Validation of a Mathematical Model for Green Algae (Raphidocelis Subcapitata) Growth and Implications for a Coupled Dynamical System with Daphnia Magna

Abstract

Toxicity testing in populations probes for responses in demographic variables to anthropogenic or natural chemical changes in the environment. Importantly, these tests are primarily performed on species in isolation of adjacent tropic levels in their ecosystem. The development and validation of coupled species models may aid in predicting adverse outcomes at the ecosystems level. Here, we aim to validate a model for the population dynamics of the green algae Raphidocelis subcapitata, a planktonic species that is often used as a primary food source in toxicity experiments for the fresh water crustacean Daphnia magna. We collected longitudinal data from three replicate population experiments of R. subcapitata. We used this data with statistical model comparison tests and uncertainty quantification techniques to compare the performance of four models: the Logistic model, the Bernoulli model, the Gompertz model, and a discretization of the Logistic model. Overall, our results suggest that the logistic model is the most accurate continuous model for R. subcapitata population growth. We then implement the numerical discretization showing how the continuous logistic model for algae can be coupled to a previously validated discrete-time population model for D. magna.

Keywords

• algae growth models
• uncertainty quantification
• asymptotic theory
• bootstrapping
• model comparison tests
• Raphidocelis subcapitata
• Daphnia magna