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.
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