We study non-neutral stochastic community models, and show that the presence of non-neutral processes is detectable if sample size is large enough and/or the amplitude of the effect is strong enough.

The power of a statistical test generally depends on three factors: first, the sample size ; second, statistical significance as measured by the threshold p-value used to assess significance; and third, the effect size, which quantifies departures from the null hypothesis.

Our results highlight the fact that the parameter I plays a more complicated role for these models than the sample size in standard power calculations, because the power does not always increase monotonically with I (Fig.

This means that the community size I plays a nonlinear role and is not a straight analogue of the sample size in standard statistical tests, so statistical power does not necessarily increase monotonically with I.

Our power calculation provides an estimate of the smallest sample size that is needed to detect non-neutrality of known intensity, and of the range strengths of non-neutrality needed to reject neutrality for a given species abundance data set.

The strength of non-neutral processes affects the sample size that is required in order to have a good chance of rejecting the neutral hypothesis (see Fig.

This appears counterintuitive because statistical power should increase monotonically with sample size .

The power of a test will depend on the magnitude of the deviation from the null hypothesis —the so-called effect size—and on the quality of the data at hand, typically, sample size .

This result is likely due to the high noise level and low sampling size for that class, which dilutes discriminatory features between the mid/late exponential and stationary phases.

This is expected, since that class corresponds to samples that either are missing data or represent classes that have low sample sizes and are grouped together.

To adjust the non-biological experimental variation with the consideration of large number of datasets with a few samples, we used ComBat that is developed under Bayesian framework and is known to be robust to outliers in small sample sizes [62].

Classifier performance and sample size .

An estimator that produces estimates that are, on average, closer to the truth for a given sample size is said to be more efficient than other estimators.

We drew 30 independent samples with sample sizes 11 = 250, 500, 1000, 2000, and 4000 from each model and computed the loss €(C, Z) for each of the five estimators.

With increasing sample sizes , all estimators converged to the ground truth (zero loss) but the estimators with correct structure outperformed the others even for large samples.

Most proposed methodologies require the collection of new data sets and thus are limited in sample size , making them difficult to validate.

The majority of currently suggested approaches are limited in sample size , and require the time consuming collection of large new data sets (such as multiple biopsies from single tumours) for validation and proof of concept.

The clinical assessment of intra-tumour heterogeneity also poses a significant challenge, with current eXperimental approaches requiring multiple biopsies per tumour leaving them severely limited in sample size [17—19].