Previously, I have written about how the probabilistic approach to Qualitative Modelling (QM) (e.g. Raymond et al. 2011) can lead to contradictory predictions of species response to a management intervention, and how this is similar to the paradoxes of the Principle of Indifference that we find in the philosophy literature. A reviewer of our new manuscript (Kristensen et al. 2019) asked us an interesting and thought-provoking question: why is it that we think these contradictions matter?

They did not find the contradictory predictions of the probabilistic QM methods to be a problem because it is interesting to learn how different assumptions about how the system works (i.e. the strength of density dependence or the probability distribution of interaction strengths) change the predicted responses of species. In their view, the Boolean approach that we propose is an interesting and different method that can be used, depending on the aim of the research, but framing it as a solution to a philosophical problem seemed off-base.

First, I definitely agree that it is interesting to learn how different distributions influence system behaviour. For example, May (1972) observed that that complex food-web models with randomly-sampled interaction strengths have a low probability of being stable, and that observation prompted the wide-ranging and fruitful complexity-stability debate in ecology. There, the probabilistic approach remains a key tool (Landi et al., 2018). For example, it was later observed that food webs with a skewed distribution of interaction strengths have a higher probability of stability (e.g. McCann et al., 1998), which is the distribution we observe in nature (Paine, 1992; Wootton, 1997; Sala and Graham, 2002; Neutel et al., 2002; Emmerson and 9213 Raffaelli, 2004; Wootton and Emmerson, 2005), and is also the distribution that we’d expect given predator-prey body size difference and feeding inefficiences (Williams and Martinez, 2000; Emmerson and Raffaelli, 2004; Loeuille and Loreau, 2005). However, the question of how different distributions influence system behaviour is not the research question that our paper seeks to address.

The question for us, and ultimately all QM studies, is: how do we obtain the most useful prediction possible that fully accounts for the range of uncertainty? I think that conservation decision-makers are not so much interested in the effect of a particular assumption, but rather they need a QM method that takes into account the full range of uncertainty that all of the different but plausible assumptions represent. The different predictions are interesting in their own right, but they may complicate the decision-makers’ task by shifting the burden of resolving this meta-level of uncertainty from the QM method onto them. Worse, if plausible alternative assumptions exist, but the QM method fails to account for them, then decision-makers may be misled about how that range of uncertainty influences model predictions. These are the problems that our paper seeks to solve.

The reason that I turned to the philosophy literature is because it deals with exactly this problem in its simplest form: how to probabilistically represent complete ignorance of a parameter value. Philosophers warn us that, if we want to model ignorance of interaction-strength values probabilistically, then because of our lack of background information, we will indeed fail to account for a multitude of plausible alternative assumptions and predictions. Further, if the goal of the Qualitative Modelling approach is to account for all of the uncertainty that experts’ ignorance represents, then it must find a way to subsume all of the alternative predictions that arise from the alternative assumptions (i.e. alternative parameter spaces). Finding a way to reconcile alternative predictions from alternative parameter spaces is the PoI problem; therefore in order to solve QM problem, we must solve the philosophical problem that underlies it first.


Emmerson, M. C. and Raffaelli, D. (2004). Predator–prey body size, interaction strength and the stability of a real food web, Journal of Animal Ecology 73(3): 399-409.

Kristensen, N. P., Chisholm, R. A. and McDonald-Madden, E. (2019) Dealing with high uncertainty in qualitative network models using Boolean analysis, Methods in Ecology and Evolution, In press, (Github)

Landi, P., Minoarivelo, H. O., Brännström, Å., Hui, C. and Dieckmann, U. (2018). Complexity and stability of ecological networks: a review of the theory, Population Ecology 60(4): 319-345.

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Raymond, B., McInnes, J., Dambacher, J. M., Way, S. and Bergstrom, D. M. (2011). Qualitative modelling of invasive species eradication on subantarctic Macquarie Island, Journal of Applied Ecology 48(1): 181-191.

Sala, E. and Graham, M. (2002). Community-wide distribution of predator-prey interaction strength in kelp forests, Proceedings of the National Academy of Sciences of the United States of America 99(6): 3678–3683.

Williams, R. J. and Martinez, N. D. (2000). Simple rules yield complex food webs, Nature 404(6774): 180-183.

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Wootton, J. T. and Emmerson, M. (2005). Measurement of interaction strength in nature, Annual Review of Ecology, Evolution, and Systematics pp. 419-444.