The mathematical core of c-ECO — transforming ecological field data into threshold proximity scores that drive governance activation.
TDR produces two core outputs for each system under observation: P(Θ) — the probability that a threshold will be crossed within a defined window — and τ(P) — the estimated time remaining before that crossing.
// TDR Core Variables P(Θ) = threshold proximity score // 0.0 → 1.0 τ(P) = time-to-threshold estimate // days | months α₁ = alert threshold // P(Θ) > 0.5 α₂ = precaution threshold // P(Θ) > 0.7 α₃ = intervention threshold // P(Θ) > 0.85 τ_c = critical time minimum // emergency trigger // Band assignment IF P(Θ) < α₁ → MONITOR IF P(Θ) ≥ α₁ → ALERT → TFP instruments activated IF P(Θ) ≥ α₂ → PRECAUTION → elevated instruments IF P(Θ) ≥ α₃ → INTERVENTION IF τ(P) < τ_c → EMERGENCY
TDR draws indicators from three domains — ecological, institutional, and financial — recognising that threshold proximity in one domain rarely occurs in isolation.
Deforestation rate · Fire incidence · Rainfall anomaly · Biomass loss rate · Species abundance index · Hydrological regime deviation
Enforcement capacity index · Authority gap score · Cross-scale coordination failure · Legal instrument coverage · Institutional resilience estimate
Resource flow concentration · Extraction rate deviation · Credit exposure to threshold-sensitive assets · Sovereign risk co-movement index
Each proximity band maps to a specific set of TFP governance instruments. The band defines what activates — TDR defines when.
| Band | Condition | TFP Response | Time-to-Threshold |
|---|---|---|---|
| MONITOR | P(Θ) below alert level | Continuous observation, institutional readiness | Extended — no proximate risk |
| ALERT | P(Θ) ≥ α₁ | Enhanced monitoring, stakeholder notification, preparatory instruments | Months — elevated risk |
| PRECAUTION | P(Θ) ≥ α₂ | Precautionary legal instruments activated, resource mobilisation | Weeks — significant risk |
| INTERVENTION | P(Θ) ≥ α₃ | Full instrument deployment, mandatory coordination, elevated authority | Days — critical risk |
| EMERGENCY | τ(P) < τ_critical | Emergency protocols, maximum instrument deployment | Hours — imminent crossing |
The mathematical foundations of TDR are available through c-ECO Publications. Working documents and collaboration proposals welcome through the research team.