Photosynthesis

For a general introduction to producers, see producers.md. Macrophytes (Salvinia, Cryptocoryne, Vallisneria) share the same photosynthetic model described here but with different light sources and tissue structures; see macrophytes.md for details.

Why Photosynthesis Is the Engine That Runs Everything

Photosynthesis is the only process in the model that creates organic matter and dissolved oxygen from scratch. Every calorie of food in the food web — every milligram of algal biomass that a Daphnia eats, every bacterium that a ciliate captures — traces back to a photosynthetic event that fixed carbon from CO₂ and released O₂ into the water. If photosynthesis stops, the ecosystem has hours to days before oxygen runs out and the food web collapses.

But photosynthesis is not a simple light-in, growth-out machine. It is simultaneously limited by light intensity, CO₂ availability, nitrogen, phosphorus, temperature, and (for diatoms) dissolved silica. These limitations multiply together, so a species that is mildly short of both light and nitrogen grows far slower than one that is severely short of just one. The interplay of these constraints — which nutrient is limiting, on which surface, at what time of day — determines which producer species dominate, how much oxygen the system generates, and whether the daytime surplus can carry the ecosystem through the night.

Gross photosynthesis rate

The starting point for photosynthesis is a maximum rate called P_max, defined at each species' thermal optimum. This is the fastest a species could possibly fix carbon under perfect conditions -- plenty of light, plenty of CO2, plenty of nitrogen, no stress, and at its thermal optimum. P_max varies by species: fast-growing green periphyton have the highest rate (~2.4 doublings/day), unicellular green microalgae are next (~1.9/day), and diatoms are close behind (~1.7/day, shade-tolerant and cold-adapted).

The actual photosynthesis rate is P_max multiplied by a series of limiting factors, each between 0 and 1. They all multiply together, so multiple stresses compound (co-limitation). The gross photosynthesis for a pool of algae biomass is:

gross photosynthesis = P_max × temperature factor × light factor × CO2 factor × nutrient factor × storage factor × salinity factor × [Si factor] × current biomass

The Si factor applies only to diatoms (all other species set it to 1.0 implicitly). It follows Michaelis-Menten kinetics on dissolved silica concentration, with a half-saturation constant of about 2 µmol/L (Sommer 1986). When DSi is exhausted, Si_factor → 0 and diatom photosynthesis stops regardless of how favorable other conditions are.

For green periphyton, there is an additional space factor that reduces growth as the surface fills up (see attachment.md).

This gives units of carbon fixed per hour. On top of this, the total is capped so algae cannot consume more dissolved CO2 than actually exists in the water at that moment.

Light limitation

Algae need light to drive photosynthesis. Growth increases with light intensity but eventually plateaus -- doubling the light beyond a certain point does not double the growth. This relationship follows a saturation kinetics curve (a smooth ramp that flattens out), controlled by a light half-saturation constant. At that light level, the alga is working at half its maximum rate. Below it, growth drops off; well above it, growth is near maximum.

Different species have different light half-saturation values. Diatoms have the lowest (20 µmol/m²/s), making them the most shade-tolerant — this reflects their dominance in turbid or stratified water columns. Green periphyton are next (40). Green microalgae (the functional group representing Scenedesmus, Chlorella, etc.) is 40.

When it is dark (light = 0), photosynthesis shuts off completely. The simulator has a day/night cycle: light is on for a configurable number of hours per day, then off. During darkness, photosynthesis is zero but respiration continues.

Surface-attached algae receive reduced light compared to planktonic algae. Light reaching a surface is computed using Beer-Lambert attenuation through the water column:

surface light = incident light × geometric light fraction × exp(-(phytoplankton attenuation × [planktonic C] + background attenuation) × depth)

The geometric light fraction (0-1) represents factors like orientation and obstruction. On top of this, the water column above the surface absorbs light based on planktonic algae density, background water absorption (default 0.05 per meter), and the depth of the surface. Each surface can have its own depth; if not set, the jar's overall depth is used. This means surfaces at the bottom of a deep jar dynamically receive less light as planktonic algae grow denser.

Mat self-shading

In addition to the surface light fraction, dense mats of surface-attached algae shade themselves. When filamentous algae accumulate on a surface, light is attenuated through the mat following a Beer-Lambert law. The model computes the average light intensity across the mat depth by integrating the exponential decay:

effective light = incident light × (1 - exp(-τ)) / τ

where τ = k_mat × biomass density (mol C per m² of surface area). The mat attenuation coefficient varies by species. Unicellular algae like green microalgae (Scenedesmus, Chlorella, etc.) have no mat self-shading since they do not form coherent mats.

At low biomass densities, mat self-shading has negligible effect. As mats become dense, it progressively reduces the effective light reaching cells in the interior, limiting further growth.

CO2 limitation (carbon supply)

Algae fix dissolved CO2 into organic carbon. CO2 enters the cell by passive diffusion, and like every other limiting substrate it follows a Michaelis-Menten curve with its own half-saturation constant (K_CO2).

But CO2 is not the only carbon source available. Water also contains bicarbonate (HCO3-), which is far more abundant than dissolved CO2 at higher pH (in hard water at pH 8 the bicarbonate pool is roughly a thousand times the dissolved CO2 pool). Many algae and aquatic plants have "carbon concentrating mechanisms" (CCMs) -- active membrane pumps that grab bicarbonate from the water and feed it into the photosynthetic machinery.

Because the two carbon sources move into the cell through entirely different pathways, the model treats them as two separate Michaelis-Menten terms that add together:

CO2_factor = CO2 / (K_CO2 + CO2) + HCO3_efficiency × Zn_CA × HCO3 / (K_HCO3 + HCO3)

(capped at 1.0)

• The first term is passive CO2 diffusion. K_CO2 is small (typically 5-25 µmol/L) because diffusion is fast and tracks RuBisCO's intrinsic affinity.
• The second term is active bicarbonate uptake via the CCM. K_HCO3 is much larger (typically 200-2500 µmol/L) because the saturable transporter capacity sets the ceiling, not RuBisCO. The Zn_CA factor gates this term: carbonic anhydrase needs zinc, so a Zn-starved cell loses bicarbonate use but retains diffusional CO2.
• HCO3_efficiency is the per-species ceiling on the bicarbonate contribution -- the fraction of saturating CO2-driven photosynthesis that fully-saturating bicarbonate can substitute for.

Treating the two pathways with separate kinetics matters in hard water. A naive single-Monod-on-summed-substrate would saturate at >99% no matter what dissolved CO2 does, because bicarbonate at 15 mmol/L is ~1500× the K_CO2 of diffusion. Splitting them keeps the bicarbonate term saturated against transporter capacity, while the CO2 term still moves with the daytime CO2 drawdown. This is what produces the natural afternoon-pH-ceiling feedback: as photosynthesis pulls CO2 down, the diffusion term drops, and even a strong bicarbonate user has to slow down.

Per-species K_HCO3 ranges from ~200 µmol/L (cyanobacteria, with the most aggressive CCM transporters) up to ~2500 µmol/L (Salvinia, a C3 fern with little active uptake). Strong bicarbonate users in the model:

• Cyanobacteria: HCO3_efficiency 0.60, K_HCO3 0.2 mmol/L -- carboxysome-based CCM, the most efficient bicarbonate transport in any phototroph
• Hornwort: HCO3_efficiency 0.45, K_HCO3 0.6 mmol/L -- one of the most aggressive HCO3 strippers among freshwater macrophytes
• Vallisneria: HCO3_efficiency 0.40, K_HCO3 0.8 mmol/L -- the strongest bicarbonate user among the tracked rooted macrophytes
• Green periphyton: HCO3_efficiency 0.30, K_HCO3 0.8 mmol/L -- moderate CCM, slightly higher affinity than free-living planktonic greens
• Green microalgae: HCO3_efficiency 0.25, K_HCO3 1.0 mmol/L -- moderate CCM
• Duckweed: HCO3_efficiency 0.25, K_HCO3 1.5 mmol/L
• Diatoms: HCO3_efficiency 0.15, K_HCO3 1.2 mmol/L -- weaker CCM, leans on CO2 diffusion
• Salvinia: HCO3_efficiency 0.15, K_HCO3 2.5 mmol/L -- C3 fern with no real CCM
• Cryptocoryne: HCO3_efficiency 0.0 -- no bicarbonate use at all; relies on CO2 from sediment pore water via root aerenchyma

This means at high pH (where most dissolved inorganic carbon is bicarbonate rather than CO2), species like cyanobacteria and Hornwort have a significant advantage over species that rely mainly on diffusional CO2.

Nutrient limitation (nitrogen and phosphorus)

Algae need nitrogen to build proteins, DNA, and chlorophyll, and phosphorus to build DNA, RNA, ATP, and cell membranes. The model tracks two forms of dissolved nitrogen: ammonium (NH4) and nitrate (NO3), and one form of dissolved phosphorus: orthophosphate (PO4). Algae can use either nitrogen form, but they prefer ammonium because it takes less energy -- nitrate has to be chemically reduced before it can be used, and that reduction requires energy from light.

Every algal class in the model uses internal-quota Droop kinetics for both nitrogen and phosphorus. Each cell carries a separate luxury reservoir (representing polyphosphate granules for P, cyanophycin granules / vacuolar nitrate / free amino acids for N) at every growth location. Two things are decoupled from each other:

• Luxury uptake from PO4, NH4, and NO3 fills the corresponding reservoir at a saturating rate, gated by how full it already is. Cells aggressively pull nutrients from the water when their reservoir is empty and water-column nutrients are available — the canonical "post-bloom water clarity" effect, where a green-water bloom can drain dissolved P to nM levels even though the cells are not currently dividing.
• Growth is gated by the cellular quota Q = stored / biomass C through the Droop factor 1 - Q_min/Q, falling to zero as Q approaches Q_min and to its maximum near Q_max.

This decoupling produces realistic delays that an older single-Monod scheme cannot. When water-column N or P crashes, cells continue growing on stored reserves for several days before the quota draws down enough to halt division — typically 3–7 days for greens, longer for cyanobacteria with their large cyanophycin reservoirs. When the nutrient returns (water change, mineralization pulse), cells take 12–48 h to refill reservoirs before division resumes. This is the lag structure that hobbyists observe in real systems and that earlier model versions compressed into one time step.

How much each class can stockpile

Each algal class keeps its nitrogen and phosphorus reserves in different organelles, and that sets how big a reserve it can build (Reynolds 2006; Sterner & Elser 2002; Healey 1973):

Diatoms store the most phosphorus, packing polyphosphate granules that can reach roughly 5% of their cell carbon. Cyanobacteria store the most nitrogen: cyanophycin (a polymer of arginine and aspartate) can hold about a quarter of their cellular carbon as nitrogen. That cyanophycin reserve is also where nitrogen-fixing cyanobacteria stash the nitrogen they fix, and it drives the canonical post-bloom pattern where a cyanobacterial mat keeps fixing N₂ for days after the ammonium and nitrate in the water are gone. The exact minimum and maximum quotas for each class are tabulated in the Parameter Reference.

Macrophytes store reserves too. Floating fronds (Salvinia, duckweed) and rootless submerged stems (Hornwort) play the same internal-reserve game as algae — stockpiling phosphorus and nitrogen inside their tissue and then growing on the reserve for several days after the water column crashes. Their reserves are smaller than a cyanobacterium's, because vascular plants lack a dedicated nitrogen-storage protein like cyanophycin, but the dynamics have the same shape: they take up nutrients aggressively when starved tissue meets a fresh supply (Paterson et al. 2020 on duckweed polyphosphate; Pedersen et al. 2013 on submerged-plant phosphate affinity). Rooted macrophytes (Vallisneria, Cryptocoryne) draw on two supplies at once — nutrients from the water column through their leaves and from the sediment pore water through their roots.

Stocking up while the water empties

The transporters that fill these reserves have a higher affinity for scarce nutrients than the machinery that gates growth. They keep pulling phosphate, ammonium, and nitrate from the water down to a few thousandths of a milligram per litre — well below the level that would still support cell division. This is what produces the "drain-to-nanomolar" signature of eutrophic lakes and the eerily empty water column left behind after an aquarium bloom: the cells are still stocking their reserves long after the water looks stripped. The exact uptake half-saturations are listed in the Parameter Reference.

Combined nutrient limitation (Liebig's law)

The Droop factors for nitrogen and phosphorus are combined with each other (and with the Liebig gates on K, Si, and Fe where present) by taking the minimum of the per-element gates: growth is controlled by the most constrained reservoir. The combined nutrient factor replaces the nitrogen-only factor in the photosynthesis equation above.

Uptake partitioning between NH4 and NO3

The total N luxury uptake rate is partitioned between the two nitrogen forms by a weighted preference. Each form has its own Michaelis-Menten affinity constant. On top of this, nitrate uptake is scaled by a light-dependent preference factor. In darkness, algae strongly prefer ammonium (nitrate preference drops to ~10 % of its light value), because nitrate reduction needs light-derived energy. In full light, nitrate preference rises (to ~50–60 % of the ammonium weight). The final uptake is split between the two sources proportionally to these weights, with the same Mo-cofactor gate that governs nitrate reductase activity.

Photosynthetic-quotient (PQ) correction at the uptake side

When algae assimilate nitrate, the reduction of NO3 to NH4 inside the cell requires extra electrons from water splitting, producing 2 mol O2 per mol NO3 reduced. Under the Droop scheme this PQ correction is applied at the moment of luxury uptake (when nitrate is actually being reduced), not at growth time, which preserves the correct stoichiometric coupling between uptake and O2 evolution even when uptake and growth are temporally separated.

Initial-quota seeding

Each scenario can set how full the phosphorus and nitrogen reserves are when the simulation begins. By default they start half-full — representing "average tank water" cells that are neither pre-loaded nor pre-starved. A scenario can instead start the cells almost empty (so that the arrival of a nutrient pulse shows up unambiguously) or nearly full (so that a starvation lag does), which is how the calibration scenarios isolate each effect.

Photorespiration

This is an important and somewhat counterintuitive process. The key enzyme in photosynthesis, RuBisCO, is not perfectly specific for CO2 -- it can also grab O2 by mistake. When it grabs O2 instead of CO2, the result is a wasteful process called photorespiration that consumes energy without producing useful carbon. Think of it like an engine that occasionally misfires -- the machinery is running, but some of the cycles produce nothing useful and actually waste fuel.

The ratio of useful work to wasted work depends on the ratio of O2 to CO2 at the enzyme. When O2 is high relative to CO2 (which can happen in a sealed jar where photosynthesis has been pumping out oxygen and consuming CO2), photorespiration becomes significant.

Each species has a "RuBisCO specificity factor" that describes how good its RuBisCO is at preferring CO2 over O2. Higher values mean better selectivity:

• Green microalgae and green periphyton: 80

The model computes two correction factors from the O2/CO2 ratio and the specificity factor:

1. Net carbon factor: How much of the gross carbon fixation actually results in usable carbon. Each oxygenation event wastes about half a carbon unit through a recovery pathway (the glycolate pathway). This factor can drop to zero at very high O2/CO2 ratios, meaning photosynthesis produces nothing useful.

2. Net O2 factor: How much oxygen is actually produced. This is worse than the carbon factor because each oxygenation event consumes about 1.5 units of O2 (1 at RuBisCO itself plus 0.5 at a downstream enzyme). This factor can actually go negative, meaning the photosynthetic machinery is consuming more oxygen than it produces -- a net O2 sink even though the light reactions are running.

In practical terms, photorespiration becomes noticeable in sealed systems where O2 builds up and CO2 gets depleted. It acts as a natural brake on runaway oxygen production.

Carbon-concentrating mechanisms relieve photorespiration

There is an important interaction between the CCM (bicarbonate use, above) and photorespiration. The whole point of a carbon-concentrating mechanism is to pump CO2 up at the RuBisCO active site — so a cell that is meeting its carbon demand through bicarbonate is also presenting RuBisCO with far more CO2 than the bulk-water dissolved-CO2 level would suggest. A strong bicarbonate user should therefore suffer little photorespiration even when ambient dissolved CO2 is low, because internally CO2 is concentrated.

The model captures this without a separate parameter: the O2/CO2 competition reads an effective CO2 equal to the level that would, by passive diffusion alone, produce the carbon-supply factor the cell actually achieved (K_CO2 × CO2_factor / (1 − CO2_factor)), capped at 10× ambient (aquatic CCM internal:external CO2 ratios run ~3–40×; Raven 1991, Maberly & Madsen 2002). By construction this reduces exactly to ambient CO2 for a species with no bicarbonate use (Cryptocoryne, with HCO3_efficiency = 0), so the relief is self-targeting: it only lifts photorespiration for the degree of CCM activity actually in play. For a strong stripper like Hornwort in soft, ambient-CO2 water this is the difference between losing ~20% of fixed carbon to photorespiration and losing almost none — which is what lets a low-tech submerged plant be a (modest) ammonia sink rather than barely covering its own maintenance respiration.

Temperature response

Photosynthesis: thermal optimum curve

Photosynthesis does not increase monotonically with temperature. Real algae have an optimal temperature for photosynthesis and decline sharply above it. The model uses a thermal optimum curve:

• Below T_opt: Photosynthetic rate follows Q10 scaling downward from the peak. At 10 degrees below T_opt, the rate is roughly half.
• At the thermal optimum: Photosynthetic rate is at its maximum (the maximum rate is defined at this temperature, following standard phycological convention).
• Above T_opt: Photosynthetic rate declines linearly to zero at T_max (the lethal high temperature). This models protein denaturation and membrane damage at supraoptimal temperatures.

The thermal optima vary considerably by species:

This means cool-water species like centric diatoms (T_opt = 16°C) photosynthesize at reduced rates when run at 25°C, which is well above their optimum. This is scientifically correct -- the old monotonic Q10 model erroneously treated them as producing at peak rate at any temperature above their reference.

Respiration and mortality: Q10 scaling

Respiration and mortality still use simple Q10 scaling (monotonic increase with temperature), since these processes do not have a sharp thermal optimum like photosynthesis. Respiration Q10 ranges from 2.1 to 2.2 across species, which is slightly higher than the Q10 used for photosynthesis below T_opt -- this means at very warm temperatures, respiration increases faster than photosynthesis, creating an energy deficit.

Salinity response

All algae species in the V1 (freshwater-only) product have a Gaussian (bell-curve) salinity response centered at low salinity (0.5-2 PSU) with narrow tolerance. They grow best in fresh or nearly fresh water, and growth drops off at higher salinities.

Respiration

Maintenance respiration is the ongoing energy cost of staying alive. It runs 24 hours a day, during both light and dark periods, consuming oxygen and releasing CO2 at a 1:1 ratio. The rate is proportional to the organism's total carbon biomass, scaled by temperature via Q10. Respiration Q10 ranges from 2.1 to 2.2 across species, which is slightly higher than for photosynthesis -- this means respiration increases with temperature slightly faster than photosynthesis does. At very warm temperatures, algae can find themselves in an energy deficit where respiration outpaces photosynthesis.

O2 limitation on respiration

Respiration requires oxygen. When dissolved O2 is low, respiration slows down following Michaelis-Menten kinetics with a half-saturation constant (K_O2_respiration). Algae have moderate O2 affinity (~0.4-0.5 mg/L half-saturation), allowing them to maintain respiration at low oxygen levels.

Osmoregulation cost

For species in water that differs from their optimal salinity, osmoregulation — maintaining internal ion balance — costs extra energy. The model increases respiration by a factor proportional to how far the current salinity is from the species' optimum. For example, at 40 PSU deviation with a cost of 0.002 per PSU, respiration increases by 8%.

The per-PSU cost varies by species:

• Green microalgae: 0.003

DOC excretion

Algae actively excrete a fraction of their photosynthetically fixed carbon as dissolved organic compounds (DOC). This includes glycerol, polysaccharides, amino acids, and other small molecules that leak or are secreted through the cell membrane. The literature reports 5-30% of fixed carbon being excreted (Fogg, 1983).

The model applies a DOC excretion fraction to net photosynthetic carbon fixation. The excreted carbon is routed to the dissolved organic matter (DOM) pool, where it becomes available to heterotrophic bacteria. The CO2 consumed during fixation is not affected -- the cell consumed the CO2 to build the molecule, then excreted it as organic carbon rather than incorporating it into biomass.

Excretion fractions vary by species:

This means the carbon available for growth (and thus nitrogen and phosphorus uptake) is reduced by the excretion fraction. A species with 10% DOC excretion grows 10% slower than it would without excretion, but the excreted carbon fuels the microbial loop.

Stoichiometry

The model tracks how photosynthesis moves specific nutrients between pools:

• Carbon: For every unit of net carbon fixed, one unit of dissolved inorganic carbon (DIC) is consumed from the water.
• Oxygen: For every unit of gross carbon fixation, one unit of O2 is produced (before photorespiration adjustments). After photorespiration, the net O2 production may be less than gross, or even negative. Additionally, when algae assimilate nitrate (NO3), the reduction of NO3 to NH4 inside the cell requires extra electrons from water splitting, producing 2 extra mol O2 per mol NO3 assimilated. This PQ (photosynthetic quotient) correction means systems where algae rely heavily on nitrate produce slightly more O2 than those using ammonium.
• Nitrogen: For every unit of nitrogen taken up, cn_ratio units of carbon are incorporated into structural biomass. Any extra fixed carbon beyond this goes to storage (tracked as an increased C:N ratio).
• Phosphorus: For every unit of carbon fixed, P uptake is determined stoichiometrically: P = C / (C:N ratio x N:P ratio). All species use a molar N:P ratio of 16 (Redfield ratio). Phosphorus uptake is capped at available PO4.
• Alkalinity: Taking up ammonium (NH4) decreases alkalinity. Taking up nitrate (NO3) increases alkalinity. Phosphate uptake does not significantly affect alkalinity. This affects pH -- systems where algae primarily consume ammonium will tend to acidify, while those where algae consume nitrate will tend to become more alkaline.
• Respiration: Consumes O2 and releases CO2 (added back to DIC) at a 1:1 ratio.

Mortality losses: senescence, environmental stress, and viral lysis

Photosynthesis builds biomass; three loss processes tear it down. Background mortality (senescence) is a small constant rate of about 5% per day, capturing the cellular wear that ends a cell's life even under perfect conditions. Environmental stress mortality adds extra deaths when temperature, salinity, pH, or hypoxia push the species past its tolerance. Both apply equally to planktonic and surface-attached cells.

Planktonic phytoplankton face a third loss term that surface-attached cells do not: viral lysis. Cyanophages, chloroviruses, and diatom-infecting viruses encounter free-swimming host cells in proportion to host density, so the lysis rate climbs as a bloom develops — and frequently terminates it before grazing or nutrient depletion would. The simulator caps cyanobacterial viral lysis at about 60%/day (driven by the ferocity of cyanophages on Microcystis-type blooms; see Suttle 2007), and green-algal / diatom viral lysis at about 30%/day. Realised rates at typical aquarium bloom densities sit around 10–25%/day.

Lysed cells release their cytoplasm as labile DOM, not particulate detritus — the viral shunt. This DOM is rapidly consumed by heterotrophic bacteria, who release inorganic N and P back to the water column, where surviving algae and biofilm cells can take it up again. So a viral phytoplankton crash is not a clean removal of biomass: it triggers a transient bacterial bloom and accelerated nutrient turnover, often visible in the simulator output as a bacterial spike following an algal peak. Surface-attached (biofilm) algae are exempt from viral lysis in the model — pelagic viruses don't penetrate the EPS matrix at meaningful rates — which gives benthic forms a competitive opening when planktonic competitors crash.

For full mortality details (including environmental-stress curves, additive stacking, and the parameter values for each density-dependent term), see Mortality Mechanisms.

Extinction threshold

To prevent unrealistic behavior where a tiny trace of biomass (representing a fraction of a single cell) can regrow into a full population, the model supports an extinction threshold. If the total nitrogen biomass of a species drops below this threshold (configured in milligrams of nitrogen per species), photosynthesis is disabled -- the maximum growth rate is set to zero. The remaining biomass continues to die via normal mortality processes until it reaches zero.

This ensures that populations can go locally extinct rather than always recovering from infinitesimal levels. The threshold is configurable per species in the scenario YAML file.

Summary of species differences

Further Reading

• Macrophytes -- macrophyte-specific photosynthesis details (root CO2 uptake, shoot-root partitioning)
• Algae Settlement and Surface Dynamics -- how surface position and light affect attached algae growth
• Biofilm Nutrient Enrichment -- why surface-attached producers grow faster than expected from bulk water nutrients
• Carbon Cycle -- the complete carbon budget including DIC fixation and organic carbon pools
• Oxygen Cycle -- O2 production from photosynthesis and the day/night balance
• Light and Temperature -- the physical light model driving photosynthetic rates