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Simultaneous changes in the concentrations of vegetative cells of the dinoflagellate Ceratium hirundinella in the Blelham Enclosures A, B and C, during 1980. Cyst production, noted in the figure, generally marks the termination of vegetative growth. Redrawn with permission from Lund and Reynolds (1982).

Simultaneous changes in the concentrations of vegetative cells of the dinoflagellate Ceratium hirundinella in the Blelham Enclosures A, B and C, during 1980. Cyst production, noted in the figure, generally marks the termination of vegetative growth. Redrawn with permission from Lund and Reynolds (1982).

terrestrial replenishment (Fig. 5.11). Thus, the inorganic carbon supply to phytoplankton in these experiments depended upon internal recycling, augmented by whatever dissolved from the air at the water surface. Thus, rising pH is a useful surrogate of carbon deficiency in the enclosures (experiments in 1978 attempted to relieve the deficiency with additions of bicarbonate; they did increase carbon but did not reduce pH). The species-specific distributions of histograms in Fig. 5.17 peak in range 9.0-9.5, simply because that is also the range reached most frequently during the maxima encouraged by fertiliser additions; it is not necessarily indicative of any algal preference for this range. However, it is evident that Fragilaria, Cryptomonas, Eudorina, Ankyra, Ceratium and, especially, Anabaena, Microcystis and Staurastrum pingue were all able all to function at pH levels up to 1 point higher. The observation matches those of Talling (1976) concerning differential insensitivity to carbon dioxide shortage; all these species are known or suspected for the efficiency of their carbon-concentration mechanisms (Section 3.4.3). The apparent failure of the chrysophytes Uroglena and Dinobryon to maintain growth at pH levels <9 aroused the suspicion that these algae might be obligate users of carbon dioxide (Reynolds, 1986b), as indeed, has since been verified in the laboratory (Saxby-Rouen et al., 1998).

These response patterns require careful interpretation and their subjectivity to the experimental design must be taken into account. The species responding to the conditions contrived are, almost exclusively, the ones that are already well established in the lake and/or the experimental enclosures. The observed performances are not necessarily those of the nature's 'best-fit'

organism so much as those of them that were there were able to contend effectively with the conditions imposed. Yet, in many ways, these relative performances do, most probably, distinguish sufficiently among the traits and adaptabilities of a number of common types of plankter for their basic ecological preferences and sensitivities to be recognised and identified in further, more focussed testing.

We see that enrichment with nutrient seems to be beneficial to most species, raising the ceiling of attainable biomass and, in many instances, releasing the growth rate from the restriction of nutrients. This may not be universally so, for some of the inherently slow-growing, self-regulating species, like Ceratium hirundinella, have adaptations for supporting their growth requirements under nutrient-segregated conditions and growth rate is not necessarily enhanced by nutrient abundance. The growth-rate performances achieved by Ceratium in each of the three enclosures during 1980 were ultimately comparable (see Fig. 5.18: 0.092 d-1 in Enclosure A, 0.098 d-1 in Enclosure B and 0.105 d-1 in Enclosure C), even though the non-physical growth conditions were quite disparate. That the yields were quite different is influenced by the length of time that cell division was maintained in situ. This was partly influenced by resource availability and, as is now known, by resource renewal in the graded Enclosure C (Fig. 5.11; Reynolds, 1996b). The major influence, however, is the source of excysting inocula. The uniformly deep sediments of Enclosures A and B supported many fewer surviving cysts than those of Enclosure C, whereas recruitment of 'germinating' gymnoceratia (see Section 5.4.6) was also relatively stronger in Enclosure C. It is interesting, indeed, that Lund (1978) had

Figure 5.19

The maximum fraction of the summer standing phytoplankton biomass in Blelham enclosures contributed by nitrogen-fixing species of Anabaena and Aphanizomenon in each enclosure-year, plotted against the corresponding areal loading rates of nitrogen and phosphorus. Their relative abundance generally coincides with low nitrogen and moderate phosphorus availability but not on a low N : P ratio per se. Redrawn with permission from Reynolds (1986b).

regarded the enclosures as being somehow hostile to Ceratium, for the alga had never become so numerous as in the lake outside. As Fig. 5.18 demonstrates, there is nothing about these enclosures that interferes with growth. Isolation of the water from that of the lake, except during winter opening, evidently made it difficult for Ceratium to invade in numbers. The point about Enclosure C is that the presence of shallow sediments assisted the success of perennation and reinfection of the water column in the spring. This pertinent biological observation was, obviously, quite peripheral to the design and purpose of the experiment.

The behaviour of Anabaena, a supposed indicator of carbon-deficient eutrophic waters, and its apparent preference for less-enriched conditions may also be explained from more detailed analysis. Suspecting a performance influenced by the ratio of available nitrogen to available phosphorus, the maximum fractional abundance of Anabaena spp. (plus the smaller amounts of Aphanizomenon) in any given enclosure year was plotted against the coordinates of the nitrogen and phosphorus supplied (Fig. 5.19). Anabaena spp. featured in most annual sequences observed in the enclosures but only occasionally did it produce dominant populations. Moreover, when levels of DIN had fallen much below 100 |g N l-1 (~7 |M), populations developed substantial heterocyst frequencies (maximum, 7% of all cells). In terms of N and P loads, however, Anabaena and Aphanizomenon abundances are clustered within one corner of the N ver sus P field of Fig. 5.19, corresponding to loadings of 6-10 g N m-2 (0.45-0.71 mol m-2) and 0.19-1.2 g P m-2 (6-38 mmol m-2), but with no clear dependence on N : P (actual ratios 12-118). At higher loads of N and P (but with ratios still in the order of 10-20), the species were hardly represented at all. Thus seasonal dominance by these species has failed to come about under conditions in which neither nitrogen nor phosphorus was likely to have been limiting plankton growth. What can be said is that, at the low nitrogen concentrations limiting non-N-fixing species, the yields of Anabaena and Aphanizomenon are broadly proportional to phosphorus loadings up to ~1 g (or ~30 mmol) P m-2. At higher levels of N and P, there will always be faster-growing species - such as Ankyra, Chlorella, Plagioselmis, Cryptomonas, even Eudorina - poised to outperform them.

Finally, additional information is available from the enclosure work to amplify the specific growth performances under persistent and relatively low phosphorus concentrations. Coenochlor-is fottii featured prominently in a number of the sequences (it was then referred to Sphaero-cystis schroeteri). It was relatively more common in the summer periods when phosphorus was strongly regulating biomass and growth (see especially Reynolds et al., 1985) but absolutely larger populations and sustained growth rates were observed at greater nutrient availabilities (Reynolds et al., 1983b, 1984). With the imposition of artificial mixing, the alga was again found to be tolerant but only for so long as the water was clear and the ratio of Secchi-disk depth to mixed depth (zs/zm) was near or greater than 1. Noting rather smaller numbers of Oocystis aff. lacustris, Coenococcus, Crucigeniella and the tetrasporalean Pseudosphaerocystis lacus-tris (formerly Gemellicystis neglecta) showed similar responses to imposed variations in nutrients and insolation, Reynolds (1988a) grouped all these non-motile, mucilaginous colonial Chloro-phyceae in a single morphological-functional group of non-motile, light-sensitive, mucilage-bound species. It is their behavioural traits with respect to threshold light levels that tend to exclude them from turbid or deep-mixed water columns and to give them a common association with oligotrophic lakes. For the common chrys-ophyte species of Dinobryon, Synura and Uroglena, the apparently similar association with nutrient poverty in the enclosures is not due to any intolerance of high nutrients but to an unrelieved dependence upon the supply of carbon dioxide, which, in the soft-water confines of the Blelham enclosures, is readily outstripped by demand (Saxby-Rouen et al., 1998).

5.5.4 Temporal changes in performance selection

There is clearly a good match between how the various species studied in the controlled field conditions of the Blelham enclosures and the sorts of trait characteristics and strategic adaptations identifiable among the properties revealed in earlier sections (especially pp. 31-34). In particular, a distinction is to be made between the manner in which species develop their populations in response to what are perceived by them to be favourable conditions. On the one hand, there are species that specialise in rapid, invasive growth, building up stocks at the expense of freely available resources and high photon fluxes, and which, by analogy to the terminology of Grime (1979, 2001), we have defined r-selected C-strategists (see Box 5.1). Besides the examples of Ankyra and Chlorella, Asterionella and some of the other freshwater diatoms that are tolerant of intermittent and poor average insolation (.-strategist traits) are also strongly r-selected over other R-type species such as Plankto-thrix agardhii. The slower growth but often

Time

I Differing demographic behaviours in exploiting favourable growth opportunities: species grow either rapidly and invasively (1) or more slowly to build a conserved, acquisitive population (2). Slow accumulation of biomass may be offset by the recruitment of pre-formed propagules from a perennial seed bank (3). Modified after Reynolds (1997a).

Time

I Differing demographic behaviours in exploiting favourable growth opportunities: species grow either rapidly and invasively (1) or more slowly to build a conserved, acquisitive population (2). Slow accumulation of biomass may be offset by the recruitment of pre-formed propagules from a perennial seed bank (3). Modified after Reynolds (1997a).

higher-biomass-achieving K-selected trait of many larger algae, represented by Curve 2 in Fig. 5.20, which, initially, lags behind the performance of more r-selected species (Curve 1) is characteristic of the performances of S- and CS-strategists. However, it is also clear that some of the self-regulating S-strategists, such as Ceratium and Microcystis, are obliged to grow so relatively slowly that eventual abundance in the plankton is influenced by the recruitment of sufficient peren-nating propagules at the initiation of the next period of growth. This very strong K-selected feature is represented by Curve 3 in Fig. 5.20.

We may venture further than this by superimposing the triangular ordination of species traits (e.g. of Fig. 5.9) and overlaying this on a notional plot to describe the interaction of mixing and nutrient availability in the near-surface waters (see Fig. 5.21). The loops and arrows are inserted to show how temporal seasonal variations in the coordinates of nutrient availability and mixing might select for particular performances and relevant traits and adaptations. These are notional and unquantified at this stage of the development and the representation is qualitative but they illustrate some general points that need to be made. The two large loops (marked a and b) reflect the transitions that might be observed over a year in a seasonally stratified (not necessarily temperate) lake. At overturn, there is a

Relative mixing

I Notional representation of Grime's CSR triangle on axes representing relative nutrient abundance and water-column mixing, showing the adaptive traits most likely to be selected by changing environmental conditions. The loops represent time tracks of selective pressures acting through the year in (a) oligotrophic lakes, (b) eutrophic lakes, (c) and (d) in smaller, enriched systems; (e) is the anticipated course of autogenic succession. Redrawn from Reynolds (1988a).

rapid rightward shift on the mixing axis with an upward drift as dissolved nutrients are redis-persed from depth. The best-performing species here and throughout the bloom period are likely also to show the traits and growth responses of R-strategist species: the limits of their morphological and behavioural adaptations are more suited to coping with low average insolation. The onset of themal stratification is represented by a lurch to the left, where conditions of low relative mixing and high relative nutrients obtain and which, initially, are open to exploitation by fast-growing C-strategist species. Their activity depletes the resources and may lead, eventually, to the partitioning of availability and to the dependence upon increasingly effective Sstrategist adaptations to access them. Note that the more severe and ongoing is the insolation or resource deficiency, the closer are the trajectories to the apices of the CSR triangle, where the relevant adaptations become ever more important. As a consequence, the few that have them are alone able to perform successfully at all. The potential diversity of surviving species is finally 'squeezed out'

at the extremes. The converse is that variability is good for maintaining high diversity as more specific performances are accommodated. The constrained cycles of (say) an enriched water column subject to variable stratification or of persistently mixed, resource-cycling systems may also be represented in this scheme (respectively, c and d). Other factors notwithstanding, the effects of population growth should follow the direction of the arrow (marked e) as nutrients are withdrawn from the water and the increasing biomass reduces light penetration and the relative mixed depth is increased.

The traces provide adequate summaries of changes in seasonal dominance in given lakes and, to an extent, they may reflect longer-term changes in phytoplankton in response to nutrient enrichment or restoration measures. In the naturally eutrophic, nutrient- and baserich kataglacial lakes of northern Europe and North America (see, for instance, Nauwerck, 1963; Lin, 1972; Kling, 1975; Reynolds, 1980a), the annual cycle of phytoplankton dominance features (i) vernal diatoms (which may include any or all of Asterionella formosa, Fragilaria crotonen-sis, Stephanodiscus rotula, Aulacoseira ambigua from the R apex of the triangle), followed by (ii) a burst of readily grazeable, plainly C-strategist nanoplankton (e.g. chlorellids, Ankyra, Chlamy-domonas, Plagioselmis), and/or (iii) by populations of colonial Volvocales (e.g. Eudorina, Pandorina -best classed as CS strategists) and increasingly more S-strategist Anabaena spp., Microcystis or Cer-atium). The cycle is completed by (iv) assemblages of diatoms (Fragilaria, Aulacoseira granulata) and desmids (Closterium aciculare and several species of Staurastrum).

In the nutrient- and base-deficient lakes of the English Lake District (Pearsall, 1932), the oligotrophic subalpine lakes of Carinthia (Findenegg, 1943) and the more oligotrophic lakes of New York and Connecticut studied by Huszar and Caraco (1998), as well, in all probability, similar lakes throughout the temperate regions (Reynolds, 1984a, b), the vernal plankton is typically dominated by Cyclotella-Urosolenia diatom associations (R or CR strategists). These may be replaced typically by such chrysophytes as Dino-bryon, Mallomonas or Synura (RS strategists) and/or by colonial Chlorophyceae (CS strategists), then by S-strategist dinoflagellates (Peridinium umbon-atum, P. willei or Ceratium spp.) and, finally, by R or SR desmids such as Cosmarium and Staurodesmus.

Between the oligotrophic and eutrophic systems are ranged the lakes of intermediate status (mesotrophic lakes), as well as several deep alpine lakes of central Europe (Sommer, 1986; Salmaso, 2000; Morabito et al., 2002) Here, the vernal phase is characterised by R-strategist diatoms featuring perhaps Aulacoseira islandica or A. sub-arctica, as well, perhaps, as Asterionella, Fragilaria or Cyclotella radiosa. There is a late-spring phase of C strategists (e.g. Plagioselmis, Chrysochro-mulina), followed either by a phase of colonial Chlorophyceae-Chrysophyceae or, especially in deeper lakes, S-strategist Ceratium or Peri-dinium, or by the Cyanobacteria Gomphosphaeria or Woronichinia, or again perhaps by potentially nitrogen-fixing Anabaena solitaria, A. lemmerman-nii or Aphanizomenon gracile. Late-summer mixing may favour R-strategist diatoms (notably including Tabellaría flocculosa or T. fenestrata), desmids or the filamentous non-diatoms (such as Mougeotia, Binuclearia, Geminella). The outstanding algae of the deep mesotrophic systems, however, are the RS-strategist Planktothrix rubescens/mougeotii group which both tolerate winter mixing and exploit deep stratified layers in summer.

The cycles in Fig. 5.21 are not tracked at an even rate, neither are they precisely identical each year. Progress may proceed by a series of lurches, whereas interannual variability can divert the sequence to differing extents. However, the growth and potential dominance of phyto-plankton adheres closely to the model tracking (Reynolds and Reynolds, 1985). The cycle may be completed in less than a year: the description of Berman et al. (1992) of the periodicity of phyto-plankton of Lake Kinneret follows a mesotrophic path before stalling in summer deep on the left-hand (nutrient) axis of Fig. 5.21. It does not really move on until wind-driven mixing or autumn rains relieve the severe nutrient (nitrogen and phosphorus) deficiency. The cycle may also be recapitulated: Lewis' (1978a) detailed description of the seasonal changes in the plankton of Lake Lanao, Philippines, could reasonably represented by track (b) in Fig. 5.21 but it would be completed within 4-6 months before being short-cut back to an earlier stage. Even in temperate lakes and reservoirs subject to extreme fluctuations in mixed depth on scales of 5-50 days, alternations between phases of increase and dominance by R species (Stephanodiscus, Synedra) and C-S groupings (cryptomonads, Chlamydomonas, Oocys-tis, Aphanizomenon) are clearly distinguishable (Haffner et al., 1980; Ferguson and Harper, 1982). Again, in nutrient-rich lakes where the alternations result in the lake being either predominantly mixed or stratified, so the dominating species would be (respectively) R species (as in Embalse Rapel, Chile: Cabrera et al., 1977) or C species (as in Montezuma Well, Arizona: Boucher et al., 1984). These possibilities comply with the track marked (c) in Fig. 5.21. Examples of enriched shallow or exposed lakes that are more or less continuously mixed seem to be dominated by the K-selected R strategists (Planktotrix agardhii, Limnothrix redekei, Pseudanabaena spp.: Gibson et al, 1971; Berger, 1984, 1989; Reynolds, 1994b) are represented in Fig. 5.21 by track (d).

It is not yet possible to apply the same approach to temporal changes in the marine phytoplankton with a similar level of investigative evidence, as the resolution of temporal changes is less clear. On the other hand, it is a testable hypothesis that similar performanceled drivers, influenced by similar morphological adaptations to analogous liqiud environments, govern the spatial and temporal differences in the growth of phytoplankton in the sea. There is good supporting evidence that this may be the case. Smayda (2000, 2002) has shown that the wide diversity among the dinoflagel-lates may be rationalised against an ecological pattern that invokes morphology. Whereas the smaller, non-armoured adinophytes (such as Pro-rocentrum) and gymnodinioids (Gymnodinium, Gyro-dinium, Heterocapsa spp.) that are characteristic of shallow, enriched coastal waters have unmistake-ably C-like morphologies and growth-rate potential, the larger, armoured and highly motile cera-tians have clear S tendencies. In the open ocean, Smayda (2002) distinguishes among dinoflagel-lates associated preferentially with fronts and upwellings (Alexandrium, Karenia) and those of post-upwelling relaxation waters (Gymnodinium catenatum, Lingulodinium polyedrum). Sstrategist dinoflagellates are also prominent in the oligotrophia, stratified tropical oceanic flora, where self-regulation, high motility and photoadaptative capabilities distinguish such dinoflagellates as Amphisolenia and Ornithocercus. The buoyancy-regulating adinophytes of the genus Pyrocystis are most remarkable in showing parallel adaptations to limnetic Planktothrix rubescens and in similarly constituting a mid-water shade flora, deep in the light gradient of the tropical ocean.

It is interesting to speculate on the range of adaptations among the planktic diatoms of the sea. Most are non-motile and (presumably) reliant upon vertical mixing for residence in the near-surface waters. Thalassiosira nordenski-oldii, Chaetoceros compressus and Skeletonema cost-atum are all chain-forming diatoms featuring in the spring blooms of North Atlantic shelf waters. The attenuate forms of species of Rhizosol-enia, Cerataulina, Nitzschia and Asterionella japonica are conspicuous in the neritic areas. All these diatoms can be accommodated in the understanding of R-strategist ecologies. However, there are also centric diatoms such as Cyclotella capsia that occur predominantly in shallow eutrophic coastal waters and estuarine areas, along with, arguably, C-strategist green algae (Dunaliella, Nannochloris), cryptomonads, the dinoflagellate Prorocentrum, the euglenoid Eutreptia and the haptophytes Chrysochromulina and Isochrysis. In another direction of adaptive radiation, the very large, self-regulating Ethmodiscus rex, belonging to the tropical shade flora, shows the typical properties of an S-strategist species.

Many coccolithophorids are small and are regarded, somewhat 'uncritically' (Raymont, 1980), as nanoplankton. Emiliana huxleyi, Gephyro-capsa oceanica and Cyclococcolithus fragilis are, indeed, small C-like species of open water, which they inhabit with nanoplanktic flagellates, including the prasinophyte Micromonas, the chlorophytes Carteria and Nannochloris, the cryptophytes Hemiselmis and Rhodomonas and the haptophytes Pavlova and Isochrysis. The nitrogen-fixing, vertically migrating Cyanobac-terium Trichodesmium displays strong S-strategist characteristics. The picoplanktic Cyanobacteria Synechococcus and, especially, Prochlorococcus, reign supreme over vast areas of ultraoligotrophic ocean, as archetypes of the newly proposed SS strategy.

Seasonal changes in the plankton flora of the English Channel, described by Holligan and Harbour (1977), show a clear tendency for vernal diatom-dominated (supposedly . -strategist) assemblages to be displaced by more mixed diatom-dinoflagellate (CR?) associations (Rhizosol-enia spp.; Gyrodinium, Heterocapsa, Prorocentrum) in early summer and by green flagellates (Carteria, Dunaliella, Nannochloris) or (S?) ceratians (Ceratium fusus, C. tripos) in mid to late summer. In enriched near-shore areas, the haptophyte Phaeocystis, in its colonial life-history stage, may dominate the early summer succession, in a manner strongly reminiscent of the abundance of volvocalean CS strategists in eutrophic lakes.

A satisfying aspect of the performances of phytoplankton in both the sea and fresh waters is the superior influence of morphological and (presumably) physiological criteria over phylogenetic affinities. This is a powerful statement attesting to evolutionary adaptations for relatively specialised lifestyles and for the radiative potential latent within all major phyletic divisions of the photosynthetic microorganisms.

5.5.5 Modelling growth rates in field

There has for long been a requirement for robust, predictive models of phytoplankton. Nowadays, the element of stochasticity of environmental events is appreciated as a near-insuperable bar to accurate predictions of sufficient precision. However, considerable use can be made of the regressions fitted to growth performances in the laboratory and the philosophy of strategic adaptations to drive predictive solutions to which of certain kinds of alga will grow in particular water bodies and under which conditions.

This section is not intended to provide a guide or a review of different modelling approaches. These are available elsewhere (Jorgensen, 1995, 1999). The purpose here is to refer to some of the approaches addressed specifically to modelling growth and performance of phytoplank-ton and to promote the use of models that invoke them. It is worth first repeating the obvious, however, that different models attempt to do different things. These may be in-and-out 'black-box functions', such as Eq. (4.15), where an input (in this case, biologically available phosphorus) generates a yield (in this case, phyto-plankton chlorophyll) on the basis of pragmatic observation, without any attention to the explicative processes. These internal linkages may be investigated, imitated and submitted to empirical model explanations, for instance, those which link the generation of phytoplankton biomass to photosynthetic behaviour in the underwater light field. The various explanative equations of (say) Smith (1936), Talling (1957c), Pahl-Wostl and Imboden (1990) predict, with accuracy, precision and increasing detail, the photosynthetic carbon yield as a function of light and respiration. They are, nevertheless, restricted in their effectiveness to cases where anabolic processes are simultaneously constrained by some other factor (carbon or nutrient supply). What is then needed is the further sets of precisely quantifiable algorithms that will describe these further processes (many of which are available) and their incorporation into a supermodel to simulate the interactions among all the components. In a third type of model, the broad function of the system ('the box') is predicted from a knowledge of the fundamental mechanisms and limitations (such as genomic information and energy efficiency), as elegantly employed in Jorgensen's (1997, 2002) own structural-dynamic models of ecosystem organisation and thermodynamics.

Each of these approaches, even when applied directly to phytoplankton ecology, has its inherent weaknesses and these have long been recognised (Levins, 1966). The first type simulates an indirect relationship with accuracy and some precision but lacks general applicability. The second has a small number of variables and yields accurate and often precise information but only under very conditioned circumstances. The third achieves accuracy and applicability through generality, at the cost of all precision.

Modelling philosophy and (certainly) computing power has moved on. Several attempts to compound specific process models of the second type into more comprehensive growth simulations have been rather unsuccessful, except where one or other of the components contin uously overrides the others. This was the case in the models of growth of filamentous Cyanobac-teria in an enriched, monomictic lake (Jiménez Montealegre et al., 1995) or deep in the light gradient of the ZUrichsee (Bright and Walsby, 2000). A most promising modern development has come through the exploration of linkages (stimulus, responses) and the probabilistic analysis of effects (likely reaction) through artificial neural networks (ANNs) (see Recknagel et al., 1997). Like the nerve connectivities they resemble, these models can be 'trained' against real data in order to predict outcomes with modified variables. Recknagel's (1997) own application to interpret the variability in the phytoplank-ton periodicity in Kasumigaura-Ko in Japan provides an excellent indication of the power of this approach. Its further development is at an early stage but the use of 'supervised' and 'unsuper-vised' learning algorithms to interpret field data, through 'self-organising maps' of close interrelationships (Park et al., 2003), promises to overcome some of the difficulties experienced with other compound models. Prediction of 'top-line' outcomes based on 'bottom-line' capacities is generally difficult without knowledge of intermediate processes. The fundamental truth is that algal growth rate is not a continuous function of nutrient supply or uptake, or of the ability to fix carbon in the light. Below the 'threshold' values discussed in Section 5.4.5, growth cannot for long exceed the weakest capacity. On the other hand, capacity in excess of the threshold saturates processing: it does not make organisms grow faster.

So, how can the growth rates of natural populations in the field be modelled? The approach advocated by Reynolds and Irish (1997) was to suppose that the photautotrophic plankter does not grow anywhere better than it does in the contrived culture conditions in the laboratory. Given that the best growth performances of given species occur under ideal culture conditions, that they are consistent and that between-species differences in growth rate are systematic (Reynolds, 1984b), an 'upper base line' for simulating natural population growth could be proposed (Reynolds, 1989b). Three equations were invoked to predict attainable growth rate in the field. In the best traditions of Eppley's (1972) model of phytoplankton growth, two of the equations set the growth potential to water temperature. The first equation (5.5) predicts replication rate at a standard 20 °C as a function of algal morphology. The second equation (5.6) provides the information to adjust specific growth rate to other temperatures. These predictions are applied to an inoculum (or, in reiterations) to the incremented standing crop to simulate day-on-day accumulation. This has to be linked, through a loop in the model logic, to an inventory of resource supply, which checks that a given daily increment is sustainable and, if so, to permit the growth step to be completed. A further feedback loop deducts the consumption from the pool of available resources.

Insofar as the depth-integration of light intensity and the duration of daylight impose, almost everywhere on the surface of the planet, a subideal environment with respect to continuously light-saturated cultures, the sensitivity of species-specific growth sensitivity to insolation is written into the third of the model equations. The original model supposed that the insolation-limited specific growth rate is in proportion to the fraction of the day that the alga spends in the light:

where the daily sum of photoperiods, £tp, comes from:

where hm is the mixed depth and hp is the height of the light compensated water column, which, following Talling (1957c; see also Section 3.5.3) is solved as:

where I 0 is the daily mean irradiance immediately beneath the water surface (in ^mol photon m-2 s-1) and s is the coefficient of exponential light attenuation with depth. The onset of light limitation of growth, Ik is here related specifically to the alga via Eq. (5.12):

Thus, the solution to Eq. (5.9) incorporated in to the growth-rate model is:

Equation (5.13) is thus the third of the three equations written into the model that eventually became known as PROTECH. It remained under development and testing for several years, but this central core has remained intact. An important adjustment in respect of dark respiration was incorporated into the model that was eventually published (Reynolds et al., 2001). This followed the important steps of sensitivity testing, authentication and validation (Elliott et al., 1999a, 2000a). It has been used to make realistic reconstructions of phytoplankton cycles of abundance and composition (by functional type) in lakes and reservoirs (Elliott et al., 2000a; Lewis et al., 2002). It has been applied to simulate succession in undisturbed environments (Elliott et al., 2000b) and to investigate the minimum size of inoculum for the growth rate still to enable an alga to attain dominance (Elliott et al., 2001b). Vertical mixing can be used as a variable to disturb community assembly (Elliott et al., 2001a) and to evaluate selective impacts of intearctions between variations in mixing depth and in surface irradiance (Elliott et al., 2002). PROTECH models exist with differing physical drivers (PROTECH-C, PROTECH-D), that work in coastal waters (PROTECH-M) and which are dedicated to (specific) rivers (RIVERPROTECH). Versions have been prepared for numerous UK and European lakes and reservoirs, with accumulating success. At time of the writing, summary papers are still in press.

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