Tensor-Based Detection of Developmental Regime Shifts in C. elegans

Developmental bifurcations are difficult to predict due to latent phenotypic heterogeneity. Traditional models like Boolean networks often fail to capture the continuous accumulation of stress preceding these shifts. We introduce a Tensor Deviation Framework (TDF) that quantifies latent variance via a deviation tensor $\mathcal{D} = \langle \pobs, \resid, \tng \rangle$. This formalism integrates genotype, phenotype, and environment into a unified state space ($V_G \otimes V_F \otimes V_E$), allowing for a rigorous calculation of stability metrics. Applied to the \textit{C. elegans} dauer pathway (n=191), we detect a pre-regime-shift signature in DAF mutants under optimal conditions ($\|\pobs - \resid\| = 0.34$, $H=0.43$, $p<0.001$). Environmental stress triggers a first-order transition at $\tng = 147$ generations to a dauer attractor. We identify specific temporal operators for developmental robustness and environmental forcing. Out-of-sample validation shows 12\% prediction error and a Detection Advantage Index (DAI) of 0.74, significantly outperforming ARIMA and Boolean networks. TDF provides a generalizable, quantitative early-warning system for developmental plasticity that can be applied to other complex biological bifurcations. \textbf{Keywords:}\textit{C. elegans}, developmental plasticity, tensor algebra, regime shifts, early-warning signals