal growthis presented in which carbon fixation and cell division aredifferent functions of assimilated nutrient. The model successfullydescribes key features of the growth of Isochrysis galbana inammonium-limited batch culture under continuous illuminationand in light/dark cycles. The incorporation of a nutrient processingtime allows the simulation of a time lag between net carbonfixation and cell division, and enables the model to describechanges in the mean carbon content and carbon/nitrogen ratioof the cells. The model can be completely parameterized fromstandard batch culture experiments.     

The spatial and temporal dynamics of deep chlorophyll layers in high-mountain lakes: effects of nutrients, grazing and herbivore nutrient recycling as growth determinants

Deep chlorophyll layers (DCL) are a common feature of oligotrophiclakes, yet the mechanisms that form and maintain them are notunderstood fully. These phytoplankton populations occur in themetalimnia of lakes where light levels are moderate to low,and where nutrient levels and zooplankton grazing pressure aredifferent than in the epilimnion. To test the importance ofnutrients and grazing pressure for algal growth in differentlake strata, microcosm experiments and monitoring were conductedin two oligotrophic lakes in the Rocky Mountains of North Americathat contain DCL. In situ microcosm experiments with naturalphytoplankton communities from three depth strata were conductedwith macronutrient additions and with and without the naturalzooplankton grazing communities. Alkaline phosphatase assaysand the in situ microcosm experiments indicated less nutrientlimitation in the metalimnia than in the epilimnia of both lakes.Zooplankton grazing in the experiments decreased algal populationgrowth rates by as much as 6% day^–1, with impacts shiftingto progressively deeper strata over the summer. Zooplanktongrazing losses, however, were partially offset by nutrient recyclingthat increased algal growth rates. Depth-differential nutrientdeficiency and zooplankton grazing and recycling interactedto maintain the DCL in these lakes.     

Species-specific algal responses to zooplankton: experimental and field observations in three nutrient-limited lakes

A series of 4-day manipulations of zooplankton biomass and nutrientavailability was performed in enclosures in three lakes to determinespecies-specific algal responses to herbivory and nutrient enrichment.Algal performance in enclosures was compared to the relationshipsbetween weekly algal growth rates and the zooplankton in situ.When in situ growth rates were significant functions of zooplanktonbiomass, the responses were generally consistent with responsesin the enclosure experiments. The importance of both nutrientsand zooplankton in mediating algal growth was demonstrated bynumerous observations: strong algal community response to enrichment,unimodal or positive responses of certain algal taxa to zooplanktonbiomass, differences in degree of nutrient limitation amongthe algal response types, lack of nutrient limitation of non-grazedalgal taxa and a preponderance of taxa with no net responseto increasing zooplankton biomass. Variation in the zooplanktoncommunity may be the largest source of variability in nutrientsupply rate during summer in stratified lakes, and causes substationalvariability in the algae. Algae responded more strongly to changesin zooplankton composition than to changes in zooplankton biomass.We conclude that, due to the close coupling of phytoplanktonand zooplankton communities in these nutrient-limited lakes,major compositional changes in the zooplankton have greatereffects on the algae than do changes in biomass of grazers alreadypresent. ¹Present address: Division of Environmental Studies, Universityof California, Davis, CA 95616, USA ²Present address: Division of Biological Sciences, Universityof California, Davis, CA 95616, USA     

Comparison of different algal carbon estimates by use of the Droop-model for nutrient limited growth

Three different estimates of algal carbon were derived fromfield experiments in plastic enclosures and tested as measureof algal biomass in the growth model of Droop. Fresh weightderived carbon and total paniculate organic carbon correctedfor detritus were both found to behave as good estimates ofalgal biomass in the model, while total paniculate organic carbondid not. The study also provided results which suggested thatthe relation between growth rate and endogenous phosphorus differedfor two species involved. Growth was maintained at lower Q_p-ratiosin Staurastrum dominated communities compared with communitiesconsisting mainly of Anabaena flos-aquae.     

Forecasting of environmental risk maps of coastal algal blooms

We present the elements of an algal bloom risk forecast system which aims to provide a scientific prognosis of the likelihood of an algal bloom occurrence as a function of: (a) the nutrient concentration; and (b) the forecasted wind and tide-induced vertical mixing relative to the critical value defined by the environmental and algal growth conditions. The model is validated with high frequency field observations of algal blooms in recent years and only requires the input of readily available field measurements of water column transparency, nutrient concentration, representative maximum algal growth rate, and a simple estimate of vertical mixing as a function of tidal range, wind speed, and density stratification. The forecasted region-wide risk maps successfully predicted the observed algal bloom occurrences in Hong Kong waters over the past 20 years, with a correct prognosis rate of 87%. It is shown that algal blooms are to a large extent controlled by the interaction of physical and biological processes. This work provides a general framework to interpret the complex spatial and temporal dynamics of observed algal blooms, and paves the way for the development of real time algal bloom risk forecast systems.     

Nutrient-Limited Growth Rates: Roles of Nutrient-Use Efficiency and of Adaptations to Increase Uptake Rate

When stressed by low nutrient availability, young sunflowerplants (Helianthus annuus) showed responses seen in many otherspecies: increases in root uptake capacity (V^max, l/K_m), root:shoot ratio, and putative nutrient-use efficiency, nUE=l/(tissuenutrient content). A straightforward mechanistic model is derivedfor relative growth rate (RGR) in solution culture in termsof these factors. A linear regression based on the model indicatesa negative role for nUE, which violates a premise of the model.A revised model proposes that primary adaptations are only inuptake rate and growth or nutrient allocations, and these actthrough the photosynthetic utility of nutrient. The tissue nutrientcontent and associated nUE become dependent quantities. Thepredictions for RGR, as tested by linear regression, are improved.The model predicts that nUE can increase as external solutionconcentration decreases, but decreases with increased uptakeadaptations in one given environment. The decrease in nUE compromisespotential gains in RGR from uptake adaptations, and makes increasesin root: shoot ratio a nearly insignificant contributor to earlyRGR. The model and associated regression analyses are generalizedfor additional adaptations such as increased root fineness andfor different quantitative ways that a nutrient may limit photosynthesis.The model and analyses are also generalized to plant growthin soil and growth without functional balance between root andshoot. Key words: Relative growth rate, Helianthus annuus, nutrient stress, nutrient use efficiency, functional balance     

Simulating pH effects in an algal‐growth hydrodynamics model1

Models and numerical simulations are relatively inexpensive tools that can be used to enhance economic competitiveness through operation and system optimization to minimize energy and resource consumption, while maximizing algal oil yield. This work uses modified versions of the U.S. Environmental Protection Agency's Environmental Fluid Dynamics Code (EFDC) in conjunction with the U.S. Army Corp of Engineers' water‐quality code (CE‐QUAL) to simulate flow hydrodynamics coupled to algal growth kinetics. The model allows the flexibility of manipulating a host of variables associated with algal growth such as temperature, light intensity, and nutrient availability. pH of the medium is a newly added operational parameter governing algal growth that affects algal photosynthesis, differential availability of inorganic forms of carbon, enzyme activity in algae cell walls, and oil production rates. A single‐layer algal‐growth/hydrodynamic model without pH limitation was verified by comparing solution curves of algal biomass and phosphorus concentrations to an analytical solution. Media pH, now included in the model as a growth‐limiting factor, can be entered as a measured value or calculated based on CO₂ concentrations. Upon adding the ability to limit growth due to pH, physically reasonable results have been obtained from the model both with and without pH limitation. When the model was used to simulate algal growth from a pond experiment in the greenhouse, a least‐squares fitting technique yielded a maximum algal production (subsequently modulated by limitation factors) of 1.05 d^?1. Overall, the measured and simulated biomass concentrations in the greenhouse pond were in close agreement.     

Modelling the effects on phytoplankton communities of changing mixed depth and background extinction coefficient on three contrasting lakes in the English Lake District

1. The process‐based phytoplankton community model, PROTECH, was used to model the response of algal biomass to a range of mixed layer depths and extinction coefficients for three contrasting lakes: Blelham Tarn (eutrophic), Bassenthwaite Lake (mesotrophic) and Ullswater (oligotrophic). 2. As expected, in most cases biomass and diversity decreased with decreasing light availability caused by increasing the mixed depth and background extinction coefficient. The communities were generally dominated by phytoplankton tolerant of low light. Further, more novel, factors were identified, however. 3. In Blelham Tarn in the second half of the year, biomass and diversity did not generally decline with deeper mixing and the community was dominated by nitrogen‐fixing phytoplankton because that nutrient was limiting to growth. 4. In Bassenthwaite Lake, changing mixed depth influenced the retention time so that, as the mixed depth declined, the flushing rate in the mixed layer increased to the point that only fast‐growing phytoplankton could dominate. 5. In the oligotrophic Ullswater, changing the mixed depth had a greater effect through nutrient supply rather than light availability. This effect was observed when the mixed layer was relatively shallow (<5.5 m) and the driver for this was that the inflowing nutrients were added to a smaller volume of water, thus increasing nutrient concentrations and algal growth. 6. Therefore, whilst changes in mixed depth generally affect the phytoplankton via commonly recognized factors (light availability, sedimentation rate), it also affected phytoplankton growth and community composition through other important factors such as retention time and nutrient supply.     

The relative importance of light and nutrient limitation of phytoplankton growth: a simple index of coastal ecosystem sensitivity to nutrient enrichment

Anthropogenic nutrient enrichment of the coastal zone is now a well-established fact. However, there is still uncertainty about the mechanisms through which nutrient enrichment can disrupt biological communities and ecosystem processes in the coastal zone. For example, while some estuaries exhibit classic symptoms of acute eutrophication, including enhanced production of algal biomass, other nutrient-rich estuaries maintain low algal biomass and primary production. This implies that large differences exist among coastal ecosystems in the rates and patterns of nutrient assimilation and cycling. Part of this variability comes from differences among ecosystems in the other resource that can limit algal growth and production – the light energy required for photosynthesis. Complete understanding of the eutrophication process requires consideration of the interacting effects of light and nutrients, including the role of light availability as a regulator of the expression of eutrophication. A simple index of the relative strength of light and nutrient limitation of algal growth can be derived from models that describe growth rate as a function of these resources. This index can then be used as one diagnostic to classify the sensitivity of coastal ecosystems to the harmful effects of eutrophication. Here I illustrate the application of this diagnostic with light and nutrient measurements made in three California estuaries and two Dutch estuaries.     

Consumer-dependent responses of lake ecosystems to nutrient loading

The nutrient loading concept proposes that algal biomass, waterclarity and the processes of lake eutrophication are a functionof nutrient loading. We hypothesized that grazers play an importantrole in determining the impacts of nutrient loading on algalbiomass and water clarity, and the overall eutrophication process.To test how the contrasting grazer communities modify the fateof nutrients, we added nutrients (nitrate and phosphate) ata known loading rate to four large enclosures, but in two ofthe four enclosures large cladoceran grazers (Daphnia >1mm mean length) were allowed to develop by removing the planktivorousfish. In the remaining two enclosures, the development of largeDaphnia was prevented by adding planktivorous fish. The concentrationsof epilimnetic total phosphorus (TP) increased at a similarrate in all four enclosures. However, the daily accumulationof added phosphate into the participate or planktonic forms,especially into plankton <20 µm, was three times fasterwhen large Daphnia were absent than when large Daphnia wereabundant. In the enclosures with large Daphnia, added phosphatewas accumulated in the dissolved pool instead. At a constantnutrient loading, algal biomass (chlorophyll a) increased fourtimes faster in the enclosures without large Daphnia than inthose with large Daphnia. Similarly, Secchi depth declined from3.5 to <1 m when Daphnia were absent, but did not declinewhen Daphnia were common. Our results demonstrate that the samenutrient loading and the resultant increase in epilimnetic TPdo not produce the same trophic conditions, as indicated byalgal biomass and water clarity, if the grazers of the majorassimilators of nutrients (the fraction of plankton edible toDaphnia) are different. We suggest that stratified lake ecosystemshaving functionally dominant large grazer communities may beless prone to eutrophication than those lacking large grazers.Consistent with the nutrient loading concept, epilimnetic concentrationsof phosphorus increase proportionately with increased loadingof phosphorus, but the trophic conditions of ecosystems indicatedby algal biomass and water clarity do not follow the same patternsunder contrasting conditions of grazer communities. We suggestthat models predicting algal biomass from loading rates shouldaccount for the role of grazers.     

Positive feedbacks between bottom-up and top-down controls promote the formation and toxicity of ecosystem disruptive algal blooms: A modeling study

Harmful algal blooms that disrupt and degrade ecosystems (ecosystem disruptive algal blooms, EDABs) are occurring with greater frequency and severity with eutrophication and other adverse anthropogenic alterations of coastal systems. EDAB events have been hypothesized to be caused by positive feedback interactions involving differential growth of competing algal species, low grazing mortality rates on EDAB species, and resulting decreases in nutrient inputs from grazer-mediated nutrient cycling as the EDAB event progresses. Here we develop a stoichiometric nutrient–phytoplankton–zooplankton (NPZ) model to test a conceptual positive feedback mechanism linked to increased cell toxicity and resultant decreases in grazing mortality rates in EDAB species under nutrient limitation of growth rate. As our model EDAB alga, we chose the slow-growing, toxic dinoflagellate Karenia brevis, whose toxin levels have been shown to increase with nutrient (nitrogen) limitation of specific growth rate. This species was competed with two high-nutrient adapted, faster-growing diatoms (Thalassiosira pseudonana and Thalassiosira weissflogii) using recently published data for relationships among nutrient (ammonium) concentration, carbon normalized ammonium uptake rates, cellular nitrogen:carbon (N:C) ratios, and specific growth rate. The model results support the proposed positive feedback mechanism for EDAB formation and toxicity. In all cases the toxic bloom was preceded by one or more pre-blooms of fast-growing diatoms, which drew dissolved nutrients to low growth rate-limiting levels, and stimulated the population growth of zooplankton grazers. Low specific grazing rates on the toxic, nutrient-limited EDAB species then promoted the population growth of this species, which further decreased grazing rates, grazing-linked nutrient recycling, nutrient concentrations, and algal specific growth rates. The nutrient limitation of growth rate further increased toxin concentrations in the EDAB algae, which further decreased grazing-linked nutrient recycling rates and nutrient concentrations, and caused an even greater nutrient limitation of growth rate and even higher toxin levels in the EDAB algae. This chain of interactions represented a positive feedback that resulted in the formation of a high-biomass toxic bloom, with low, nutrient-limited specific growth rates and associated high cellular C:N and toxin:C ratios. Together the elevated C:N and toxin:C ratios in the EDAB algae resulted in very high bloom toxicity. The positive feedbacks and resulting bloom formation and toxicity were increased by long water residence times, which increased the relative importance of grazing-linked nutrient recycling to the overall supply of limiting nutrient (N).     

An investigation of non-steady-state algal growth. I. An experimental model ecosystem

In order to test rigorously the transient behaviour of mathematical models of algal growth, detailed laboratory data sets with good temporal resolution are required. A series of algal growth experiments was conducted in transient conditions. Monoculture growth of, and competition for nutrients between, three contrasting species of phytoplankton (the diatom Thalassiosira pseudonana, the harmful flagellate Heterosigma carterae and the toxic dinoflagellate Alexandrium minutum) were investigated in different temperature, light and nutrient regimes. Although growth dynamics were qualitatively similar in batch culture, quantitative differences were evident in the growth response of the different species when grown in single yield-limiting nutrient conditions in identical physical conditions. Quantities such as the carbon:nitrogen (C:N) ratio and C and N per cell varied between species and within species under different growth conditions. Such results have particular significance to the development of mathematical models, which commonly represent algal populations as a single homogeneous group using a single currency such as numbers, C or N. Changes in light and temperature regime influenced algal growth: Alexandrium failed to grow at low temperatures, while specific growth rates of Thalassiosira were more sensitive to changes in temperature than those of Heterosigma. Changes in the dominant organism(s) and/or its size or nutrient status may influence the transfer of nutrients within the food web. Commonly, mathematical models make cell growth a function of a single yield-limiting nutrient. Decreased growth rates and high residual nutrient concentrations in competition experiments indicate that this approach is unlikely to be successful in conditions of limited supply of more than one nutrient, where multiple nutrient stresses will be significant.      

Response of an algal assemblage to nutrient enrichment and shading in a Hawaiian stream

To investigate the effects of nitrate enrichment, phosphate enrichment, and light availability on benthic algae, nutrient-diffusing clay flowerpots were colonized with algae at two sites in a Hawaiian stream during spring and autumn 2002 using a randomized factorial design. The algal assemblage that developed under the experimental conditions was investigated by determining biomass (ash-free dry mass and chlorophyll a concentrations) and composition of the diatom assemblage. In situ pulse amplitude-modulated fluorometry was also used to model photosynthetic rate of the algal assemblage. Algal biomass and maximum photosynthetic rate were significantly higher at the unshaded site than at the shaded site. These parameters were higher at the unshaded site with either nitrate, or to a lesser degree, nitrate plus phosphate enrichment. Analysis of similarity of diatom assemblages showed significant differences between shaded and unshaded sites, as well as between spring and autumn experiments, but not between nutrient treatments. However, several individual species of diatoms responded significantly to nitrate enrichment. These results demonstrate that light availability (shaded vs. unshaded) is the primary limiting factor to algal growth in this stream, with nitrogen as a secondary limiting factor.     

Modelling time-series of photosynthesis and comparisons with the fluorescence yield in Chlorella vulgaris: a study of adaptation, inhibition and recovery

Time-series of ¹⁴C uptake and fluorescence yield (i.e., thefluorescence enhancement after addition of the photosyntheticinhibitor DCMU) were measured in Chorella vulgaris at variouslight intensities. Adaptation and recovery processes after alterationof the light intensity were also studied. At a constant lightintensity, both the rate of ¹⁴C uptake and the fluorescenceyield decreased with time. Comparison of time-series data of¹⁴C uptake at different light intensities showed that this phenomenonconsisted of several processes (i.e., at low light intensitiessmall changes in uptake rates were mainly due to photoadaptation,while at higher light intensities relatively larger changesoccurred, as result of photoinhibition). Transfer of an algalsample to low light intensities after a period of exposure toinhibiting light intensities resulted in an exponential recoveryof the ¹⁴C uptake rate with time, coupled with an exponentialrecovery of the fluorescence yield. A mechanistic model is presented,which describes the algal ¹⁴C uptake rate as a function of timeand light intensity. The model includes adaptation, inhibitionand recovery. Six parameters, characterising the algal suspension,have to be estimated from the results of one P versus I curveand one time-series ¹⁴C uptake, which includes a period of recovery.Using these parameters the model can predict the time-courseof ¹⁴C uptake at every constant light intensity, as well aswhen the light intensity is changed during the experiment. Whenapplied to a culture of C. vulgaris, the theoretical valuesclosely approach the actual measurements. The resemblance betweenthe measured time-series of fluorescence yield and the rateof ¹⁴C uptake indicates, that the changes in the rate of ¹⁴Cuptake are due to changes in the photosynthetic apparatus, ratherthan to changes of diffusion of ¹⁴C into the cell.     

Gastropod grazers and nutrients,but not light,interact in determining periphytic algal diversity

The potential interactions of grazing, nutrients and light in influencing autotroph species diversity have not previously been considered. Earlier studies have shown that grazing and nutrients interact in determining autotroph species diversity, since grazing decreases species diversity when nutrients (i.e. N or P) limit autotroph growth, but increases it when nutrients are replete. We hypothesized that increased light intensities would intensify the interactions between grazing and nutrients on algal species diversity, resulting in even stronger reductions in algal species diversity through grazing under nutrient–poor conditions, and to even stronger increases of algal species diversity through grazing under nutrient-rich conditions. We studied the effects of grazing (absent, present), nutrients (ambient, N + P enriched) and light (low light, high light) on benthic algal diversity and periphyton C:nutrient ratios (which can indicate algal nutrient limitation) in a factorial laboratory experiment, using the gastropod grazer Viviparus viviparus. Grazing decreased algal biomass and algal diversity, but increased C:P and N:P ratios of periphyton. Grazing also affected periphyton species composition, by decreasing the proportion of Spirogyra sp. and increasing the proportion of species in the Chaetophorales. Grazing effects on diversity as well as on periphyton N:P ratios were weakened when nutrients were added (interaction between grazing and nutrients). Chlorophyll a (Chl a) per area increased with nutrient addition and decreased with high light intensities. Light did not increase the strength of the interaction between grazing and nutrients on periphytic algal diversity. This study shows that nutrient addition substantially reduced the negative effects of grazing on periphytic algal diversity, whereas light did not interact with grazing or nutrient enrichment in determining periphytic algal diversity.     

Phytoplankton–zooplankton dynamics in periodic environments taking into account eutrophication

In this paper, we derive and analyze a mathematical model for the interactions between phytoplankton and zooplankton in a periodic environment, in which the growth rate and the intrinsic carrying-capacity of phytoplankton are changing with respect to time and nutrient concentration. A threshold value: “Predator’s average growth rate” is introduced and it is proved that the phytoplankton–zooplankton ecosystem is permanent (both populations survive cronically) and possesses a periodic solution if and only if the value is positive. We use TP (Total Phosphorus) concentration to mark the degree of eutrophication. Based on experimental data, we fit the growth rate function and the environmental carrying capacity function with temperature and nutrient concentration as independent variables. Using measured data of temperature on water bodies we fit a periodic temperature function of time, and this leads the growth rate and intrinsic carrying-capacity of phytoplankton to be periodic functions of time. Thus we establish a periodic system with TP concentration as parameter. The simulation results reveal a high diversity of population levels of the ecosystem that are mainly sensitive to TP concentration and the death-rate of zooplankton. It illustrates that the eruption of algal bloom is mainly resulted from the increasing of nutrient concentration while zooplankton only plays a role to alleviate the scale of algal bloom, which might be used to explain the mechanism of algal bloom occurrence in many natural waters. What is more, our results provide a better understanding of the traditional manipulation method.     

DYPHORA--a dynamic model for the rate of photosynthesis of algae

Experimental data obtained from different cultures of phytoplanktonindicate that photosynthesis (P) depends on light intensity(I) in a dynamic way. Therefore, static P/I curves relatingphotosynthesis to the instantaneous light may not be adequateto describe the activity of algal cells in lakes or oceans wheremixing can cause a complex pattern of light variation. The modelDYPHORA (DYnamic model for the PHOtosynthetic Rate of Algae)describes the response of photosynthesis to light using twocharacteristic times, the response time to increasing light(_r), and the light inhibition decay time (_r). The model agreeswell with available experiments if _r is chosen between 0.5 and5 min, and _r, between 30 and 120 min. It explains the occurrenceof the well-documented afternoon depression as well as the decreaseof integrated long-term rates of photosynthesis with increasinglight. Although the presented comparison of experimental dataand model results cannot serve as a proof for DYPHORA in a strictsense, the structural relationship between P and I can neverthelesspoint out inadequacies in the common interpretation of staticP/I relationships. The model can also serve as a tool to testhypotheses regarding the selective role of mixing in the competitionbetween algal species.     

The snail <Emphasis Type="Italic">Potamopyrgus antipodarum</Emphasis> grows faster and is more active in the shade,independent of food quality

Ecological stoichiometry has advanced food web ecology by emphasising the importance of food quality over food quantity for herbivores. Here, we focus on the effects of abiotic factors such as nutrients and light (known to influence food quality) on grazer growth rates. As model organism we used the mudsnail Potamopyrgus antipodarum that is native to New Zealand but invasive elsewhere. In a stream channel experiment in New Zealand, we manipulated light (two levels) and nutrients (four levels) to achieve a range of primary producer carbon: nutrient ratios and added mudsnails (3 densities + ungrazed control) to 128 periphyton covered stream channels in a 2 × 4 × 4 full factorial design. We measured snail growth rate and activity, food quality and nutritional imbalance, to test the predictions that (1) less light and more nutrients increase periphyton food quality and thus snail growth rates, and (2) less crowding leads to higher food availability and thus higher snail growth rates. We found that snail growth rates were higher under low light than under high light intensities and this difference increased with increasing nutrient addition. These changes in growth rate were not mediated by food quality in terms of periphyton nutrient ratios. Furthermore, experimental treatments strongly affected snail behaviour. Snails grazed more actively in the low light treatments, and thus it is more likely that snail growth rates were directly affected by light levels, maybe as a result of innate predator avoidance behaviour or as a reaction to high UV intensities. We conclude that in our stream channels snail growth rate was limited by factors other than food quality and quantity such as UV exposure, algal defences or the relatively low ambient water temperature.     

Physico-chemical control of the growth of a diatom, Asterionella formosa Hass., in a shallow eutrophic lake

Physico-chemical environmental control of the growth rate ofan algal population, the pennate diatom Asterionella formasaHass., was investigated for a year in natural water. This speciesoccurred in vegetative form in the water column all the time,although its population density varied by five orders of magnitudefrom a maximum of 1.4?10⁶ cells l^–1 in February to a minimumof 0.8?10¹ cells l^–1 in August. A mathematical model ofa combination of multiplicative and Liebig types suggested thatvegetative cells were severely limited in their growth rate,reaching almost 80% depression of the maximum rate between Decemberand February by low temperatures and nearly 50% depression inwarm seasons by light intensity. Nutrient limitations were onlyobserved in May, August and September, although they were notas great as by temperature and light intensity in the studylake. Population changing rates of A.formosa determined in thelake were low and agreed well with the estimated growth ratesduring winter, but those in summer were low and disagreed withthe estimated high growth rates. This suggests that populationchange of the species was highly dependent upon the specificgrowth rate in winter, but other factors became predominantin summer.     

Infection of the diatom Asterionella by a chytrid. II. Effects of light on survival and epidemic development of the parasite

A model is formulated to investigate the ability of chytridparasites to survive or become epidemic within populations oftheir algal hosts The model is used for an analysis of the effectsof light on the occurrence of Rhizophydium planktonicum Canteremend., a chytrid parasite of the freshwater diatom Asterionellaformosa Hass., using the information on the growth parametersof host and parasite presented in the first part of this article(J. Plankton Res ., 13, 103–117). According to the model,conditions for survival of the parasite are optimal when thehost grows at saturating light conditions. Under limiting lightconditions, Rhizophydium needs higher host densities in orderto maintain itself. The parasite is not able to survive prolongedperiods of severe light limitation of the host Epidemic development,however, turned out to be facilitated by a moderate light limitationof the host. Both light saturation and severe light limitationhamper epidemic development, but in the first case, epidemicdevelopment is still possible at sufficiently high host densities.