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Chains were run for 10 million generations with topology and model parameter estimates sampled every 1000 generations.
We first derived four equations describing the relationship of t and s from the four empirical rate reduction hypotheses (Eq. 5 8, see Results), and fitted them to 1,500 sets of corresponding t and s estimates, sampled from their posterior distributions consisting of 15,000 datasets.
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The non-parametric bootstrap method estimates sampling distribution by taking repeated samples with replacement from the original participant data [ 39].
Estimated sampling location origin of sample using the SAM.
We estimated sampling errors using the Taylor series linearized method.
The SAM accurately estimated sampling location origin in 58% of assignments.
Variance was estimated using the Taylor series expansion theory to estimate sampling errors based on the complex sampling [ 42].
Conditional probabilities were estimated sampling the MCMC process every 10 iterations after 2,500 burn-in iterations (sample size 750).
We were unable to perform a formal meta-analysis because several critical components (e.g., variance estimates, sample size, repeated sampling of each reef, etc).
To reflect national population estimates, sample weights were applied in all analyses.
Few studies have examined the accuracy of estimates, sample size or power analysis in binary multilevel regression [ 5, 15].
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