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Abstract Molecular ecology regularly requires the analysis of count data that reflect the relative abundance of features of a composition (e.g., taxa in a community, gene transcripts in a tissue). The sampling process that generates these data can be modelled using the multinomial distribution. Replicate multinomial samples inform the relative abundances of features in an underlying Dirichlet distribution. These distributions together form a hierarchical model for relative abundances among replicates and sampling groups. This type of Dirichlet‐multinomial modelling (DMM) has been described previously, but its benefits and limitations are largely untested. With simulated data, we quantified the ability of DMM to detect differences in proportions between treatment and control groups, and compared the efficacy of three computational methods to implement DMM—Hamiltonian Monte Carlo (HMC), variational inference (VI), and Gibbs Markov chain Monte Carlo. We report that DMM was better able to detect shifts in relative abundances than analogous analytical tools, while identifying an acceptably low number of false positives. Among methods for implementing DMM, HMC provided the most accurate estimates of relative abundances, and VI was the most computationally efficient. The sensitivity of DMM was exemplified through analysis of previously published data describing lung microbiomes. We report that DMM identified several potentially pathogenic, bacterial taxa as more abundant in the lungs of children who aspirated foreign material during swallowing; these differences went undetected with different statistical approaches. Our results suggest that DMM has strong potential as a statistical method to guide inference in molecular ecology. 

Abstract Non‐random mating among individuals can lead to spatial clustering of genetically similar individuals and population stratification. This deviation from panmixia is commonly observed in natural populations. Consequently, individuals can have parentage in single populations or involving hybridization between differentiated populations. Accounting for this mixture and structure is important when mapping the genetics of traits and learning about the formative evolutionary processes that shape genetic variation among individuals and populations. Stratified genetic relatedness among individuals is commonly quantified using estimates of ancestry that are derived from a statistical model. Development of these models for polyploid and mixed‐ploidy individuals and populations has lagged behind those for diploids. Here, we extend and test a hierarchical Bayesian model, calledentropy, which can use low‐depth sequence data to estimate genotype and ancestry parameters in autopolyploid and mixed‐ploidy individuals (including sex chromosomes and autosomes within individuals). Our analysis of simulated data illustrated the trade‐off between sequencing depth and genome coverage and found lower error associated with low‐depth sequencing across a larger fraction of the genome than with high‐depth sequencing across a smaller fraction of the genome. The model has high accuracy and sensitivity as verified with simulated data and through analysis of admixture among populations of diploid and tetraploidArabidopsis arenosa.