You are the reserve manager. Over 200 days, steer the lagoon's water level and salinity so that brine-shrimp food thrives, the colony synchronises, builds nests above the flood line and raises chicks to flight.
The science
Water and salt. The lagoon volume V(h) and surface area A(h) come from the real bed height grid of the 3-D model (hypsometry): dV/dt = Qin − Qout − E·A(h) + P·A(h) with weir outflow Qout = A(h) (h − hw)/τ (τ = 1.5 d). Salt is carried by the flows and left behind by evaporation: dS/dt = (QinSin − QoutS − S dV/dt)/V, well mixed, no stratification. Without outflow S·V is conserved, so evaporating a lagoon makes it saltier; with a steady throughflow S = QinSin/Qout.
Food. Brine shrimp and algae (the filter-feeding diet) follow logistic growth dF/dt = r(S)F(1 − F/K(S)) − Nfeed f/V; r and K peak near S ≈ 90 ppt and fall steeply in fresher or hypersaline water (a bell curve; model values). Birds filter at the Holling type II rate f = fmax F/(Kf + F), reduced when the feeding area (depth 5-40 cm) is crowded (2.5 m² per bird). Body condition changes with intake relative to need; birds starving below 0.25 leave.
Synchrony. Breeding readiness is a population of coupled phase oscillators (mean-field Kuramoto model) dθi/dt = ωi + K r sin(ψ − θi) with natural spreads ω uniformly in [−γ, γ] and coupling K proportional to colony size. Below the critical coupling Kc = 4γ/π the colony stays incoherent (r ≈ 0); above it, r jumps (a first-order transition for a uniform spread). Nest building starts when the stimulus G = r + 0.6 condition + 0.4 water suitability exceeds 1.3. This is why small colonies often fail to breed at all.
Nests, eggs, chicks. One egg per nest, laid 5 days after the nest is started, incubation 28 days, 70 days to fledging. Eggs and chicks are tracked as age cohorts; losses: flooding when the water passes the nest height (0.55 m), predation (rises with colony stress), abandonment (low synchrony, stress), starvation (low parental condition). The accounting identity laid = hatched + lost + remaining is checked below.
Simplifications and model values. Zero-dimensional lagoon (no wind mixing or stratification), flat food distribution, all rates are illustrative round numbers, no real site; the real birds' needs and the ranges of salinity vary by species and place. No violence is shown: predation and loss are only counted. Models built with Blender, scene by Three.js.