“…To evaluate the effects of HAB on each species ( i ) at the regional scale ( ES REGION,i ) and each functional group ( j ) at each shore ( k ) ( ES SHORE,j,k ), we calculated the effect sizes ( ES ) of the abundance ( A ) from the pre-HAB period (2004–2020) to the post-HAB period (2021) with the following formulas (Iwasaki et al ., 2016; Noda et al ., 2017; Iwasaki & Noda, 2017; Ishida et al ., 2023):
where log ( A REGION,i,post − HAB ) represents the log 10 (abundance) of each species in the post-HAB year, log ( Ā REGION,i,pre−HAB ) and SD ( log ( A REGION,i,pre−HAB )) represent the mean and standard deviation of the log 10 (abundance) of each species during the pre-HAB period, respectively; log ( A REGION,j,k,post − HAB + 0.5) represents the log 10 (abundance + 0.5) of each functional group at each shore in the post-HAB year, log ( Ā REGION,j,k,pre − HAB + 0.5) and SD log ( A REGION,j,k,pre − HAB + 0.5) represent the mean and standard deviation of log 10 (abundance + 0.5) of each functional group at each shore during the pre-HAB period, respectively. An effect size greater than 1.96 in absolute value suggests that the abundance in the post-HAB year changed significantly compared with the pre-HAB period.…”