JPR Advance Access originally published online on November 23, 2005
Journal of Plankton Research 2005 27(12):1205-1210; doi:10.1093/plankt/fbi099
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HORIZONS |
Castles built on sand: dysfunctionality in plankton models and the inadequacy of dialogue between biologists and modellers
Institute of Environmental Sustainability, Wallace Building, University of Swansea, Swansea SA2 8PP, UK
Corresponding Author: k.j.flynn{at}swansea.ac.uk
Received September 14, 2005; accepted in principle October 17, 2005; accepted for publication November 6, 2005; published online November 23, 2005
Communicating editor: I.R. Jenkinson
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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Although lip service is often paid to the involvement of modellers in the design of biological experiments and to a lesser degree to a role for biologists in construction of dynamic models, on closer examination the ultimate communication failings and associated waste of effort are all too obvious. Biologists need to work with modellers to ensure that data collected are more amenable to modelling (notably C-N-P biomass, rather than just Chl, or organism numbers), to measure the fate of non- or lesser-limiting nutrients, and the release/production of particulate and dissolved organics from organisms. Modellers should not omit representations of biological behaviour unless it is demonstrated (empirically and/or mathematically) that it is safe to do so; the performance of each part of an ecosystem model should be demonstrated as being fit for purpose and not dysfunctional. Modelling should be accepted as a research tool within biology and ecology with just as much emphasis as enjoyed by statistical and molecular methods.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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In a preceding Horizons article (Anderson, 2005
), the development of models describing plankton functional types has been questioned both with respect to the necessity for them and our ability to construct them. In the present contribution, some more basic issues are raised that strike at the heart of the biology-modelling interface. This is not intended as a pointing-the-finger-at-the-group-to-blame exercise (hence the thin referencing). We are all, to some extent or other, guilty, but we do need to do something about it else we are in real danger of continuing to waste a lot of effort. Indeed, we have been wasting a lot of effort; arguments over the interaction between biologists and modellers are by no means new (Morales, 1972; Stearns, 1972) but still little seems to have changed.
Simple models, such as nutrient-phytoplankton-zooplankton (NPZ; Fasham, 1993), make a lot of assumptions, using functions that are clearly highly questionable from a biological standpoint. That NPZ models have been so successful is perhaps in part because two (or more) wrongs do indeed sometimes make a right, and perhaps because being so simple, failings are more willingly accepted or not even recognized. The description of the physical environment is also simplistic, but physics and chemistry are sciences blessed with laws so at least the implications can be more carefully considered. Biology is a grey science, with no laws per se and little structure. Continuing technological advancement in computing capacity has been matched by an increased complexity of ecosystem models describing marine planktonic systems (e.g. Blackford et al., 2004). The description of the physical environment has developed such that 3D descriptions are now far from unusual (e.g. Proctor et al., 2003). But how have the biological descriptions developed?
The answer, in large measure, is by inclusion of more nutrients and of additional functional groups (diatoms, flagellates, micro- and mesozooplankton and so on; Anderson, 2005). Typically, this has been attained by bolting together the same old functions (Monod, quota, etc.) used in the simpler models. Are these descriptions still adequate for the task at hand? After all, one would not attempt to make a supersonic plane by bolting together a collection of subsonic aircraft; instead the performance, and often the failings, of components are reassessed when run in the new environment. That something is indeed amiss is apparent from the lack of pro rata enhancement in simulation capacity (Anderson, 2005). Where are we going wrong?
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WHY BIOLOGISTS NEED MODELS, AND MODELLERS NEED BIOLOGISTS |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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Why do we study systems, conduct experiments and collect data? Aside from the all important philosophical arguments for setting and testing hypotheses, many data are collected to quantify natural history hence enabling comparisons between studies, backed by numerous statistical approaches. It is easy to explore the almost endless biological variety without any recourse to modelling. So, why should biologists be concerned about models? Models provide a supreme dynamic test of knowledge; if you can not model a system well then it is likely that you do not understand it very well either. Understanding, making nature more intelligible, is at the very heart of science. In turn, models aid biological study by helping to identify critical processes. And then there are the all important prediction and ‘what-if?’ tests to which models so readily avail themselves and which can be used to aid the design of logistically complex biological studies.
Biologists often do not collect data of much value for modelling (Miller, 2004). Modellers are often frustrated by the effort expended in conducting biological experiments over weeks or months and yet not measuring critical parameters that would enable a modelling approach to be applied. Biologists may well argue that they are working to their own agenda, with their own hypotheses and could not possibly second guess what data a modeller may want. The question is, how do biologists know that what they are measuring is even sufficient to tackle their own hypotheses? For example, if you are trying to determine the percentage of C fixed that is released as dissolved organic C, unless you attempt a mass balance you cannot be sure that you have adequately characterized the system you are studying. The process of constructing a model, let alone trying to parameterize and use it, will alert biologists to such issues. On the other side of the coin, biologists who examine models can often find fault in model structure. With justification they may ask what is the sense in running models, let alone comparing models, that do not behave sensibly? There is also the issue of the time scales of biological sampling and of simulation output. Logistically, it is impossible to be everywhere all the time, yet models can output to resolutions measured in seconds and metres rather than to hours or days and kilometres. However, resolution in models is not always greater than that in biology. For example, while diel/diurnal events are important biologically the light–dark cycle is not always explicitly described in models, and, indeed, it may not be justified to do so but at the least that case should be demonstrated (Flynn and Fasham, 2003).
Unfortunately, all this neither spurs the biologists to furnish more and better data nor does it stop the modellers from carrying on with an in-depth analysis of a model bearing little connection to reality, in some instances attempting to forecast events of global consequence. It is perhaps this latter point, that people (notably politicians) with even less understanding of the pitfalls of experimental and theoretical ecology (modelling) may make important decisions based on results from simulations, that is a most powerful argument for improving the biology-modelling interface.
The potential value of modelling to biology, a science that so often lacks direction, is (or should be) clear. However, this potential can only be realized if the form and output of biological models are representative of biological processes. Inevitably, a model must be a simplified representation of reality, but who is best placed to judge what should or should not be represented and whether the representation is any good? The answer has to be biologists and ecologists.
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WHAT WE NEED |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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If modellers are to help ecologists, they need conceptual understanding, problems to answer and wide ranging complete data sets describing the system under consideration. What they get is poor or conflicting conceptual understanding (often reflecting biological uncertainty), little commonality in units (numbers, Chl, dry weight, C, protein, biovolume), incomplete mass balance (e.g. dissolved inorganic N + particulate organic N + dissolved organic N), poor time series and poor coverage of environmentally important organisms grown under environmentally relevant conditions.
Biologists need guidance on what to measure and how frequently, and an indication of the significance of processes, leading to guidance on what experiments to next conduct. What they get from modellers is demands for data rather than guidance on what to measure, and models that appear to be gobbledygook with gross simplifications made with little if any biological justification. The structure in models may be biologically flawed (Flynn, 2003) or based on factoids that are not necessarily well founded (‘small organisms are better at nutrient acquisition and grow faster’; ‘one species does it so let us assume all do it’). Unless biologists make public their concerns, the modeller may not be aware of the faults, but that is not likely unless biologists make more effort to engage with modellers.
Biologists and modellers need to make a cycle of studies but typically the cycle is truncated to a line; review, experiment, model [end]. In part, this fits with the short duration of research grants but that is really just an excuse. The bigger problem is simply that the linkage fails, because there is an inadequate dialogue. Biologists usually do not understand the mathematical justification for model structures. Mathematicians usually do not understand, or cannot/do not want to reproduce, the subtleties of biological interactions. Mathematicians often prefer simple (empirical) models; biologists like structured (mechanistic) models, provided they are written in any language other than algebra.
While there is no correct way to model, there are certainly incorrect, dysfunctional approaches. A dysfunctional model gives an output that is contrary to what is expected. Sometimes this may be obvious (Monod versus quota models for Si use by diatoms; Flynn, 2003, 2005) while others may have important ramifications under certain situations (ratio-based prey selectivity functions; Gentleman et al., 2003). Just because a model gives a fit to a particular data set does not guarantee that the structure is not dysfunctional, that it will not behave in some aberrant way when operated outside of the data envelope on which it was tuned. Failing may be masked by some other feature overcompensating in balance; thus an over representation of grazing may compensate for an inadequate description of algal bloom aggregation and sinking. Dysfunctionality becomes increasingly important in complex models because the ‘cheats’ that simple models employ to keep them on track are often removed; you do not need to worry about prey selection on diatoms versus dinoflagellates if you do not describe these groups in your model. This is part of the problem discussed by Anderson (Anderson, 2005).
It is not good enough that a plankton model is mathematically sound, that it yields comforting results when subjected to sensitivity analyses, and the like, or even that it fits some particular data set. The ‘virtual’ plankton must behave in a way becoming of real plankton and only informed biologists can make that judgement. Without doubt, it would help if sessions at conferences were mixed rather than putting the modellers into their own room. Molecular biology used to be separated like this but not any more. As a consequence molecular methods (which at heart are little more than a kit of chemical recipes) have found real important ecological applications as well as in taxonomy and physiology. But then at least molecular biology is a biology. Mathematical biology seems like a contradiction in terms to many people. While mathematical modelling is older than molecular biology, it has yet to become a mainstream biological subject. Interestingly, there is another profound difference between modelling and molecular biology; while the latter tends to resolve organisms into ever smaller groups (species, subspecies), by tradition if not by necessity modelling tends to group organisms together according to functionality within the ecosystem (Anderson, 2005). Modelling has a potential role in helping to identify those phenotypic features of greatest importance in ecology and hence features of greatest selective importance.
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UNWANTED DETAIL VERSUS UNJUSTIFIED SIMPLIFICATION |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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If one follows the philosophical view that simple arguments are more powerful because they are easier to falsify, then one should always construct simple models. Simple models are also easier to tune and conduct sensitivity analyses, and engage in all the other mathematical ‘games’, that modellers may play and which so confuse biologists. However, it is inappropriate to apply the conventional Karl Popper style of scientific philosophy (driven by falsification) to modelling, because no single model will ever be appropriate for all test situations. Arguably, what is more important is that the behaviour of each submodel is never wrong; it may not be as good as it could be but at least the direction should never be opposite to expectations. An example is the misuse of quota models to describe Si-dependant diatom growth (Flynn, 2003
, 2005). The adequacy of model fits to biological data can be highly subjective (Rykiel, 1996) because, while it may be easy to decide whether one model fit is better than another, determining whether either describe the system adequately is another matter altogether. For sure, models should be a simple as possible; Occam’s razor (include only what is necessary) is the cornerstone of much modelling activity. However, ultimately who is best placed to judge what is necessary and whether an omission is justified? Biologists and biogeochemists of course, though they certainly may need help to keep things in perspective, else every little facet may be deemed as desirable if not essential.
Modelling has an important role here, in helping us all to identify facets of nature that exert greatest leverage on the processes of interest. However, you are unlikely to convince a biologist that a particular ecophysiological trait is of little or no consequence in the grand scheme of things by demonstrating it with a model based on flawed assumptions. Modellers typically get all worked up about the number of variables and where estimates for constants and descriptions of functions will come from. But what is the sense in having a nice neat little model if it does not do the right things? Modellers need to demonstrate to biologists why they have made what ever simplifications they have made. By the same token, modellers should not increase complexity by just adding poorly justified biological detail in an attempt to improve ‘realism’ (Anderson, 2005).
A critical factor in biological systems is feedback. It pervades every facet of life from the simplest biochemical process through to complex behavioural patterns. To ignore feedback is to consider that biology is just a series of simple chemical reactions. Indeed, there are models that do exactly that, they make analogies to chemistry (e.g. Baird et al., 2001). Such approaches are not without merit; if they were acceptable then we should be able to write simple rules for biology, because chemistry is a rule-driven science. However, biology, even (or perhaps, especially) at the microbial level, does not appear to be that simple. Models with feedback controls are more complex (though the equations themselves are mathematically trivial), but if the feedbacks are correctly constructed, they are more likely to always behave sensibly and hence should be safer in prediction of extreme events. To construct these mechanistic, physiologically based models, we need biological information.
Unfortunately, most biological information is not in the form of a nice parametric data set; it exists as a general perception, as the combination of many pieces of information. Arguably, it is as important, if not more, for a model to behave in a general appropriate fashion than to mimic exactly behaviour of a perhaps atypical species. Non-parametric knowledge, the direction of a response to a stimulation and so on, is important, and modellers should not ignore it. However, to use it they need a good understanding of biology. I used to believe that modellers were best trained by taking mathematicians and teaching them bits of biology. I was wrong. Biology is such a large diffuse subject that it is impossible to know which bits of it a mathematician is likely to need; it is difficult enough for a biologist. No, it is better to take biologists and train them to do modelling. This also makes them think about what to measure in their experiments, so making them better biologists.
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SOME EXAMPLE PROBLEMS |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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A good biological model is one that behaves in a way that a biologist would understand and appreciate. Confidence by biologists in models thus requires that biological components are demonstrably not flawed in their operation. This is both with respect to the description of components that are present and also for justification of the absence of components. In the following I will seek, briefly, to identify common problems in both biological and modelling approaches for different plankton groups.
I have written before on the subject of the importance of model structure for descriptions of multi-nutrient phytoplankton growth dynamics, that different outputs may occur under dynamic situations, even though behaviour under steady state may be similar (Flynn, 2001, 2003, 2005). The fate of the lesser limiting nutrients is every bit as important as that of the limiting nutrient, yet how many biologists measure the concentrations of the non-limiting nutrients? Another common failing is measurement of biomass as chlorophyll (Chl : C varies 10-fold with nutrient and light availability; Kruskopf and Flynn, in press), or cell number (cell size varies with nutrient status); modellers typically need C-biomass and indeed ecosystem energetics work on C. This leads to perhaps the single greatest problem, estimates of growth and production rates. Typically modellers need biomass-specific rates; rates calculated from Chl may be easily in error by 2–4 fold. There is similar confusion between nutrient transport kinetics and growth kinetics (Flynn, 1998). Topics that need urgent attention are kinetics of dual nutrient limitation (appreciating that the impact of nutrient ratios must depend on the concentration of those nutrients) and processes affecting the magnitude and form of DOM release.
There are several crippling problems for the modelling of zooplankton activity. While the literature abounds with respiration and ingestion rates (etc.), most is all but useless for modelling as it is expressed per individual rather than per unit of biomass. Although there are various transforms from dry weight and so on (Harris et al., 2000), these are not as satisfactory as having raw data in C units. At the least, it would be much safer if the biologists provided such transformed data rather than risk modellers employing inappropriate transforms in error. There is also too much emphasis on the activity of adult female mesozooplankton (often associated with egg production), ignoring the importance of the activities of other stages, and especially of juveniles.
Secondly, there is the lack of data, non-parametric or parametric, describing the handling of prey of different nutrient status, a problem especially great in marine systems. The stoichiometric (C:N:P nutrient status) quality and biomass-based quantity of prey supplied are rarely documented. This is an important topic not only because the stoichiometric relationship between predator and prey has an immediate impact on the interaction between these organisms (Hessen and Andersen, 1992) but because of other factors associated with food quality that affect prey rejection or switching (Mitra and Flynn, 2005). Stoichiometric-based zooplankton models have concentrated on matters affecting the simple implications of stoichiometric disparity, ignoring other (perhaps equally or more significant) impacts of prey quality and quantity on zooplankton growth and nutrient cycling. Changes in assimilation and gross growth efficiency with prey quality and quantity also affect the form of material voided and hence the support of microbial activity.
In models, purporting to explicitly describe the growth and death of functional groups of phytoplankton, prey selection and rejection by zooplankton must surely warrant further attention. The more complex the model, with more explicit inclusion of behavioural functions, the more important it becomes that those functions are described adequately. And the more important it is that biologists provide suitable data sets for model validation, not just for modelling per se but to enhance their understanding of ecology.
Of the three main groups of plankton, bacteria are probably the most difficult to model. We know very little about even the biomass of marine bacteria (Herndl et al., 2005) let alone about their nutrition, having to assume their physiological regulation is akin to that in medically important bacteria. Bacteria can select between both inorganic and organic nutrients of great variety. The resultant feedbacks are complex with control mechanisms linked to fast-acting metabolite repression (Titgemeyer and Hillen, 2002). This complex physiology is poorly represented in models with some quite bizarre constructs. This is compounded by an incomplete knowledge of the production of nutrients (notably dissolved organic matter, DOM) by other organisms. Indeed, one could argue that until we understand and can manage to model the phytoplanktonic and zooplanktonic production of DOM adequately, there remains little urgency in resolving processes that consume that DOM. Much description of DOM is couched in terms of lability (Carlson et al., 2002), without describing the actual chemical composition and forgetting that a compound is only biologically labile if there is an organism present that can use it. There are also few data for biomass-specific gross growth rates and growth efficiencies, and we do not know whether the impact of P-stress on growth is as significant as it appears to be in non-planktonic bacteria (Pirt, 1982). While a biologist may point out the problems in model construction, there are few data for a modeller to structure an informed alternative view.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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In totality, it is perhaps hardly surprising that modellers are tempted to simplify and take ‘shortcuts’ or that biologists claim that models do not represent reality. Biologists and modellers need to talk together at the outset of experimental design, and they (and indeed grant awarding bodies) need to appreciate the importance of complete data sets without there necessarily being some immediate earth-shattering new ‘result’. Perhaps journals, if not grant awarding bodies, should require data to be deposited in forms more suitable for data mining and modelling. One may also ask whether journals should accept modelling papers without a complete transcript of the code (even if just as an ASCII text dump); it is all too easy to omit details and introduce typographic errors in traditional descriptions of models in papers that render reconstruction of models impossible. For their part, modellers need to engage in a more proactive way with biologists for model construction, taking joint decisions on simplification and omissions. Biologists should also be involved in data selection for model verification; data may be flawed, inappropriate, or otherwise have serious reliability issues. There are instances where it becomes obvious during the attempted modelling of a system that the biologists has made errors; a good example is where microalgae adhere to the walls of culture vessels and hence a proportion of the system nutrient goes ‘missing’. The model may thus not fit the data, because the data are inaccurate or otherwise inadequate, not because of flaws in the model per se. Both biologist and modeller learn from such interactions.
To return to the issue of complexity and simulation adequacy (Anderson, 2005), for each organism type simulated we should ask the following:
- Is the form of each model component dysfunctional?
- When run alone do model organisms always exhibit sensible behaviour both with respect to what they do and what they do not do?
- What components of physiology have been omitted, why, and has that omission been shown to be safe under all realistic scenarios for which this model may be run?
We should remember that over application of Occam’s razor results in you cutting your own throat; biological features should be omitted only after careful consideration. Just as it is dangerous to run models beyond their original operational envelope, so it is equally dangerous to swap submodels into other simulators as the original caveats for their operation may be compromised. Traditional Monod and quota models were developed for single nutrient steady-state situations yet are frequently at the heart of multi-nutrient dynamic simulations; that is potentially dangerous as their responses may be wrong leading to further errors as the fate of nutrients is incorrectly simulated (Flynn, 2003, 2005).
Finally, perhaps we should ask a more basic question. Should we study biology or population ecology divorced from concurrent modelling activity? We would not dream of undertaking biological studies without an eye towards the use of statistics, so why ignore models? If statistics in biology can be compared to a lamp-post supporting a drunkard, then models can be compared to the light helping to guide the way forward. However, it takes a biologist to show the modeller in which direction the light needs to be shone. We need each other.
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FOOTNOTES |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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Written responses to this article should be submitted to Ian Jenkinson at ian.jenkinson@wanadoo.fr within six months of print publication. For further information, please see the Editorial ‘Horizons’ in Journal of Plankton Research, Volume 26, Number 3, Page 257.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONWHY BIOLOGISTS NEED MODELS,...WHAT WE NEEDUNWANTED DETAIL VERSUS...SOME EXAMPLE PROBLEMSCONCLUSIONSFOOTNOTESREFERENCES |
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Kruskopf, M. and Flynn, K. J. (in press) Chlorophyll content and fluorescence responses cannot be used to gauge reliably phytoplankton biomass, nutrient status or growth rate. New Phytol. doi: 10.1111/j.1469-8137.2005.01601.x.
Miller, C. B. (2004) Biological Oceanography. Blackwell, Malden, Massachusetts.
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Proctor, R., Holt, J. T., Allen, J. I. et al. (2003) Nutrient fluxes and budgets for the North west European Shelf from a 3-dimensional model. Sci. Total Environ., 314, 769–785.
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