## 5 Discussion
Since all models were confounded with this possibility for human error, we can assume that human error did not influence the analysis by favoring one model over any other. In future work, more accurate and consistent cell counts may be performed with a flow cytometer. Alternatively, a spectrophotometer may be used to approximate algae concentrations. Overall, we suggest that the population growth of _Raphidocelis subcapitata_ is most accurately modeled using the Logistic equation among the simple growth models we investigated. It is important to note that our findings are limited to controlled laboratory settings with unchanging temperature, constant photoperiod, and no change in nutrient availability. For example, we did not consider the possible influence of photoperiod (light/dark) conditions on algae growth. We also did not consider the affect of limiting nutrients such as carbon, nitrogen, phosphorous, or sulfur. The models we investigated here represent our first approximation of algae growth and seemed to fit the data well even without considering how light affects algae growth and that the affect of limiting nutrients could be described by saturating algae growth. The simplifying assumption we made that growth parameters are independent of light conditions may be investigated in future work to yield a closer fit to the data. Our work here serves the purpose of coupling our green algae model with one of zooplankton (_D. magna_) population growth in a laboratory setting, e.g., for toxicity testing, but should not be directly extrapolated to populations in lakes. In order to develop an accurate model of community fluctuations in the field, we will need to consider predation by various zooplankton and microbes, competition with other algae, nutrient fluctuation, abiotic drivers, and habitat heterogeneity. This study is, however, a useful step toward developing a more comprehensive model. In particular, our results showing that a coupling a validated green algae model with a validated daphnia model are important because it exemplifies the possibility of using a mathematical model to recapitulate the oscillatory dynamics seen in nature. In contrast, the previously validated daphnia model that did not include algae dynamics was not able to produce oscillations and only resulted in steady state behavior [5], a result that did not account for the broader range of plankton dynamics seen in natural systems [1]. We note that our ultimate goal is to validate a coupled continuous time daphnia/algae model since continuous time models, such as the Sinko-Streifer model, are described by partial differential equations (PDEs) with a continuously structured variable and can be more amenable to the estimation of age-dependent parameters than a discretely structured model [14; 15; 16; 17]. In this work, we investigated the dynamics of a coupled algae/daphnia discrete-time model as a coarse approximation to understand the qualitative impact of including a dynamic food source on daphnia populations. Our finding that increasing the density-dependent survival constant (\(c\)) in a coupled predator-prey model yields oscillatory dynamics compliments previous work that has predicted limit cycles based on increased mortality [18]. In an ecological setting, changes in the parameter \(c\) could reflect differing nutrient (algae) requirements on the density-dependent survival of daphnia due to differences in species size (e.g., _Daphnia pulex vs. Daphnia magma_) or other increased sources of density-dependent mortality such as predation on daphnia. Changes in \(c\) may also be induced toxicologically. For example, endocrine toxins are known to alter the molt cycle of adult daphids through incomplete ecdysis [19], which may have an indirect affect on density-dependent survival by lowering competition for algae.