Seasonal Light and Temperature Timing in a Stoichiometric Food Web

Seasonal fluctuations in light and temperature can significantly impact the interactions within a food web, particularly in relation to consumer performance and the availability of favorable food quantity and elemental quality. To account for these seasonal changes, researchers have extended a closed-phosphorus model which includes pelagic and benthic producers, varying producer phosphorus quotas, and a shared Daphnia grazer. The model now allows for adjustable phase differences in annual light and temperature cycles.

The previous version of this preprint had a grazer-free boundary that was not isolated. To parameterize the annual periodic extension of this boundary, researchers used the fraction of producer phosphorus in phytoplankton and derived a unique positive annual producer orbit for every fixed allocation. Linearization in the rare-grazer direction resulted in an exact conditional Floquet exponent, which was then decomposed into a mean-rate term and a covariance term. This decomposition helped identify the effect of seasonal timing on consumer growth.

A reconstructed descriptive thermal proxy was used, which relied on quasi-acclimated filtration-capacity means taken from the official Muller et al. dataset. However, this proxy only provided a relative response shape over a temperature range of 15-25 degrees Celsius, rather than an absolute ingestion calibration.

In a representative configuration, changing the phase of the seasonal light and temperature distributions while maintaining the same annual patterns led to a change in the invasion exponent. This change ranged from -0.00382 to 0.01486 day^-1, with corresponding annual multipliers of 0.248 and 227. The constant-mean-ingestion exponent turned out to be positive, indicating that adverse timing covariance was responsible for the negative case.

The result of this study does not provide a global theorem of persistence or extinction, but rather a local invasion criterion for specific grazer-free cycles. Within the boundaries of this parameterized problem, relative seasonal timing can alter the sign of infinitesimal consumer growth, demonstrating the importance of considering seasonal timing in understanding seasonal food-web interactions.