Temporal integration of systemic signals governs biological size and phase transitions

For over a century, developmental phase transitions such as metamorphosis and puberty have been presumed to be triggered by instantaneous spatial size thresholds1-9. Here we overturn this paradigm, demonstrating that biological size and life-history progression are governed by continuous temporal integration. Diverse biological transitions can be understood as manifestations of a single integral threshold mechanism. Our genetic analysis of Myoglianin (Myo), which is a muscle- and glia-derived TGF-β factor10 inducing metamorphosis in the cricket Gryllus bimaculatus, reveals a striking paradox: partial reduction leads to gigantism11,12, whereas complete myo knockout causes permanent developmental arrest13. This proves Myo acts as an essential temporal licensing signal. We formulate the Epigenetic Integration Clock (EIC) model, wherein systemic signals are continuously integrated into an epigenetic state. Phase transitions occur only upon reaching a critical threshold, yielding the Area-Constancy Rule of Epigenetics (Size × Duration ≈ constant). During vertebrate evolution, this temporal integration was decoupled from spatial constraints via the subfunctionalization of Myo into Myostatin (GDF8)14 and GDF1115, enabling extreme body size allometries. This rule naturally derives the quarter-power scaling law of lifespan and resolves the vernalization and the source-sink paradox in plant agronomy. Ultimately, the EIC reveals temporal epigenetic integration as the fundamental principle coupling growth, aging, and biological time across taxa.