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Appl. Sci. 2016, 6(5), 155; doi:10.3390/app6050155

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

1
Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212, USA
2
Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, USA
3
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8212, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Yang Kuang
Received: 31 March 2016 / Revised: 29 April 2016 / Accepted: 5 May 2016 / Published: 18 May 2016
(This article belongs to the Special Issue Dynamical Models of Biology and Medicine)
View Full-Text   |   Download PDF [1155 KB, uploaded 18 May 2016]   |  

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. View Full-Text
Keywords: algae growth models; uncertainty quantification; asymptotic theory; bootstrapping; model comparison tests; Raphidocelis subcapitata; Daphnia magna algae growth models; uncertainty quantification; asymptotic theory; bootstrapping; model comparison tests; Raphidocelis subcapitata; Daphnia magna
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Stemkovski, M.; Baraldi, R.; Flores, K.B.; Banks, H. Validation of a Mathematical Model for Green Algae (Raphidocelis Subcapitata) Growth and Implications for a Coupled Dynamical System with Daphnia Magna. Appl. Sci. 2016, 6, 155.

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