1 Validation methods for trophic niche models 2 3 To assign links between nodes (species), we used trophic niche-space models (e.g., [1]). 4 Each of these models has two quantile regressions that define the prey-size range a 5 predator of a given size is predicted to consume. Species whose body mass is within the 6 range of a predator’s prey size, as identified by the trophic niche-space model, are predicted 7 to be prey, while those outside the range are predicted not to be eaten. 8 9 The broad taxonomy of a predator helps to predict predation interactions [2]. To optimize 10 our trophic niche-space model, we therefore tested whether including taxonomic class of 11 predators improved the fit of quantile regressions. Using trophic (to identify which species 12 were predators), body mass, and taxonomic data, we fitted and compared five quantile 13 regression models (including a null model) to the GloBI data. In each model, we log10- 14 transformed the dependent variable prey body mass, and included for the independent 15 variables different combinations of log10-transformed predator body mass, predator class, 16 and the interaction between these variables (Supplementary Table S4). We log10- 17 transformed both predator and prey body mass to linearize the relationship between these 18 variables. We fit the five quantile regressions to the upper and lower 5% of prey body mass, 19 and compared model fits using the Bayesian information criterion (BIC). The predator body 20 mass*predator class model fit the 95th quantile data best, whereas the predator body mass 21 + predator class model fit the 5th quantile data marginally better than the aforementioned 22 interaction model (Supplementary Figure S2, Supplementary Table S4). 23 24 Next, we compared the performance of two trophic niche-space models using empirical 25 data and the true skill statistic (i.e., model validation). The true skill statistic assesses how 26 well a model predicts present and absent links [1,3]: ("# − %&) 27 (" + &)(% + #) 28 where a = number of predicted links observed, b = number of predicted links not observed, 29 c = number of links observed but not predicted, and d = number of links predicted to be 30 absent and not observed. 31 32 The two trophic niche models we compared were: (1) the simple body-size model originally 33 developed by Gravel et al. [1], and (2) our new model based on the quantile regressions 34 with the lowest BIC (i.e., predator body mass*predator class for the upper limit and 35 predator body mass + predator class for the lower limit). We applied these trophic niche 36 models to two empirical datasets for validation. In the first validation, we split the GloBI 37 interaction data into training and validation datasets; we randomly assigned 75% of the 38 interactions in the GloBI interaction dataset to the training dataset, and 25% to the 39 validation dataset. Because GloBI only includes observed predator-prey interactions, we 40 needed to generate ‘observed absent’ links to calculate the true skill statistic. We generated 41 these absent links by randomly selecting pairs of species in the validation data that were not 42 observed in trophic interactions with each other, making the same number of these absent 43 links as there were observed links (1:1 ratio). We randomly generated 100 training and 44 validation datasets in this way, and recorded the performance (true skill statistics) of the 45 two trophic niche models on these sets. 46 47 The second dataset we used to validate our trophic niche models was a real-world food web 48 from the Serengeti (de Visser et al., 2011, S. de Visser, unpublished data). This is probably 49 the most highly resolved, diverse terrestrial vertebrate food web that has been documented 50 and published; it describes one of the most intact ecosystems today, and one that includes 51 much of its Late Pleistocene megafauna (i.e., it is more analogous to Late Pleistocene 52 assemblages in Australia in this regard). While it is the most detailed diverse terrestrial 53 vertebrate food web in existence, it consists of functional/trophic species groups rather 54 than individual species. We ran the validation analyses on the Serengeti food web in the 55 same way as described for the GloBI training/validation datasets, only in this case we: (1) 56 used the full GloBI dataset as the training data (i.e., to define the trophic-niche-space 57 models), (2) assumed all unobserved links between pairs of species were absent links, (3) 58 ran the analysis only once on the full Serengeti dataset, and (4) prohibited impossible links 59 based on each species’ diet — we only treated species as predators if they preyed on 60 vertebrates; we did not allow impossible links from vertebrates to strictly herbivorous or 61 insectivorous species (e.g., water buffalo are strictly herbivorous, and so we did not assign 62 vertebrate prey to this species). 63 64 In both the GloBI and Serengeti validations, the new model performed better than the 65 simple body-size model (i.e., true skill statistics for the new model and the simple model 66 were 0.38 vs 0.37, and 0.60 vs 0.58 for the GloBI and Serengeti data, respectively). Thus, we 67 adopted the new model that incorporates body size and predator class to infer trophic links. 68 Both trophic niche models are good at identifying potential links, but they almost always 69 overestimate the number of functional links. This is because predators are unlikely to 70 consume all prey within their size range — some species are not palatable, are dangerous, 71 too rare, difficult to capture, use different microhabitats, or have other ecological 72 characteristics that make them unsuitable for regular consumption [e.g., 5]. To build a 73 network with a more realistic structure, this overestimation needs to be considered. We 74 used the Serengeti validation food web to estimate how much our trophic niche model 75 overpredicted links so we could correct for overprediction when building trophic networks. 76 First, we tested whether there was a relationship between the number of prey predicted 77 and the proportion of predicted links that were actually observed by fitting a least-squares 78 regression to these variables; we found no association (t25 = -1.119, p = 0.27; Akaike 79 information criterion weights: 0.42 and 0.58 for the slope and intercept-only models, 80 respectively, giving an evidence ratio = 0.42/0.58 = 0.72). We then fit a kernel density to the 81 overestimation data to guide the removal of a proportion of each predator’s trophic links 82 when building networks from species lists (described in Methods). The number of observed 83 links divided by the number of predicted links per predatory species had a mean of 0.22 84 (range: 0.02 to 0.62). 85 86 References 87 1. Gravel d, Poisot T, Albouy C, Velez L, Mouillot d. 2013 Inferring food web structure from 88 predator-prey body size relationships. Methods Ecol. Evol. 4, 1083–1090. 89 (doi:10.1111/2041-210X.12103) 90 2. Eklof A, Helmus MR, Moore M, Allesina S. 2012 Relevance of evolutionary history for food 91 web structure. Proc. R. Soc. B 279, 1588–1596. (doi:10.1098/rspb.2011.2149) 92 3. Allouche O, Tsoar A, Kadmon R. 2006 Assessing the accuracy of species distribution 93 models: prevalence, kappa and the true skill statistic (TSS): Assessing the accuracy of 94 distribution models. J. Appl. Ecol. 43, 1223–1232. (doi:10.1111/j.1365- 95 2664.2006.01214.x) 96 4. de Visser SN, Freymann BP, Olff H. 2011 The Serengeti food web: empirical quantification 97 and analysis of topological changes under increasing human impact: Topological changes 98 under human impact. J. Anim. Ecol. 80, 484–494. (doi:10.1111/j.1365-2656.2010.01787.x) 99 5. Marples NM, Speed MP, Thomas RJ. 2018 An individual-based profitability spectrum for 100 understanding interactions between predators and their prey. Biological Journal of the 101 Linnean Society 125, 1–13. (doi:10.1093/biolinnean/bly088) 102 Supplementary Figure Captions Figure S1. Flowchart displaying the steps we used to build ecological network models of Late Pleistocene Naracoorte, and how we assessed node vulnerability to bottom-up cascades and relative position in the network. Figure S2. Predator/prey body-size relationships. Title indicates predator class. The red lines on the scatter plots show upper and lower quantile regressions. Figure S3. Contributions of network metrics to PC1 in the principal component analysis. Figure S4. Contributions of network metrics to PC2 in the principal component analysis. Figure S5. Naracoorte temperature and precipitation anomalies (relative to 1000 years ago) over the last 120,000 years. We hindcasted these climate variables for the Naracoorte region using a transient LOVECLIM Earth-system model1,2. The dotted vertical lines indicate the estimated date of megafauna extinction in this region (~ 44,000 years ago). Temperature reached a minimum immediately before the megafauna extinct (left panel), whereas the amount and rate of change in precipitation were not extreme at this time compared to earlier or later (right panel). 1Goosse, H. et al. Description of the Earth system model of intermediate complexity LOVECLIM version 1.2. Geosci. Model Dev. 3, 603–633 (2010). 2Saltré, F. et al. Climate-human interaction associated with southeast Australian megafauna extinction patterns. Nat. Commun. 10, 5311 (2019). Figure S6. Network metrics from the 1000 ecological network models of Late Pleistocene Naracoorte. Figure S7. Body mass versus number of links (node degree) for vertebrates from the ecological network models of Late Pleistocene Naracoorte.