May 20, 2018, Sunday

# MBW:Modeling the coupling of ocean ecology and biogeochemistry

Paper review by Mariah Walton based on Dutkiewicz, S., M. J. Follows, and J. G. Bragg (2009), Modeling the coupling of ocean ecology and biogeochemistry, Global Biogeochem. Cycles, 23, GB4017, doi:10.1029/2008GB003405.[1]

# Executive Summary

In this paper the authors use a biogeochemistry enabled General Circulation Model to look at phytoplankton colonies in the world ocean and their relationship to their chief growth-promoting resources: light, temperature, and nutrients. Focusing primarily on nutrients, Dutkiewicz et al attempt to answer the question "to what extent is resource competition theory a qualitative and quantitative tool with which to interpret this complex and flexible ecosystem model?" They do this by first looking at single resource scenario, where light and temperature are held constant, and then a multiple resource scenario which is a much closer analog to the real ocean. They find that resource competition does explain the dominant distribution of broad phytoplankton types, particularly if phytoplankton are classified only by their ability to compete with limited and abundant resources respectively. Competition theory becomes a less useful metric however when looking at the polar and subpolar regions, due to high seasonality and imbalances between nutrient concentrations and productivity.

# Overview

• Mathematics used:
• The main mathemamatical model used in this study is the general circulation model. This model simulates the observed nutrient patterns and these patterns effect on phytoplankton
• A monod function is also used to represent resource competition.
• Type of model:
• Population model using differential equations to describe macronutrient populations and phytoplankton populations.
• Biological system studied:
• 78 phytoplankton types in the world's oceans.
• Both single resource and multiple resource are studied.

# Biological System

The focus of this paper is phytoplankton communities. Phytoplankton are microscopic, plant-like organisms that live in the mixed layer of the ocean (upper 0 – 350 m). They grow by converting carbon dioxide to carbohydrates through photosynthesis, and are the keystone of the ocean carbon cycle. Phytoplankton communities are typically described as a ‘biological pump’, converting inorganic carbon (mostly in the form of aqueous HCO3- and gaseous CO2) into organic carbon, which then sinks to the ocean floor. As it sinks, this organic carbon dissolves, ‘remineralizing’ into inorganic carbon, which is eventually carried back to the surface by the deep ocean circulation. The small portion of organic carbon that does not remineralize is deposited on the sea floor and sequestered in sediment. Because the ocean circulates on a much longer time scale than the atmosphere, this biological pump can act as a temporary carbon reservoir. [2]

Phytoplankton growth is dependent on three primary factors: temperature, light, and nutrient supply. Temperature and light follow a fairly regular seasonal cycle, making nutrients the greatest source of productivity interannual variability. Phytoplankton take up three primary nutrients—carbon, nitrogen, and phosphorous--according to the Redfield ratio (on a global average), but are also heavily dependent on other nutrients such as iron and silica, depending on the species.

Our ability to model the effect of changes in ocean nutrients on phytoplankton communities has grown in importance with rising concerns about global climate change and the sensitivity of the ocean biological pump to these changes. Here Dutkiewicz et al explore the utility of a relatively simplistic resource competition theory model to map the distribution of different phytoplankton communities in the world ocean, and their sensitivities to changes in the resource environment and in physiological characteristics.

# Math/Modeling Approach

To assess the extent to which phytoplankton communities are dominated by resource competition, Dutkiewicz et al use a General Circulation model to simulate observed nutrient patterns in the world ocean and to simulate 78 phytoplankton types. From this simulation they calculate steady state equilibrium nutrient patterns according to resource competition theory, and compare that distribution to the actual steady state nutrient concentrations in the model

## General Circulation Model (GCM)

The model used is a three dimensional, course resolution configuration of the MITgcm[3], with bathymetric and hydrographic constraints imposed from ECCO-GODAE[4][5] state estimates. The model is gridded on a 1° lat x 1° lon scale with 24 depths. The Biogeochemistry traced is inorganic and organic nitrogen and carbon, phosphorus, iron, and silica. Biology modeled are 39 paired phytoplankton types (78 total), and 2 grazers—grazers being zooplankton that consume phytoplankton.

Carbon and nitrogen are tracked through their transformation and remineralization between organic and inorganic forms. Living organic material is lost through excretion and mortality, becoming dissolved organic detritus, and then becoming inorganic through respiration. These transformations are calculated in each grid cell, and then transport mechanisms (sinking, ocean circulation) move nutrients and different forms of carbon from one grid cell to another. Each phytoplankton type has a set of parameters for light-dependent, temperature-dependent, and resource-dependent growth, as well as specific loss terms for sinking, grazing, other mortality, and transport (advection by ocean circulation). The values of these parameters are taken from empirical observations or from plausible ranges of values based on empirical observations. The resulting distribution of surface nutrients, biomass, and production is plausible, and previous research[6] has verified the model analogues of some specific phytoplankton types—most notably Prochlorococcus.

## Competition Theory

Resource competition is exactly what it sounds like—different species compete for the same resources, such that the dominant species are those best able to cope with the resource supply. Here resource supply is divided into two categories—abundant or limited—and phytoplankton are similarly delineated, with K-type organisms being those best able to compete for limited resources, and r-type those most able to take advantage of abundant resources. In its most simplified form resource competition can be represented mathematically by a Monod function:

${\frac {dN}{dt}}=-\mu _{{m}}{\frac {N}{N+\kappa _{{N}}}}P+S$

${\frac {dP}{dt}}=\mu _{{m}}{\frac {N}{N+\kappa _{N}}}P-mP$

And at equilibrium:

${\bar {N}}={\frac {\kappa _{{N}}m}{\mu _{{m}}-m}}=R^{*}$

${\bar {P}}={\frac {S}{m}}$

Where:

$N$= population of a single macronutrient,

$P$= population of a single photoautotroph (phytoplankton),

$\mu _{{m}}$ = maximum growth rate,

$\kappa _{{N}}$ = nutrient half-saturation constant

$S$= nutrient supply,

$m$= mortality rate,

$R^{*}={\bar {N}}$ = equilibrium (S.S.) resource concentration, and

${\bar {P}}$ = equilibrium photoautotroph population.

In the lower limit, where nutrients are exhausted by the organisms present, N should approach the lowest R* amongst those organisms, and P will be determined by nutrient supply, S. In the upper limit, when resources are abundant such that ${\frac {N}{N+\kappa _{{N}}}}=1$ and the grazer population is small, P becomes dependent on the growth rate only.

Competition theory is first examined in a simplified form, looking at a single limiting resource, and then used to break down the full, multiple resource model.

### Single Resource

Dutkiewicz et al look at phosphorous in the single resource case. The model is initialized with 39 phytoplankton ‘species’ pairs, where light and temperature sensitivity is constant between species, but the nutrient sensitivity is set so that one of each pair is a K-type competitor, and the other is an r-type competitor. The GCM is run with this simplified single nutrient scenario for 10 years, after which the system is essentially at steady state and little change occurs. The resulting distribution of all K and r-type subsets of each species is then compared to the nutrient distribution and the mixed layer to look for relationships. To assess the extent to which competition explains variability, the authors calculate R*and compare it to the ‘actual’ nutrient concentration N. When calculating R* they use a slightly modified version of the original competition theory equations that incorporate a more complicated loss term:

$j}^* =\frac{\kappa_{N_{1_{j}}} L_{j}}{v_{j} – L_{j}$

where $v_{{j}}=\mu _{{max_{{j}}}}\gamma _{{j}}^{2}\gamma _{{j}}^{I}$and $L_{{j}}=m_{{j}}^{p}+{\frac {1}{P_{{j}}}}{\frac {\delta w_{{j}}^{p}P_{{j}}}{\delta z}}+g_{{max_{{j}}}}{\frac {\eta _{{j}}}{A_{{1}}}}{\frac {A_{{1}}}{A_{{1}}+\kappa _{{1}}^{P}}}Z_{{1}}$

So the growth term $v_{{j}}$ is a function of all ‘resources’, and $L_{{j}}$ includes mortality, sinking, and grazing.

### Multiple Resource

In the multiple resource model we add variable light and temperature sensitivities for each species, and introduce the other nutrients: NOx, Fe, and silica. Nutrient sensitivity is set such that phytoplankton fall into four groups: (1) large, fast growing with high $\kappa _{{N}}$, (2) same, but which use silica (diatom analogs), (3) small, slow growing with small R*, and (4) same, but which cannot use nitrate and have a lower $\kappa _{{N}}$ (Prochlorococcus analogs). Ten simulations were run varying the distribution of these sensitivities, and the ensemble of these simulations is what the authors use in their analysis.

Figure 1 summarizes the differences in sensitivities between the single and multiple resource cases. Green and black lines are K-strategy, red lines are r-strategy. Note that withe the single resource, light and temperature sensitivity are constant between K and r-type groups, while in the multiple resource model they vary, giving each species a different productivity window.

# Results and Analysis

## Single Resource

Dutkiewicz et al use $(N_{1}-R*_{m}in)/N_{1}$ as their metric for equilibrium, where a value of one indicates that the ‘actual’ nutrient concentration equals that predicted from competition theory. They found that K strategy species dominate in the tropics and subtropics, and r strategists dominate at the poles (Fig 2, Fig 5). The authors tie this distribution to the stability of the mixed layer: the equatorial regions have very little seasonal changes in temperature, and therefore a more constant mixed layer depth, where as the poles have strong seasonal contrasts which lead to very large changes in mixed layer depth.

A Hovmoller diagram (Fig 4) of a Pacific Ocean transect shows another seasonal effect: the ‘equilibrium’ region (where N approximately equals R*min), extends closer to the poles during each hemisphere’s respective summer. This is due to seasonal productivity: during a summer, light and temperature increase at one pole, which increases productivity and nutrient utilization, such that R* begins to approach N. This only works up to a point however, as the poles, and particularly the Southern Ocean, have naturally elevated nutrient concentrations which cause N to far exceed R*.

## Multiple Resource

The multiple resource case is more difficult to break down. If the large phytoplankton types are labeled as r-strategy, and the small as K-strategy then the multiple resource simulation has almost the same distribution as the single resource (Fig 8). When all four model groups are mapped separately, we see a more gradual transition between regimes (Fig11). Diatom analogues dominate the Southern Ocean and northern Pacific, other large phytoplankton dominate the North Atlantic and buffer the diatom zones, small phytoplankton dominate the equator and subtropics, and the Prochlorococcus analogues transition into the subtropics.

This intuitively makes sense, but is the result of a more complicated nutrient pattern. The equatorial Pacific is iron depleted ($Fe), while the equatorial Atlantic is nitrate depleted (Fig 9), so the K-strategy dominance seen in the tropics in Figure 8 is a result of two limiting resources, not one. Further, the diatom dominated areas are iron depleted, but nitrate rich, while the Prochlorococcus dominated areas are nitrate depleted, but iron rich.

The authors conclude that resource competition theory can accurately explain and predict the distribution of broad classes of phytoplankton in the world ocean, but that it remains most useful in the tropical/subtropical regions where equilibrium roughly holds true.

# Discussion of Recent Paper Citing

Link, Bragg JG, Dutkiewicz S, Jahn O, Follows MJ, Chisholm SW (2010) Modeling Selective Pressures on Phytoplankton in the Global Ocean. PLoS ONE 5(3): e9569. doi:10.1371/journal.pone.0009569 here.

This paper discusses the pressures put on phytoplankton in the world's oceans. There are diverse forces (physical, biogeochemical, ecological, and mutational) at play. Particularly, the scientist look at two types of picophytoplankton: Synechococcus and Prochlorococcus. The main trait studied is their ability to use Nitrogen. The Synechococcus have an ability to use nitrogen, while the closely related Prochlorococcus, do not have that same ability.

The main citation discussed is related to iron in the tropical Pacific. Although there are concentrations of both Nitrate and Nitrite in the ocean in this region, the picophytoplankton do not use it. This is because the main limiting factor for growth is iron in this region. With iron being the limiting factor, the population is relatively insensitive to Nitrogen.