A Philosophical Analysis of Theoretical Food Web Ecology

Updated on March 28, 2018
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Lili is a Ph.D. student in Theoretical Ecology at the University of Michigan. She has a Masters from the University of Arizona.

A Highly Influential Paper in Food Web Ecology

In the 2000 Nature article ‘Simple rules yield complex food webs,’ Richard J. Williams and Neo D. Martinez introduced the ‘niche model,’ a structural food web model that performed at least an order of magnitude better than previous models. Since then, the publication has accrued 946 citations and stimulated much research. Despite many proposed improvements, the niche model is still the benchmark standard for analyzing empirical food webs and testing the structural fits, computational tractability, and ecological relevance of new food web models.

An Empirical Food Web

A visualization of the empirically-recorded food web of Little Rock Lake, Wisconsin. 997 feedings links (lines) betw 92 taxa (nodes). Color indicates the trophic level of the taxon: (from bottom to top) algae, zooplankton, insects, and fishes.
A visualization of the empirically-recorded food web of Little Rock Lake, Wisconsin. 997 feedings links (lines) betw 92 taxa (nodes). Color indicates the trophic level of the taxon: (from bottom to top) algae, zooplankton, insects, and fishes. | Source

A Visual Illustration of the Niche Model


But Is It "Popperian"?

However, philosopher of science Karl Popper may not have been so enchanted. Williams and Martinez did not explicitly pose hypotheses nor state whether its attempting to reject or support them. The paper implicitly hypothesized that the niche model will better predict twelve properties of seven empirical food webs than previous models, the ‘random’ and ‘cascade’ models. Empirical data was used to test the three food web models and then data was collected and analyzed on the performance of the models. The results indicate that indeed, the average normalized error for the niche model was 0.22 with a standard deviation of 1.8, an order of magnitude better fit to empirical food webs than the cascade model with average normalized error of -3.0 and standard deviation of 14.1. The random model performed much worse with average normalized error of 27.1 and standard deviation of 202. After presenting their results, Williams and Martinez explicitly stated their assumptions and discussed the ecological and computational ramifications of those assumptions. Later perspectives found implicit mathematical assumptions not discussed in the original paper but also have not managed to dramatically improve the original niche model performance.

This method certainly cannot be described as “strong inference.”

The Process of Building Structural Food Web Models

Besides the disapproval Popper would have had to not listing and addressing hypotheses explicitly, he may criticize the whole philosophy behind Williams and Martinez’s model, and therefore the form of their attempt to uncover the mechanisms behind food web assembly, organization, stability, and interconnectedness. Generally, the nature of the model building procedure used in their paper can be described in the following steps:

  1. making ad hoc assumptions,
  2. building a model using those assumptions but also possibly encoding other information, trends, or properties unintentionally,
  3. comparing the model to empirical data and other models,
  4. temporarily accepting the model that is the least bad,
  5. analyzing the model’s structure to determine aspects that make it fit better and aspects that make it fit worse, and finally
  6. attempting to incorporate these discoveries into a new model that also makes ad hoc assumptions
  7. (repeat).

This process, like Platt’s generalization of Popper’s philosophy published in the 1964 Science article ‘Strong Inference,’ is also iterative and so should eventually lead to an optimally predictive model. However, it is fundamentally different from Platt’s process which seeks to iteratively falsify and refine mutually exclusive hypotheses until one is the only remaining explanation. The method used by Williams and Martinez 2000 seeks to simply refine, not necessarily falsify, models until the best approximation is achieved. This method certainly cannot be described as “strong inference.”

Strong inference may even hinder the process of model building for complex, context-dependent, and interconnected systems like food webs.

Does It Matter?

That said, the model building process used by Williams and Martinez 2000 is still efficient and will still reach an optimal conclusion. Furthermore, it avoids the pitfalls of attempting to rule out ‘mutually exclusive’ models, when in fact the optimally predictive model may incorporate structural or qualitative features of more than one of the seemingly ‘mutually exclusive’ models. Indeed, the niche model can be best described as a modified ‘cascade model’ with certain assumptions of the cascade model relaxed and others strengthened. But this modification of the strength of assumptions in the cascade model has led to the currently best description of food web structure—a description that has stood up through 15 years of advances in data and computational tools. So even though it was out-performed by the niche model by an order of magnitude, can the cascade model be said to have been ‘falsified’? By trying to compare mutually exclusive models, would Williams and Martinez have missed the nuance in the quality of assumptions that led to a successful model? It is unclear what Popper would think, but Williams and Martinez 2000 is a prime example of the alternative ways science can progress (and even progress efficiently) outside of the bounds of strong inference. As hinted at in this case, strong inference may even hinder the process of model building for complex, context-dependent, and interconnected systems like food webs.


"Neo D. Martinez." Google Scholar. N.p., n.d. Web. 21 Sept. 2015.<http://scholar.google.com/citations?user=M2XGNO4AAAAJ&hl=en>.

Pascual, Mercedes. “Computational Ecology: From the Complex to the Simple and Back.” PLoS Computational Biology, vol. 1, no. 2, 2005, doi:10.1371/journal.pcbi.0010018.

Pascual, Mercedes, and Jennifer A. Dunne. Ecological Networks: Linking Structure to Dynamics in Food Webs. New York: Oxford UP, 2006. Print. 21 Sept. 2015.

Platt, J. R. "Strong Inference: Certain Systematic Methods of Scientific Thinking May Produce Much More Rapid Progress than Others." Science 146.3642 (1964): 347-53. Web. 21 Sept. 2015.

Shea, Brendan. “Karl Popper: Philosophy of Science.” Internet Encyclopedia of Philosophy, www.iep.utm.edu/pop-sci/.

Williams, Richard J., and Neo D. Martinez. "Simple Rules Yield Complex Food Webs." Nature 404.6774 (2000): 180-83. Web. 21 Sept. 2015.

© 2018 Lili Adams


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