Role of food web structures

Drs. L. D. J. Kuijper, Dr. B. W. Kooi, Prof. Dr. S. A. L. M. Kooijman ,

As shown in many natural ecosystems as well as in theoretical exercises, food webs can become unstable when the environment changes. For example, eutrophication with phosphorous has shifted many crystal clear lakes, dominated by water fleas and vascular plants, into muddy pools saturated with blue-green algae. But what exactly drives these changes in trophic structure? In order to make intelligible decisions in conservation biology, we need to fundamentally understand how ecosystems respond to environmental change.

Trophic structure

Organisms interact with each other, and they also interact with their environment. The nature of these interactions, or in other words the ecosystem's architecture, has been shown to be a very important determinant for the dynamic behavior of ecosystems. Classic studies (e.g. Pimm and Lawton) predict that increasing complexity leads to food web destabilization and that, therefore, complex food webs should actually be rare in nature! However, the models involved were extremely simplistic (Lotka-Volterra models with randomized interaction parameters). It was well possible that it was the omission of biological detail that led to the observed destabilization, and not the architecture of the models. Later, improved computer power made it possible to perform numerical bifurcation analysis of food web models with more biological detail. This readily led to a new view, holding that weak trophic interactions may in fact lead to more stable food web structures.

Weak interactions

Strong trophic interactions are quite apparent. Aphids feeding on phloem juices have a strong link with the plants they feed on. The classic food chain (flower-wabbit-cat picture) comprises strong interactions exclusively. As shown by the arrows, the herbivore can only eat plants and the carnivore can only eat herbivores. However, if the carnivore is replaced with an omnivorous species (such as in the flower-wabbit-bear picture) there exist two links towards the highest trophic level, one from the shared resource, and one from the herbivore to the carnivore. If, for instance, only a small fraction of the carnivore's food is from vegetable origin, then the link between the plants and the omnivore species is said to be weak. Weak links are omnipresent in nature, and therefore, if we are to understand dynamics of natural food webs, we should also establish their dynamic effects in model studies.

We studied the effect of an omnivorous link on the dynamics of a mathematical food web model, and compared the results obtained, to similar results derived from a model of a classic food chain. In this case, we used a microbial food web, living in a chemostat, where non-living resources are supplied at a constant rate, and all of the chemostat's constituents are continuously flushed out at a fixed rate to maintain a constant volume. The food web structure is as follows: a producer utilizes the non-living resources, a predator feeds upon producers and an omnivorous species eats predators, as well as producers. It appeared that indeed, the replacement of a top-predator by an omnivore reduced the food-web's potential to oscillate or act chaotically. Enrichment with resources (compare with eutrophication) caused the food web to become unstable, but especially when the omnivore was only weakly linked to the producer species, this effect was far less severe than in the food chain.

Multiple nutrients at play

The former results hold when a single resource dictates the production of the lowest trophic level. However, in reality many nutrients are required for biomass production. The classic law holds that the element which is in shortest relative supply limits the growth of an organism, and in the model above, the dynamics of the population. Now we should remember the food chain where increasing the amount of a single resource (in this case glucose) led to food web instability. But what if this resource ceases to be the limiting one at lower supplies than those that lead to food web destabilization? Increasing glucose availability may cause another compound, let's say manganese, to become limiting, in which case one would not expect much effect from increasing the supply of sugars any further.

The presence of the many non-limiting nutrients in real ecosystems may impose weak interactions on food webs. Maybe, after all, we should not expect food webs to destabilize when we add more resources. Or maybe we need better models that deal with multiple nutrients in the environment, and establish the effects of increasing the particular resources.

Synthesizing units

Traditional methods for modeling multiple nutrient limitation have problems in their mathematical tractability, due to inconvenient switches imposed on those models. In the late nineties, Bas Kooijman proposed a way to circumvent these problems. He assumed that the transformation from the required nutrients into metabolites or biomass is analogous to enzymatic reactions, where substrates are transformed into products. Underlying is the assumption that organisms require all nutrients in fixed proportions for any given process. With slight simplifications from the mathematical formulation of enzyme kinetics, it appears to be possible to have simple equations for modeling stoichiometry in a population/ecosystem context. The Synthesizing Unit (SU) was born. The scheme of the SU shows how it works by taking a very simple example. Suppose that the blue triangle and the red square are packages of substrates, in just the quantities required for the production of some compound. These substrates are, for instance, reserves which are mobilized in the organism. At any time, the SU notices a flux of squares and triangles, and it will pick them up in a process called association. However, when the SU is saturated with blue triangles, it can not bind another of those; it has to wait until it binds a red square and if that happens, production starts. In this case, a nice green circle is produced, but, as things are in nature, this transformation will hardly be 100% efficient and some by-products, indicated as brown stars appear as well. If there is an excess of blue triangles coinciding with a lack of red squares, production is slow. The production is fastest when all substrates are present in the proper proportions.

A stoichiometric model of a food web

The methods above make it possible to create a mathematical food web model in which multiple nutrient limitation is dealt with in a convenient way. We analyzed a model of a small food chain, where algae use minerals of different kinds in order to grow, while grazers feed on these algae. Meanwhile, thanks to realistic formulations of biochemical transformations, unused by-products of any organism, as well as detritus of deceased organisms, can be traced and recycled in the environment, where micro-organisms reduce these compounds to minerals that can be taken up by the algae again. We modeled a fully functional marine ecosystem, including the copepod Acartia tonsa and the diatom Thalassiosira weissfloggii, in this way (see the food-web diagram), and parameterized it using literature data. The model physiologically based model of Acartia tonsa was created in cooperation with Tom Anderson from the Southampton Oceanography Center. We ended up with a number of surprising conclusions. First of all, the food web destabilized at high levels of nitrogen-enrichment, however, if carbon was added in excess to the food web, it remained stable. If carbon however was depleted, the food-web destabilized again. This suggests that a proper relative availability of potentially limiting compounds is important to food web stability, and that the classic "paradox of enrichment" is only an exponent of that. Furthermore, we could see that nutrient limitation on the lowest trophic level did not necessarily lead to limitation at higher trophic levels. Apparently, looking at food webs in a more nutritionally detailed manner enables us to fine-tune our classic ideas on nutrient enrichment and limitation.

Retrospection

What is presented above is elaborated on in my thesis called "The role of trophic flows in food web dynamics". It can be downloaded from this site for free. Do not hesitate to contact me for any questions about the subject, or about my work at the Vrije Universiteit.

For more info on this project, see the Kuijper, 2004.


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