75 Article

Modelling phytoplankton dynamics in fresh waters: affirmation of the PROTECH approach to simulation

J. Alex Elliott1, Anthony E. Irish2,3 and Colin S. Reynolds2,4 1 Centre for Ecology and Hydrology (CEH) Lancaster, Library Avenue, Bailrigg, Lancaster, LA1 4AP, UK. Email: [email protected] 2 Formerly of CEH and Freshwater Biological Association, The Ferry Landing, Ambleside, LA22 0LP, UK 3 3 Lake Road, Ambleside, LA22 0AD, UK 4 18 Applerigg, Kendal, LA9 6EA, UK

Received 13 November 2009; accepted 3 March 2010; published 21 June 2010

Abstract

Twenty years after model equations describing the in situ growth rates of phytoplankton were first devised and eight since their successful incorporation into a computer simulation was first published, we set out to affirm the general validity and utility of PROTECHP ( hytoplankton RespOnses To Environmental Change). Elaborated originally for commercial purposes, PROTECH has been shown to be capable of simulating simultaneous seasonal fluctuations in the standing crops of several contrasting species of alga, making it attractive for testing the impacts of various simulated regimes for managing the growth conditions. These have been sufficiently convincing to persuade us to use PROTECH as a research tool; over a number of years, it has been used to simulate such ‘traditional’ problems of ecology as succession, competitive exclusion and species diversity, in the context of intermediate disturbance. In this paper, we review critically the workings of the model, especially how complex but consistent outcomes emerge in compliance with simple trait-based rules of community assembly. We affirm that temperature-specific growth rates of algae are strongly influenced by algal morphology, that slender species are tolerant of low average light exposure and that periodicity is related to species-specific characteristics of motility and buoyant behaviour. The results of some applications of PROTECH are presented, simulating responses of the phytoplankton community to adjustments in nutrient loading, light penetration and hydrological flushing rates; an explicit investigation of the sensitivity of population responses of Cyanobacteria to eutrophication is also reported, in the context of varying availabilities of combined inorganic nitrogen.

Considering future developments of PROTECH, we affirm the virtues of its central growth equations; we anticipate that future applications will mostly depend upon improved representation of the physical environments it seeks to simulate and that these may more frequently relate to aquatic systems other than the lakes and reservoirs for which it was originally devised.

Keywords: Phytoplankton; modelling; lake; climate change; functional groups; morphology.

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 © Freshwater Biological Association 2010 76 Elliott, J.A., Irish, A.E. & Reynolds, C.S.

Introduction With the availability of modern computing power, there is no obvious reason why these model approaches There has long been an implicit desire among limnologists should not be combined, but there have been few attempts to be able to construct reasonable models that simulate to do this. While there is a foundation of understanding of the dynamics of phytoplankton populations in lakes and the mechanisms by which natural communities are both reservoirs. In recent years, various directives on protecting selected and assembled, there remains a conceptual hiatus ecological quality and providing guidance on the maximum between the basic scientific knowledge of processes and levels of cyanobacterial toxins to be permitted in water the ability to apply them to the practical requirements of supplied for drinking has turned desire into an explicit managers, regulators and legislators for critical information. requirement. Yet ‘significant barriers to progress’ (Reynolds In 2001, we published a paper (Reynolds et al., et al., 2001) in formulating suitable models persist: despite 2001) intimating an alternative approach to modelling a widespread and comprehensive understanding of the phytoplankton dynamics. We had already been anabolic processes supporting phytoplankton growth – clear using for commercial purposes a family of models examples include the relationship between photosynthesis under the collective name, PROTECH (Phytoplankton and underwater light intensity, duration and penetration RespOnses To Environmental CHange). Essentially, (Talling, 1971) and the requirement and rates of uptake of these programmes had been built around the equations essential nutrients (Dugdale, 1967; Droop, 1974; Tilman of Reynolds (1989), which relate the growth dynamics et al., 1982) - few workers have been able satisfactorily of various phytoplankton species, grown in the to extrapolate likely actual rates of cell replication and laboratory under controlled idealised conditions, to their population recruitment. Population assembly is countered morphological characterisation in terms of cell volume by losses, measurement of which is tedious and prone to and surface area. In PROTECH, these relationships are wide inaccuracies (Jassby & Goldman, 1974). As to the applied, in defined sequence, to simulate the potential forces governing the selection, dynamic variation and the rates of change in biomass of each of these species, as well diversity of emergent assemblages, the general appreciation as others of given size and shape, in a contrived, virtual has probably altered little since Tilman (1996) declared that habitat. The major novelty in its construction was to ‘largely, they remain mysteries’. assume that the phytoplankton will always recruit new The component processes resulting in recognisable generations of individuals in natural environments, at outcomes or patterns are acknowledged to be complicated. the potential rates observed consistently in the laboratory, There is currently available an array of modelling under the identical conditions of temperature, insolation approaches that have been devised to rationalise, and resource availability. It was further assumed that the describe and predict the behaviour of populations. rates of biomass losses (through mortality, sedimentation, Mostly, these have been found not to be altogether consumption by grazing zooplankton) apply at rates also helpful: according to Reynolds’ (1999) overview, the determined experimentally on captive populations in large models then on offer fell among three categories: enclosures (Reynolds et al., 1982; see also later). In this way, • those that simulate as far as possible precise inputs environmental constraints, where they apply, detract from and responses but, thus, lack generality; optimal species-specific performances. Where manifestly • those that focus on particular or isolated processes they do not apply, the maximum attainable growth rate is and whose outputs may be precise but limited in assumed to be maintained for so long as it is sustainable. application; and Thus, it is not necessary to know the cell-specific rates of • those that require limited information inputs to derive photosynthesis or of nutrient uptake: it is self-evident that general, principled outputs but give little information the anabolic requirements of the self-replicating cells are about any particular site. simultaneously fulfilled. It is important, however, that

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 77 the model is able to recognise the onset of critical resource a short résumé of its uses as a commercial tool and as an aid depletion and the points where light fluxes or nutrient to understanding the current and projected behaviour of availabilities might fail to saturate the maximum rates of natural waters in the face of eutrophication and of climate assimilative deployment. In other words, the achievable change. We look again at the functions in the model which rates of specific growth become subject to control by are crucial to its ability to discriminate among the properties the resource supply; that is, they become ‘limited’ by of individual species that favour their dominance under it. Applying these principles to the dynamic changes in particular environmental conditions, or at particular times of species-specific phytoplankton populations, the logic of the year. We shall look at some of the versions of PROTECH PROTECH is that it subtracts losses and the deficiencies and of the success of one of its derivations, the Swedish of poor performance from a verifiable maximum growth PROTBAS model (PROTech-Based Algal Simulations). rate, thereby avoiding the extrapolation of recruitment We consider the application of PROTECH’s outputs to rates from component processes (photosynthetic rate, issues of fundamental ecological significance, including nutrient uptake rate) that may well over-saturate competition, alternative dominance, succession, diversity considerably the actual growth rate achievable. and disturbance. Finally, we remark upon how, with a The model has continued to be applied, not just to an growing awareness of its capabilities through numerous ever-increasing range of real management problems at and varied studies, confidence in the authenticity and specific world-wide locations but also to the investigation reliability of PROTECH outputs to simulate the dynamics of a number of more general ecological problems. It of freshwater phytoplankton has steadily accrued. has been used to simulate actual, observed variations in phytoplankton mass and composition in a number The rationale and development of of lakes, of varying depths, dimensions and hydraulic PROTECH displacements. It has been adapted for use in latitudes from the tropics to the Arctic, and to address wider limnological The logic of PROTECH starts with the premise that issues than just those concerning phytoplankton alone. individual species of phytoplankton have known, or Pragmatically speaking, the model can be claimed to potentially definable, maximum performances, subject have performed adequately in simulating observable to growth opportunities, water temperature, and an events in the majority of cases in which it has been tested. adequate supply of light and nutrients. A number of Although the mechanics, programme code and the run- historic systematic datasets have been published that speeds of the model have been steadily improved and report the growth rates of algal species grown under diversified, we can emphasise that, so far, it has not been idealised laboratory conditions, with steady, pre- at all necessary to modify the original base equations determined temperature, constant saturating light and describing algal growth; these remain, unchanged, at in media designed to supply the spectrum of nutritional the centre of all PROTECH iterations and, in essence, requirements (e.g. Hoogenhout & Amesz, 1965; Dauta, underpin a testable hypothesis that has yet to be disproved. 1982; Butterwick et al., 2005). Although relevant growth- We believe that it is now an appropriate time to performance data are available for scarcely more than draw attention both to the utility and to the versatility of a dozen named species, the small number of published PROTECH simulations. In this review, we will summarise observations referring to the same species reveal a high briefly the rationale and development of the model; we consistency in the rates of increase derived for given emphasise that, following the initial embodiment of its species. These rates are determined from appropriate driving equations into a computer programme and the serial measurements of accumulating biomass indices (for creation of a process-based model, the essential PROTECH instance, as cell concentration, biovolume, mass or suitable formulation has now been in use for two decades. We give analogue thereof, such as turbidity or pigmentation).

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 78 Elliott, J.A., Irish, A.E. & Reynolds, C.S.

Initially, the numerical increase is predictably exponential different size–growth rate relationships from those (1, 2, 4, 8 ... etc); the progression is normalised on a of unicells (most recently, that of Nielsen, 2006), our logarithmic scale and the distinctive statistic to be solved is evidence is that equation (3) adequately describes the the exponent of increase, r, to a predetermined base (10, 2 growth performance of planktonic coenobial diatoms, or, as is now conventional, the natural logarithmic (ln) base, like Asterionella, the individual cells of which have little e). Thus, while growth is maintained, r is the rate of change mutual physical contact, and of the open-structured in an initial cell biomass, N0, over a period of t days: colonial chrysophyte, Dinobryon. Moreover, it stretches to the mucilage-swathed colonies of green algae like Eudorina rt Nt = N0.e and the Cyanobacteria Microcystis and Anabaena, so long as (1) the representative surface-area and volume measurements Thus: adopted are those of the complete colony unit, together with any bounding mucilage. Even the relatively large

r = {ln (Nt / N0)}/t colonial cyanobacterium, Gloeotrichia, has proven possible (2) to simulate (Elliott et al., 2007). OnlyVolvox has been found where Nt is the biomass aftert days. to depart from the versatile s/v base description (unless the Again, based on rather limited data, it is evident that inside surface of the hollow colony is included); a separate the maximum rates of increase in single-celled species model is available (Reynolds, 1983) but it is not included of phytoplankton, at a constant 20 °C (or r20), generally as an option in PROTECH. Volvox is, so far, the only alga vary, from around 0.2 per day, sufficient to double the whose dynamics are known not to be readily amenable to biomass in 3.47 days, to 2.2 per day (sufficient to support PROTECH simulation. one doubling in under 7.6 hours). Moreover, interspecific differences in growth rate have been shown to be, in part, Temperature adjustment a function of algal size and morphology (e.g. Schlesinger et al., 1983; Nielsen, 2006; Kruk et al., 2009). Specifically, The second core equation in PROTECH addresses the growth rates are best correlated with the surface area-to- sensitivity of growth performances of named species volume ratios (s/v) of the algae (be that an individual cell or to water temperature, again in cultures subject to colony). The equation (3) of Reynolds (1989) asserts that: continuously saturating light and nutrient concentrations. The variations in maximum growth rate were found also 0.325 r20 = 1.142 (s/v) to be best correlated with the ratio of unit surface area to (3). volume (Reynolds, 1989). For the small, high-(s/v) species It has been shown by Elliott et al. (2000) that equation (3) and for larger ones whose distortions from the spherical explains 52 % of the total variance within the original data; form imparts an enhanced (s/v) ratio, growth rate roughly it was adopted as the base equation in the PROTECH halves per 10 °C temperature decrease; among the larger model, where it is used in the form: species having low (s/v), the growth response to lower temperatures is greater, yielding a steeper plot of replication

log r20 = a + b log (s/v) rate against temperature. Based upon the relationship (4) of β, the slope of specific temperature sensitivity to s( /v) where the standard value of the regression intercept a = (Reynolds, 1989), the PROTECH-model coding calculates log (1.142) and the standard value of the slope b = 0.325. It the maximum daily replication rate possible (rθ) at a given is relevant to point out that the original dataset included temperature (θ, °C) from the model-predicted replication Cyanobacteria, diatoms, green algae and dinoflagellates. rate at 20 °C, using equation (5): Despite reports suggesting that colonial species show

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 79

log rθ = log r20 + β [1000 / (273 + 20) - 1000 / (273 + θ)] has to be compensated if the alga is to grow in markedly (5) sub-saturating light fields. In this context, it is opportune where: to point out that such ‘respirational consumption’ is sometimes relatively very large and has to be accounted β = 3.378 - 2.505 log (s/v) as ‘loss’ in wholly anabolic models. In PROTECH, the (6). metabolic balance allows a basal respiration rate, set The coefficient of correlation of equation (6) is 0.84; the originally and justified by Reynolds et al. (2001) at 5.5 % equation explains 70 % of the variance in the original data. of the maximum light-saturated growth rate, which is included in the model calculation of the rate of replication. Growth-rate constraints: model adjustment In practice, the maximum temperature-dependent growth for suboptimal light conditions rate is increased by a factor of 1.055, then this is subject to the downward adjustment for the truncated photoperiods Phytoplankton rarely perform in the wild as they do in spent in sub-saturating light fields, before the respiratory culture, not least because the natural environment is less loss is deducted over the entire daily time-step. Self- benign than the laboratory in offering conditions that evidently, the calculation of growth rate in continuous light are manifestly not constant, being subject to fluctuations yields the original result; any time spent in the darkness or on scales at least as small as seconds (Reynolds, 1990). beyond the depth of light saturation is encompassed; the PROTECH can do little more than average and integrate longer the period of light deprivation, the more the rate variability to its own scale (i.e. a day). At night, the whole of cell replication relative to the light-saturated growth water column is in darkness. During the daylight period, is depressed. Moreover, the model allows the result to it is not certain that there will always be sufficient light to fall, quite properly, to negative values (cells are dying!). saturate growth rate; below the surface, the attenuation In the established terminology of phytoplankton and scatter of downwelling light have the effect of a dynamics (see, e.g. Jassby & Goldman, 1974), respiration sharp vertical fall in light intensity and, except in very is a legitimate, major ‘loss process’. In PROTECH, the shallow lakes, a corresponding decline with increasing connotation of ‘loss’ is in terms of shedding biomass, depth in the likelihood of light levels being able to saturate as intact, whole cells. Nevertheless, it is important growth rates. Given that phytoplankton may be entrained to emphasise the precision of the distinct terms used: simultaneously in turbulent circulations and that they are the ‘saturated growth rate’ (r’θ), is the species- and carried through this light gradient, it is natural that they temperature-specific maximum growth rate that is experience fluctuating light levels. Even in quite shallow achievable by that species at that temperature; the lakes, it is inevitable that vertical mixing takes them to ‘rate of replication’ (r) is the rate at which new cells are depths where the light does not saturate photosynthesis. formed and potentially recruited to the population, and Growth rate does not depend on instantaneous saturation which may be close to r’, or may be substantially lower of photosynthesis; rather it is a function of the light- when either the light or the nutrient supply is unable independent growth process being supplied with sufficient to saturate the maximum rate possible. The observable photosynthate to sustain growth over the division cycle. If ‘net rate of population increase’ (rn), takes into account vertical entrainment between higher and lower levels of the rates at which newly replicated cells, together with incident light results in this requirement being no longer others in the population, are subject to being lost from the satisfied, then growth rate is proportionately reduced. population, as a consequence of settlement, consumption Moreover, the metabolic costs of growth and as food by animals, and other mortalities. Note that: maintenance, which, of course, persist into darkness, (rn) ≤ (r) ≤ (r’θ) emphasise that there is an ongoing respirational loss that (7).

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 80 Elliott, J.A., Irish, A.E. & Reynolds, C.S.

The integral impact on phytoplankton growth in sub- where m is the maximum unit dimension of the alga, in ideal light fields is addressed as a function of the photoperiod, μm. The term (ms / v) is dimensionless; its value is least for which is the probable aggregate of time that algae entrained a sphere but rather greater in elongated cells and filaments. in the surface-mixed layer are exposed to light adequate to In PROTECH, equation (11) is solved as: saturate their growth demands. Allowance is made for the hours of night-time darkness and for the proportion of the log r = log (0.257) + 0.236 log (ms / v) daylight period that algae are circulated to depths greater (12). than that where penetrating light is just sufficient still to The point where light saturates specific growth rate is then be able to saturate the maximum rate of growth, r’θ. We solved from: supposed the fastest light-compensated, daily replication rate that is sustainable can be expressed in the form: Ik = (r’θ,I) /αr (13)

(r’θ,I) = r’θ Σtp / 24 from which equation (8) is solved by substitution; when hm

(8) > hp : where Σtp is the aggregate of the daily photoperiods (in 0.236 hours); it is calculated as the product of the day length, (r’θ,I) = [(r’θ) Γ / 24hm] [ln (2 I’0 × 0.257 (ms / v) )] / ε Γ (sunrise to sunset, in hours), and the ratio between the (14). depth of the light-compensated water column (hp) and the Otherwise, when hp ≥ hm: depth to which surface mixing reaches (hm):

(r’θ,I) = r’θ Γ / 24

Σtp = Γ (hp / hm) (15).

(9). The value ascribed to hm , the mixed depth, may be drawn The concept of a depth of ‘light compensation’ was from any of several sources. If sufficiently frequent real adopted, and modelled in PROTECH, following Talling’s temperature profiles are available (for instance, from (1957) seminal treatment: automatic monitoring stations: see Rouen et al., 2001), changes in mixed depth may be evident from sharp

hp = ln (I’0 / [0.5 Ik]) / ε vertical changes in temperature, and can be written in (10) to the model programme. Alternatively, simulations of where ε is the coefficient of vertical light attenuation- (m 1), mixed-depth variations can be derived from sophisticated

I’0 is the daytime-averaged photon flux across the water thermal structure models (Elliott et al., 2007) that combine -2 -1 surface (mol photons m s ) and Ik is the photon flux the effects of geographical latitude, solar declination, required to saturate the maximum growth rate. The latter cloud cover and heat absorption by water. In the earliest is a property of the alga, not the environment. On the basis versions of PROTECH, a continuously uniform mixed of laboratory experiments with 12 contrasted species of depth had to be assumed; this was acceptable in the case algae, Reynolds (1989) had found that their specific rates of the shallow lakes on which the biological model was of growth at markedly sub-saturating light intensities (αr) initially tested. In order to apply the logic to stratifying is a correlative of algal unit morphology (coefficient of lakes, we set up routines to estimate heat income to the correlation, 0.57): lake surface, based on the solar constant (the solar flux perpendicular to the top of the atmosphere) and used a 0.236 αr = 0.257 (ms / v) series of subtractive factors that related to latitude, the day (11) of the year and the maximum angle of incidence, and the further atmospheric absorption and backscattering of solar

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 81 energy by cloud. Assuming that the calculated flux to the found in the mixed layer. In order to allow for these water column, corrected for surface reflection, is distributed effects, an eddy-diffusivity subroutine was embodied into instantaneously in the surface wind-mixed layer, the heat the model, now styled PROTECH-D (D for diffusivity). imparted to the water raises its temperature according to PROTECH-D thus uses the same functions as the its specific-heat properties. Warming reduces its density, earlier PROTECH versions to calculate mixed depth but making it liable to float on colder water and more difficult also simulates extra mixing below this layer. It does this to mix downwards. The forces of warming and mixing are by using a single value of ‘background’ eddy-diffusivity 2 -1 neatly counterposed in the Monin-Obukhov equation (as (Kd, m d ); Kd actually changes with depth (Wetzel, presented by Imberger, 1985). The PROTECH-C model 1983), but this is already captured by the PROTECH used daily iterations of wind forcing and heat income as mixed depth routines, hence the simplification to a single known inputs to solve the mixed depth. For manipulative value. The value is determined using the following convenience, the vertical profile was broken into 10 cm equation (see Elliott & Thackeray, 2004, for its derivation): blocks, measuring upwards from the lake bottom. Rather 1.4383 than point temperatures, we derived a layered structure, Kd = 0.0045 zmax each slice having its own mean temperature, updated at (16) each iteration. The near instantaneous outputs, though where zmax is the maximum depth (in m). intuitively reasonable, still needed to incorporate the The Kd value is then used to calculate the net fluxes cumulative effects of stored heat on the thermal structure (Fn) of heat and nutrient concentrations between groups existing at the end of each day and to test its resistance of 10 cm layers (called metalayers) in the hypolimnion: to forced mixing on a daily basis. Thus, we introduced to PROTECH-C a daily calculation of the mixing energy Fn = (Kd / (zb - za)).(Cb - Ca).An delivered to the base of the existing structure by the (17) current day’s forcing. If sufficiently strong, it was allowed where z is the central depth (in m) of the metalayer above (za) to incorporate deeper layers in turn, until the balance of or below (zb) the point of flux,C is the mean concentration/

Monin-Obukhov components was recovered, albeit at value of the solute/heat in the metalayer above (Ca) or 2 a greater depth. Otherwise, the accumulated structure below (Cb), and An is the area (in m ) of contact between was allowed to survive, with accumulated income being the two metalayers. The end result is a smoothing of the confined only in the upper, mixed part. With a good heat temperature profile below the mixed layer and a realistic income as well, the structure was reinforced with new, means of representing the slow upward flux of nutrients stable layers being inserted towards the surface. from the high concentrations in the hypolimnion towards Though the sharply angled isotherms of the season- the upper mixed layers of the water column. long graphical representations are intuitively unfamiliar Other adaptations to the physical properties of the to limnologists, the simulations of stratification were water column have been made for specific case-studies. adequate to drive PROTECH dynamics in each layer. The For example, Myponga Reservoir in Australia had two onset of warming, of thermocline formation, the extent active surface mixers for which allowance had to be of down-mixing events through the summer, and the made (Lewis et al., 2002, 2003). These mixers moved eventual collapse of stratification in autumn may all be water from the surface down through a 13 m draft tube satisfactorily simulated. However, such a simplification into the hypolimnion at a flow rate of 7 3m s-1. Adopting was not always appropriate, particularly in deeper lakes this flow rate, a known volume of water could thus be (> 10-15 m deep) where the redistribution of heat and transferred each day to the appropriate depth in the chemicals in the hypolimnion could still be subjected hypolimnion. This then brought about temperature to mixing forces, albeit considerably weaker than those

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 82 Elliott, J.A., Irish, A.E. & Reynolds, C.S. changes and instabilities in the water column, increasing where K is the biomass-specific aliquot of each resource the probability of destabilisation and mixing occurring. considered and r now represents the expression r’ (θ, I). Another example was the challenge to PROTECH to If the aggregate demand can be met, the growth simulate the dynamics of the phytoplankton community of recruitment is allowed in full and the new simulated biomass Lake Erken in Sweden, requiring an allowance for the effects is taken to the next time step. The judgement of sufficiency of inverse stratification under the winter ice-cover (Elliott et is not just that there is absolutely more available than can al., 2007). This was achieved by fixing the mixed depth to support the potential growth, but that the rate of uptake be no deeper than 0.5 m below the surface during ice-cover. of the given nutrient by the alga is likely to saturate the growth demand. The evidence is that despite (or, perhaps, Growth-rate constraints: adjustment for because of) algae having powerful uptake capacities, suboptimal nutrient conditions failure to saturate the growth demand is not observed to occur until the target nutrient is very nearly exhausted. In nature, the ability to increase the standing biomass Below the level of saturation, the nutrient-limited may become subject to an insufficiency of the intracellular growth rates that are possible in nature are allowed in reserve of sustaining nutrients and, ultimately, of the PROTECH simulations. For the relatively small number bathing medium to supply them. Indeed, the rate of supply of species for which nutrient-limited growth kinetics of nutrients may directly regulate the rate of cell assembly, have been published, it is simple enough to encode the at which point it may truly be said to limit the growth rate. relevant equations. In our models, however, we used a Measurements of critical nutrient concentration provide more general approach that overcomes the lack of species- an important indication of imminent limitation of growth specific information and that also provides a basis for rate of one or more species but growth may be maintained, imitating disproportionate sharing of resource among possibly for another two or three cell divisions by the its competitors. Once the calculated growth increment intracellular store, generally of unknown size. The coding depletes nutrient to a level at which uptake rate is likely of PROTECH merely anticipates limitation by certain to impinge upon growth rate (default concentrations: elements only – phosphorus, nitrogen and silicon – through 3 μg L-1 bioavailable phosphorus; 80 μg L-1 dissolved calculating at each iteration the aggregate nutrient demand inorganic combined nitrogen; 234 μg L-1 soluble reactive that is required to sustain the biomass increment permitted silicon), the available limiting resource is shared among at the water temperature and light conditions obtaining. the species in proportion to their specific demands. The The model adopts as standard the mean stoichiometry of nutrient is thus exhausted and becomes simultaneously all live phytoplankton biomass, ideally constituting these limiting to all species trying to grow in the simulated elements in the ratio proposed by Stumm & Morgan water mass. Thereafter, such recruitment as may (1981): 50 g carbon : 8.3 g nitrogen : 1.2 g phosphorus : 1 g occur must rely on fresh inputs or the recycling of the chlorophyll. This ratio is based on measurements made limiting nutrient. The logic steps that are applied are: on well-resourced cell material, is only an approximate (i) solve the possible resource demand of the new biomass average, is variable in time and moves significantly in that may be sustained by the calculated light- and response to a persistent deficiency of supply of any of the temperature-determined growth; named resources. The potential growth demand is easily (ii) solve the requirement of nutrients to sustain this new calculated as the sum of demand of each of the first eight biomass; species, written as: (iii) subtract this solution (ii) from the resource remaining, or, in the event that any of the nutrient available would be r Σ(i=8) [KN0,i (e - 1)] exhausted by potential demand, share the entire remainder (18) of the limiting nutrient among the demanding algae

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 83 in the proportions of the calculated chemical demand. dearth of good information on which to formulate generic The allocation thus made now supports only a severely programs. The approach of PROTECH represents a restricted (nutrient-limited) growth rate. Exception is made gross simplification of the real world, yet it can give a in the case of all non-diatomaceous species, which have no reasonable, resource-sensitive estimate of the impacts on substantial skeletal requirement for silicon. Dinitrogen- phytoplankton. It works by assuming that only cladoceran fixing Cyanobacteria (such as Anabaena or Aphanizomenon Crustacea (specifically daphniids) are sufficiently spp.) are similarly assumed to be able to maintain growth consumptive and recruited adequately to be capable despite shortages of combined inorganic nitrogen (this of generating the rates of removal that are frequently is not a correct assumption in all circumstances; see, for observed to regulate phytoplankton biomass. This is not to instance, Diaz et al., 2007), at least until shortage of another say, of course, that we disregard the role of other Crustacea nutrient, such as phosphorus, intervenes. (copepods), rotifers and ciliates, only that their effects on the phytoplankton are not separately distinguished. Loss rates of formed biomass Fortuitously, Daphnia is one of the few animals for which there are adequate data referring to its energy requirements, Phytoplankton population dynamics are further subject to growth efficiency, growth rate, and rate of feeding - all of ongoing mortalities, especially as a consequence of sinking which rely on the filtration of food particles from a feeding out to deeper, uninsolated water and/or of consumption current that it generates itself - along with the temperature by pelagic grazers. Loss rates of phytoplankton may, sensitivities of all these processes (summarised in Gliwicz, indeed, be so high that they can greatly exceed the rates 2003; Lampert, 2007). The size selection of particles, of recruitment to growing populations, so that numbers itself a function of animal size, and the corresponding simultaneously decline. PROTECH is constructed to vulnerability of algae to selection by size, are simplified to estimate the scale of these losses on extant populations. a single function. Suitable foods, those having individual maximal dimensions of ≤ 50 μm, are effectively diluted Grazing losses from suspension by the contemporary aggregate filtration rate. The concentration of algae remaining as the starting Many kinds of animal – mostly grouped as zooplankton population for the next iteration is calculated. At the same – derive a substantial part of their nutrition through direct time, the aggregate filtration rate is raised simultaneously, consumption of phytoplankton. Many of these do so by a factor derived from the increase in individual filtration by ingesting algal cells intact, provided that they are of rates of growing daphniids and from the recruitment of suitable size and shape. The significance of grazing losses new generations of consuming juveniles. For further details on phytoplankton is thus conditioned by three factors: the of the formulation, please consult Reynolds et al. (2001). abilities and predilections of the animals in determining For the present context it is sufficient to point to which algae are selected as food; the amount of food authentic PROTECH simulations of the increased required to satisfy the animals’ individual requirements for aggregate daily filtration rate in response to rising water energy, growth and recruitment; and the prevalence of the temperatures, from being almost negligible to processing grazer itself, its impact on the food resource always being over 50 % of the total water volume, within four weeks, the product of individual demand and numbers present. or the equivalent of two cohorts of Daphnia recruiting to Moreover, it must be accepted that growing populations of the plankton. The numerical deduction is equivalent to growing individual zooplankters are liable to lead to time- 500 mL per litre of lake water filtered clear of ingestible dependent increases in the consumer pressure exerted on algae each day. Expressed in the same natural the phytoplankton. In reality, this is a formidable set of logarithms as growth rate, the loss rate (in this case, criteria for the modeller to simulate, as there is a relative rg = - 0.693 d-1) is compounded in the calculated rate

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 84 Elliott, J.A., Irish, A.E. & Reynolds, C.S. of net increase (which may easily become Table 1. Summary of PROTECH instructions governing vertical movements of phytoplankton in a hypothetical case study. In all cases of either moving up or negative) in the relevant algal populations. down, if the top or bottom layer (i.e. 0.1 m PROTECH layer) is encountered the It is evident that, in these simulations, algae movement is stopped; if it is the bottom layer the phytoplankton is lost. larger than 50 μm are not subject to this loss Phytoplankton Light condition Movement (m d-1) and that they can soon dominate over faster (µmol photon m-2 s -1) growing organisms that happen to be actively Nearly neutrally-buoyant, grazed. When the numbers of consumable non-motile life-forms foods are exhausted, the consumption rate is Paulschulzia and all sink 0.1 unsustainable and the animals ‘starve’, much Monoraphidium as they would do in the wild. It should be noted also that PROTECH calculates the Non-buoyant non-motile content of nitrogen and phosphorus of the diatoms algae removed as food and releases this Asterionella ≤ 500 sink 0.2 instantaneously into the nutrient pool in the > 500 sink 1.0 water, at each new iteration. It is accepted Aulacoseira ≤ 500 sink 0.8 that this is an exaggeration of the true rate that > 500 sink 1.0 Daphnia grazing is able to recycle nutrients. So far, PROTECH models do not Buoyancy-regulating anticipate or allow for the consumption of Cyanobacteria Daphnia by fish or other predators, but such functions are in the process of being tested. Planktothrix > 30 sink 0.1 ≤ 30 but > 10 no move Sinking losses and the effects of ≤ 10 rise 0.1 vertical motility Anabaena and > 100 sink 0.3 Aphanizomenon The effects of loss from suspension on ≤ 100 but > 30 sink 0.1 the population ecology of non-motile ≤ 30 but > 10 no move phytoplankton (especially diatoms) have ≤ 10 rise 0.1 been systematically accommodated and, like the impact of grazing on natural populations, Swimming flagellates expressed in conveniently subtractable Cryptomonas > 100 rise 0.1 logarithmic terms (Reynolds et al., 1982, ≤ 100 rise 2.0 and others). The sinking-loss subroutine of PROTECH performs the relatively simple mathematics of property of the mixed-layer depth. So long as the depth of a predictably variable alga sinking rate (a property of the mixing does not penetrate further, the settlement in deeper particle) exported across the lower boundary of each 10 cm layers is not homogenised by daily mixing but allowed to slice. For most of the latter, of course, exports to depth are progress to completion. A subroutine has been prepared more or less compensated by imports from above. There that simultaneously cumulates the sinking losses. is no replacement at the top, while those at the bottom are The simulation is acceptably realistic in simulating the considered to be removed. Those surviving the exports accelerated sinking losses of diatoms following the onset are uniformly re-integrated at the next daily iteration, the of stratification (fewer 10 cm layers) and to the often rapid total now being effectively diluted, at a loss rate that is a proliferation of diatoms that is possible when the sinking

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 85 losses of diatoms are correspondingly 20 a) minimised by deeper mixing and the PlanktothriPlanktothrix x 18 integration of more 10 cm layers. The AsterionellAsterionella a

) 16

3 AnabaenAnabaena a reproducibility of simulations was - m AphanizomenoAphanizomenon n 14 PaulschulziPaulschulzia a improved early on by allowing for the (mg (mg 12 AulacoseriAulacoseira a a acceleration of ‘stressed’ individuals, 10 MonoraphidiuMonoraphidium m for instance, those subject to prolonged CryptomonaCryptomonas s 8 exposure to high near-surface light 6 Chlorophyll levels, as occurs when there is an abrupt 4 fall in mixing intensity. The approach 2 works, albeit less spectacularly, for 0 other non-motile algae (desmid species, 1 31 61 91 121 151 181 211 241 271 301 331 361 non-motile colonies of chlorophyte, 20 b) such as Coenochloris). For algae that PlanktothriPlanktothrix x 18 AsterionellAsterionella a are motile – by virtue of possessing ) 16

3 AnabaenAnabaena a - flagella – or, like many planktonic m 14 AphanizomenoAphanizomenon n Cyanobacteria, self-regulate their PaulschulziPaulschulzia a (mg (mg 12 AulacoseriAulacoseira a a buoyancy by intracellular gas vesicles, 10 MonoraphidiuMonoraphidium m CryptomonaCryptomonas s there is the additional possibility that 8 they can be moved upwards as well 6

Chlorophyll as downwards. Rates of individual 4 movements are sensitive, especially to 2 light, and in the case of larger motile 0 algae, to nutrient availability. A set of 1 31 61 91 121 151 181 211 241 271 301 331 361 species-specific movement instructions, Fig. 1. Illustration of the movement characteristics in PROTECH for phytoplankton all provided to each alga used in the Figwith 1 the same morphology of a) Asterionella and b) Cryptomonas. The legends indicate simulation, is summarised in Table 1. which movement characteristics were applied (see Table 1). For this review, we devised an illustration of the Having now created the phytoplankton assemblage, we importance of motility on the outcome of PROTECH ran PROTECH over a simulated year and observed how simulations. We imagined a community of eight the various types separated out, purely as a result of the phytoplankton types, all of which occur frequently in differences in their movement characteristics Fig.( 1). The Windermere, but ascribing to them identical morphological figure shows two results tracing annual fluctuations in properties and behavioural logic (grazed/diatom/nitrogen- the biomass of each of the eight species in the top 5 m of fixer) and all entering the daily inoculum in identical the water column using the species-specific movement proportions. Essentially, each of the eight types is a ‘clone’ characteristics but the same morphology. In Fig. 1a, of the other. Using the growth equations presented above all the species have the morphology of Asterionella; in would determine that they all grow in exactly the same Fig. 1b, they all comply with the model’s Cryptomonas. way. Now, we assign to each phytoplankter its species- Firstly, we were able to show that phytoplankton given the specific characteristics of movement from the PROTECH same movement instructions did indeed produce identical library (Table 1). The species that obey similar rules of daily amounts of chlorophyll (e.g. the Anabaena movement movement should then also grow in very similar ways; type is not visible because it coincides exactly with that of if they do not, then it is the modelling that is at fault! Aphanizomenon). Secondly, the effect of distinct movement

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 86 Elliott, J.A., Irish, A.E. & Reynolds, C.S. characteristics is also clear in that the ‘clone’ populations limitation of growth: the low-light specialists (R-types) produced different amounts of biomass over the year, the perform relatively better than other types under conditions traces separating quite early in the sequence. However, it is of increased turbidity and critically diminished availability, also clear from comparison between the two plots that the while low-nutrient specialists (S-types) excel over others morphology used also affects the population responses of in the face of reduced or vertically segregated nutrient the various ‘clones’. For example, the Asterionella ‘clones’ supplies. grew earlier in the year than did the Cryptomonas types, Obviously, beyond these tests, any application demonstrating well the superior growth characteristics of PROTECH to a given system requires some under low average light intensities that previous work has common sense approach in judging its ability to attributed to the attenuated cell shape (Reynolds, 1989). simulate the key dynamics of the species selected. In The example demonstrates ably that the characteristics this way, PROTECH is very much an ‘expert’ model. of indigenous movement play an important, probably decisive role in the dynamics and succession of individual Sensitivity species, plainly supplementing, if not overriding, population responses to such familiar constraints The key growth equations (4), (6) and (12), discussed above, as nutrient availability and consumer pressures. lie at the heart of the biological philosophy of PROTECH. Given their importance, it was crucial to test the sensitivity The testing of PROTECH of their parameters and how variations could affect the important factors simulated, such as overall biomass produced and growth rate. Elliott et al. (1999b) achieved Verification just this, revealing that equations (4) and (6), in particular, are robust, reflecting perhaps the statistical strength of the Whilst PROTECH is essentially a phytoplankton original underpinning correlations. The light function community model, the initial testing of its assumptions (equation (12)) was the most sensitive but still required involved single-species runs, under a range of changing changes in the parameters of greater than 20 to 30 % to environments (Elliott et al., 1999a). Predictions of which produce large deviations from the relationships originally species types would be favoured by the modelled fitted. The conclusion of the study was that, as all three conditions were compared to the actual results of these functions work together to calculate a given species’ studies; the C-S-R phytoplankton functional classification, growth rate, the compounded rate overall was probably developed by Reynolds (1988), was used as a shorthand more robust than some of the equations taken individually. for the species introduced into these predictions. Thus, However, the operator of PROTECH needs to apply the model was run at various fixed temperatures, surface common sense and be wary of the fact that, of the three key irradiances, mixing depths, daylengths and imposed equations, the light function is the most sensitive. conditions of nutrient limitation. The performances of the simulated species were compared to the intuitive Validation expectations of each. Whereas good conditions of light and nutrient availability favour the rapid recruitment of To demonstrate the suitability of a model, it is usual to seek small-celled, high-sv-1 species (previously anticipated in to compare its outputs against relevant and comparable their grouping by Reynolds, 1988, as C-types), longer runs observed data (e.g. total phytoplankton biomass, species show PROTECH to be capable of capturing the impacts of counts). Such evaluations may vary from a simple visual changed circumstances such as the growing competition comparison (whether the modelled outputs look similar for diminished availability of light or the onset of nutrient to those observed), to a full statistical analysis, using

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 87 either regressions or Nash- Table 2. List of lakes and reservoirs where PROTECH has been applied and tested in peer-reviewed studies. The trophic status of the water body is also indicated. Sutcliffe comparisons (Elliott et al., 2000). Water body (Country) Trophic status Reference Elliott et al., 2006; Bernhardt Although PROTECH has Bassenthwaite Lake (UK) Mesotrophic/Eutrophic habitually been subject to et al., 2008 such validations during Blelham Tarn (UK) Eutrophic Elliott et al., 2000 the course of its various El Gergal Reservoir (Spain) Eutrophic Elliott et al., 2005 applications to particular Esthwaite Water (UK) Eutrophic Elliott, 2010 lakes and reservoirs, we take Lake Erken (Sweden) Mesotrophic Elliott et al., 2007 a single, typical example Loch Leven (UK) Mesotrophic/Eutrophic Elliott & May, 2008 of a simulation of the Myponga Reservoir (Australia) Eutrophic Lewis et al., 2002 phytoplankton periodicity QE II Reservoir (UK) Eutrophic Reynolds et al., 2005 in Bassenthwaite Lake, Ullswater (UK) Oligotrophic Bernhardt et al., 2008 Cumbria, undertaken at Wastwater (UK) Oligotrophic Elliott & Thackeray, 2004 the initiation of the study by Elliott et al. (2006). As the research set out to show how changing nutrient and water temperature affect the amount and timing of the dominant phytoplankton in the lake, it was necessary to provide convincing validation against real data, not only on overall biomass (Fig. 2) but also species composition (Fig. 3). PROTECH captured Fig. 2. Comparison of observed chlorophyll a (mg m-3) values (crosses) and PROTECH simulations (solid reasonably well the line) for Bassenthwaite Lake (1991). (After Elliott et al., 2006). changes in total chlorophyll but it was at the species level Applications of PROTECH that it succeeded best, simulating particularly well the annual responses of that year’s dominant phytoplankton Given the ability of PROTECH to simulate key aspects of species which were as diverse as Chlorella, Asterionella, the dynamic performances of various species, based upon Plagioselmis and Anabaena. It is this demonstrable and their morphological and physiological traits, the model validated capability to simulate biomass fluctuations and, has proved valuable to the exploration and prediction simultaneously, to distinguish realistically among the of phytoplankton sensitivity to environmental changes. adaptations of its major constituents the selective criteria that Below we present some apposite examples. influence the eventual assemblage composition, that gives PROTECH its reputation to reconstruct the phytoplankton ecology of many different lake systems Table ( 2).

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 88 Elliott, J.A., Irish, A.E. & Reynolds, C.S.

Diversity and the Intermediate Disturbance Hypothesis

Understanding changes in ecosystem diversity has been a challenge for ecologists for decades and numerous theories and concepts have been created. One such example is the Intermediate Disturbance Hypothesis (IDH), ably encapsulated in Connell’s (1978) landmark paper on the species diversity associated with coral reefs and tropical forests. The IDH states that the highest diversity is maintained at intermediate scales of disturbance. At low levels of disturbance, competitive exclusion will reduce diversity (autogenic selection), whereas at high levels of disturbance, only a few specialised colonist species will be able to cope with the rapidly changing environment (abiotic selection). Therefore, at intermediate disturbance levels, a mixture of functional types is represented and, potentially, at high levels of diversity. The relationship is usually represented by a smooth, humpback-shaped curve of species diversity against time. The IDH has been found to apply to the development of phytoplankton communities (e.g. Padisák et al., 1993) and is, thus, ripe for investigation using PROTECH (Elliott et al., 2001). In this particular study, the development of an assemblage of eight contrasted species of phytoplankton was simulated in a virtual controlled lake system. A 15 m deep lake was set to be constantly stratified with a 5 m mixed layer, its temperature fixed at 10 °C and insolation maximised with 24 hours of daylight, without cloud cover or any seasonal variation. This heavily controlled environment provided an experimental background onto which a single form of Fig. 3. Comparison of observed chlorophyll a (mg m-3; solid diamonds with error bars of 2 s.e.) and PROTECH simulations (solid line) for the four most abundant disturbance could be applied but with minimal phytoplankton in Bassenthwaite Lake (1991). (a) Chlorella; (b) Asterionella; (c) compound effects from other variables. Plagioselmis; (d) Anabaena. (After Elliott et al., 2006).

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 89

A realistic form of disturbance was used, that of mixing would give warning and perhaps time for a conservation of the full water column for a fixed length of time (i.e. 3, 5 or strategy to be implemented. However, if the IDH is best 7 days); thus, the 5 m mixed layer was altered to one mixed described by a cliff-shaped curve as suggested by the to 15 m, before restoring the stratification at the end of the PROTECH study, no such warning decline might be disturbance period. After observing the effects of a single observed before a catastrophic collapse occurs. Sadly for mixing, the model was run again to include additional the long-term function of lakes, the latter effect is all too mixings, the number of such events being sequentially familiar, particularly in shallow lakes (Scheffer, 1998). increased with each re-run of the model, until the lake was, effectively, fully mixed throughout the whole year. Evaluating the impacts of climate change For each of these runs the annual mean Shannon diversity (H”) was calculated; the results are plotted against the A growing concern in ecology over the last decade has number of disturbance (‘forcing’) events (see Fig. 4). been to understand how the predicted effects of climate What was immediately evident from these results change might affect freshwater ecosystems. Regarding was that the pattern of diversity was in broad support phytoplankton, research has focused on two main areas: of that predicted by the IDH. However, there was one changes in species phenology (e.g. the timing of spring significant difference in the shape of the curve when the blooms: see Adrian et al., 2006; Thackeray et al., 2008) and number of mixing events increased from 31 to 32 year-1. the possible increases in the abundance of Cyanobacteria At this point the community diversity decreased by over species (Paerl & Huisman, 2008). half because one species emerged as dominant to all others In tackling these issues using PROTECH, two (Planktothrix in this case). This kind of sudden change approaches have been taken. The first uses the results from causing a discontinuous response to a steadily changing a Regional Climate Model (RCM) that had been run using driving variable is not uncommon in ecology, particularly various climate scenarios (Elliott et al., 2005). However, in alternative stable state theory (e.g. Noy-Meir, 1975; because the RCM outputs were for 50 km grid squares, it May, 1977; Scheffer, 1998). The implications, though, was necessary to downscale the weather and to correct for for environmental managers are stark. For example, if a altitude. Furthermore, present-day RCM outputs needed humpback-shaped curve best describes the IDH, then to be tested for their ability to drive realistic phytoplankton it would be expected that a gradual decline in diversity responses in a simulated lake (Bassenthwaite Lake was again would be observed as the pressure from some disturbing selected). Using the downscaled weather data, PROTECH force increased (e.g. nutrient enrichment, pollution) which was run for 20 years under present-day climatic conditions and 20 years under the Intergovernmental Panel on Climate Change’s A2 ‘worst-case’ prediction of global climate change (IPCC, 2000). Comparisons between these two runs showed little difference in the overall amount of phytoplankton produced, although there was a tendency towards slightly increased production in the spring and reduced biomass in the summer under an altered climate. The former effect was attributable to increased water temperatures in spring (caused by higher air temperatures) while the summer decline reflects Fig. 4. Species diversity relationships between annual mean species diversity (H”) and the forcing frequency. (After Elliott et al., 2001). depleted nutrient availability, caused by the

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 90 Elliott, J.A., Irish, A.E. & Reynolds, C.S. uptake of the increased production in the spring. It was couple of key drivers and assessing the lake’s sensitivity clear from this study that nutrients are an important factor to such changes. Serial PROTECH runs were executed, in determining phytoplankton responses to climate change. again based on the characteristics of Bassenthwaite Lake, The observation led directly to a further study which in which both water temperature and nutrient loading employed the second approach to the exploration of were systematically varied, as a means of evaluating the climate-change effects on phytoplankton. This approach sensitivity of the phytoplankton to each. The method did not require RCM input and simply involved re- involved taking a single year-long simulation, successfully running a given present day simulate but changing a validated against observed data, and re-running it with increased or decreased water temperature and nutrient loads. A number of phytoplankton metrics were examined, including timing of peaks, annual mean species biomass, diversity and maximum percentage Cyanobacteria abundance. Considering the outputs describing the biomass of individual phytoplankters and, in particular, the timings of the respective peaks of each of the three most prevalent species, it was evident that changing both nutrient load and temperature had synergistic effects. Thus, the spring peaks of Plagioselmis and Chlorella each occurred later with increasing nutrient Fig. 5. The change in timing (Julian day) of the simulated spring peak with changing load but that of Asterionella was earlier (Fig. 5); nutrient (phosphorus) load for three phytoplankton (Plagioselmis, Asterionella and on the other hand, increased temperatures Chlorella) in Bassenthwaite Lake, 1991. (After Elliott et al., 2006). allowed the spring peaks of all three algae to advance. In reality, such changes have been observed to occur in many lakes in Europe and been attributed to climate change-driven factors, such as the earlier break-up of winter ice cover (Adrian et al., 2006). However, more recent studies on the long-term spring phenology of some dominant phytoplankton in Bassenthwaite Lake and Windermere demonstrate that whilst climatic influences can be important (e.g. water temperature), nutrient availability can have a considerable influence on peak timing, by averting the onset of growth-rate limitation, and that such responses are species specific (Thackeray et al., 2008; Meis et al., 2009). Another important metric to have reacted to both variables was Cyanobacteria abundance (Fig. 6). This showed a marked increase in Fig. 6. The maximum annual percentage abundance of Cyanobacteria with proportion with both increasing temperature changing water temperature and phosphorus load. (After Elliott et al., 2006).

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 91 and enhanced nutrient load. It is also evident that the forcing it to add extra phosphorus into the hypolimnion relative dominance of Cyanobacteria to higher temperatures using observed rates and observations to calibrate the alone is increased - by around 6.5 % per 1 °C rise. The model. The consequence of low inflows and weak implications for lake management are clear - even if nutrient replenishment of combined sources of inorganic nitrogen loads to the lake were to remain at their current level, the is an incipient nutrient limitation of phytoplankton, with relative abundance of Cyanobacteria seems set to increase. the further consequence, as at Loch Leven, of changes in Whether a similar response is to be expected across the abundance of dinitrogen-fixing Cyanobacteria. Thus, a wide range of differing lake habitats is something local factors of nutrient supply can be shown to affect that further, lake-specific PROTECH simulations might the response of the phytoplankton community to the establish. In another investigation of ‘lake sensitivity’, consequences of climate change. Making broad predictions applied to Loch Leven (Elliott & May, 2008), it was revealed about how lakes are likely to respond will be challenging; the that outcomes are rarely straightforward. Simulations of intervention of compounding local factors, such as nutrient the responses of phytoplankton to altered temperatures availability, elevates the importance of well-based models. were run in conjunction with altered loads of phosphorus and of altered simultaneous loads of nitrogen and The influence of retention time phosphorus. The results of this study showed that nutrients had the greatest effect on similar phytoplankton The hydrological retention (or residence) time of a metrics to those shown in the Bassenthwaite studies: lake can be important in influencing its ecology (Kalff, outcomes attributable to increased water temperatures 2002). The mechanisms at work are a balance between were small. Furthermore, the importance of late gain (e.g. increased nutrient supply) and loss processes summer nitrogen limitation in the lake was identified as (e.g. flushing out of phytoplankton and nutrients: a key factor, because it determined whether dinitrogen- Søballe & Kimmel, 1987). In trying to understand these fixing Cyanobacteria could dominate the community. balancing factors, Jones & Elliott (2007) developed some In another ‘lake sensitivity’ study, this time on Esthwaite of the inherent concepts for a renewed iteration of the Water (Elliott, 2010), the combined effects of changing Vollenweider phosphorus-load model (Vollenweider & water temperature and hydrological retention time were Kerekes, 1980). This showed that the nutrient-gain and evaluated, the latter being clearly related to possible future -loss impacts of altered retention time are dependent on changes in rainfall. Again, key phytoplankton metrics were whether the proximal source of phosphorus is a discrete calculated and averaged annually and seasonally, and it was point of entry (e.g. sewage discharge, sediment releases) clear that the sensitivity of the simulated phytoplankton or is diffuse (e.g. agriculturally-derived nutrients). In the to selected varying driving factors varied greatly with the PROTECH simulations they ran, Jones & Elliott (2007; time of the year. The phytoplankton was more sensitive see also Elliott et al., 2009) found that only in lakes having in summer and autumn, with maximum percentage annual retention times of under ca. 90 to 100 days could abundance of Cyanobacteria generally increasing with variability in retention be expressed in the phytoplankton higher temperature (in agreement with the results from the community supported. Furthermore, at most times of the Bassenthwaite Lake study: Elliott et al., 2006) and decreasing year, instantaneous retention times that are shorter than flushing rate. However, importance of the latter had less to this have an increasingly negative effect on phytoplankton do with the direct removal of phytoplankton by flushing populations. than with a lesser input of nutrients, especially of nitrogen. However, there is a significant exception to this finding During the summer, considerable amounts of phosphorus that applies when the main source of nutrients is diffuse are released from the sediments (Drake & Heaney, 1987) and the supply is limiting. Under these conditions, usually and this was mimicked in the PROTECH simulation by found in the summer months, increased inflow (shorter

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 Fig. 6 92 Elliott, J.A., Irish, A.E. & Reynolds, C.S.

Point_Diffuse

Fig. 7. Response of the mean chlorophyll a (mg m-3) for the summer in Bassenthwaite Lake (1996) to changing retention time (days) with varying ratios of point–diffuse sources of phosphorus (e.g. 100_0 = 100 % point). (After Elliott et al., 2009). retention time) may support a larger phytoplankton availability can be one of the drivers behind these changes,

biomass by supplying vital nutrients when in critical light availability and sedimentation may also be important

demand (Fig. 7). Conversely, under low flow conditions, factors. In an earlier study, in which mixed depth and

biomass declines when diffuse sources dominate but light availability were varied to alter the underwater light may increase if point sources dominate. The practical field, Elliott et al. (2002) showed PROTECH to be capable consequence highlighted by these studies is that the of simulating the population dynamics of several species responses to changing flushing rate are greatest in (e.g. Asterionella), including the temporary formation of waters that are already very sensitive to the source of deep-water maxima by some species (Reynolds, 2006). the nutrients and to its relationship to the inflow. With Building on this, a broader analysis was conducted testing predicted changes in future rainfall patterns, the likely the importance of changing mixed depth and turbidity in responses of otherwise similar lakes to, for example, a three contrasting lakes (Bernhardt et al., 2008). summer drought could be quite different, depending Using one example each of an oligotrophic, a mesotrophic on the split between point and diffuse nutrient sources. and a eutrophic lake, the study created a fixed period of stratification for each lake that began on 1 April and ended The influence of mixed depth and turbidity on 30 September. The mixed-layer depth was altered by 1 m for each run and also the background extinction coefficient It is well recognised in limnology that the timing of of the water was accorded four different values, as a proxy stratification formation and collapse can have profound for altered turbidity. The responses of the functional effects on phytoplankton communities, especially those types in the simulated communities and the overall of deeper lakes (Kalff, 2002). Whilst a change in nutrient species diversity were assessed for either half of the year.

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4 Modelling phytoplankton dynamics in fresh waters 93

The first most obvious result from this analysis was We emphasise again the enduring nature of the core that the simulated oligotrophic lake (based on Ullswater) formulations. All the improvements made to date and showed little sensitivity to either changing mixed depth or most of the additions likely to be made in the future turbidity because nutrient limitations were the dominant probably concern the mathematical description of the controlling force in the lake. In fact, the only slight effect simulated physical environments in which the biological was a simulated increase in phytoplankton biomass and equations are set to operate. The multilayered concept diversity at very shallow mixing depths (< 4 m) because the of horizontal slices was introduced into PROTECH-C for inflowing nutrients, which in PROTECH are always added operator convenience rather than limnological authenticity to the upper mixed layer, were entrained into a decreasing and, though the outputs are acceptable, neither the volume of water, this increasing their concentration. development of a diffusivity-informed water column, Another indirect effect of altering mixed depth was nor our (unpublished) attempts to link PROTECH to observed in the mesotrophic lake, which was based on the outputs of DYRESM1 (Imberger & Patterson, 1981) Bassenthwaite Lake. In this case, the shallower mixed have quite overcome the current weaknesses attaching to depths favoured the preponderance of small, faster- prescriptions of the physical medium. However, some of growing species to increase in the phytoplankton. Again the specific areas we are developing include adding oxygen because PROTECH adds the inflows into the mixed layer, concentration predictions to the model’s suite of outputs, this caused increased flushing of the mixed layer and which will allow the addition of a sediment nutrient flux increased proportionate net losses of the slower-growing routine to be applied. Also, we are working with other species, leaving more resources available for the smaller colleagues to expand the grazing functions in PROTECH phytoplankton. However, despite these unexpected in order to begin to simulate zooplankton populations and but interesting insights, the simulations supported the communities. It is not clear, either, that CAEDYM2, the conclusions of other field and experimental studies. model of Hamilton & Schladow (1997), which is driven Generally, cylindrical species tolerant of deep mixing and directly by DYRESM outputs but generates its own view low-light conditions, grouped as R-types by Reynolds of phytoplankton dynamics, produces simulations very (1988), dominated under conditions of diminished light different from those of PROTECH. availability, when turbidity was high or mixing was The model works well enough in shallow, non- deep. In fact, such species produced the largest blooms stratifying water columns (Reynolds et al., 2001). We at intermediate levels of mixing, thereby matching the also know that it can be used successfully using real findings of Reynolds et al. (1983) and of Diehl et al. (2002, measurements of thermal structure which can now be 2005). These studies recognised that, at very shallow supplied from automatic buoys (e.g. Rouen et al., 2001); mixing depths, sinking loss has a net negative effect on most these may yield so many data that their integration for use phytoplankton and, at very deep mixing depths, the shortage in PROTECH may be something of a luxury. Markensten of light restricts growth of even the most tolerant species. & Pierson (2007) devised a model (called PROTBAS, for PROTech-Based Algal Simulations) which, as its name The future of PROTECH implies, simulates the simultaneous variations in the biomass of several algae against recorded field data. We believe that the series of applications outlined in They used this with considerable success to reconstruct this paper will convey some of the confidence we have the variations in the phytoplankton assemblage, through acquired in using the PROTECH model formulations. consecutive years of contrasted weather conditions, in a They have helped us to improve the versatility of the large, exposed shallow basin at the western end of Lake model to simulate phytoplankton dynamics in systems 1 Dynamic Reservoir Simulation Model far from those for which its use was originally designed. 2 Computational Aquatic Ecosystem Dynamics Model

DOI: 10.1608/FRJ-3.1.4 Freshwater Reviews (2010) 3, pp. 75-96 94 Elliott, J.A., Irish, A.E. & Reynolds, C.S.

Mälaren, Sweden. To a dedicated formulation of the Drake, J.C. & Heaney, S.I. (1987). Occurrence of phosphorus and its physics, they added a subroutine to estimate the variations potential remobilization in the littoral sediments of a productive in light extinction that result from wind action and attendant lake. Freshwater Biology 17, 513-523. entrainment and resuspension of detritus from the bottom Droop, M.R. (1974). The nutrient status of algal cells in continuous sediments, as well as those attributed to the enhanced culture. Journal of the Marine Biological Association of the United discharges from inflowing rivers. They also modified Kingdom 54, 825-855. the regeneration terms applying to nitrogen and silica. Dugdale, R.C. (1967). Nutrient limitation in the sea: dynamics, These diversions apart, it seems that the immediate identification and significance.Limnology and Oceanography 12, future of PROTECH will continue to be divided between 685-695. making simulations of phytoplankton dynamics in specific Elliott, J.A. (2010). The seasonal sensitivity of Cyanobacteria and lakes and reservoirs (which are increasingly likely to be other phytoplankton to changes in flushing rate and water outside the UK) and to using emergence-based operating temperature. Global Change Biology 16, 864-876. rules (Reynolds & Elliott, 2010) in the simulation of some Elliott, J.A. & May, L. (2008). The sensitivity of phytoplankton of the ongoing issues contended in theoretical ecology. in Loch Leven (UK) to changes in nutrient load and water temperature. Freshwater Biology 53, 32-41. References Elliott, J.A. & Thackeray, S.J. (2004). The simulation of phytoplankton in shallow and deep lakes using PROTECH. Adrian, R., Wilhelm, S. & Gerten, D. (2006). Life-history traits of Ecological Modelling 178, 357-369. lake plankton species may govern their phenological response Elliott, J.A., Reynolds, C.S., Irish, A.E. & Tett, P. (1999a). to climate warming. Global Change Biology 12, 652-661. Exploring the potential of the PROTECH model to investigate Bernhardt, J., Elliott, J.A. & Jones, I.D. (2008). Modelling the effects phytoplankton community theory. Hydrobiologia 414, 37-43. on phytoplankton communities of changing mixed depth and Elliott, J.A., Irish, A.E., Reynolds, C.S. & Tett, P. (1999b). Sensitivity background extinction coefficient on three contrasting lakes in analysis of PROTECH, a new approach in phytoplankton the English Lake District. Freshwater Biology 53, 2573-2586. modelling. Hydrobiologia 414, 45-51. Butterwick, C., Heaney, S.I. & Talling, J.F. (2005). Diversity in the Elliott, J.A., Irish, A.E., Reynolds, C.S. & Tett, P. (2000). Modelling influence of temperature on the growth rates of freshwater freshwater phytoplankton communities: an exercise in algae. Freshwater Biology 50, 291-300. validation. Ecological Modelling 128, 19-26. Connell, J.H. (1978). Diversity in tropical rain forests and coral Elliott, J.A., Irish, A.E. & Reynolds, C.S. (2001). The effects of vertical reefs. Science 199, 1302-1310. mixing on a phytoplankton community: a modelling approach Dauta, A. (1982). Conditions de développement du phytoplancton: to the Intermediate Disturbance Hypothesis. Freshwater Biology étude comparative du comportement de huit espèces en culture. 46, 1291-1297. I. Détermination des paramètres de croissance en fonction de la Elliott, J.A., Irish, A.E. & Reynolds, C.S. (2002). Predicting the lumière et de la température. Annales de Limnologie 18, 217-262. spatial dominance of phytoplankton in a light limited and Diaz, M., Pedrozo, F., Reynolds, C. & Temporetti, P. (2007). incompletely mixed eutrophic water column using the Chemical composition and the nitrogen-regulated trophic state PROTECH model. Freshwater Biology 47, 433-440. of Patagonian lakes. Limnologica 37, 17-27. Elliott, J.A., Escot, C., Basanta-Alves, A. & Cruz-Pizarro, L. (2005). Diehl, S., Berger, S., Ptacnik, R. & Wild, A. (2002). Phytoplankton, Simulations of phytoplankton dynamics in El Gergal reservoir, light, and nutrients in a gradient of mixing depths: field southern Spain (PROTECH). In: New Tools for the Monitoring, experiments. Ecology 83, 399-411. Modelling & Management of Fresh Waters (eds K. Rouen & G. Diehl, S., Berger, S. & Woehrl, R. (2005). Flexible nutrient George). Freshwater Forum 23, 78-92. stoichiometry mediates environmental influences on Elliott, J.A., Jones, I.D. & Thackeray, S.J. (2006). Testing the phytoplankton and its resources. Ecology 86, 2931-2945. sensitivity of phytoplankton communities to changes in

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water temperature and nutrient load, in a temperate lake. Reynolds, C.S. (2003). Modelling the effects of artificial mixing Hydrobiologia 559, 401-411. and copper sulphate dosing on phytoplankton in an Australian Elliott, J.A., Persson, I., Thackeray, S.J. & Blenckner, T. (2007). reservoir. Lakes & Reservoirs: Research and Management 8, 31-40. Phytoplankton modelling of Lake Erken, Sweden by linking Markensten, H. & Pierson, D.C. (2007). Weather driven influences the models PROBE and PROTECH. Ecological Modelling 202, on phytoplankton succession in a shallow lake during 421-426. contrasting years: application of PROTBAS. Ecological Modelling Elliott, J.A., Jones, I.D. & Page, T. (2009). The importance of 207, 128-136. nutrient source in determining the influence of retention time on May, R.M. (1977). Thresholds and breakpoints in ecosystems with phytoplankton: an explorative modelling study of a naturally a multiplicity of stable states. Nature 269, 471-477. well-flushed lake. Hydrobiologia 627, 129-142. Meis, S., Thackeray, S.J. & Jones, I.D. (2009). Effects of recent Gliwicz, Z.M. (2003). Between Hazards of Starvation and Risk of climate change on phytoplankton phenology in a temperate Predation: The Ecology of Offshore. Excellence in Ecology, Book 12, lake. Freshwater Biology 54, 1888-1898. ed. O. Kinne. International Ecology Institute, Oldendorf/Luhe, Nielsen, S.L. (2006). Size-dependent growth rates in eukaryotic Germany. 379 pp. and prokaryotic algae exemplified by green-algae between Hamilton, D.P. & Schladow, S.G. (1997). Prediction of water unicells and colonial growth forms. Journal of Plankton Research quality in lakes and reservoirs. 1. Model description. Ecological 28, 489-498. Modelling 96, 91-110. Noy-Meir, I. (1975). Stability of grazing systems: an application of Hoogenhout, H. & Amesz, J. (1965). Growth rates of photosynthetic predator-prey graphs. Journal of Ecology 63, 459-481. microorganisms in laboratory cultures. Archiv für Mikrobiologie Padisák, J., Reynolds, C.S. & Sommer, U. (eds) (1993). The 50, 10-25. Intermediate Disturbance Hypothesis in phytoplankton Imberger, J. (1985). Thermal characteristics of standing waters: an ecology. Hydrobiologia 249, 135-156. illustration of dynamic processes. Hydrobiologia 15, 7-29. Paerl, H.W. & Huisman, J. (2008). Blooms like it hot. Science 320, Imberger, J. & Patterson, J.C. (1981). A dynamic reservoir 57-58. simulation model – DYRESM. In: Transport Models for Inland and Reynolds, C.S. (1983). Growth-rate responses of Volvox aureus Coastal Waters (ed. H.B. Fisher), pp. 310-361. Academic Press, Ehrenb. (Chlorophyta, Volvocales) to variability in the physical New York. environment. British Phycological Journal 18, 433-442. IPCC (2000). Special Report on Emissions Scenarios. Eds N. Reynolds, C.S. (1988). Functional morphology and the adaptive Nakicenovic & R. Swart (Intergovernmental Panel on Climate strategies of freshwater phytoplankton. 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Reynolds, C.S., Wiseman, S.W., Godfrey, B.M. & Butterwick, C. (1983). Some effects of artificial mixing on the dynamics of phytoplankton populations in large limnetic enclosures. Journal of Plankton Research 5, 203-234. Reynolds, C.S., Irish, A.E. & Elliott, J.A. (2001). The ecological basis for simulating phytoplankton responses to environmental change (PROTECH). Ecological Modelling 140, 271-291. Reynolds, C.S., Irish, A.E. & Elliott, J.A. (2005). A modelling approach to the development of an active management strategy for the Queen Elizabeth II reservoir. In: New Tools for the Monitoring, Modelling & Management of Fresh Waters (eds K. Author Profile Rouen & G. George). Freshwater Forum 23, 105-125. Alex Elliott is a research scientist in the Lake Ecosystem Rouen, M.A., George, D.G. & Hewitt, D.P. (2001). Using an Group at the Centre for Ecology and Hydrology. He automatic monitoring station to assess the impact of episodic has been developing and applying the PROTECH mixing on the seasonal succession of phytoplankton. model for over ten years and continues to expand its Verhandlungen der Internationalen Vereinigung für theoretische und angewandte Limnologie 27, 2972-2976. application throughout the world. Scheffer, M. (1998). Ecology of Shallow Lakes. Chapman & Hall, Anthony (Tony) E. Irish joined the Freshwater London. 357 pp. Biological Association, Windermere Laboratory, in Schlesinger, D.A., Molot, L.A. & Shuter, B.J. (1983). Specific growth rates of freshwater algae in relation to cell size and light intensity. 1973 to work on the Blelham Tarn enclosures after Canadian Journal of Fisheries and Aquatic Sciences 38, 1052-1058. completing research on a shallow Staffordshire Søballe, D.M. & Kimmel, B.L. (1987). A large-scale comparison of lake under the guidance of Dr. John Lund. His first factors influencing phytoplankton abundance in rivers, lakes, computer simulation model, based on Blelham Tarn, and impoundments. Ecology 68, 1943-1954. was written in 1975 and the data generated processed Stumm, W. & Morgan, J.P. (1981). Aquatic Chemistry. 2nd edition, by graphics computer software. In 1982 he designed John Wiley, New York. 1040 pp. Talling, J.F. (1957). The phytoplankton population as a compound Relational Data Bases to store the long-term data sets photosynthetic system. New Phytologist 56, 133-149. collected from studies on the English Lakes. This Talling, J.F. (1971). The underwater light climate as a controlling technology was later adapted by him for storing factor in the production ecology of freshwater phytoplankton. and manipulating the very large data sets produced Mitteilungen der Internationalen Vereinigung für theoretische und by the various Protech series of models he wrote in angewandte Limnologie 19, 214-243. Fortran IV. In 2002 Tony left the Centre of Ecology Tilman, D. (1996). Biodiversity: population versus ecosystem stability. Ecology 77, 350-363. and Hydrology, Windermere Laboratory, to follow a Tilman, D., Kilham, S.S. & Kilham, P. (1982). Phytoplankton career in commerce. community ecology: the role of limiting nutrients. Annual Colin S. Reynolds has retired recently from the Reviews of Ecology and Systematics 13, 349-372. Thackeray, S.J., Jones, I.D. & Maberly, S.C. (2008). Long-term Centre for Ecology and Hydrology, Windermere change in the phenology of spring phytoplankton: species- Laboratory, where he had been appointed as a research specific responses to nutrient enrichment and climate change. scientist by the Freshwater Biological Association in Journal of Ecology 96, 523-535. 1970, and where he had previously been a research Vollenweider, R.A. & Kerekes, J. (1980). The loading concept as student to Dr John Lund. Colin has had short phases basis for controlling eutrophication philosophy and preliminary in the water industry and as a teacher of ecology but results of the OECD programme on eutrophication. Progress in Water Technology 12, 5-38. most of his time has been devoted to dynamics and Wetzel, R.G. (1983). Limnology. 2nd edition, Saunders College selection in the freshwater phytoplankton. As an Publishing. 439 pp. honorary fellow of both CEH and the FBA, he is still engaged in research.

© Freshwater Biological Association 2010 DOI: 10.1608/FRJ-3.1.4