22 23 24 Summary statement: We apply a thermal performance curve approach to a variety of fitness 25 related parameters in a reef building coral across its geographic range and various functions to 26 improve our understanding of the inherent variability in thermal tolerance.Abstract 32 Temperature drives biological responses that scale from the cellular to ecosystem levels 33 and thermal sensitivity will shape organismal functions and population dynamics as the world 34 warms. Reef building corals are sensitive to temperature due to their endosymbiotic relationship 35 with single celled dinoflagellates, with mass mortality events increasing in frequency and 36 magnitude. The purpose of this study was to quantify the thermal sensitivity of important 37 physiological functions of a Caribbean reef-building coral, Orbicella franksi through the 38 measurement of thermal performance curves (TPCs). We compared TPC metrics (thermal 39 optimum, critical maximum, activation energy, deactivation energy, and rate at a standardized 40 temperature) between two populations at the northern and southern extent of the geographic range 41 of this species. We further compared essential coral organismal processes (gross photosynthesis, 42 respiration, and calcification) within a site to determine which function is most sensitive to thermal 43 stress using a hierarchical Bayesian modeling approach. We found evidence for differences in 44 thermal performance, which could be due to thermal adaptation or acclimatization, with higher 45 TPC metrics (thermal optimum and critical maximum) in warmer Panama, compared to cooler 46 Bermuda. We also documented the hierarchy in thermal sensitivity of essential organismal 47 functions within a population, with respiration less sensitive than photosynthesis, which was less 48 sensitive than calcification. Understanding thermal performance of corals is essential for 49 projecting coral reef futures, given that key biological functions necessary to sustain coral reef 50 ecosystems are thermally-mediated. 51 52 53 89 worldwide over the last 30 years (from ~60% to <20% on some reefs), in large part due to ocean 90warming (Bruno and Selig, 2007; De'ath et al., 2012; Gardner et al., 2003; Hughes et al., 2018a) 91 causing mass bleaching, or the loss of the corals' symbiotic dinoflagellates and their nutritional 92 4 benefits to the host (Oakley and Davy, 2018). While there are numerous local causes of coral loss 93 (e.g., pollution, destructive fishing practices, tourism, etc.), the single most detrimental stressor to 94 date is thermal stress from anomalous heating events (i.e., heatwaves) and its associated 95 complications (i.e., bleaching, disease, reduced calcification etc.; (DeCarlo et al., 2017; Harvell et 96 al., 2002; Hughes et al., 2017)). Reef building corals and their dinoflagellate symbionts live close 97 to their physiological thermal maximum and, as a result, warming of 1°C or more above local 98 mean monthly maxima can reduce fitness and cause tissue loss or whole-colony...