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Supplementary Online Materials Page 1. Table of contents 2. Materials and Methods 20. Figure S1 – Contour plot of estimated temperature change in Mexico. 21. Figure S2 – Phylogeny used in PIC analysis of Sceloporus lizard extinctions 23. Figure S3 – Phylogeny used in Phylogenetic Independent Contrasts analysis of lineage survival, Tb, Tair and reproductive mode 24. Figure S4 – Te for the Yucatán ground-truth of Sceloporus serrifer extinctions 25. Figure S5 – Temperature change at weather stations in the interior Yucatán peninsula 27. Figure S6 – Phylogeny of Phrynosomatidae used in Phylogenetic Independent Contrasts analysis of Tb and CTmax 28. Figure S7 – Phylogenetic Independent Contrasts for Tb and CTmax of the Phrynosomatidae 29. Figure S8 – Phylogeny of lizard families and reconstruction of thermoregulatory mode 31. Figure S9 – Map showing georeferenced Tb values and sites used to validate the extinction model 32. Table S1 – Geo-referenced data on extinction of Sceloporus lizards 40. Table S2 – Geo-referenced data on Mexican weather stations 44. Table S3 – Parametric climate surfaces for Tmax for México 46. Table S4 – Data set for Phylogenetic Independent Contrasts analysis of lineage survival, Tb, Tair and reproductive mode 48. Table S5 – Data set for Phylogenetic Independent Contrasts analysis of Tb and CTmax 50. Table S6 – Geo-referenced data on Tb for lizard families 75. Table S7 – Local extinctions in biotas of South America, Europe, Africa and Australia 85. Table S8 – Correspondence between local population extinction and species extinction 86. Literature cited 1 Materials and Methods Resurvey of Sceloporus localities in Mexico From 2002-2008, we resurveyed localities for Sceloporus lizard species, at sites previously described in the literature or based on our own field studies from 1980-1995. We specifically excluded any cases of extinction where habitat modification was the cause and only included sites characterized by intact habitat as described in historical surveys. We quadrupled sampling effort (hours × personnel) relative to past surveys in cases of putative extinction events to ensure that we minimized registration of false extinction records. Sceloporus lizards are heliophilic ectotherms and quite conspicuous during morning hours when they bask and engage in elaborate push-up displays, which enhances the probability of detection, especially during the breeding season when we conducted field surveys. Thus, erroneous extinction events are unlikely compared to other lizard species that have cryptic activity patterns. We resurveyed 46 species at 200 localities. We registered a total of 24 extinctions, or 12% of all populations surveyed (Table S1). Phylogenetic inference in the Phrynosomatidae Because species with adjacent ranges might be related phylogenetically, we used methods of phylogenetic independent contrasts (PIC) to determine associations among extinction risk, geography, climate and thermal adaptations like viviparity and Tb. We mapped extinctions on a phylogeny to account for phylogenetic structure in the pattern of extinctions (Figure S2). Phylogeny used for mapping extinctions was based on based on a Sceloporine super tree (S1) and phylogenies for subclades (S2, S3). We obtained most of the data for the Tb of Sceloporus from Andrew’s (S4) review, but we also included Garrick’s (S5) Tb measure for S. cyanogenys (the control values), as well as our own measurements. We also used a phylogeny for the Phrynosomatidae to reconstruct evolutionary changes in the Critical Thermal Maximum (S6), CTmax, as a function of Tb. For CTmax and Tb of the Phrynosomatidae, we used data from Table S4 for Tb of Sceloporus and reviewed additional data in the literature for Tb and CTmax across the Phrynosomatidae (S7-S22). The phylogeny is based on the Sceloporine super tree (S1) and phylogenies for subclades (S23), and a more recent Phrynosomatidae phylogeny that includes 2 evolutionary branch lengths based on 2 mtDNA genes and 5 nuclear genes (S24). This recent phylogeny confirms the topology of the Sceloporine super tree based on diverse genetic data (S1). We computed phylogenetic independent contrasts (PIC) (Figure S4) using the PDAP (S25) module of Mesquite (S26) and branch lengths are based on the Phrynosomatidae phylogeny (S24). Details on Yucatán ground-truth and the thermal physiological model of extinction Thermal models designed to mimic thermal properties of basking lizards estimate operative model temperatures, Te [(S27) PVC pipe size, 2.5×15cm, grey primer paint to match reflectance of S. serrifer], were connected to a HOBOTEMP™ and deployed at 4 sites in the Yucatán. We recorded average model temperature, Te, every h over a 4-month period (Jan-May). Geographical coordinates of the ground-truth for persistent (Izamal, Conkal) and extinct sites (Chumpan, Uxmal) in the interior of the Yucatán peninsula are: Izamal, Yucatán, 20° 53' 48.2'' N; 88° 47' 10.4'' W, 22m elevation; Conkal, Yucatán, 21° 03' 46.1'' N; 89° 32' 09.2'' W, 9 m elev.; Chumpan, Campeche, 18° 12' 42.3'' N; 91° 30' 45.7'' W, 10m elev.; and Uxmal, Yucatán, 20° 27' 37.2'' N; 89° 44' 38.7'' W, and 47m elev. Three weather stations (Mérida, Valladolid, Chetumal see Fig. S5) are close to the sites. A plot of the change in Tmax over the last 36 years at these stations is shown for the months of January to May (Fig S5). A total of 14 of 15 station×months registered significant increases in Tmax. The four S. serrifer sites in our ground-truth of extinction and thermal physiology are closest to the Mérida weather station. We used temperature records from the Mérida station (Jan-Apr 2009) to compute the functional relationship between hr in activity time, which is the cumulative h each day when Te > Tb preferred (Tb preferred =31°C for S. serrifer) (Fig. 4B). We related hr on a daily basis to the Tmax observed at Mérida on a daily basis and fitted the following highly significant linear regression equation (Figure S4B): hr[Te >Tb preferred] = slope × (Tmax) + intercept1 (Equation S1). This equation has a high goodness-of-fit to a linear equation with no evidence of non-linearity (e.g., quadratic or cubic terms). Notice that if we standardize Eqn. S1 in terms of Tb preferred (e.g., where Tmax – Tb, preferred is the x-variate) before carrying out the model fit we obtain a more general equation for lizards: 3 hr[Te >Tb preferred] = slope × (Tmax – Tb, preferred) + intercept2 (Equation S2). Given data on Tb, preferred, Equation S2 can be extended to any species of lizard. Data on Tb preferred is actually quite rare, because it requires measurement in a laboratory thermal gradient under standard conditions (S28). However, measurements of activity body temperatures (Tb), which are highly correlated with Tb preferred (S28), are available for almost all of the species in our extinction survey and Tb is highly correlated with extinction (Tb is also highly correlated with Tb preferred, see analysis Table S6). To extend our physiological model of extinction to other Sceloporus we substituted Tb from Table S4 for Tb preferred. When a Tb value for a species was unavailable, we used nearest ancestor reconstruction to estimate values (only a few species required ancestor reconstruction, c.f., species listed in Table S1 vs. Table S4). Figure S4A suggests a value of hr ~ 4 h (March-April average), based on persistent S. serrifer populations that are on the verge of extinction. We explored this assumption by varying hr from 1 to 12 h in 0.1 h increments to compute the overall fit of the model (e.g., deviations of extinction model from observed data). Based on this statistical estimation procedure, a value of hr =3.85 h provides the best fit between observed and predicted extinctions. This calibration suggests that a value of hr =3.85 h during critical reproductive periods may be general for heliothermic Sceloporus species. In the future, this assumption could be tested by exploring other factors known to influence Te and thermal activity limits such as body size, habitat preference, and perch height (S27, S28) and with Te estimates of other species located at sites on the verge of extinction. Nevertheless, the goodness-of-fit of the model in predicting extinctions is exceptional (see text). We also varied the two critical months used to compute hr, but March and April provided the best fit for both reproductive modes. This is intuitively appealing because if it gets too hot early in the season, it will be exceptionally hot in May-July and thus only the early season hr (i.e., critical period of reproduction) sends a population to the tipping point of extinction. It might be more appropriate to compute the cumulative hours Te exceeds CTmax (Fig. S4C). However, CTmax values are rarely reported in the primary literature (N=11, Table S5) compared to Tb values (N=26, Table S4). Moreover, Tmax recorded at weather stations, which is the most widely reported measure of environmental temperature in climate databases, rarely exceeded CTmax values (Fig. S4C), 4 thus potentially generating large errors of inference in relating hr to Tmax-CTmax. In contrast, Tmax often exceeds Tb, providing residuals (e.g., Tmax - Tb, Fig. S4BC) for estimating a functional relationship with hr. Thus, the relationship between Tb - Tmax (Equation S2) performs well in predicting extinction, while CTmax - Tmax performs poorly. Finally CTmax is correlated with Tb in PIC regression analysis (Table S5, Fig. S7). A Physiological model for extinction risk and Tb and global climate models of Tmax i. Overview of the Global Simulation Model We used global climate surfaces from the WORLDCLIM web site (S30) (www.worldclim.org) (for the years 1975, 2020, 2050, 2080) to derive Tmax (°C) at a given latitude and longitude (10-arc minute resolution). We also used WORLDCLIM predictions for Tmax in the year 2050 and 2080 under three scenarios for climate change (IPPC 3rd Assessment).