In looking at the diversity within an environment, Is it possible for Shannon and Simpson's indices to show significant variation among the samples while the relative abundance of major OTUs are not significant. Need clarification.
What do you mean by "relative abundance of Major OTUs"? I suspect that you have based the definition of major OTUs on some defined cut-off (>1%, 2% etc).
Well, the adjuged "minor" OTUs that have been removed form your OTUs count table (to obtain major OTUs) may be driving the significant differences observed between communities. Have you performed a Beta-diversity analysis (PCoA, PERMANOVA, PERMDISP) on the OTU count table and Unifrac Distances?
Also, what kind of statistical tests have you performed? Remember that microbiome data are sparse and not normally distributed. You may want to use tests that do not assume normality of your data. I would recommend Wilcoxon test (for two groups), Kruskal-Wallis Test (for more than two groups).
Although significant differences in diversity indices has been observed, this does not necessarily mean that significant relative abundance shifts have occurred within one or a few OTUs. The changes that you observe in microbial community diversity may actually be associated with many small shifts in relative abundances across many OTUs. As Obinna has mentioned, these shifts may have occurred in rare/"minor" OTUs in your dataset, which highlights the importance of including both the core/"major" and rare/"minor" OTUs in your analyses going forward.
I would recommend running a statistical analysis which takes into account community structure (e.g. analysis of molecular variance (AMOVA)) to try and help you to explain these complex dynamics.
Thanks Obinna and Jolinda for your answers. I have included the "minor OTUs" and also used the Kruskal-Wallis Test. This has helped out greatly. Thank you very much