2.4.1. Great Barrier Reef

One live unfed gnathiid (stage three, 15 d), two adult males (alive, 15 d; dead, 29 d) and three adult females (alive, 15 and 24 d; dead, 16 d) were excluded from the data. These gnathiids were excluded because they were adults and thus their longevity would be different to that of the juveniles. The single juvenile that was still alive when we terminated the experiment was omitted for simplicity and consistency. We categorized the three juvenile stages based on their headwidth (stage one: 0.14–0.2, stage two: 0.21–0.24, stage three: 0.25–0.32 mm) [77]. Due to the large difference in sample size per unfed/fed status (based on the presence of an engorged gut), we conducted separate analyses for unfed (*n* = 1133) and fed gnathiids (*n* = 87).

To test whether survival of gnathiids differed among temperature treatments, we used a proportional hazards Cox mixed-effects model with temperature treatment and gnathiid juvenile stage as categorical fixed effects, aquarium as a random factor, and gnathiid headwidth as a covariate (Table 1 and Table S3). We used ambient temperature (29 ◦C) and juvenile stage one as the baselines for the analyses. We used the function "coxme" in the package "coxme" [110,111] and function "Anova" in the package "car" [112]. We tested the Cox model assumption of proportionality using the Global test statistic in the function "coxph" and "cox.zph" in the package "coxme" and graphically using a smoothed spline plot of the Shoenfeld residuals relative to time (see Tables S3 and S4 for results and Figures S4 and S5 for spline plots).


**Table 1. Great Barrier Reef;** Analysis of deviance table (Type II tests) for unfed gnathiid survival among temperature treatments and juvenile stages for Cox model. Bolded values are ones mentioned in main text. \*\*\* *p* < 0.001.
