Different sources of uncertainty are known to affect our ability to predict ecological dynamics (Petchey et al. 2015). However, the consequences of uncertainty on prediction biases have been less investigated, especially when predictions are scaled up to higher levels of organisation as is commonly done in ecology for instance. The study of Orr et al. (2020) addresses this issue. It shows that, in complex systems, the uncertainty of unbiased predictions at a lower level of organisation (e.g. species level) leads to a bias towards underestimation of change at higher level of organisation (e.g. ecosystem level). This bias is strengthened by larger uncertainty and by higher dimensionality of the system.
This general result has large implications for many fields of science, from economics to energy supply or demography. In ecology, as discussed in this study, these results imply that the uncertainty of predictions of species’ change increases the probability of underestimation of changes of diversity and stability at community and ecosystem levels, especially when species richness is high. The uncertainty of predictions of species’ change also increases the probability of underestimation of change when multiple ecosystem functions are considered at once, or when the combined effect of multiple stressors is considered.
The consequences of species diversity on ecosystem functions and stability have received considerable attention during the last decades (e.g. Cardinale et al. 2012, Kéfi et al. 2019). However, since the bias towards underestimation of change increases with species diversity, future studies will need to investigate how the general statistical effect outlined by Orr et al. might affect our understanding of the well-known relationships between species diversity and ecosystem functioning and stability in response to perturbations.
Cardinale BJ, Duffy JE, Gonzalez A, Hooper DU, Perrings C, Venail P, Narwani A, Mace GM, Tilman D, Wardle DA, Kinzig AP, Daily GC, Loreau M, Grace JB, Larigauderie A, Srivastava DS, Naeem S (2012) Biodiversity loss and its impact on humanity. Nature, 486, 59–67. https://doi.org/10.1038/nature11148
Kéfi S, Domínguez‐García V, Donohue I, Fontaine C, Thébault E, Dakos V (2019) Advancing our understanding of ecological stability. Ecology Letters, 22, 1349–1356. https://doi.org/10.1111/ele.13340
Orr JA, Piggott JJ, Jackson A, Arnoldi J-F (2020) Why scaling up uncertain predictions to higher levels of organisation will underestimate change. bioRxiv, 2020.05.26.117200. https://doi.org/10.1101/2020.05.26.117200
Petchey OL, Pontarp M, Massie TM, Kéfi S, Ozgul A, Weilenmann M, Palamara GM, Altermatt F, Matthews B, Levine JM, Childs DZ, McGill BJ, Schaepman ME, Schmid B, Spaak P, Beckerman AP, Pennekamp F, Pearse IS (2015) The ecological forecast horizon, and examples of its uses and determinants. Ecology Letters, 18, 597–611. https://doi.org/10.1111/ele.12443
I have now received two reviews of your manuscript. Both reviewers and I are in agreement that this is an interesting study considering how scaling up uncertain predictions of individual properties in complex systems affects the estimation of system-level properties. The results have important implications in ecology as well as in other research disciplines. However, several issues have been identified which, in my views, require revision before recommendation. Such revised contribution would need to address all of the reviewer comments. In particular, reviewer #1 raises an issue regarding the assumptions on the specific distribution of the “error” used in the mathematical derivation. In addition, reviewer #2 highlights several points that would deserve to be further clarified and discussed (e.g. further discussion of the implications of the results for other research areas, including consequences of intraspecific variations).
In addition to the comments of the reviewers, I have a few additional suggestions to help improve the clarity of the manuscript:
Figure 2: When reading first the manuscript, I didn’t understand the meaning of the blue and red circles in this figure, and globally this figure is rather difficult to understand. This part only becomes clear when reading the next section with Figure 3. I would suggest either removing this figure, or simplifying it by summarizing more the main steps and goals of the approach taken in the manuscript (as an illustration for the end of the introduction).
Box 1 is very useful but it is cited only rarely in the text. I think further reference to this box would be very helpful to remind readers of critical steps and definitions of the approach (e.g. how change is measured at the system level in the geometrical approach).
Legend of Figure 3: in (c), please explain what corresponds to x and y in the equation and what it means (i.e. expected relationship between error and underestimation as derived from equation 4). From what I understood, the dashed red lines and the black points correspond to (mean – sd) and (mean + sd) and not to the values of the variances. This needs to be clarified. In addition, I would also explain that “underestimation” refers to the relative magnitude of underestimation as defined in equation (2).
Legend of Figure 4, “The variance around the mean expectation was accurately predicted using the IPR instead of species richness”: I would explain why more clearly in the text. Indeed, if the variance around the mean expectation was well predicted by species richness, we would have the same variance in the two studied cases of biomass distribution as they have the same number of species.
Line 442 page 21: “we still see below”
Line 470 page 23: “probability of underestimation” instead of “probability of synergism”
Examples page 25: it is not fully clear how these examples are related to what is presented in the main text, this would need to be clarified. More globally, I think the appendices could be linked a little more clearly to the main text.
Appendix page 29: This is not fully clear how the different aggregate functions are defined here. For instance, do they depend on species biomass or on other species properties? This point would deserve to be explained in the main text too.
I am looking forward to seeing your revised manuscript addressing the reviewers’ comments, along with a point-by-point response.
Best wishes, Elisa Thébault