Seasonal Light and Temperature Timing in a Stoichiometric Food Web
Seasonal food-web interactions can depend on whether consumer performance is high when food quantity and elemental quality are favorable. We extend a closed-phosphorus model containing pelagic and benthic producers, variable producer phosphorus quotas, and a shared Daphnia grazer by allowing annual light and temperature cycles to have an adjustable phase difference. The previous light-seasonality preprint has a nonisolated grazer-free boundary. We parameterize its annual periodic extension by the fraction of producer phosphorus in phytoplankton and derive the unique positive annual producer orbit for every fixed allocation. Linearization in the rare-grazer direction then gives an exact conditional Floquet exponent. Its decomposition into a mean-rate term and a covariance term identifies the effect of seasonal timing. A reconstructed descriptive thermal proxy uses quasi-acclimated filtration-capacity means from the official Muller et al. dataset; it supplies only a relative response shape over 15-25 degrees C, not an absolute ingestion calibration. In a representative configuration, changing phase while preserving the annual light and temperature distributions changes the invasion exponent from -0.00382 to 0.01486 day^-1, with annual multipliers 0.248 and 227, respectively. The constant-mean-ingestion exponent is positive, so the negative case is generated by adverse timing covariance. Sign reversal persists across a range of phosphorus allocations, but not across the entire boundary family. The result is a local invasion criterion for specified grazer-free cycles, not a theorem of global persistence or extinction. Within this parameterized boundary problem, relative seasonal timing can change the sign of infinitesimal consumer growth.