## 1 Introduction  
Studies of the population dynamics of phytoplankton and their zooplankton predators in lentiic 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]. The same lake may exhibit stability on a given year but switch to oscillation during the following year, and vice versa. A variety of explanations have been proposed for this behavior in the field, including predator-prey interactions, temperature fluctuations, and external influences on nutrient content [2; 3; 4]. 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 population growth of zooplankton such as _Daphnia magna_[5] and may be an important factor when modeling population dynamics that are observed in lakes and other ecosystems.  
The aim of the present study is to validate and parametrize continuous models for the growth of green algae (_Raphidocelis subcapitata_) in the absence of predation by zooplankton. The broader goal is to couple a validated green algae model with a validated discrete-time population model for _Daphnia magna_[5], and ultimately with an analogous continuous-time model, in order to investigate the possibility of oscillations in the laboratory setting similar to those found in lenti environments. In our previous study of _D. magna_ population dynamics [5], we carried out laboratory experiments in which green algae were fed to _D. magna_ populations on a daily basis, and populations were reared in media optimized for daphnia survival, but not necessarily ideal for algae growth. In particular, it was not known whether green algae could proliferate in daphnia media to an extent that would affect daphnia population dynamics. Thus, it is of central importance to quantitate the rate at which green algae grow in daphnia media and whether this growth has the potential to significantly alter the fecundity and survival of daphnia. In theory, such changes would thereby affect the quantification of population level risk assessments involving experimental exposure of daphnia populations to environmental perturbations, e.g., toxins or temperature change.  
We tested several commonly used growth models for organisms with a limiting nutrient: the Gompertz, the Logistic (continuous and discretized), and the Bernoulli population models. We note that the Bernoulli model is a generalization of the continuous Logistic model, which allows for nested model comparison. Each model has been used to describe populations across many scenarios associated with saturated growth processes in biology. We collected experimental data from three replicates of green algae grown in isolation of predation. We describe goodness of fit of several mathematical models for green algae growth in the context of asymptotic theory and bootstrapping techniques. We provide estimated parameter values and computed confidence intervals for the model predictions. Finally, we implement a numerical scheme that can be used to approximate the concentration of green algae on a daily time scale in order to combine the continuous green algae model that we had the most confidence in with a discrete time population model for _Daphnia magna_. We performed simulations of an unvalidated coupled green algae and daphnia model in order to explore the possible effects of green algae growth on daphnia population dynamics.