17Population structure influences genealogical patterns, however data 18 pertaining to how populations are structured are often unavailable or 19 not directly observable. Inference of population structure is highly 20 important in molecular epidemiology where pathogen phylogenetics is 21 increasingly used to infer transmission patterns and detect outbreaks. 22 Discrepancies between observed and idealised genealogies, such as those 23 generated by the coalescent process, can be quantified, and where 24 significant differences occur, may reveal the action of natural selection, 25 host population structure, or other demographic and epidemiological 26 heterogeneities. We have developed a fast non-parametric statistical test 27 for detection of cryptic population structure in time-scaled phylogenetic 28 trees. The test is based on contrasting estimated phylogenies with the 29 theoretically expected phylodynamic ordering of common ancestors in 30 two clades within a coalescent framework. These statistical tests have 31 also motivated the development of algorithms which can be used to 32 quickly screen a phylogenetic tree for clades which are likely to share a 33 distinct demographic or epidemiological history. Epidemiological 34 applications include identification of outbreaks in vulnerable host 35 populations or rapid expansion of genotypes with a fitness advantage.36To demonstrate the utility of these methods for outbreak detection, we 37 applied the new methods to large phylogenies reconstructed from 38 thousands of HIV-1 partial pol sequences. This revealed the presence of 39 clades which had grown rapidly in the recent past, and was significantly 40 concentrated in young men, suggesting recent and rapid transmission in 41 that group. Furthermore, to demonstrate the utility of these methods 42 for the study of antimicrobial resistance, we applied the new methods to 43 a large phylogeny reconstructed from whole genome Neisseria 44 gonorrhoeae sequences. We find that population structure detected 45 using these methods closely overlaps with the appearance and expansion 46 of mutations conferring antimicrobial resistance. 48 diversity is a longstanding problem in population genetics. When information 49 about how lineages are sampled is available, primarily geographic location, a 50 variety of statistics are available for describing the magnitude and role of 51 population structure (Hartl et al. 1997). In pathogen phylogenetics, such 52 geographic 'meta-data' has been instrumental in enabling the inference of 53 transmission rates over space (Dudas et al. 2017), host species (Lam et al. 54 2015), and even individual hosts (De Maio et al. 2018). Population structure 55 shapes genetic diversity, but can the existence of structure be inferred directly 56 from genetic data in the absence of structural covariates associated with each 57 lineage, such as if the geographic location or host species of a lineage is 58 unknown? 59 The problem of detecting and quantifying such 'cryptic' population 60 structure has become a pr...