Year 0Coral cover 0 %Recruits 0Juveniles 0Small 0Mature 0Growth rate λ 1Heat stress calmFPS 0

Drag to orbit, wheel or pinch to zoom. Each coral on the plot stands for the colonies of its stage (counts per 100 m², scaled to fit); pale corals are bleached. The three lenses show a larval cloud, a polyp and its algae symbionts.

Planulae

Polyp

Symbionts

Coral Life-Cycle Lab: From Planula to Colony with a Stage Matrix

A drifting larva becomes a polyp, a branching colony and a mature head. Which step of the life cycle decides whether the reef grows or shrinks?

Environment

Larvae and habitat

Time

Live readouts

Stable stage mix (blue) vs current (orange)

Most important transitions (elasticity of λ)

Colonies per 100 m² by stage

Coral cover (%)

Experiments

Each button projects the expected (deterministic) reef for many settings and tabulates the result.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; four camera presets.
Sliders change the environment immediately; the matrix and λ are recomputed every year. "Chance" switches between random births and deaths (small reefs fluctuate) and the smooth expected values.
"Outplant" adds 10 small colonies, like coral gardening.
Time scale = simulated years per real second.

The science

Stage matrix. Colonies per 100 m² are grouped into recruit polyps R, juveniles J, small colonies S and mature colonies M. One year of life is the projection n(t+1) = A n(t), with survival s_i, growth probability g_i (stay: s(1−g), advance: s g) and fecundity entries from S and M: larvae per colony × settlement success. The yearly planula stage is folded into those entries.

Growth rate and stable mix. The dominant eigenvalue λ (power iteration) is the long-run yearly growth factor; its right eigenvector w is the stable stage distribution and the left eigenvector v the reproductive value. Elasticity e_ij = (a_ij/λ)(v_i w_j)/(v·w) shows which transition changes λ most and always sums to 1. Net reproductive rate R₀ = ρ(F (I − T)⁻¹); λ > 1 exactly when R₀ > 1.

Environment. Heat stress in degree heating weeks (DHW) raises bleaching mortality as a logistic curve centred at DHW 6, scaled by a vulnerability per stage; acidification enters through a calcification factor (Ω_arag − 1)/(3.3 − 1) that slows growth and settlement; habitat quality (clean substrate, grazers keeping algae down) scales settlement; space limits recruitment as 1 − cover/0.8. All parameter values are illustrative model numbers [перевірити за джерелом], not data for any real reef.

Simplifications: one species, no shrinkage or fragmentation, no explicit spawning timing, no larval dispersal between reefs (an optional larval import term stands in), no disease, no adaptation or symbiont switching. Assets built with Blender; scene by Three.js.