Examining the diversity maxima of marine macrophytes and their relationship with a continuous environmental stress gradient in the Northern Ryukyu Archipelago

In coastal marine ecosystems, the environmental stress model (ESM) predicts that the central measures (i.e., the mean or median) of species richness are highest at intermediate stresses (e.g., intermediate levels of light and wave exposure). It is now appropriate to examine ESM over larger spatial scales beyond a single shoreline, using a continuous stress scale, and non-central measures of species richness. The relationship between marine macrophyte richness and a continuous stress gradient (i.e., hydrodynamic stress) from 210 sites in the Northern Ryukyu Archipelago were examined. Expectile regression splines were used to determine how non-central measures of richness vary with stress. Species richness peaked at intermediate stresses and this feature was strongest at the higher expectiles (i.e., in the upper tails of the distribution of species richness). The fitted expectile regressions converged at the highest and lowest stress, and were widely spaced at intermediate values. This suggests that environmental stress, as determined, is the process that controls species richness at low and high stress. A provisional analysis assuming a Gumbel distribution to model the extreme values of species richness mirrored the patterns elucidated by the expectile regression. Expectile regression and extreme value approaches may provide a means of predicting the occurrence of species richness maxima at the regional scale.