The debate has focused on the rise of jellyfish blooms and their
mean abundance (3, 13–16); thus, we examined both the distribution
of the annual standardized abundance and maximal jellyfish
values (i.e., blooms or data >90th percentile for each location) over
time using linear mixed model (LMM) and generalized linear
mixed model (GLMM) analyses that incorporate random effects
and nonlinear components and are adjusted for temporal autocorrelation
(heterogeneous AR1 estimates). The fact that timeseries
start and end at different years imposes limitations on the
analysis, as this results in differences in the sets of data available for
analysis in any single year. We used three approaches to determine
whether standardized jellyfish abundances have significantly increased
over time. First, we determined whether there was a significant
departure from the expected zero linear slope of standardized
abundance over time (i.e., the baseline) by comparing
between slopes of linear regressions from individual datasets over
the time period 1874–2011, as well as three consecutive time
periods: 1874–1939, 1940–1969, and 1970–2011. The second approach
involved GLMM (logistic) analyses of binary data to test
whether there was a change in the likelihood (odds) of observing
a higher vs. lower proportion of jellyfish over time. Third, we
computed effect sizes, as the ln [(Jp1/Jp2)/D], where Jp1 andJp2 are
the predicted jellyfish data for start and end years and D is the
number of decades in the time series (see Methods for summary),
allowing comparison of changes across datasets based on different
metrics (22). Because effect sizes deviated from a normal distribution
and no suitable transformation to normalize the data were
found, we used a nonparametric median test to test whether populations
showing significant increases or decreases over time differed
in effect size. To reject the null hypothesis of no global increase
in jellyfish, all three of these analyses combined should yield