Maximum likelihood estimation and natural pairwise estimating equations are identical for three sequences and a symmetric 2-state substitution model.

Consider the problem of estimating the branch lengths in a symmetric 2-state substitution model with a known topology and a general, clock-like or star-shaped tree with three leaves. We show that the maximum likelihood estimates are analytically tractable and can be obtained from pairwise sequence comparisons. Furthermore, we demonstrate that this property does not generalize to larger state spaces, more complex models or larger trees.

Evaluation of population structure inferred by principal component analysis or the admixture model.

Principal component analysis (PCA) is commonly used in genetics to infer and visualize population structure and admixture between populations. PCA is often interpreted in a way similar to inferred admixture proportions, where it is assumed that individuals belong to one of several possible populations or are admixed between these populations. We propose a new method to assess the statistical fit of PCA (interpreted as a model spanned by the top principal components) and to show that violations of the PCA assumptions affect the fit.

Estimating admixture pedigrees of recent hybrids without a contiguous reference genome.

The genome of recently admixed individuals or hybrids has characteristic genetic patterns that can be used to learn about their recent admixture history. One of these are patterns of interancestry heterozygosity, which can be inferred from SNP data from either called genotypes or genotype likelihoods, without the need for information on genomic location. This makes them applicable to a wide range of data that are often used in evolutionary and conservation genomic studies, such as low-depth sequencing mapped to scaffolds and reduced representation sequencing.

A reaction network scheme for hidden Markov model parameter learning.

With a view towards artificial cells, molecular communication systems, molecular multiagent systems and federated learning, we propose a novel reaction network scheme (termed the Baum-Welch (BW) reaction network) that learns parameters for hidden Markov models (HMMs). All variables including inputs and outputs are encoded by separate species. Each reaction in the scheme changes only one molecule of one species to one molecule of another.

Estimation of site frequency spectra from low-coverage sequencing data using stochastic EM reduces overfitting, runtime, and memory usage.

The site frequency spectrum is an important summary statistic in population genetics used for inference on demographic history and selection. However, estimation of the site frequency spectrum from called genotypes introduces bias when working with low-coverage sequencing data. Methods exist for addressing this issue but sometimes suffer from 2 problems.

Fast reactions with non-interacting species in stochastic reaction networks.

We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex.

Identification of Hidden Population Structure in Time-Scaled Phylogenies.

Population structure influences genealogical patterns, however, data pertaining to how populations are structured are often unavailable or not directly observable. Inference of population structure is highly important in molecular epidemiology where pathogen phylogenetics is increasingly used to infer transmission patterns and detect outbreaks. Discrepancies between observed and idealized genealogies, such as those generated by the coalescent process, can be quantified, and where significant differences occur, may reveal the action of natural selection, host population structure, or other demographic and epidemiological heterogeneities.

Addition of flow reactions preserving multistationarity and bistability.

We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology.

General theory for stochastic admixture graphs and F-statistics.

We provide a general mathematical framework based on the theory of graphical models to study admixture graphs. Admixture graphs are used to describe the ancestral relationships between past and present populations, allowing for population merges and migration events, by means of gene flow. We give various mathematical properties of admixture graphs with particular focus on properties of the so-called F-statistics.

Node balanced steady states: Unifying and generalizing complex and detailed balanced steady states.

We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex.

Some properties of the conditioned reconstructed process with Bernoulli sampling.

In many areas of genetics it is of relevance to consider a population of individuals that is founded by a single individual in the past. One model for such a scenario is the conditioned reconstructed process with Bernoulli sampling that describes the evolution of a population of individuals that originates from a single individual. Several aspects of this reconstructed process are studied, in particular the Markov structure of the process.

Powerful Inference with the D-Statistic on Low-Coverage Whole-Genome Data.

The detection of ancient gene flow between human populations is an important issue in population genetics. A common tool for detecting ancient admixture events is the D-statistic. The D-statistic is based on the hypothesis of a genetic relationship that involves four populations, whose correctness is assessed by evaluating specific coincidences of alleles between the groups.

Identifying parameter regions for multistationarity.

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature.

Intermediates and Generic Convergence to Equilibria.

Known graphical conditions for the generic and global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure to simplify the network, making the graphical conditions considerably easier to check.

epiG: statistical inference and profiling of DNA methylation from whole-genome bisulfite sequencing data.

The study of epigenetic heterogeneity at the level of individual cells and in whole populations is the key to understanding cellular differentiation, organismal development, and the evolution of cancer. We develop a statistical method, epiG, to infer and differentiate between different epi-allelic haplotypes, annotated with CpG methylation status and DNA polymorphisms, from whole-genome bisulfite sequencing data, and nucleosome occupancy from NOMe-seq data. We demonstrate the capabilities of the method by inferring allele-specific methylation and nucleosome occupancy in cell lines, and colon and tumor samples, and by benchmarking the method against independent experimental data.

Challenges in microbial ecology: building predictive understanding of community function and dynamics.

The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth's soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited.

Core signalling motif displaying multistability through multi-state enzymes.

Bistability, and more generally multistability, is a key system dynamics feature enabling decision-making and memory in cells. Deciphering the molecular determinants of multistability is thus crucial for a better understanding of cellular pathways and their (re)engineering in synthetic biology. Here, we show that a key motif found predominantly in eukaryotic signalling systems, namely a futile signalling cycle, can display bistability when featuring a two-state kinase.

Intermediates, catalysts, persistence, and boundary steady states.

For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We describe two graphical procedures for simplifying reaction networks without breaking known necessary or sufficient conditions for persistence, by iteratively removing so-called intermediates and catalysts from the network. The procedures are easy to apply and, in many cases, lead to highly simplified network structures, such as monomolecular networks.

LandScape: a simple method to aggregate p-values and other stochastic variables without a priori grouping.

In many areas of science it is custom to perform many, potentially millions, of tests simultaneously. To gain statistical power it is common to group tests based on a priori criteria such as predefined regions or by sliding windows. However, it is not straightforward to choose grouping criteria and the results might depend on the chosen criteria.

Graphical reduction of reaction networks by linear elimination of species.

The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are assumed effectively to be at steady state with respect to the "slow" species. Under this assumption the steady state equations can be used to eliminate the "fast" variables and a new ODE system with only the slow species can be obtained.

Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks.

We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.

Finding the positive feedback loops underlying multi-stationarity.

Background: Bistability is ubiquitous in biological systems. For example, bistability is found in many reaction networks that involve the control and execution of important biological functions, such as signaling processes. Positive feedback loops, composed of species and reactions, are necessary for bistability, and generally for multi-stationarity, to occur.

Phosphorelay of non-orthodox two component systems functions through a bi-molecular mechanism in vivo: the case of ArcB.

Two-component systems play a central part in bacterial signal transduction. Phosphorelay mechanisms have been linked to more robust and ultra-sensitive signalling dynamics. The molecular machinery that facilitates such a signalling is, however, only understood in outline.