Module 1

Epipelagic (0–200 m) — The Sunlit Zone

Where sunlight drives the photosynthetic engine of the ocean and fuels the entire marine food web

1.1 Phytoplankton Biochemistry & Photosynthetic Pigments

Phytoplankton are the foundation of marine ecosystems, responsible for approximately 50% of global net primary production (~50 Gt C/yr). Their photosynthetic apparatus contains a suite of light-harvesting pigments tuned to different wavelengths:

Chlorophyll a (all phytoplankton)

Universal photosynthetic pigment. Absorption peaks at 430 nm (blue) and 680 nm (red). The primary electron donor in both Photosystem I and II. Concentration in surface ocean: 0.01–30 mg/m$^3$ (oligotrophic gyres to coastal upwelling).

Chlorophyll b (green algae, euglenoids)

Accessory pigment absorbing at 455 nm and 640 nm, filling the “green gap” of Chl a. Transfers energy to Chl a via resonance energy transfer (FRET). Chl b/a ratio increases under low light as cells invest in light harvesting.

Carotenoids (all phytoplankton)

Absorb 400–550 nm (blue-green). Dual function: light harvesting (fucoxanthin in diatoms) and photoprotection (quenching singlet oxygen and triplet chlorophyll under excess light). Include $\beta$-carotene, zeaxanthin, peridinin.

Phycobilins (cyanobacteria, red algae)

Water-soluble pigments organised in phycobilisomes. Phycoerythrin (absorbs 490–570 nm, green) and phycocyanin (absorbs 610–640 nm, orange-red). Allow efficient harvesting of green light that penetrates deepest in coastal waters.

Photosynthesis-Irradiance (P-I) Curve

The relationship between photosynthetic rate $P$ and irradiance $I$ is described by the hyperbolic tangent model (Jassby & Platt, 1976):

$ P = P_{\max} \cdot \tanh\!\left(\frac{\alpha I}{P_{\max}}\right) $

$P_{\max}$: light-saturated rate (mg C/mg Chl/hr), $\alpha$: initial slope (photosynthetic efficiency)

Derivation: At low irradiance, photosynthesis is light-limited: $P \approx \alpha I$ (linear). The slope $\alpha$ depends on the quantum yield of photosynthesis and the absorption cross-section of pigments. At high irradiance, the rate saturates at $P_{\max}$, limited by the Calvin cycle's capacity to fix CO$_2$ (RuBisCO turnover rate). The light saturation parameter is:

$ I_k = \frac{P_{\max}}{\alpha} $

Irradiance at which light-limited and light-saturated rates intersect

With photoinhibition at very high irradiances, the Platt et al. (1980) model adds a decay term:

$ P = P_s \left(1 - e^{-\alpha I / P_s}\right) e^{-\beta I / P_s} $

$\beta$: photoinhibition parameter; $P_s$: hypothetical maximum without inhibition

Major Phytoplankton Groups & Strategies

Diatoms (Bacillariophyceae): silica frustules, dominant in nutrient-rich upwelling zones and spring blooms. Fast growth (up to 2–3 divisions/day). Major carbon exporters via heavy sinking. Require dissolved silica: Si:N:P $\approx$ 15:16:1.
Dinoflagellates (Dinophyceae): two flagella, mixotrophy common. Slower growth but resist grazing via toxins (saxitoxin, brevetoxin). Cause harmful algal blooms. Some form symbioses (zooxanthellae in corals).
Coccolithophores (Haptophyta): calcium carbonate plates (coccoliths). Emiliania huxleyi is the most abundant. Produce DMS (dimethyl sulphide) affecting cloud formation. CaCO$_3$ production: $\text{Ca}^{2+} + 2\text{HCO}_3^- \to \text{CaCO}_3 + \text{CO}_2 + \text{H}_2\text{O}$.
Cyanobacteria (Prochlorococcus, Synechococcus): smallest phytoplankton (0.5–2 $\mu$m). Prochlorococcus is the most abundant phototroph on Earth (~3 $\times$ 10$^{27}$ cells). Dominates oligotrophic gyres. Some fix N$_2$ (Trichodesmium).

1.2 Primary Production & Sverdrup's Critical Depth

Net primary production (NPP) is the organic carbon available to the food web after phytoplankton respiration:

$ \text{NPP} = \text{GPP} - R_{\text{phyto}} $

Global ocean NPP $\approx$ 50 Gt C/yr (about half of global NPP)

GPP is integrated over the euphotic zone:

$ \text{GPP} = \int_0^{z_{eu}} P(I(z)) \cdot [\text{Chl}](z)\,dz $

Sverdrup's Critical Depth Model

Harald Sverdrup (1953) explained why spring blooms occur: phytoplankton can accumulate only when the mixed layer depth $z_{\text{ML}}$ is shallower than the critical depth $z_{\text{cr}}$. The critical depth is where vertically integrated photosynthesis equals integrated respiration:

$ \int_0^{z_{\text{cr}}} P(I_0\,e^{-K_d z})\,dz = \int_0^{z_{\text{cr}}} R\,dz = R \cdot z_{\text{cr}} $

Using the linear approximation $P \approx \alpha I$ (valid when $z_{\text{cr}}$ extends well below the compensation depth where light is low):

$ \alpha I_0 \int_0^{z_{\text{cr}}} e^{-K_d z}\,dz = R \cdot z_{\text{cr}} $

$ \frac{\alpha I_0}{K_d}\left(1 - e^{-K_d z_{\text{cr}}}\right) = R \cdot z_{\text{cr}} $

For large $z_{\text{cr}}$, $e^{-K_d z_{\text{cr}}} \to 0$, giving the approximate critical depth:

$ z_{\text{cr}} \approx \frac{\alpha I_0}{K_d \cdot R} $

In winter, deep mixing ($z_{\text{ML}} > z_{\text{cr}}$) carries phytoplankton below the compensation depth on average — losses exceed gains. In spring, solar heating stratifies the surface, shoaling the mixed layer above $z_{\text{cr}}$ and triggering the bloom. This process is critical for understanding climate-biodiversity feedbacks, since the timing and magnitude of spring blooms affect the entire food web.

1.3 The Microbial Loop

The classical food chain (phytoplankton $\to$ zooplankton $\to$ fish) misses a major pathway discovered by Azam et al. (1983). Up to 50% of primary production passes through dissolved organic matter (DOM) and is recovered by heterotrophic bacteria:

The microbial loop pathway:

Phytoplankton exude DOM (10–50% of fixed C) $\to$ heterotrophic bacteria assimilate DOM$\to$ heterotrophic nanoflagellates (HNF) graze bacteria $\to$ ciliates graze HNF$\to$ microzooplankton $\to$ mesozooplankton. At each step, CO$_2$is respired and DOM is released, partially recycling carbon.

Bacterial Growth Efficiency (BGE)

The bacterial growth efficiency determines how much DOM is converted to bacterial biomass versus respired as CO$_2$:

$ \text{BGE} = \frac{BP}{BP + BR} = \frac{BP}{BCD} $

BP = bacterial production, BR = bacterial respiration, BCD = bacterial carbon demand

Typical BGE values: 10–30% in oligotrophic waters, 30–60% in productive coastal waters. Lower BGE means more carbon is respired and less is transferred to higher trophic levels. This makes the microbial loop an important carbon sink but an inefficient food source.

Viral Lysis and the “Viral Shunt”

Marine viruses (bacteriophages) kill 10–40% of bacteria per day, releasing cellular contents as DOM. This viral shunt short-circuits carbon transfer to higher trophic levels and keeps DOM recycling within the microbial loop:

$ \text{Lysis rate} = \phi \cdot B \cdot V \cdot k_{\text{ads}} $

$\phi$: burst size (~25–100 virions/cell), B: bacterial abundance, V: viral abundance, $k_{\text{ads}}$: adsorption rate

Viral abundances in the ocean are enormous: ~10$^7$ per mL in surface waters, exceeding bacterial counts by ~10:1. The total marine virosphere contains an estimated ~10$^{30}$ particles.

1.4 Zooplankton Grazing & Carbon Export

Mesozooplankton (200 $\mu$m–2 cm) are the primary grazers linking phytoplankton to higher trophic levels. The dominant groups include copepods (most abundant multicellular animals on Earth), krill, and salps.

Holling Type II Functional Response

The ingestion rate of a zooplankter as a function of food concentration follows a saturating (Michaelis-Menten type) curve, known as the Holling Type II functional response:

$ I = I_{\max} \cdot \frac{C}{C + K_{1/2}} $

$I_{\max}$: maximum ingestion rate, C: food concentration, $K_{1/2}$: half-saturation constant

Derivation: The grazer spends time both searching for and handling (capturing, ingesting, digesting) prey. If $a$ is the search rate (clearance rate, L/day) and$h$ is the handling time per prey item, then the fraction of time spent searching is$1/(1 + ahC)$ and:

$ I = \frac{aC}{1 + ahC} = \frac{(1/h) \cdot C}{C + 1/(ah)} $

So $I_{\max} = 1/h$ and $K_{1/2} = 1/(ah)$

Fecal Pellets and the Biological Carbon Pump

Zooplankton fecal pellets are dense, compact particles that sink rapidly (50–200 m/day for copepods, up to 1000 m/day for salps). They are a major vehicle for carbon export from the euphotic zone to the deep ocean. The export ratio (e-ratio) describes the fraction of NPP that sinks below the euphotic zone:

$ e = \frac{F_{\text{export}}(z_{eu})}{\text{NPP}} \approx 0.05\text{--}0.25 $

The rest is remineralised in the euphotic zone, recycling nutrients for further production. This biological carbon pump is a critical mechanism for sequestering atmospheric CO$_2$ in the deep ocean, with direct relevance toclimate carbon feedbacks.

1.5 Food Web Energetics & Trophic Transfer

Energy transfer between trophic levels is inherently inefficient. The Lindeman efficiency (trophic transfer efficiency) is typically ~10%:

$ \eta_n = \frac{P_{n+1}}{P_n} \approx 0.10 $

Lindeman (1942): production at level n+1 / production at level n

Derivation of the “10% rule”: Of the energy ingested by a consumer, approximately 20–30% is lost as undigested material (faeces), 40–60% is respired for metabolism, and only 10–20% is converted to new biomass (growth):

$ P_{n+1} = I_n \cdot AE \cdot GGE = P_n \cdot \eta_n $

AE = assimilation efficiency (~70%), GGE = gross growth efficiency (~15%)

After $n$ trophic levels, the available energy is $P_n = P_1 \cdot \eta^{n-1}$. This limits food chains to typically 4–5 levels:

Level 1 (phytoplankton): 100% of NPP = 50 Gt C/yr
Level 2 (herbivorous zooplankton): ~10% = 5 Gt C/yr
Level 3 (planktivorous fish): ~1% = 0.5 Gt C/yr
Level 4 (piscivorous fish): ~0.1% = 0.05 Gt C/yr
Level 5 (apex predators): ~0.01% = 0.005 Gt C/yr

At level 5, only 0.01% of the original primary production remains — insufficient to support a viable 6th trophic level in most ecosystems.

1.6 Harmful Algal Blooms & Droop Model

Some phytoplankton produce potent toxins, especially under bloom conditions. Key toxin-producing groups and their toxins:

Saxitoxin (STX): produced by Alexandrium spp. Blocks voltage-gated Na$^+$ channels (IC$_{50} \sim$ 10 nM). Causes paralytic shellfish poisoning (PSP). One of the most toxic natural substances.
Brevetoxin: produced by Karenia brevis (Florida red tides). Activates voltage-gated Na$^+$ channels, causing neurotoxic shellfish poisoning (NSP).
Domoic acid: produced by diatom Pseudo-nitzschia. Glutamate analogue causing amnesic shellfish poisoning (ASP). Bioaccumulates in anchovies and sardines.

Droop Model for Nutrient-Limited Growth

The Droop (cell quota) model describes growth rate as a function of intracellular nutrient content rather than external concentration:

$ \mu = \mu_{\max}' \left(1 - \frac{Q_{\min}}{Q}\right) $

$\mu$: specific growth rate, $Q$: cell quota (nutrient/cell), $Q_{\min}$: minimum quota for growth

Coupled with nutrient uptake kinetics (Michaelis-Menten):

$ V = V_{\max} \cdot \frac{S}{S + K_S} $

Nutrient uptake rate V as a function of external concentration S

The Droop model explains luxury uptake: cells can store excess nutrients ($Q \gg Q_{\min}$) when nutrients are abundant, allowing continued growth after external nutrients are depleted. This decoupling between uptake and growth is crucial for understanding bloom dynamics, including HABs that exploit pulsed nutrient inputs.

1.7 Nutrient Limitation & the Iron Hypothesis

While nitrogen and phosphorus are the primary limiting nutrients in most of the ocean (governed by the Redfield ratio), three vast regions remain High-Nutrient, Low-Chlorophyll (HNLC) — the Southern Ocean, the subarctic Pacific, and the equatorial Pacific. John Martin's (1990) iron hypothesisdemonstrated that dissolved iron limits phytoplankton growth in these regions:

$ \mu = \mu_{\max} \cdot \min\!\left(\frac{N}{N + K_N},\; \frac{P}{P + K_P},\; \frac{\text{Fe}}{\text{Fe} + K_{\text{Fe}}}\right) $

Liebig's law of the minimum applied to multi-nutrient limitation

Iron is required for photosynthetic electron transport (ferredoxin, cytochromes), nitrogen fixation (nitrogenase contains 38 Fe atoms), and nitrate reduction. Typical concentrations:

Surface dissolved Fe in HNLC waters: 0.02–0.2 nmol/L
Half-saturation constant for phytoplankton: $K_{\text{Fe}} \approx 0.1\text{--}0.5\;\text{nmol/L}$
Iron sources: aeolian dust (Saharan, Australian), sediment resuspension, hydrothermal vents

Iron fertilisation experiments (IronEx, SOIREE, SOFeX) confirmed that adding dissolved iron to HNLC waters triggers massive phytoplankton blooms. However, the efficiency of carbon export is debated: most bloom carbon may be remineralised in the upper ocean rather than exported to depth. This remains an active area ofclimate-biodiversity research.

Nitrogen Fixation and New Production

New production (Dugdale & Goering, 1967) is fuelled by allochthonous nitrogen sources: upwelled nitrate, atmospheric deposition, and biological N$_2$fixation. The f-ratio describes the fraction of total production that is “new”:

$ f = \frac{\text{New production}}{\text{Total production}} = \frac{\rho_{\text{NO}_3^-}}{\rho_{\text{NO}_3^-} + \rho_{\text{NH}_4^+}} $

Oligotrophic gyres: f $\approx$ 0.1; upwelling regions: f $\approx$ 0.5–0.8

At steady state, the f-ratio equals the export ratio (Eppley & Peterson, 1979), linking surface nutrient cycling to the efficiency of the biological carbon pump. Cyanobacterial nitrogen fixation by Trichodesmium and unicellular diazotrophs adds ~100–200 Tg N/yr to the ocean, partially decoupling the marine nitrogen cycle from external inputs.

Silica Limitation in Diatoms

Diatoms require dissolved silicic acid Si(OH)$_4$ for their frustules. The extended Redfield ratio for diatoms is C:Si:N:P = 106:15:16:1. In regions where silica is depleted before nitrate (e.g., after the spring diatom bloom), the phytoplankton community shifts to non-siliceous species (dinoflagellates, coccolithophores, small flagellates). This succession from diatoms to smaller cells reduces the efficiency of carbon export, since small cells sink slowly and are efficiently grazed by microzooplankton rather than producing large, fast-sinking aggregates.

1.8 DMS Production & the CLAW Hypothesis

Phytoplankton, particularly coccolithophores and dinoflagellates, produce dimethylsulfoniopropionate (DMSP) as an osmolyte and cryoprotectant. When cells are grazed or lysed, DMSP is cleaved by bacterial enzymes to dimethyl sulphide (DMS):

$ \text{DMSP} \xrightarrow{\text{DMSP lyase}} \text{DMS} + \text{acrylate} $

DMS is the largest natural source of sulphur to the atmosphere (~28 Tg S/yr). Once ventilated to the atmosphere, DMS is oxidised to sulphate aerosols that serve as cloud condensation nuclei (CCN), increasing cloud albedo and potentially cooling the planet. This is the basis of the CLAW hypothesis (Charlson, Lovelock, Andreae, Warren, 1987):

Warming $\to$ increased phytoplankton growth $\to$ more DMSP/DMS production$\to$ more CCN $\to$ brighter clouds $\to$ higher albedo$\to$ cooling (negative feedback)

While elegant, the CLAW hypothesis remains debated. Observational evidence suggests the feedback is weaker than originally proposed, partly because DMS emissions depend on complex ecological interactions (grazing, viral lysis, bacterial consumption) rather than simply on phytoplankton biomass. Nevertheless, marine DMS remains a key factor inclimate feedback analysis.

Epipelagic Food Web with Carbon Fluxes

A schematic of the epipelagic food web showing the classical grazing chain, the microbial loop, and carbon flux estimates in Gt C/yr:

1.9 Ocean Colour Remote Sensing

Satellite ocean colour sensors (SeaWiFS, MODIS, OLCI) measure the spectral reflectance of the ocean surface to estimate chlorophyll-a concentration and primary productivity from space. The principle relies on the fact that phytoplankton pigments absorb blue light (440 nm) and reflect green (550 nm):

$ \log_{10}[\text{Chl}] = a_0 + a_1 R + a_2 R^2 + a_3 R^3 + a_4 R^4 $

OC4 algorithm: $R = \log_{10}\!\left(\max\!\left(\frac{R_{rs}(443)}{R_{rs}(555)}, \frac{R_{rs}(490)}{R_{rs}(555)}\right)\right)$

The remote sensing reflectance $R_{rs}(\lambda)$ is the ratio of water-leaving radiance to downwelling irradiance just above the surface. It depends on the inherent optical properties (IOPs) of the water: absorption $a(\lambda)$ and backscattering $b_b(\lambda)$:

$ R_{rs}(\lambda) \propto \frac{b_b(\lambda)}{a(\lambda) + b_b(\lambda)} $

These satellite observations have revealed global patterns of ocean productivity: the most productive regions are coastal upwelling zones (Peru, Benguela, California), high-latitude spring blooms, and equatorial divergence zones. Oligotrophic subtropical gyres appear as vast blue deserts with Chl-a <0.1 mg/m$^3$. Long-term trends from satellite data suggest oligotrophic gyres are expanding under warming, with implications forclimate-driven biodiversity changes.

Simulation: P-I Curves & Sverdrup Critical Depth

Photosynthesis-irradiance curves for different phytoplankton groups and the critical depth model for spring bloom initiation:

Python

script.py128 lines

import numpy as np
import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 2, figsize=(16, 12))
fig.patch.set_facecolor('#0a0a1a')

# --- Panel 1: P-I curves for different phytoplankton ---
ax = axes[0, 0]
I = np.linspace(0, 1500, 500)  # umol photons/m2/s

# Jassby-Platt tanh model: P = Pmax * tanh(alpha*I/Pmax)
groups = [
    ('Diatoms', 8.0, 0.04, '#34d399'),
    ('Dinoflagellates', 4.0, 0.02, '#f87171'),
    ('Coccolithophores', 5.0, 0.03, '#fbbf24'),
    ('Prochlorococcus', 2.5, 0.06, '#818cf8'),
]
for name, Pmax, alpha, color in groups:
    P = Pmax * np.tanh(alpha * I / Pmax)
    ax.plot(I, P, color=color, linewidth=2.5, label=f'{name} (P$_{{max}}$={Pmax})')
    Ik = Pmax / alpha
    ax.plot(Ik, Pmax * np.tanh(1), 'o', color=color, markersize=6)
    ax.axvline(Ik, color=color, linestyle=':', alpha=0.3)

ax.set_xlabel('Irradiance (\u03bcmol photons/m\u00b2/s)', color='white', fontsize=11)
ax.set_ylabel('P (mg C/mg Chl/hr)', color='white', fontsize=11)
ax.set_title('Photosynthesis-Irradiance (P-I) Curves', color='#60a5fa', fontsize=13, fontweight='bold')
ax.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af')

# --- Panel 2: P-I with photoinhibition (Platt model) ---
ax = axes[0, 1]
for beta_val, color, label in [(0, '#34d399', 'No inhibition (\u03b2=0)'),
                                 (0.005, '#fbbf24', 'Mild (\u03b2=0.005)'),
                                 (0.015, '#fb923c', 'Moderate (\u03b2=0.015)'),
                                 (0.04, '#f87171', 'Severe (\u03b2=0.04)')]:
    Ps = 6.0
    alpha_p = 0.04
    P = Ps * (1 - np.exp(-alpha_p * I / Ps)) * np.exp(-beta_val * I / Ps)
    ax.plot(I, P, color=color, linewidth=2, label=label)

ax.set_xlabel('Irradiance (\u03bcmol photons/m\u00b2/s)', color='white', fontsize=11)
ax.set_ylabel('P (mg C/mg Chl/hr)', color='white', fontsize=11)
ax.set_title('Photoinhibition (Platt et al. 1980)', color='#60a5fa', fontsize=13, fontweight='bold')
ax.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af')

# --- Panel 3: Sverdrup critical depth model ---
ax = axes[1, 0]
z = np.linspace(0, 400, 500)
I0 = 800  # surface PAR
Kd = 0.05
alpha_sv = 0.03
R = 0.5  # respiration rate

# Photosynthesis rate vs depth
I_z = I0 * np.exp(-Kd * z)
P_z = alpha_sv * I_z  # linear approximation

ax.plot(P_z, z, color='#34d399', linewidth=2.5, label='Gross photosynthesis')
ax.axvline(R, color='#f87171', linewidth=2, linestyle='--', label=f'Respiration R={R}')

# Critical depth
z_cr = alpha_sv * I0 / (Kd * R)
z_comp = -np.log(R / (alpha_sv * I0)) / Kd
ax.axhline(z_comp, color='#fbbf24', linestyle=':', alpha=0.7, linewidth=1.5, label=f'Compensation depth = {z_comp:.0f} m')
ax.axhline(z_cr, color='#818cf8', linestyle='--', alpha=0.7, linewidth=1.5, label=f'Critical depth = {z_cr:.0f} m')

# Shading: net production vs net loss
ax.fill_betweenx(z[P_z > R], R, P_z[P_z > R], alpha=0.15, color='#34d399')
ax.fill_betweenx(z[P_z < R], P_z[P_z < R], R, alpha=0.1, color='#f87171')

# Mixed layer depths (scenarios)
for ml, ls, lbl in [(50, '-', 'ML=50 m (bloom!)'), (200, '--', 'ML=200 m (no bloom)')]:
    ax.axhline(ml, color='#60a5fa', linestyle=ls, alpha=0.5, linewidth=1)
    ax.text(2.5, ml+5, lbl, color='#93c5fd', fontsize=8)

ax.set_xlabel('Rate (mg C/mg Chl/hr)', color='white', fontsize=11)
ax.set_ylabel('Depth (m)', color='white', fontsize=11)
ax.set_title('Sverdrup Critical Depth Model', color='#60a5fa', fontsize=13, fontweight='bold')
ax.legend(fontsize=8, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white', loc='lower right')
ax.invert_yaxis()
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af')

# --- Panel 4: Seasonal bloom cycle ---
ax = axes[1, 1]
months = np.arange(1, 13)
month_labels = ['J','F','M','A','M','J','J','A','S','O','N','D']

# Mixed layer depth (deep winter, shallow summer)
ml_depth = 250 - 200 * np.sin(np.pi * (months - 2) / 6)**2
ml_depth = np.clip(ml_depth, 20, 300)

# Critical depth (increases with solar angle)
I0_monthly = 200 + 600 * np.sin(np.pi * (months - 1) / 12)**2
z_cr_monthly = alpha_sv * I0_monthly / (Kd * R)

# Chl a (bloom when ML < zcr)
bloom = np.where(ml_depth < z_cr_monthly, (z_cr_monthly - ml_depth) / z_cr_monthly * 10, 0.2)

ax2 = ax.twinx()
ax.bar(months - 0.15, ml_depth, 0.3, color='#60a5fa', alpha=0.6, label='Mixed layer depth')
ax.bar(months + 0.15, z_cr_monthly, 0.3, color='#818cf8', alpha=0.4, label='Critical depth')
ax2.plot(months, bloom, 'o-', color='#34d399', linewidth=2.5, markersize=6, label='Chl a')

ax.set_xlabel('Month', color='white', fontsize=11)
ax.set_xticks(months)
ax.set_xticklabels(month_labels)
ax.set_ylabel('Depth (m)', color='#93c5fd', fontsize=11)
ax2.set_ylabel('Chl a (mg/m\u00b3)', color='#6ee7b7', fontsize=11)
ax.set_title('Spring Bloom: ML vs Critical Depth', color='#60a5fa', fontsize=13, fontweight='bold')
ax.invert_yaxis()
ax.legend(loc='lower left', fontsize=8, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax2.legend(loc='upper right', fontsize=8, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax2.tick_params(colors='#6ee7b7')
ax.grid(True, alpha=0.2, color='#1e40af')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
print('P-I curve and Sverdrup simulation complete')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation: Microbial Loop & Trophic Transfer Efficiency

Carbon flow through the microbial loop and the classical food chain, plus trophic transfer efficiency analysis:

Python

script.py128 lines

import numpy as np
import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 2, figsize=(16, 12))
fig.patch.set_facecolor('#0a0a1a')

# --- Panel 1: Microbial loop carbon flow ---
ax = axes[0, 0]
# Simplified carbon flow model
NPP = 50.0  # Gt C/yr (total ocean NPP)
DOM_fraction = 0.30  # fraction going to DOM
grazing_fraction = 0.50  # direct grazing
sinking_fraction = 0.20  # sinking/other

BGE_values = np.linspace(0.05, 0.60, 200)
DOM_input = NPP * DOM_fraction  # 15 Gt C/yr

# Bacterial production = DOM_input * BGE
bact_prod = DOM_input * BGE_values
bact_resp = DOM_input * (1 - BGE_values)

# Carbon reaching mesozooplankton via microbial loop
# (BGE * flagellate_eff * ciliate_eff)
flag_eff = 0.30
cil_eff = 0.30
to_mesozoo = bact_prod * flag_eff * cil_eff

ax.plot(BGE_values * 100, bact_prod, color='#34d399', linewidth=2, label='Bacterial production')
ax.plot(BGE_values * 100, bact_resp, color='#f87171', linewidth=2, label='Bacterial respiration (CO\u2082)')
ax.plot(BGE_values * 100, to_mesozoo, color='#fbbf24', linewidth=2, label='Reaching mesozooplankton')
ax.axvspan(10, 30, alpha=0.08, color='#60a5fa')
ax.text(20, 12, 'Oligotrophic
BGE', color='#93c5fd', fontsize=8, ha='center')
ax.axvspan(30, 50, alpha=0.08, color='#34d399')
ax.text(40, 12, 'Productive
BGE', color='#6ee7b7', fontsize=8, ha='center')

ax.set_xlabel('Bacterial Growth Efficiency (%)', color='white', fontsize=11)
ax.set_ylabel('Carbon flux (Gt C/yr)', color='white', fontsize=11)
ax.set_title('Microbial Loop Carbon Partitioning', color='#60a5fa', fontsize=13, fontweight='bold')
ax.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af')

# --- Panel 2: Holling Type II functional response ---
ax = axes[0, 1]
C = np.linspace(0, 500, 500)  # food concentration (ug C/L)

for Imax, Khalf, color, label in [
    (50, 50, '#34d399', 'Copepod (I=50, K=50)'),
    (100, 150, '#60a5fa', 'Krill (I=100, K=150)'),
    (200, 30, '#fbbf24', 'Salp (I=200, K=30)'),
    (30, 200, '#f87171', 'Appendicularian (I=30, K=200)')]:
    I_rate = Imax * C / (C + Khalf)
    ax.plot(C, I_rate, color=color, linewidth=2.5, label=label)
    ax.axhline(Imax, color=color, linestyle=':', alpha=0.2)
    ax.plot(Khalf, Imax/2, 'o', color=color, markersize=5)

ax.set_xlabel('Food concentration (\u03bcg C/L)', color='white', fontsize=11)
ax.set_ylabel('Ingestion rate (\u03bcg C/ind/day)', color='white', fontsize=11)
ax.set_title('Holling Type II Functional Response', color='#60a5fa', fontsize=13, fontweight='bold')
ax.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af')

# --- Panel 3: Trophic pyramid ---
ax = axes[1, 0]
levels = ['Phytoplankton
(NPP)', 'Herbivorous
zooplankton', 'Planktivorous
fish', 'Piscivorous
fish', 'Apex
predators']
efficiencies = [1.0, 0.10, 0.10, 0.10, 0.10]

production = [50.0]
for e in efficiencies[1:]:
    production.append(production[-1] * e)

colors_bar = ['#34d399', '#60a5fa', '#818cf8', '#fbbf24', '#f87171']
y_pos = np.arange(len(levels))
bars = ax.barh(y_pos, production, color=colors_bar, height=0.6, edgecolor='white', linewidth=0.5)

for i, (p, level) in enumerate(zip(production, levels)):
    if p > 0.1:
        ax.text(p + 0.3, i, f'{p:.2f} Gt C/yr', color='white', fontsize=10, va='center')
    else:
        ax.text(p + 0.01, i, f'{p:.4f} Gt C/yr', color='white', fontsize=10, va='center')

ax.set_yticks(y_pos)
ax.set_yticklabels(levels, fontsize=10)
ax.set_xlabel('Production (Gt C/yr)', color='white', fontsize=11)
ax.set_title('Trophic Pyramid (\u03b7 = 10%)', color='#60a5fa', fontsize=13, fontweight='bold')
ax.set_xscale('log')
ax.set_xlim(0.001, 100)
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af', axis='x')
ax.invert_yaxis()

# --- Panel 4: Sensitivity to trophic transfer efficiency ---
ax = axes[1, 1]
eta_range = np.linspace(0.05, 0.25, 200)
for level, color, label in [(2, '#60a5fa', 'Level 2 (herbivores)'),
                             (3, '#818cf8', 'Level 3 (planktivores)'),
                             (4, '#fbbf24', 'Level 4 (piscivores)'),
                             (5, '#f87171', 'Level 5 (apex)')]:
    P_level = 50 * eta_range**(level - 1)
    ax.plot(eta_range * 100, P_level, color=color, linewidth=2, label=label)

ax.axvline(10, color='white', linestyle='--', alpha=0.3, linewidth=1)
ax.text(10.5, 20, '\u03b7 = 10%
(typical)', color='#94a3b8', fontsize=9)
ax.set_xlabel('Trophic transfer efficiency \u03b7 (%)', color='white', fontsize=11)
ax.set_ylabel('Production (Gt C/yr)', color='white', fontsize=11)
ax.set_title('Production vs Transfer Efficiency', color='#60a5fa', fontsize=13, fontweight='bold')
ax.legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#1e40af', labelcolor='white')
ax.set_yscale('log')
ax.set_ylim(1e-4, 100)
ax.set_facecolor('#0f0f2a')
ax.tick_params(colors='white')
ax.grid(True, alpha=0.2, color='#1e40af')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
print('Microbial loop and trophic transfer simulation complete')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

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Droop, M. R. (1973). Some thoughts on nutrient limitation in algae. Journal of Phycology, 9(3), 264–272.
Falkowski, P. G. & Raven, J. A. (2007). Aquatic Photosynthesis (2nd ed.). Princeton University Press.
Suttle, C. A. (2007). Marine viruses — major players in the global ecosystem. Nature Reviews Microbiology, 5, 801–812.