Linking individual-based modelling and Dynamic Energy Budget theory: lessons for ecology and ecotoxicology
Benjamin Martin, PhD project, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
My research deals with bridging the gap between risk assessment and management. Currently within the EU risk is typically assessed at the level of the individual through standardized tests either on survival, or some individual life history output such as reproduction. Risk management, or at least the goals of risk management within the EU are to protect populations, communities, and ecosystems and the services they provide. Thus bridging the gap between risk assessment and management, entails understanding how effects observed at the individual level (in standardized tests) related to those at higher levels of biological organisation. My research, focuses specifically of bridging the gap between dynamics at the individual and population level.
To extrapolate from effects at the individual level to the population level I use Individual-based models (IBMs). As the words “individual-based” suggest, the focus of IBMs is on individuals. IBMs are developed by trying to specify as simply as possible, how individual processes (growth, reproduction, dispersal, etc.) are influenced by both the environment (food availability, temperature), and the characteristics of the individual (size, age). The level of detail, and the number of processes considered in an IBM depends on the research question you want to address with an IBM. For the case of understanding how toxicants alter population dynamics, at minimum our IBMs need to capture how individuals growth, reproduce, and survive as a function of the food and toxicant in the environment. Once you have defined the behavior of individuals, you can then run computer simulations with different environmental conditions, including the presence of a toxicant. Population-level patterns, such as the density or size structure of a population over time emerge from the behavior of individuals.
Because the processes important for population dynamics (growth, reproduction, and survival) are dependent on energy, and the laws of thermodynamics gives us reliable constrains, using energy-budgets are a useful foundation for IBMs. As the basis for my IBMs, I use an exisitng mass balance approach, the Dynamic Energy Budget theory (http://www.bio.vu.nl/thb/deb/). Often a toxicant can cause sub-lethal effects at lower doses than mortality is observed. These sub-lethal effects often reduce the amount individual grows or reproduces. Using an energy budget approach we can consider these effects, by linking the internal concentration of a toxicant to a change in a parameter that alters the energy fluxes within an organisms and ultimately leads to different growth and reproduction trajectories. For example a toxicant may reduce the feeding rate of an organism. The figures below demonstrate how a reduction in feeding activity can lead to reductions in growth and reproduction.
The dynamic energy budget theory has been used extensively at the individual level, however DEB has been rarely used in a dynamic population context. To facilitate and encourage further use of this powerful approach at the population level we developed DEB-IBM, a generic an accessible implementation of Dynamic Energy Budget theory. We implemented the DEB-IBM in Netlogo (http://ccl.northwestern.edu/netlogo/), a free and easy to programming environment designed specifically for the implementation of IBMs. The DEB-IBM framework was recent published in Methods in Ecology and Evolution where the paper can be freely downloaded: http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2011.00168.x/abstract
The program, a detailed model description, and a user manual showing how the model can be adapted to specific research questions can be downloaded here: DEB-IBM
We used the DEB-IBM framework to extrapolate from individuals to population with Daphnia magna. Our inital work focused on testing whether the model when parameterized at the individual-level was able to predict population dynamics. We used experimental population data from (Preuss 2009) to compare model predictions against. We found that the model parameterized at the individual-level was able to accurately predict dynamics during the population growth phase. However after the population peak, model predictions and experimental observation diverged (figure below, left panel). We hypothesizes that this was due to starvation related mortality not being correctly considered in the model. We then tested a series of starvation submodel that had different size dependence (eg. juveniles are more vulnerable to starvation, equal starvation tolerance, or adults more vulnerable). We found that the model and data agreed best at the population level when starvation vulnerability was greatest for juveniles.
With the additional 1 parameter starvation submodel, the DEB-IBM model was able to predict population dynamics (both total density and size structure) at multiple food levels and intital conditions.
We are now in the process of using this model for predicting the effects of pesticides and comparing how different physiological modes of action at the individual level translate to the population level.