Erratum to: Thermal–mechanical behaviour of chitosan–cellulose derivative thermoreversible hydrogel films

CH, Chitosan; HPMC, (Hydroxypropyl)methyl cellulose; FT, Freeze-thaw; SC, Solvent casting; CH:HPMC (X:Y), pH Z, FT/SC, Chitosan and (hydroxypropyl)methyl cellulose hydrogel, at X and Y proportion (0-100), at Z pH (3.0-4.0) and prepared by freeze-thaw or solvent casting techniques; DSC, Differential scanning calorimetry; MDSC, Temperature modulated Differential scanning calorimetry; Tg, glass transition temperature; ΔH, enthalpy change; TGA, Thermogravimetric Analysis; TG, Thermogravimetry; DTG, Derivative or Differential thermogravimetry; σ, Tensile strength; ε, elongation at break; DMA, Dynamic mechanical analysis; X-Ray, X-radiation, FTIR-ATR, Attenuated total reflectance Fourier transform infrared spectroscopy; SEM, Scanning electron microscopy.The authors are thankful to the Chemistry and Physic Centres at Minho University (Pest-C/QUI/UI0686/2013 and PEST-C/FIS/UI607/2013), CNPq, FAPESP and CAPES for the financial support of this research. Sandra Cerqueira Barros and Carlos M. Costa acknowledge the Portuguese Foundation for Science and Technology for the Post-Doc and PhD grants provided (SFRH/BPD/85399/2012 and SFRH/BD/68499/2010) and M. M. Silva acknowledges to CNPq, for the mobility grant provided by this institution. The authors of this paper are grateful to the Company Devan-Micropolis, S.A., for the material support, namely the natural polymers chitosan (CH) and (hydroxypropyl)methyl cellulose (HPMC) employed in this study. JLGR acknowledges the support of Ministerio de Economía y Competitividad, MINECO, through the MAT2013-46467-C4-1-R project. CIBER-BBN is an initiative funded by the VI National R&D&i Plan 2008-2011, Iniciativa Ingenio 2010, Consolider Program, CIBER Actions and financed by the Instituto de Salud Carlos III with assistance from the European Regional Development Fund

Statistical analysis of co-occurrence patterns in microbial presence-absence datasets.

Drawing on a long history in macroecology, correlation analysis of microbiome datasets is becoming a common practice for identifying relationships or shared ecological niches among bacterial taxa. However, many of the statistical issues that plague such analyses in macroscale communities remain unresolved for microbial communities. Here, we discuss problems in the analysis of microbial species correlations based on presence-absence data. We focus on presence-absence data because this information is more readily obtainable from sequencing studies, especially for whole-genome sequencing, where abundance estimation is still in its infancy. First, we show how Pearson's correlation coefficient (r) and Jaccard's index (J)-two of the most common metrics for correlation analysis of presence-absence data-can contradict each other when applied to a typical microbiome dataset. In our dataset, for example, 14% of species-pairs predicted to be significantly correlated by r were not predicted to be significantly correlated using J, while 37.4% of species-pairs predicted to be significantly correlated by J were not predicted to be significantly correlated using r. Mismatch was particularly common among species-pairs with at least one rare species (<10% prevalence), explaining why r and J might differ more strongly in microbiome datasets, where there are large numbers of rare taxa. Indeed 74% of all species-pairs in our study had at least one rare species. Next, we show how Pearson's correlation coefficient can result in artificial inflation of positive taxon relationships and how this is a particular problem for microbiome studies. We then illustrate how Jaccard's index of similarity (J) can yield improvements over Pearson's correlation coefficient. However, the standard null model for Jaccard's index is flawed, and thus introduces its own set of spurious conclusions. We thus identify a better null model based on a hypergeometric distribution, which appropriately corrects for species prevalence. This model is available from recent statistics literature, and can be used for evaluating the significance of any value of an empirically observed Jaccard's index. The resulting simple, yet effective method for handling correlation analysis of microbial presence-absence datasets provides a robust means of testing and finding relationships and/or shared environmental responses among microbial taxa