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Appendix S1. Daily parameter estimates from mark-recapture analysis of solitary humpback whales, Perlas Islands, Panama. The model used was the open-population Cormack-Jolly-Seber, allowing animals to depart the study area each day with probability ε; the number of animals present in the study area each day (N), departing prior to the next day (L), and ε all were allowed to vary following Gaussian (N, L) or logit-Gaussian (ε) hyperdistributions. The number entering the study area prior to each day (R), was calculated by subtraction and was not modeled with a hyperdistribution. Daily variation in ε was scant, that is, the model almost collapsed to a constant ε. Observed = number of distinct animals photographed each day. CI = 95% credible intervals. Hyperparameters and the estimated detection probability δ, which was modeled as constant every day, are given in Appendix S2. Gaps in the sequence (e.g., 16 August 2005) are days animals were not observed, so on those days L, R, and ε refer to two-day totals; since the model allowed daily variation in all three parameters, this violates no assumptions.

Appendix S2. Hyperparameters for daily population size N, departures L, detection probability δ, and departure probability ε from the mark-recapture model for solitary humpback whales, Perlas Islands, Panama. Credible intervals are given in parentheses. Since no annual term was included, there is only one hypermean (μ) and hyper-standard deviation (σ) per variable. Since daily arrivals were calculated by subtraction, no hyperdistribution was used for R. In the case of departure probability, the hyperparameters were estimated for a Gaussian distribution of logit(ε), but the values presented here have been back-transformed (inverse-logit) to probabilities. In the case of SD(ε), this meant adding the mean of the logit to the SD of the logit then back-transforming and substracting the back-transformed mean. There was no hyperdistribution for δ: it was assumed constant every day, and the value under μ is thus not a hypermean but simply the best estimate.

Appendix S3. Daily parameter estimates from mark-recapture analysis of humpback whale calves, Perlas Islands, Panama. The model used was the open-population Cormack-Jolly-Seber, allowing animals to depart the study area each day with probability ε. As for solitary animals, a model was attempted allowing daily variation in the number of animals present in the study area each day (N), departing prior to the next day (L), and ε, but for calves, all hyperdistributions collapsed to point estimates, meaning the data were insufficient to detect daily variation. Without hyperdistributions, the estimates presented are simply the best point estimates of daily numbers.

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