We employed LR and ML methods to build ecometric models relating turtle community body size distributions to temperature and precipitation. Our linear models used single- and two-variable predictors from turtle community size mean, SD, maximum, minimum, range, and skewness (SI Appendix ).
We adapted the ML approach from ref. 8 , to output the most likely value for the environmental variable for a given trait distribution based on the observed environmental values across turtle communities in a training dataset. This method does not require a predictable relationship between the ecometric statistic values and the estimated climate variable. We extensively tested different techniques for building ML models, using 75% of the available community samples at global and continental scales to train the models and the remaining 25% of data points to test their predictive performance. (SI Appendix ).
We compared models built using community sampling points drawn from three different geographic datasets. The first dataset is species range maps from the Turtle Taxonomy Working Group (65 ), and the second is species occurrence points from the Global Biodiversity Information Facility database (https://www.GBIF.org ), both of which we used to assemble communities at a set of global sampling points spaced at 50 km across the terrestrial globe. The third input dataset we used is range maps derived from SDMs (66 ). SDMs have not previously been employed in ecometric modeling, but their estimates of geographic areas where environmental conditions are suitable for each species can improve ecometric community sampling, because the SDMs output an approximation of ranges prior to human impacts on geographic distributions.
We also compared ML models using only occurrences of terrestrial or aquatic turtle species to investigate whether body size is more strongly related to climate in turtle communities from one of these habitat categories. We built additional models based only on training points on each continent and compared their predictive performance for temperature and precipitation with that of global models at test points on individual continents (Table 1 ). We provide the full ranking of models in each run and comparisons of prediction anomalies between datasets, along with all results for precipitation modeling (SI Appendix ).
We applied ecometric models to reconstruct temperature and precipitation values for each member of the Shungura Formation based on paleocommunity ecometrics. We inputted these communities into the top-performing models to estimate temperature and precipitation at the member stratigraphic scale.
We adapted the ML approach from ref. 8 , to output the most likely value for the environmental variable for a given trait distribution based on the observed environmental values across turtle communities in a training dataset. This method does not require a predictable relationship between the ecometric statistic values and the estimated climate variable. We extensively tested different techniques for building ML models, using 75% of the available community samples at global and continental scales to train the models and the remaining 25% of data points to test their predictive performance. (
We compared models built using community sampling points drawn from three different geographic datasets. The first dataset is species range maps from the Turtle Taxonomy Working Group (65 ), and the second is species occurrence points from the Global Biodiversity Information Facility database (
We also compared ML models using only occurrences of terrestrial or aquatic turtle species to investigate whether body size is more strongly related to climate in turtle communities from one of these habitat categories. We built additional models based only on training points on each continent and compared their predictive performance for temperature and precipitation with that of global models at test points on individual continents (
We applied ecometric models to reconstruct temperature and precipitation values for each member of the Shungura Formation based on paleocommunity ecometrics. We inputted these communities into the top-performing models to estimate temperature and precipitation at the member stratigraphic scale.
