The ecosystem model

When I started working with the ecosystem model PCLake, a model that describes the food web of shallow lakes, I first thought it was a better representation of a species community than the food web model. Because PCLake not only takes into account species and their interactions, but also describes the environment and how that interacts with the food web. For example, it takes into account the seasonal cycling of temperature and light dynamics: essential when the model is run over time. Furthermore, not only carbon fluxes are described, but also the cycles of inorganic nutrients such as phosphorus and nitrogen. It encompasses sedimentation and resedimentation, stoichiometry, oxygen dynamics, bioturbation, etcetera.

However, as I started to work with the model, I realised that all this model complexity comes with a cost: it has become a black box. For example, the underlying causes for the regime shift in shallow lakes that the model shows are hard to find, almost as hard as it would be in a real lake, because there are thousands of potential causes, both direct and indirect. The advantage of a modelling approach is that in theory one could actually examine all these thousands of potential causes in a systematic way. Only this would take a very long time. As a side note, compared to the ecosystem model the supposedly less complex food web model still has a level of complexity that it might actually be regarded as a black box as well. For example, if I changed a single interaction strength and watched

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what that did to food web stability (Chapter 2), I often could not explain why stability responded to that changing interaction strength in a particular way. For a two species model, such responses in stability to changing parameters or interactions strengths can be analytically resolved, but for an 18 species model, this is practically impossible.

Still, PCLake allows running the model under different scenarios, by which we can test hypotheses and make predictions. In chapter 4, I used PCLake to investigate what the effects of herbivorous birds are on macrophyte biomass and whether these birds have the potential to facilitate a sudden transition, or catastrophic shift, from a clear to a turbid water state. The outcome was that the impact through bird herbivory becomes greater along the nutrient loading axis, and that catastrophic shifts are indeed facilitated by that. In field studies and experimental set-ups with exclosures, this is rather difficult to observe or to test. The difficulty lies in the different circumstances under which field or experimental studies are performed, which can lead to different conclusions regarding the significance of bird herbivory to macrophytes. In this case, but also in general, using a model is a perfect way to do ‘experiments’ under controlled circumstances. For example, the effects of bird herbivory can be tested for any density of birds, in any time of the year, and under all ‘field conditions’. Once all the conditions have been set, they remain the same throughout the analysis: there will be no sudden change in temperature, no sudden outbreak of a disease, or other unexpected disturbances that could disrupt an experiment. That I used an ecosystem model for this particular question was necessary, given the many biotic and abiotic processes that are known to play a role in the critical transitions in shallow lakes.

There are many differences between the ecosystem model and the food web model. For one, these two models differ in how the species interactions are mathematically defined. The food web model employs proportional type I functional responses, while the ecosystem model employs saturating type II and III functional responses. There is also a difference in model complexity, if you express model complexity in terms of number of equations or parameters. Because the ecosystem model also covers abiotic processes, such as light conditions, temperature, and inorganic nutrient flows explicitly, the number of equations (> 60 for state variables only) and parameters (>400) is much higher than in the food web model (maximum number of equations used here was 19, maximum number of parameters was 52). Because there are so many differences between both models, one would expect the mathematical stability properties of both models to be quite different. Yet, we saw in chapter 5 that both models in fact did give comparable results, when used to analyse what happens to the stability of the clear-water state during eutrophication and the stability of the turbid state during re-oligotrophication.

Regarding the use of type I functional response in the food web model, this

linear functional response is considered to be not very realistic, because it implies that there is no limit to the amount of resource a consumer can eat (which is taken into account by a

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type II functional response). In addition, other factors such as encounter rate at low prey densities or density dependent prey selection (covered by a type III functional response) cause the response of a predator's feeding rate to the number of prey to be nonlinear. So given the somewhat unrealistic assumptions that underlie the type I functional response, are they appropriate to use in food web models? I would say that it depends on the type of analysis that you want to perform. For example, for a time series analysis, I would not recommend to use the food web model with linear functional responses, but to use an ecosystem model instead. However, for local stability analysis the food web model is of value, because I think that it can be seen as a simpler representation of an unknown, more complex model. I think that the results from chapter 5 support this statement. Both the ecosystem model and the food web model show the same result: the stability of the clear- water state decreases under eutrophication. These models are completely different in the (mathematical) way they are defined and in their complexity and yet, decreasing food web stability signalled the critical transition in the lake. So for stability analysis, I would say that generalized Lotka-Volterra models and the interaction strength matrix approach can be used very well to understand how ecosystem states change in terms of their stability (see also