1 Eastern S. Pacic Synechococcus sp. Bloom maximum 90 10
9 1 Central N. Atlantic Synechococcus sp. Summer depth range 0.1 { 75 10
9 1 Sargasso Sea Synechococcus sp. Autumn depth range 0.1 { 10 10
9 2 Equatorial Pacic Synechococcus sp. HNLC surface waters 10 10
9 3 Baltic Sea Bacterioplankton Spring{autumn range 0.6 { 2.4 10
12 4 Buzzards Bay, USA Bacterioplankton Annual range 0.3 { 10.9 10
12 5 Western S. Atlantic E. huxleyi Spring bloom range 0.2 { 609 10
6 6 Central N. Atlantic E. huxleyi Early summer range 0.03 { 20 10
9
7 Buzzards Bay, USA Dinoagellates Annual range 0.5 { 225 10
6 8 Buzzards Bay, USA Tintinnids Mean annual range 0.4 { 1.2 10
6
9 Suruga Bay, Japan Mesozooplankton Annual range 0.02 { 4 10
3 10 California Current Mesozooplankton Early summer range 0 { 2 10
3
Table 1.2: Observed ranges of densities for several plankton groups from the literature. Densities measured in cells m;3. Mesozooplankton densities in individuals m;3. Sources : 1. Waterbury et al. (1986) 2. Wells, Price & Bruland (1994) 3. Zweifel, Norrman & Hagstrom (1993) 4. Turner & Borkman (1993) 5. Gayoso (1995) 6. Balchet al. (1996) 7. Pierce & Turner (1994a) 8. Pierce & Turner (1994b) 9. Omori & Ikeda (1992) 10. Huntleyet al. (1995). See text for further details.
seasonal thermocline. As such, the assumption of plankton as evenly mixed through the surface mixed layer is not unreasonable.
The biological processes considered by most plankton models usually occur over time scales ranging from hours up to days. While seasonal cycles and certain biological phenomena occur over obviously longer periods (e.g. the duration of the planktivorous Blue Whale's gestation is approximately one year), processes key to the models used in this thesis (cell division, nutrient uptake, grazing, excretion, decomposition, sinking) occur over relatively short periods of time (minutes to hours) and are usually assumed to be adequately represented by exponential rates.
The assumption of identical inhabitants is perhaps the least defensible in the case of the models used in this thesis. The three biological state variables (phytoplankton, zooplankton and bacteria) used by Fasham (1993), are intended to cover a size spectrum of organisms from prokaryotes up to metazoans (approximately 1 m ! 1 mm), and a trophic spectrum which includes photosynthetic autotrophs, detritivores, grazers, cannibals, and predators (and frequently organisms which indulge in more than one of these lifestyles). The continuous range of size (which encompasses dierences in uptake rates, locomotory ability, vulnerability, et cetera) and the variety in life history, nutrient requirement, prey
preference, and behaviour further complicates attempts to describe plankton systems with a small num- ber of functional groups. However, modellers have found that even simple models, which parameterise only the most important ecological processes (e.g. photosynthesis, nutrient limitation, grazing, regener- ation), can relatively successfully predict certain key features of plankton dynamics (e.g. spring blooms { Taylor et al., 1991 recurrent red tide events { Truscott & Brindley, 1994). Some researchers have found the creation of multiple nutrient, phytoplankton or zooplankton compartments necessary to more accurately capture certain features of data (Kremer & Nixon, 1978 Andersen, Nival & Harris, 1987), but the success of simpler models suggests that they still have a role to play in plankton modelling.
1.7.4 The rise of computational power
As already stated, the Lotka{Volterra model introduced earlier is somewhat unrealistic because of several of the assumptions made in its formulation. Although such assumptions may be made where knowledge of the system in question is poor, the avoidance of more realistic (and complicated) forms does allow the model to be rigorously analysed by mathematical techniques.
In the time of Lotka and Volterra, this was an important consideration, since understanding a model depended on being able to deduce its behaviour through analysis. In the latter half of this century, however, the appearance of digital computers, as well as their (so far) relentless rise in processing power, has permitted researchers to formulate models without regard for their analytical solubility. Numerical simulation of these models to examine their behaviour has become commonplace. While simulation is less powerful than rigorous analysis in terms of understanding model behaviour, it does permit the ex- amination of systems which were hitherto intractable for all practical purposes (e.g. complex ordinary or partial dierential equations, individual based models, spatially{extended systems). The work contained in this thesis, for instance, has relied almost entirely upon numerical solutions of ODE models of the plankton ecosystem.
1.7.5 Plankton modelling
The modelling of plankton populations has a history stretching back to the work of Gordon Riley in the 1940s. Riley, in common with many of his contemporaries in biological oceanography, was interested in the phenomenon of the spring phytoplankton bloom. Using the ideas of Gran about the stabilisation of the surface waters in spring, he produced a quantitative model of the phytoplankton dynamics in the North Atlantic (Riley, Stommel & Bumpus, 1949). This work was expanded later by Sverdrup (1953), but remains the basis of models of the spring phytoplankton bloom (including those in this thesis). Mann & Lazier (1991) and Fasham (1993) provide some further background to the origins of plankton modelling.
Latter{day modelling eorts address plankton behaviour across the full range of space and/or time. There is also a substantial body of more abstract theoretical work (e.g. Bascompte, Sole & Valls, 1992
Malchow, 1994 Truscott & Brindley, 1994 Rose, 1998), which explores processes from a mathematical perspective. The work in this thesis focuses on non{spatial models, and their behaviour across annual cycles of physical forcing. In contrast, other work (e.g. Davidson, Cunningham & Flynn, 1993 David- son & Cunningham, 1996) has focussed on resolving behaviour at the shorter time scales of hours to days. As indicated, there is also work which additionally focuses on spatial elements of plankton dynamics. Again, such work covers a wide range of scales, from metres to kilometres (e.g. Pascual, 1993 Malchow, 1994 Bees, Mezic & McGlade, 1997), all the way to full ocean basin simulations in general circulation models (GCMs) (e.g. Wroblewski, 1989 Sarmientoet al., 1993). Recently there has been the appearance of models in which the life histories of individual plankters are followed in both space and time (Woods & Barkmann, 1995).
The dierent models outlined above are often used to answer research questions which cannot be set- tled, or reasonably addressed, from observations. For instance, large scale GCM simulations are normally concerned with estimating total oceanic productivity over the ocean basin in question. Models at the smaller end of the spatial scale are often used to predict the consequences to plankton population dynam- ics of small to medium scale physical processes such as diusion14, advection or Langmuir circulation. Models (usually non{spatial ones similar to those in this thesis) are also commonly used to examine specic ecological questions. For example, several researchers have investigated the occurrence of so{ called \High Nutrient, Low Chlorophyll" (HNLC) regions. Since nutrients normally limit phytoplankton growth, these regions (where nutrients, for no obvious reason, go unused by phytoplankton) have long been considered anomalous, and have attracted several modelling studies (Evans & Parslow, 1985 Frost, 1987 Steele & Henderson, 1992 Fasham, 1995) which attempt to explicate them.
The research in this thesis centres around the nitrogen ecosystem model of the oceanic mixed layer described by Fasham (1993) . This model is described, mathematically and ecologically, in Chapter 2. The chapter also aims to place this model into context within plankton modelling by comparing it with several other plankton models.
1.8 Summary
This chapter has attempted to lay a foundation for the biology and physics which underlie the models that form the basis of this thesis. Additionally, sections have aimed to explain (and defend) the simpli- cations of this foundation by models. Models are, by denition, abstractions of reality.
14The term \diusion" is often used to describe processes such as active swimming, advection and wind{mixing which,