Statistical validation of structured population models for Daphnia magna

Abstract

In this study we use statistical validation techniques to verify density-dependent mechanisms hypothesized for populations of Daphnia magna. We develop structured population models that exemplify specific mechanisms, and use multi-scale experimental data in order to test their importance. We show that fecundity and survival rates are affected by both time-varying density-independent factors, such as age, and density-dependent factors, such as competition. We perform uncertainty analysis and show that our parameters are estimated with a high degree of confidence. Further, we perform a sensitivity analysis to understand how changes in fecundity and survival rates affect population size and age-structure.

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

“…. , 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).…”

“…In general, we assume that we have an inverse problem for the model observations f (t, θ) and are given n observations with the cost function described above in Equation (5). We are interested in using data to question whether the "true" parameter θ 0 can be found in a subset Ω H ⊂ Ω, for which we make the same assumptions as Banks, Hu, and Thompson [10].…”

“…We note that the continuous models described above were simulated using the ode45 algorithm in Matlab. In order to ensure that the logistic model can be coupled to a discrete time model for a D. magna population in which the population size is updated once per day [5], we investigated the logistic model using a forward Euler scheme that was discretized on an hour basis. In this paper, we refer to this discrete Euler-method logistic model as the DEL model.…”

“…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 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 lentic 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.…”