Lordosis as a Conjunctive Reflex: Testing the ARCH × Φ Model of Behavioral Expression

<ns3:p>Background Behavioral expression rarely depends on a single determinant; instead, it emerges from the convergence of neural architecture, neurohumoral state, and contextual input. The lordosis reflex in female rats is a well-characterized model requiring intact hypothalamic circuitry, ovarian steroid signaling, and somatosensory stimulation. Despite decades of empirical study, these dependencies have largely been described qualitatively, without a formal specification of how multiple necessary factors combine to permit or suppress behavioral execution. Methods We apply the ARCH × Φ framework to lordosis, modeling behavioral expression as Φ × (A × D × C), a multiplicative interaction among neural archetype (A), neurohumoral drive (D), and contextual sensory input (C), scaled by a threshold field (Φ) reflecting arousal, neuromodulatory tone, stress, and developmental state. Drawing on lesion, hormone-manipulation, and sensory-deprivation studies, we examine three canonical necessity tests: disruption of the ventromedial hypothalamus (A), ovariectomy without neurohumoral replacement (D), and removal of somatosensory context (C). We additionally perform a quantitative reanalysis of published lordosis quotient data from 10, contrasting additive, threshold-linear, and multiplicative threshold models. Results Across necessity tests, lordosis fails when any single component is reduced below threshold, even when remaining components are intact, supporting conjunctive necessity rather than additive sufficiency. Quantitative fits to classic dose–response data reveal sharp threshold transitions in expression probability that are poorly captured by additive models but well described by multiplicative formulations. Notably, probability of expression saturates rapidly once threshold is crossed, whereas magnitude measures such as lordosis duration continue to increase with hormone dose, demonstrating a dissociation between execution probability and response robustness. Progesterone selectively shifts expression probability more than magnitude, consistent with threshold modulation. Conclusions Lordosis provides a canonical testbed for conjunctive, threshold-governed behavioral control. ARCH × Φ formalizes behavioral convergence, yields falsifiable predictions, and establishes a quantitative framework for statistical model comparison.</ns3:p>