All of the phytoplankton types are initialized with identical, low biomass distributions and the phosphate field is initialized from climatology [Conkright et al., 2002]. The model is integrated forward for 10 years. After about 2 years the phytoplankton types begin to occupy clearly different biogeographical regions, and after several years exhibit a repeating seasonal cycle. Here we discuss results from the tenth year of integration. Longer integrations of the model reveal that the biogeography of the model changes very little between a decade and two hundred years, thus we consider this to be a quasi-stable state. The annual surface phosphate distribution is plausible, with elevated concentrations in upwelling regions, while subtropics and tropics are oligotrophic. Some details, for example the High-Nitrate Low-Chlorophyll (HNLC) regions, are affected by the lack of additional micronutrient controls.
2.2. Single Resource Case: R* Analysis
 We expect the steady state analysis of resource competition theory to be most applicable (if at all) in the low-seasonality, oligotrophic regions where K strategy types dominate. Assuming steady state in equation (A2) and neglecting transport terms, we develop a diagnostic R*j (see Appendix A (section A6) for derivation) which may be evaluated for each of the 78 initialized phytoplankton types (j = 1, 2,…78) in the global model. This diagnostic is analogous to R* (equation (3)) but accounts for the relatively complex loss terms (see equation (A2), though note that there is only one nutrient and one grazer in this illustrative case) which include explicit terms in Pj and Z1 which can only be determined diagnostically in the numerical model.
where for this single nutrient, single grazer case
Here the growth term, νj, is a function of temperature and light and the loss term, Lj, includes mortality, sinking and grazing. This loss term is a function of the abundance of the jth phytoplankton, the total palatability weighted abundance of phytoplankton, A1, and the abundance of the grazer Z1. In essence R* is still a combination of the phytoplankton physiology and the loss terms, however the nonlinearity means that R* is no longer independent of the phytoplankton and source terms.
 Resource competition theory, as discussed in the Introduction, suggests the following: (1) Organisms with the lowest R* will outcompete all others for a single limiting resource, and without other limiting factors will exclude them, (2) the ambient concentration of that resource will be set to the minimum R*, and (3) and the resource will vary predictably with changes in the physiology of the lowest-R* organisms. We examine the global model in the context of these hypotheses. In the following paragraphs we examine how resource competition theory helps us to interpret the model ecosystem first locally for a single grid point, then with latitude and season. Afterward we interpret the large-scale regional patterns.
 We first consider the characteristics of phytoplankton types at a single grid cell in the Equatorial Pacific in the month of February (Figure 3a). Following equation (6), R*j was diagnosed for each initialized phytoplankton type at every time step and averaged over February. We show here the positive R*j for all the phytoplankton that coexist in this grid cell. (A negative R*j can denote a phytoplankton type for whom current local losses are larger than the growth. A negative R*j can also indicates phytoplankton types for whom local losses are balanced by the neglected transport terms.) Phytoplankton abundance increases with decreasing, positive R*j. Furthermore, the local concentration of the single limiting nutrient (dashed line in Figure 3a) closely matches R*min, the lowest positive R*j of all the phytoplankton. Notably, in the illustrated global model, a single, lowest-R* organism does not exclude all others, at least on the timescale of these integrations. Instead, several K strategist species with R*j close to R*min coexist (A. Barton et al., Modeling species diversity gradients in marine phytoplankton, manuscript in preparation, 2009). Those with similar R*j and high abundances have similar light and temperature requirements. Small variations in these environmental factors offer an opportunity for each species to be fittest at some point during the year, allowing coexistence on the longer term.
Figure 3. Single resource case R* Analysis: (a) Single location (circle in Figure 5): R*j for each phytoplankton (crosses), averaged for February (0–50 m). Red dashed line indicates the February (0–50 m) averaged nutrient concentration at that location. (b) Pacific transect (line in Figure 5): R*j for each phytoplankton (blue crosses), averaged 0–50 m for February for each latitude; phytoplankton with biomass at least 10% of the maximum at that location are indicated additionally with a black circle; red dashed line indicates February (0–50 m) nutrient concentration.
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 On the other hand, the phytoplankton with higher R*j, but low abundances, are also K strategists which are not near their optimum temperature or light requirement (this will lead to a low νj and therefore high R*j). They may persist at low abundances due to lateral transport (immigration) or the timescale for their complete exclusion may be very long relative to the integration.
 Along a north-south transect in the Pacific (also for February) the ambient nutrient is almost identical to the R*j of the dominant species from −40° to the equator during the Southern Hemisphere summer (Figure 3b). However the nutrient is slightly higher than the R*j of the dominant species in the Northern Hemisphere reflecting a breakdown of the equilibrium balance assumed in equation (3) in the winter months (due to higher supply of nutrients and low growth rates during this period). Poleward of about 40° the nutrient concentration shows little or no correspondence to the R*min, as anticipated since these regions are dominated instead by the r strategists.
 The tight coupling of growth and mortality in the tropics and subtropics, consistent with equation (3), breaks down in the highly seasonal, subpolar oceans but may still be achieved during the summer period of the seasonal succession. R*min is similar to the ambient nutrient always in a tropical location (Figure 4b) but only during the summer in a higher-latitude location (Figure 4a). This is further revealed by the Hovmoller diagram (Figure 4c) of the variable (N1 − R*min)/N1, which measures the departure of the ambient concentration of the limiting resource from the minimum R* of the organisms present, along the Pacific transect (Figure 4c). When (N1 − R*min)/N1 is close to zero (green/yellow) the equilibrium assumed in equation (3) is valid. In the tropical and subtropical waters, the equilibrium holds year round, between about 25° and 40° of latitude the balance holds seasonally in the summer. Poleward of 50°N in the Northern Hemisphere (sooner in the Southern Hemisphere), seasonal variations, advection and light limitation break the simple balance and drive nutrient concentrations away from R*min.
Figure 4. Single resource case: (a) Time series of nutrient concentration (red dashed) and minimum diagnosed R*j (R*min, black solid) for 0–50 m at 211°W, 31°S (marked on Figure 5). (b) Same as above but for 211°W, 5°N. (c) Pacific transect (marked on Figure 5): Relative difference between diagnosed R*min and ambient nutrient, both averaged for 0–50 m for each month, (N1 − R*min)/N1. Contours are at (−0.5, 0.5), green/yellow shading indicates R*min close to ambient nutrient, red indicates nutrients exceed R*min, and blue indicates that nutrients are less than the R*min; no shading indicates where no reasonable value for the diagnosed R*min was found. Dotted lines indicate locations for Figures 4a and 4b.
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 We also investigate (not shown here) the applicability of resource control theory with depth, and find that diagnosed R*min is close to the ambient nutrients for the lower latitudes from the surface down to about 50 m. At greater depths, low light leads to low growth rates and nutrient supply is higher, making the steady-state assumption less reasonable, and the R*min is a less useful diagnostic. For the remainder of the paper we will consider only the annual 0–50 m averaged results to examine the large-scale picture, but keep in mind that there are interesting time and depth-varying issues.
 In a global, annually averaged, perspective, the minimum positive, R*j (R*min) of the phytoplankton types present closely anticipates the ambient concentration of the single nutrient in the tropics and subtropics. The interesting diagnostic to look at is, relatively, how much the ambient concentration of the limiting resource departs from R*min: (N1 − R*min)/N1 (Figure 5). And consistent with the inference from the single Pacific transect the difference is small in the tropics and subtropics, but the equilibrium assumption breaks down in the extratropics. The region where the theory appears to hold is a subset of the domain where K strategy types dominate. Unshaded regions are those in which the pattern of R*min is particularly noisy or consistently negative. In such regions advection, decoupling of growth and grazing, or light limitation break the simple equilibrium assumed in equation (3).
Figure 5. Single resource case: Ratio of difference to actual nutrient concentration (N1 − R*min)/(N1). Contours are at (−0.5, 0.5), green/yellow shading indicate R*min close to ambient nutrient, red indicates nutrients exceed R*min, and blue indicates that nutrients are less than the R*min. No shading indicates where no reasonable value for the diagnosed R*min was found. Transect line and circle indicate locations for Figures 3 and 4.
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2.3. Single Resource Case: Sensitivity Studies
Figure 6. Single resource case, sensitivity experiments: Ratio of macronutrient in (a) double case; (b) halved case to macronutrient in control run (Figure 5). Contours are drawn at 2 (indicating nutrient concentrations double the control experiment) and at 0.5 (indicating nutrient concentrations half of the control experiment).
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 Thus, over a large areas of this idealized global ocean model the phytoplankton types that dominate the biomass, the ambient resource concentration, and the sensitivity of the resource concentration to changes in phytoplankton physiology, are all consistent with the expectations from the simple statement of resource competition theory encapsulated in equation (3). As expected, this framework has its greatest diagnostic ability in relatively stable physical environments where the simple assumption of equilibrium between growth and mortality is an appropriate balance. Here the ecological regime where the diagnostic R* accurately describes the system is defined by a critical threshold in the annual range of mixed-layer depth (maximum mixed layer depth minus minimum) of about 250 m (Figure 7). This also reflects the transition between the extremely oligotrophic subtropical region and areas with higher surface nutrient concentration.
Figure 7. Relative stability of region: annual range of mixed layer depth (m). Mixed-layer depths are from ECCO-GODAE state estimates. [Wunsch and Heimbach, 2007]. Dashed contour indicates the region where the sensitivity studies in the single resource case show the expected linear relationship (0.5 and 2 contours from Figure 6). Solid line indicates where the Prochlorococcus analogs dominate in the multiple resource case (see Figure 11a).
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