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.
Highlights
Studies of the population dynamics of phytoplankton and their zooplankton predators in lentic habitats have found a variety of patterns
These figures contain 68% and 95% confidence bands around the fits to data. These were constructed by generating 1000 random parameter sets from a normal distribution described by the mean and standard error obtained by the asymptotic theory results, computing the model for each of these parameter sets, and calculating the respective confidence intervals from model generated points f, where k = 1, . . . , 1000 [5]
One primary difference between the fits to data that we found was that each model tends to underestimate the initial data and the Bernoulli model provided the closest fit (Figure 4)
Summary
Studies of the population dynamics of phytoplankton and their zooplankton predators in lentic habitats have found a variety of patterns. Plankton communities have been observed to either oscillate in low or high amplitude cycles or to remain relatively stable throughout the year [1]. Fewer studies have attempted to answer the question of what drives these population dynamics in the laboratory setting. Of the predator-prey models that have been proposed for plankton communities, most do not consider certain elements of zooplankton biology such as density-dependent mortality or age-specific fecundity. These traits are crucial for describing the
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