Recent advancements in next-generation sequencing have revolutionized our understanding of the human microbiome. Despite this progress, challenges persist in comprehending the microbiome's influence on disease, hindered by technical complexities in species classification, abundance estimation, and data compositionality. At the same time, the existence of macroecological laws describing the variation and diversity in microbial communities irrespective of their environment has been recently proposed using 16s data and explained by a simple phenomenological model of population dynamics. We here investigate the relationship between dysbiosis, i.e. in unhealthy individuals there are deviations from the "regular" composition of the gut microbial community, and the existence of macro-ecological emergent law in microbial communities. We first quantitatively reconstruct these patterns at the species level using shotgun data, and addressing the consequences of sampling effects and statistical errors on ecological patterns. We then ask if such patterns can discriminate between healthy and unhealthy cohorts. Concomitantly, we evaluate the efficacy of different statistical generative models, which incorporate sampling and population dynamics, to describe such patterns and distinguish which are expected by chance, versus those that are potentially informative about disease states or other biological drivers. A critical aspect of our analysis is understanding the relationship between model parameters, which have clear ecological interpretations, and the state of the gut microbiome, thereby enabling the generation of synthetic compositional data that distinctively represent healthy and unhealthy individuals. Our approach, grounded in theoretical ecology and statistical physics, allows for a robust comparison of these models with empirical data, enhancing our understanding of the strengths and limitations of simple microbial models of population dynamics. In this study, we explore emerging ecological properties in gut microbiomes. Our aim here is to determine whether these patterns can be informative of the gut microbiome (healthy or diseased) and unveil essential ingredients driving its population dynamics. Leveraging on metagenomic data and interpretable statistical models based on ecological processes, we show that not all ecological patterns are informative to characterize its states, while few are (e.g., species diversity). Eventually, thanks to the ecological interpretability of the inferred models' parameters, our analysis provides insights into the role of environmental fluctuations and carrying capacities of the gut microbiomes in both health and disease. This study offers valuable knowledge, bridging theoretical concepts with practical implications for human health.