Time-Integrated Micronutrient Adequacy and Chronic Safety: A Tissue-Reservoir Model and a Cited One-Compartment Kinetic Model with Homeostatic Absorption

A daily adequacy check asks whether one bowl meets a requirement. It cannot answer the two questions that matter over a feeding lifetime: whether adequacy survives the day-to-day variation of a real diet once tissue stores are allowed to buffer it, and whether the nutrients that accumulate stay bounded rather than drifting toward a ceiling. This paper reports two models addressing the time axis, and gives the parameter set of the second in full. The reservoir model buffers each nutrient by an exponential moving average parameterised by its biological half-life, with a smoothing constant α = 1 − e^(−1/τ) and τ ranging from 7 days for thiamine to 180 days for cobalamin. Because the correction's contribution is constant day to day while the grocery base varies, integrating over the storage horizon can only raise the effective floor relative to a single-day snapshot. Across 2,000 simulated animals over 365 days per species, the reservoir floor returned a Wilson-C95 lower bound of 99.808% for both species with no sub-90% tail at any body weight, copper the tightest nutrient at a 5th percentile of 122% (dog) and 135% (cat) of requirement. The kinetic model answers the standard objection that a moving average is a filter with no physiology. It replaces the average with a one-compartment model carrying explicit homeostatic absorption regulation and first-order clearance, and it is a strict generalisation: setting the absorption exponent p = 1 recovers the reservoir exactly, so the kinetic model can add mechanism but cannot contradict the reservoir's floor result. Its parameter set is tabulated in §4: fourteen nutrients, with the source and confidence grade for each half-life and absorption exponent, species extrapolations marked, and values not found in the literature left blank rather than estimated. Nutrients without a citable absorption curve run at p = 1, taking no regulation credit. The single parameter at which the kinetic model departs from the reservoir is copper's absorption exponent, p = 0.34, derived from a human stable-isotope tracer series. Under it, modelled tissue copper compresses toward its set-point from both directions: the feline median falls from 153% to 116% of requirement and the maximum to 125%, while the 5th percentile remains well above the floor. Section 7 sets that result against the veterinary literature on copper-associated hepatopathy and states its limits.