Dealing with the Pseudo-Replication Problem in Longitudinal Data from Posidonia Oceanica Surveys: Modeling Dependence vs. Subsampling

Abstract

Posidonia oceanica represents the key species of the most important ecosystem in subtidal habitats of the Mediterranean Sea. Being sensitive to changes in the environment, it is considered a crucial indicator of the quality of coastal marine waters. A peculiarity of P. oceanica is the presence of reiterative modules characterizing its growth, which lend themselves to back-dating techniques, allowing for the reconstruction of past history of growth variables (annual rhizome elongation and diameter, primary production, etc.). Such back-dating techniques provide, for each sampled shoot, a longitudinal series of multivariate data; this is an instance of what Hurlbert (1984) in a seminal paper defined as “pseudo-replications”, for which it becomes crucial to take into account the possible dependence of the data. A common solution to the “pseudo-replications” in the ecological literature is represented by “pseudo-replications”: given repeated measurements on the same unit, only a random sub-sample of such measurements is analyzed, in order to attenuate correlation and obtain approximately independently distributed observations, to which standard statistical methods can be applied. In its most extreme version, only one measurement is randomly drawn for each unit, i.e. the sub-sampling size is one. If on one hand sub-sampling attenuates correlation, on the other it implies a loss of information (due to the reduction of the total sample size) and then requires a higher number of sampling units to ensure a specified level of efficiency and power. In the talk, we contrast sub-sampling with the alternative approach of handling dependence directly in the modelling stage, using the class of Generalized Linear Mixed Models. We show that this approach permits remarkable gains of precision in estimation and power in testing, without requiring the increase in sample sizes involved in sub-sampling, and thus avoiding the practice of over-sampling, which has a negative impact on aquatic ecosystems.