arXiv subjects

Amy Willis

Publications and source records attributed to Amy Willis.

6 recordsLinked to original sources

arXiv2019

Estimation of cell lineage trees by maximum-likelihood phylogenetics

CRISPR technology has enabled large-scale cell lineage tracing for complex multicellular organisms by mutating synthetic genomic barcodes during organismal development. However, these sophisticated biological tools currently use ad-hoc and outmoded computational methods to reconstruct the cell lineage tree from the mutated barcodes. Because these methods are agnostic to the biological mechanism, they are unable to take full advantage of the data's structure. We propose a statistical model for the mutation process and develop a procedure to estimate the tree topology, branch lengths, and mutation parameters by iteratively applying penalized maximum likelihood estimation. In contrast to existing techniques, our method estimates time along each branch, rather than number of mutation events, thus providing a detailed account of tissue-type differentiation. Via simulations, we demonstrate that our method is substantially more accurate than existing approaches. Our reconstructed trees also better recapitulate known aspects of zebrafish development and reproduce similar results across fish replicates.

q-bio.QM↗

arXiv2017

Confidence sets for phylogenetic trees

Inferring evolutionary histories (phylogenetic trees) has important applications in biology, criminology and public health. However, phylogenetic trees are complex mathematical objects that reside in a non-Euclidean space, which complicates their analysis. While our mathematical, algorithmic, and probabilistic understanding of phylogenies in their metric space is mature, rigorous inferential infrastructure is as yet undeveloped. In this manuscript we unify recent computational and probabilistic advances to construct tree--valued confidence sets. The procedure accounts for both centre and multiple directions of tree--valued variability. We draw on block replicates to improve testing, identifying the best supported most recent ancestor of the Zika virus, and formally testing the hypothesis that a Floridian dentist with AIDS infected two of his patients with HIV. The method illustrates connections between variability in Euclidean and tree space, opening phylogenetic tree analysis to techniques available in the multivariate Euclidean setting.

stat.ME↗

arXiv2016

Species richness estimation with high diversity but spurious singletons

The presence of uncommon taxa in high-throughput sequenced ecological samples pose challenges to the microbial ecologist, bioinformatician and statistician. It is rarely certain whether these taxa are truly present in the sample or the result of sequencing errors. Unfortunately, alpha-diversity quantification relies on accurate frequency counts, which can rarely be guaranteed. We present a species richness estimation tool which predicts both the number of unobserved taxa and the number of true singletons based on the non-singleton frequency counts. This method can be treated as either inferential (for formally estimating richness) or exploratory (for assessing robustness of the richness estimate to the singleton count). If the estimate, called breakaway_nof1, is comparable to other richness estimators, this provides evidence that the richness estimate is robust to the level of quality control (eg. chimera-checking) employed in pre-processing. The function breakaway_nof1 is freely available from CRAN via the R package breakaway.

stat.ME↗

arXiv2016

Improved detection of changes in species richness in high-diversity microbial communities

High throughput sequencing (HTS) continues to expand our understanding of microbial communities, despite insufficient sequencing depths to detect all rare taxa. These low abundance taxa are not accounted for in existing methods for detecting changes in species richness. We address this with a new hierarchical model that permits rigorous testing for both heterogeneity and biodiversity changes, and simultaneously improves Type I & II error rates compared to existing methods.

stat.AP↗

arXiv2015

Inference for changes in biodiversity

We wish to formally test for changes in the taxonomic diversity of a community, especially in the presence of high latent diversity. Drawing on the meta-analysis literature, we construct a model for diversity that accounts for covariate effects as well as sampling variability. This permits inference for changes in richness with covariates and also a test for homogeneity. We argue that we can use the principles of shrinkage estimation to improve richness estimation in this nonstandard context, which is especially important given the high variance of richness estimators and the increasing abundance of community composition data. We demonstrate the methodology under simulation, in a gut microbiome study (testing for a decrease in richness with antibiotics), and in a soil microbiome study (testing for homogeneity of replicates). We believe that this is the first formal procedure for analyzing changes in species richness.

stat.ME↗

arXiv2014

Nonstandard regular variation of in-degree and out-degree in the preferential attachment model

For the directed edge preferential attachment network growth model studied by Bollobas et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails. Typically the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular variation is non-standard. Only marginal regular variation has been previously established for this distribution in the cases where the marginal tail indices are different.

math.PR↗