Evolving Improved Sampling Protocols for Dose-Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric.

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Experimental Evaluation of a Direct Fitness Effect of the De Novo Evolved Mouse Gene Pldi.

De novo evolved genes emerge from random parts of noncoding sequences and have, therefore, no homologs from which a function could be inferred. While expression analysis and knockout experiments can provide insights into the function, they do not directly test whether the gene is beneficial for its carrier. Here, we have used a seminatural environment experiment to test the fitness of the previously identified de novo evolved mouse gene Pldi, which has been implicated to have a role in sperm differentiation. We used a knockout mouse strain for this gene and competed it against its parental wildtype strain for several generations of free reproduction. We found that the knockout (ko) allele frequency decreased consistently across three replicates of the experiment. Using an approximate Bayesian computation framework that simulated the data under a demographic scenario mimicking the experiment's demography, we could estimate a selection coefficient ranging between 0.21 and 0.61 for the wildtype allele compared to the ko allele in males, under various models. This implies a relatively strong selective advantage, which would fix the new gene in less than hundred generations after its emergence.

Equivalence of variance components between standard and recursive genetic models using LDL' transformations.

BACKGROUND: Recursive models are a category of structural equation models that propose a causal relationship between traits. These models are more parameterized than multiple trait models, and they require imposing restrictions on the parameter space to ensure statistical identification. Nevertheless, in certain situations, the likelihood of recursive models and multiple trait models are equivalent. Consequently, the estimates of variance components derived from the multiple trait mixed model can be converted into estimates under several recursive models through LDL' or block-LDL' transformations. RESULTS: The procedure was employed on a dataset comprising five traits (birth weight-BW, weight at 90 days-W90, weight at 210 days-W210, cold carcass weight-CCW and conformation-CON) from the Pirenaica beef cattle breed. These phenotypic records were unequally distributed among 149,029 individuals and had a high percentage of missing data. The pedigree used consisted of 343,753 individuals. A Bayesian approach involving a multiple-trait mixed model was applied using a Gibbs sampler. The variance components obtained at each iteration of the Gibbs sampler were subsequently used to estimate the variance components within three distinct recursive models. CONCLUSIONS: The LDL' or block-LDL' transformations applied to the variance component estimates achieved from a multiple trait mixed model enabled inference across multiple sets of recursive models, with the sole prerequisite of being likelihood equivalent. Furthermore, the aforementioned transformations simplify the handling of missing data when conducting inference within the realm of recursive models.

Estimating genomic relationships of metafounders across and within breeds using maximum likelihood, pseudo-expectation-maximization maximum likelihood and increase of relationships.

BACKGROUND: The theory of "metafounders" proposes a unified framework for relationships across base populations within breeds (e.g. unknown parent groups), and base populations across breeds (crosses) together with a sensible compatibility with genomic relationships. Considering metafounders might be advantageous in pedigree best linear unbiased prediction (BLUP) or single-step genomic BLUP. Existing methods to estimate relationships across metafounders Γ are not well adapted to highly unbalanced data, genotyped individuals far from base populations, or many unknown parent groups (within breed per year of birth). METHODS: We derive likelihood methods to estimate Γ . For a single metafounder, summary statistics of pedigree and genomic relationships allow deriving a cubic equation with the real root being the maximum likelihood (ML) estimate of Γ . This equation is tested with Lacaune sheep data. For several metafounders, we split the first derivative of the complete likelihood in a term related to Γ , and a second term related to Mendelian sampling variances. Approximating the first derivative by its first term results in a pseudo-EM algorithm that iteratively updates the estimate of Γ by the corresponding block of the H-matrix. The method extends to complex situations with groups defined by year of birth, modelling the increase of Γ using estimates of the rate of increase of inbreeding ( Δ F ), resulting in an expanded Γ and in a pseudo-EM+ Δ F algorithm. We compare these methods with the generalized least squares (GLS) method using simulated data: complex crosses of two breeds in equal or unsymmetrical proportions; and in two breeds, with 10 groups per year of birth within breed. We simulate genotyping in all generations or in the last ones. RESULTS: For a single metafounder, the ML estimates of the Lacaune data corresponded to the maximum. For simulated data, when genotypes were spread across all generations, both GLS and pseudo-EM(+ Δ F ) methods were accurate. With genotypes only available in the most recent generations, the GLS method was biased, whereas the pseudo-EM(+ Δ F ) approach yielded more accurate and unbiased estimates. CONCLUSIONS: We derived ML, pseudo-EM and pseudo-EM+ Δ F methods to estimate Γ in many realistic settings. Estimates are accurate in real and simulated data and have a low computational cost.

Redefining and interpreting genomic relationships of metafounders.

Metafounders are a useful concept to characterize relationships within and across populations, and to help genetic evaluations because they help modelling the means and variances of unknown base population animals. Current definitions of metafounder relationships are sensitive to the choice of reference alleles and have not been compared to their counterparts in population genetics-namely, heterozygosities, FST coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy-Weinberg equilibrium. Then, the relationship between or within populations is a cross-product of the form Γ b , b ' = 2 n 2 p b - 1 2 p b ' - 1 ' with p being vectors of allele frequencies at n markers in populations b and b ' . This is simply the genomic relationship of two pseudo-individuals whose genotypes are equal to twice the allele frequencies. We also show that this coding is invariant to the choice of reference alleles. In addition, standard population genetics metrics (inbreeding coefficients of various forms; FST differentiation coefficients; segregation variance; and Nei's genetic distance) can be obtained from elements of matrix Γ .

Heritable epigenetic changes are constrained by the dynamics of regulatory architectures.

Interacting molecules create regulatory architectures that can persist despite turnover of molecules. Although epigenetic changes occur within the context of such architectures, there is limited understanding of how they can influence the heritability of changes. Here, I develop criteria for the heritability of regulatory architectures and use quantitative simulations of interacting regulators parsed as entities, their sensors, and the sensed properties to analyze how architectures influence heritable epigenetic changes. Information contained in regulatory architectures grows rapidly with the number of interacting molecules and its transmission requires positive feedback loops. While these architectures can recover after many epigenetic perturbations, some resulting changes can become permanently heritable. Architectures that are otherwise unstable can become heritable through periodic interactions with external regulators, which suggests that mortal somatic lineages with cells that reproducibly interact with the immortal germ lineage could make a wider variety of architectures heritable. Differential inhibition of the positive feedback loops that transmit regulatory architectures across generations can explain the gene-specific differences in heritable RNA silencing observed in the nematode Caenorhabditis elegans. More broadly, these results provide a foundation for analyzing the inheritance of epigenetic changes within the context of the regulatory architectures implemented using diverse molecules in different living systems.

Dynamics of karyotype evolution.

In the evolution of species, the karyotype changes with a timescale of tens to hundreds of thousand years. In the development of cancer, the karyotype often is modified in cancerous cells over the lifetime of an individual. Characterizing these changes and understanding the mechanisms leading to them has been of interest in a broad range of disciplines including evolution, cytogenetics, and cancer genetics. A central issue relates to the relative roles of random vs deterministic mechanisms in shaping the changes. Although it is possible that all changes result from random events followed by selection, many results point to other non-random factors that play a role in karyotype evolution. In cancer, chromosomal instability leads to characteristic changes in the karyotype, in which different individuals with a specific type of cancer display similar changes in karyotype structure over time. Statistical analyses of chromosome lengths in different species indicate that the length distribution of chromosomes is not consistent with models in which the lengths of chromosomes are random or evolve solely by simple random processes. A better understanding of the mechanisms underlying karyotype evolution should enable the development of quantitative theoretical models that combine the random and deterministic processes that can be compared to experimental determinations of the karyotype in diverse settings.

An interpretable model of pre-mRNA splicing for animal and plant genes.

Pre-mRNA splicing is a fundamental step in gene expression, conserved across eukaryotes, in which the spliceosome recognizes motifs at the 3' and 5' splice sites (SSs), excises introns, and ligates exons. SS recognition and pairing is often influenced by protein splicing factors (SFs) that bind to splicing regulatory elements (SREs). Here, we describe SMsplice, a fully interpretable model of pre-mRNA splicing that combines models of core SS motifs, SREs, and exonic and intronic length preferences. We learn models that predict SS locations with 83 to 86% accuracy in fish, insects, and plants and about 70% in mammals. Learned SRE motifs include both known SF binding motifs and unfamiliar motifs, and both motif classes are supported by genetic analyses. Our comparisons across species highlight similarities between non-mammals, increased reliance on intronic SREs in plant splicing, and a greater reliance on SREs in mammalian splicing.

Modeling homologous chromosome recognition via nonspecific interactions.

In many organisms, most notably Drosophila, homologous chromosomes associate in somatic cells, a phenomenon known as somatic pairing, which takes place without double strand breaks or strand invasion, thus requiring some other mechanism for homologs to recognize each other. Several studies have suggested a "specific button" model, in which a series of distinct regions in the genome, known as buttons, can associate with each other, mediated by different proteins that bind to these different regions. Here, we use computational modeling to evaluate an alternative "button barcode" model, in which there is only one type of recognition site or adhesion button, present in many copies in the genome, each of which can associate with any of the others with equal affinity. In this model, buttons are nonuniformly distributed, such that alignment of a chromosome with its correct homolog, compared with a nonhomolog, is energetically favored; since to achieve nonhomologous alignment, chromosomes would be required to mechanically deform in order to bring their buttons into mutual register. By simulating randomly generated nonuniform button distributions, many highly effective button barcodes can be easily found, some of which achieve virtually perfect pairing fidelity. This model is consistent with existing literature on the effect of translocations of different sizes on homolog pairing. We conclude that a button barcode model can attain highly specific homolog recognition, comparable to that seen in actual cells undergoing somatic homolog pairing, without the need for specific interactions. This model may have implications for how meiotic pairing is achieved.

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph.

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

Topology and Dynamics of Transcriptome (Dys)Regulation.

RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let us delve into the mathematical intricacies of these sequences. We have previously devised a mathematical approach for defining a "healthy" sequence. This sequence is characterized by having at most four distinct nucleotides (denoted as nt≤4). It serves as the generator of a group denoted as fp. The desired properties of this sequence are as follows: fp should be close to a free group of rank nt-1, it must be aperiodic, and fp should not have isolated singularities within its SL2(C) character variety (specifically within the corresponding Groebner basis). Now, let us explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S24. When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI Equation. In certain cases, S24 degenerates, in the sense that two punctures collapse, resulting in a "wild" dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find many applications including cancer research and the investigation of neurodegenative diseases.

SEEI: spherical evolution with feedback mechanism for identifying epistatic interactions.

BACKGROUND: Detecting epistatic interactions (EIs) involves the exploration of associations among single nucleotide polymorphisms (SNPs) and complex diseases, which is an important task in genome-wide association studies. The EI detection problem is dependent on epistasis models and corresponding optimization methods. Although various models and methods have been proposed to detect EIs, identifying EIs efficiently and accurately is still a challenge. RESULTS: Here, we propose a linear mixed statistical epistasis model (LMSE) and a spherical evolution approach with a feedback mechanism (named SEEI). The LMSE model expands the existing single epistasis models such as LR-Score, K2-Score, Mutual information, and Gini index. The SEEI includes an adaptive spherical search strategy and population updating strategy, which ensures that the algorithm is not easily trapped in local optima. We analyzed the performances of 8 random disease models, 12 disease models with marginal effects, 30 disease models without marginal effects, and 10 high-order disease models. The 60 simulated disease models and a real breast cancer dataset were used to evaluate eight algorithms (SEEI, EACO, EpiACO, FDHEIW, MP-HS-DHSI, NHSA-DHSC, SNPHarvester, CSE). Three evaluation criteria (pow1, pow2, pow3), a T-test, and a Friedman test were used to compare the performances of these algorithms. The results show that the SEEI algorithm (order 1, averages ranks = 13.125) outperformed the other algorithms in detecting EIs. CONCLUSIONS: Here, we propose an LMSE model and an evolutionary computing method (SEEI) to solve the optimization problem of the LMSE model. The proposed method performed better than the other seven algorithms tested in its ability to identify EIs in genome-wide association datasets. We identified new SNP-SNP combinations in the real breast cancer dataset and verified the results. Our findings provide new insights for the diagnosis and treatment of breast cancer. AVAILABILITY AND IMPLEMENTATION: https://github.com/scutdy/SSO/blob/master/SEEI.zip .

Detecting inbreeding depression in structured populations.

Measuring inbreeding and its consequences on fitness is central for many areas in biology including human genetics and the conservation of endangered species. However, there is no consensus on the best method, neither for quantification of inbreeding itself nor for the model to estimate its effect on specific traits. We simulated traits based on simulated genomes from a large pedigree and empirical whole-genome sequences of human data from populations with various sizes and structures (from the 1,000 Genomes project). We compare the ability of various inbreeding coefficients ([Formula: see text]) to quantify the strength of inbreeding depression: allele-sharing, two versions of the correlation of uniting gametes which differ in the weight they attribute to each locus and two identical-by-descent segments-based estimators. We also compare two models: the standard linear model and a linear mixed model (LMM) including a genetic relatedness matrix (GRM) as random effect to account for the nonindependence of observations. We find LMMs give better results in scenarios with population or family structure. Within the LMM, we compare three different GRMs and show that in homogeneous populations, there is little difference among the different [Formula: see text] and GRM for inbreeding depression quantification. However, as soon as a strong population or family structure is present, the strength of inbreeding depression can be most efficiently estimated only if i) the phenotypes are regressed on [Formula: see text] based on a weighted version of the correlation of uniting gametes, giving more weight to common alleles and ii) with the GRM obtained from an allele-sharing relatedness estimator.

Synergistic epistasis among cancer drivers can rescue early tumors from the accumulation of deleterious passengers.

Epistasis among driver mutations is pervasive and explains relevant features of cancer, such as differential therapy response and convergence towards well-characterized molecular subtypes. Furthermore, a growing body of evidence suggests that tumor development could be hampered by the accumulation of slightly deleterious passenger mutations. In this work, we combined empirical epistasis networks, computer simulations, and mathematical models to explore how synergistic interactions among driver mutations affect cancer progression under the burden of slightly deleterious passengers. We found that epistasis plays a crucial role in tumor development by promoting the transformation of precancerous clones into rapidly growing tumors through a process that is analogous to evolutionary rescue. The triggering of epistasis-driven rescue is strongly dependent on the intensity of epistasis and could be a key rate-limiting step in many tumors, contributing to their unpredictability. As a result, central genes in cancer epistasis networks appear as key intervention targets for cancer therapy.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Optimizing selection based on BLUPs or BLUEs in multiple sets of genotypes differing in their population parameters.

KEY MESSAGE: Selection response in truncation selection across multiple sets of candidates hinges on their post-selection proportions, which can deviate grossly from their initial proportions. For BLUPs, using a uniform threshold for all candidates maximizes the selection response, irrespective of differences in population parameters. Plant breeding programs typically involve multiple families from either the same or different populations, varying in means, genetic variances and prediction accuracy of BLUPs or BLUEs for true genetic values (TGVs) of candidates. We extend the classical breeder's equation for truncation selection from single to multiple sets of genotypes, indicating that the expected overall selection response ( Δ G Tot ) for TGVs depends on the selection response within individual sets and their post-selection proportions. For BLUEs, we show that maximizing Δ G Tot requires thresholds optimally tailored for each set, contingent on their population parameters. For BLUPs, we prove that Δ G Tot is maximized by applying a uniform threshold across all candidates from all sets. We provide explicit formulas for the origin of the selected candidates from different sets and show that their proportions before and after selection can differ substantially, especially for sets with inferior properties and low proportion. We discuss implications of these results for (a) optimum allocation of resources to training and prediction sets and (b) the need to counteract narrowing the genetic variation under genomic selection. For genomic selection of hybrids based on BLUPs of GCA of their parent lines, selecting distinct proportions in the two parent populations can be advantageous, if these differ substantially in the variance and/or prediction accuracy of GCA. Our study sheds light on the complex interplay of selection thresholds and population parameters for the selection response in plant breeding programs, offering insights into the effective resource management and prudent application of genomic selection for improved crop development.

Ocean to Tree: Leveraging Single-Molecule RNA-Seq to Repair Genome Gene Models and Improve Phylogenomic Analysis of Gene and Species Evolution.

Understanding gene evolution across genomes and organisms, including ctenophores, can provide unexpected biological insights. It enables powerful integrative approaches that leverage sequence diversity to advance biomedicine. Sequencing and bioinformatic tools can be inexpensive and user-friendly, but numerous options and coding can intimidate new users. Distinct challenges exist in working with data from diverse species but may go unrecognized by researchers accustomed to gold-standard genomes. Here, we provide a high-level workflow and detailed pipeline to enable animal collection, single-molecule sequencing, and phylogenomic analysis of gene and species evolution. As a demonstration, we focus on (1) PacBio RNA-seq of the genome-sequenced ctenophore Mnemiopsis leidyi, (2) diversity and evolution of the mechanosensitive ion channel Piezo in genetic models and basal-branching animals, and (3) associated challenges and solutions to working with diverse species and genomes, including gene model updating and repair using single-molecule RNA-seq. We provide a Python Jupyter Notebook version of our pipeline (GitHub Repository: Ctenophore-Ocean-To-Tree-2023 https://github.com/000generic/Ctenophore-Ocean-To-Tree-2023 ) that can be run for free in the Google Colab cloud to replicate our findings or modified for specific or greater use. Our protocol enables users to design new sequencing projects in ctenophores, marine invertebrates, or other novel organisms. It provides a simple, comprehensive platform that can ease new user entry into running their evolutionary sequence analyses.

Modelling Plasmid-Mediated Horizontal Gene Transfer in Biofilms.

In this study, we present a mathematical model for plasmid spread in a growing biofilm, formulated as a nonlocal system of partial differential equations in a 1-D free boundary domain. Plasmids are mobile genetic elements able to transfer to different phylotypes, posing a global health problem when they carry antibiotic resistance factors. We model gene transfer regulation influenced by nearby potential receptors to account for recipient-sensing. We also introduce a promotion function to account for trace metal effects on conjugation, based on literature data. The model qualitatively matches experimental results, showing that contaminants like toxic metals and antibiotics promote plasmid persistence by favoring plasmid carriers and stimulating conjugation. Even at higher contaminant concentrations inhibiting conjugation, plasmid spread persists by strongly inhibiting plasmid-free cells. The model also replicates higher plasmid density in biofilm's most active regions.

GbyE: an integrated tool for genome widely association study and genome selection based on genetic by environmental interaction.

BACKGROUND: The growth and development of organism were dependent on the effect of genetic, environment, and their interaction. In recent decades, lots of candidate additive genetic markers and genes had been detected by using genome-widely association study (GWAS). However, restricted to computing power and practical tool, the interactive effect of markers and genes were not revealed clearly. And utilization of these interactive markers is difficult in the breeding and prediction, such as genome selection (GS). RESULTS: Through the Power-FDR curve, the GbyE algorithm can detect more significant genetic loci at different levels of genetic correlation and heritability, especially at low heritability levels. The additive effect of GbyE exhibits high significance on certain chromosomes, while the interactive effect detects more significant sites on other chromosomes, which were not detected in the first two parts. In prediction accuracy testing, in most cases of heritability and genetic correlation, the majority of prediction accuracy of GbyE is significantly higher than that of the mean method, regardless of whether the rrBLUP model or BGLR model is used for statistics. The GbyE algorithm improves the prediction accuracy of the three Bayesian models BRR, BayesA, and BayesLASSO using information from genetic by environmental interaction (G × E) and increases the prediction accuracy by 9.4%, 9.1%, and 11%, respectively, relative to the Mean value method. The GbyE algorithm is significantly superior to the mean method in the absence of a single environment, regardless of the combination of heritability and genetic correlation, especially in the case of high genetic correlation and heritability. CONCLUSIONS: Therefore, this study constructed a new genotype design model program (GbyE) for GWAS and GS using Kronecker product. which was able to clearly estimate the additive and interactive effects separately. The results showed that GbyE can provide higher statistical power for the GWAS and more prediction accuracy of the GS models. In addition, GbyE gives varying degrees of improvement of prediction accuracy in three Bayesian models (BRR, BayesA, and BayesCpi). Whatever the phenotype were missed in the single environment or multiple environments, the GbyE also makes better prediction for inference population set. This study helps us understand the interactive relationship between genomic and environment in the complex traits. The GbyE source code is available at the GitHub website ( https://github.com/liu-xinrui/GbyE ).

Phylogenetic network classes through the lens of expanding covers.

It was recently shown that a large class of phylogenetic networks, the 'labellable' networks, is in bijection with the set of 'expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call 'spinal' phylogenetic networks.