Autism-related dietary preferences mediate autism-gut microbiome associations.

There is increasing interest in the potential contribution of the gut microbiome to autism spectrum disorder (ASD). However, previous studies have been underpowered and have not been designed to address potential confounding factors in a comprehensive way. We performed a large autism stool metagenomics study (n = 247) based on participants from the Australian Autism Biobank and the Queensland Twin Adolescent Brain project. We found negligible direct associations between ASD diagnosis and the gut microbiome. Instead, our data support a model whereby ASD-related restricted interests are associated with less-diverse diet, and in turn reduced microbial taxonomic diversity and looser stool consistency. In contrast to ASD diagnosis, our dataset was well powered to detect microbiome associations with traits such as age, dietary intake, and stool consistency. Overall, microbiome differences in ASD may reflect dietary preferences that relate to diagnostic features, and we caution against claims that the microbiome has a driving role in ASD.

Consistently estimating network statistics using aggregated relational data.

Collecting complete network data is expensive, time-consuming, and often infeasible. Aggregated Relational Data (ARD), which ask respondents questions of the form "How many people with trait X do you know?" provide a low-cost option when collecting complete network data is not possible. Rather than asking about connections between each pair of individuals directly, ARD collect the number of contacts the respondent knows with a given trait. Despite widespread use and a growing literature on ARD methodology, there is still no systematic understanding of when and why ARD should accurately recover features of the unobserved network. This paper provides such a characterization by deriving conditions under which statistics about the unobserved network (or functions of these statistics like regression coefficients) can be consistently estimated using ARD. We first provide consistent estimates of network model parameters for three commonly used probabilistic models: the beta-model with node-specific unobserved effects, the stochastic block model with unobserved community structure, and latent geometric space models with unobserved latent locations. A key observation is that cross-group link probabilities for a collection of (possibly unobserved) groups identify the model parameters, meaning ARD are sufficient for parameter estimation. With these estimated parameters, it is possible to simulate graphs from the fitted distribution and analyze the distribution of network statistics. We can then characterize conditions under which the simulated networks based on ARD will allow for consistent estimation of the unobserved network statistics, such as eigenvector centrality, or response functions by or of the unobserved network, such as regression coefficients.

Wide and deep neural networks achieve consistency for classification.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are consistent for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that are consistent. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and neural tangent kernels, we provide explicit activation functions that can be used to construct networks that achieve consistency. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: 1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); 2) majority vote (model predictions are given by the label of the class with the greatest representation in the training set); or 3) singular kernel classifiers (a set of classifiers containing those that achieve consistency). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Mixed Selectivity Coding of Content-Temporal Detail by Dorsomedial Posterior Parietal Neurons.

The dorsomedial posterior parietal cortex (dmPPC) is part of a higher-cognition network implicated in elaborate processes underpinning memory formation, recollection, episode reconstruction, and temporal information processing. Neural coding for complex episodic processing is however under-documented. Here, we recorded extracellular neural activities from three male rhesus macaques (Macaca mulatta) and revealed a set of neural codes of "neuroethogram" in the primate parietal cortex. Analyzing neural responses in macaque dmPPC to naturalistic videos, we discovered several groups of neurons that are sensitive to different categories of ethogram items, low-level sensory features, and saccadic eye movement. We also discovered that the processing of category and feature information by these neurons is sustained by the accumulation of temporal information over a long timescale of up to 30 s, corroborating its reported long temporal receptive windows. We performed an additional behavioral experiment with additional two male rhesus macaques and found that saccade-related activities could not account for the mixed neuronal responses elicited by the video stimuli. We further observed monkeys' scan paths and gaze consistency are modulated by video content. Taken altogether, these neural findings explain how dmPPC weaves fabrics of ongoing experiences together in real time. The high dimensionality of neural representations should motivate us to shift the focus of attention from pure selectivity neurons to mixed selectivity neurons, especially in increasingly complex naturalistic task designs.

R2-DDI: relation-aware feature refinement for drug-drug interaction prediction.

Precisely predicting the drug-drug interaction (DDI) is an important application and host research topic in drug discovery, especially for avoiding the adverse effect when using drug combination treatment for patients. Nowadays, machine learning and deep learning methods have achieved great success in DDI prediction. However, we notice that most of the works ignore the importance of the relation type when building the DDI prediction models. In this work, we propose a novel R$^2$-DDI framework, which introduces a relation-aware feature refinement module for drug representation learning. The relation feature is integrated into drug representation and refined in the framework. With the refinement features, we also incorporate the consistency training method to regularize the multi-branch predictions for better generalization. Through extensive experiments and studies, we demonstrate our R$^2$-DDI approach can significantly improve the DDI prediction performance over multiple real-world datasets and settings, and our method shows better generalization ability with the help of the feature refinement design.

Provable Boolean interaction recovery from tree ensemble obtained via random forests.

Random Forests (RFs) are at the cutting edge of supervised machine learning in terms of prediction performance, especially in genomics. Iterative RFs (iRFs) use a tree ensemble from iteratively modified RFs to obtain predictive and stable nonlinear or Boolean interactions of features. They have shown great promise for Boolean biological interaction discovery that is central to advancing functional genomics and precision medicine. However, theoretical studies into how tree-based methods discover Boolean feature interactions are missing. Inspired by the thresholding behavior in many biological processes, we first introduce a discontinuous nonlinear regression model, called the "Locally Spiky Sparse" (LSS) model. Specifically, the LSS model assumes that the regression function is a linear combination of piecewise constant Boolean interaction terms. Given an RF tree ensemble, we define a quantity called "Depth-Weighted Prevalence" (DWP) for a set of signed features S±. Intuitively speaking, DWP(S±) measures how frequently features in S± appear together in an RF tree ensemble. We prove that, with high probability, DWP(S±) attains a universal upper bound that does not involve any model coefficients, if and only if S± corresponds to a union of Boolean interactions under the LSS model. Consequentially, we show that a theoretically tractable version of the iRF procedure, called LSSFind, yields consistent interaction discovery under the LSS model as the sample size goes to infinity. Finally, simulation results show that LSSFind recovers the interactions under the LSS model, even when some assumptions are violated.

Standardizing Protein Corona Characterization in Nanomedicine: A Multicenter Study to Enhance Reproducibility and Data Homogeneity.

We recently revealed significant variability in protein corona characterization across various proteomics facilities, indicating that data sets are not comparable between independent studies. This heterogeneity mainly arises from differences in sample preparation protocols, mass spectrometry workflows, and raw data processing. To address this issue, we developed standardized protocols and unified sample preparation workflows, distributing uniform protein corona digests to several top-performing proteomics centers from our previous study. We also examined the influence of using similar mass spectrometry instruments on data homogeneity and standardized database search parameters and data processing workflows. Our findings reveal a remarkable stepwise improvement in protein corona data uniformity, increasing overlaps in protein identification from 11% to 40% across facilities using similar instruments and through a uniform database search. We identify the key parameters behind data heterogeneity and provide recommendations for designing experiments. Our findings should significantly advance the robustness of protein corona analysis for diagnostic and therapeutics applications.

Phase 3 Study Assessing Lot-to-lot Consistency of RSVPreF3 Vaccine and its Immune Response, Safety, and Reactogenicity When Co-administered with FLU-D-QIV.

BACKGROUND: A single-dose investigational respiratory syncytial virus (RSV) vaccine, RSV prefusion protein F3 (RSVPreF3), was co-administered with a single-dose quadrivalent influenza vaccine (FLU-D-QIV) in a phase 3, randomized, controlled, multicenter study in healthy, non-pregnant women aged 18-49 years. METHODS: The study was observer-blind to evaluate the lot-to-lot consistency of RSVPreF3, and single-blind to evaluate the immune response, safety, and reactogenicity of RSVPreF3 co-administered with FLU-D-QIV. RESULTS: A total of 1415 participants were included in the per-protocol set. There was a robust immune response at day 31 across each of the 3 RSVPreF3 vaccine lots; adjusted geometric mean concentration ratios (95% confidence interval [CI]) were 1.01 (0.91, 1.12), 0.93 (0.84, 1.03), and 0.92 (0.83, 1.02) for RSV1/RSV2, RSV1/RSV3, and RSV2/RSV3, respectively. For FLU-D-QIV co-administered with RSVPreF3, versus FLU-D-QIV alone at day 31, noninferiority was satisfied for 3 of 4 strains assessed, with the lower limit of the 95% CI for geometric mean ratio >0.67. CONCLUSIONS: Immunogenic consistency was demonstrated for 3 separate lots of RSVPreF3. Immunogenic noninferiority was demonstrated when comparing FLU-D-QIV administered alone, versus co-administered with RSVPreF3, for 3 strains of FLU-D-QIV. Co-administration was well tolerated, and both vaccines had clinically acceptable safety and reactogenicity profiles. CLINICAL TRIALS REGISTRATION: NCT05045144; EudraCT, 2021-000357-26.

This was a phase 3 study that compared antibodies against respiratory syncytial virus (or RSV for short) between women who were given 3 different production batches of RSV prefusion protein F3 (known as RSVPreF3) vaccine. The study also compared the antibodies between women who received either an RSV vaccine together with a flu vaccine (known as FLU-D-QIV), or a flu vaccine alone. The flu vaccine contained 4 different strains of flu virus. The study involved 1415 healthy, non-pregnant women aged 18­49 years. The antibodies checked after 31 days showed strong immune responses for all 3 RSV vaccine production batches, and similar immune responses between each of the 3 RSV vaccine production batches. The immune response of 3 of the 4 flu strains was not less when the flu vaccine was given together with the RSV vaccine than the immune response when flu vaccine was given alone and both vaccines were well tolerated.

SCPLPA: An miRNA-disease association prediction model based on spatial consistency projection and label propagation algorithm.

Identifying the association between miRNA and diseases is helpful for disease prevention, diagnosis and treatment. It is of great significance to use computational methods to predict potential human miRNA disease associations. Considering the shortcomings of existing computational methods, such as low prediction accuracy and weak generalization, we propose a new method called SCPLPA to predict miRNA-disease associations. First, a heterogeneous disease similarity network was constructed using the disease semantic similarity network and the disease Gaussian interaction spectrum kernel similarity network, while a heterogeneous miRNA similarity network was constructed using the miRNA functional similarity network and the miRNA Gaussian interaction spectrum kernel similarity network. Then, the estimated miRNA-disease association scores were evaluated by integrating the outcomes obtained by implementing label propagation algorithms in the heterogeneous disease similarity network and the heterogeneous miRNA similarity network. Finally, the spatial consistency projection algorithm of the network was used to extract miRNA disease association features to predict unverified associations between miRNA and diseases. SCPLPA was compared with four classical methods (MDHGI, NSEMDA, RFMDA and SNMFMDA), and the results of multiple evaluation metrics showed that SCPLPA exhibited the most outstanding predictive performance. Case studies have shown that SCPLPA can effectively identify miRNAs associated with colon neoplasms and kidney neoplasms. In summary, our proposed SCPLPA algorithm is easy to implement and can effectively predict miRNA disease associations, making it a reliable auxiliary tool for biomedical research.

BASE: Brain Age Standardized Evaluation.

Brain age, most commonly inferred from T1-weighted magnetic resonance images (T1w MRI), is a robust biomarker of brain health and related diseases. Superior accuracy in brain age prediction, often falling within a 2-3 year range, is achieved predominantly through deep neural networks. However, comparing study results is difficult due to differences in datasets, evaluation methodologies and metrics. Addressing this, we introduce Brain Age Standardized Evaluation (BASE), which includes (i) a standardized T1w MRI dataset including multi-site, new unseen site, test-retest and longitudinal data, and an associated (ii) evaluation protocol, including repeated model training and upon based comprehensive set of performance metrics measuring accuracy, robustness, reproducibility and consistency aspects of brain age predictions, and (iii) statistical evaluation framework based on linear mixed-effects models for rigorous performance assessment and cross-comparison. To showcase BASE, we comprehensively evaluate four deep learning based brain age models, appraising their performance in scenarios that utilize multi-site, test-retest, unseen site, and longitudinal T1w brain MRI datasets. Ensuring full reproducibility and application in future studies, we have made all associated data information and code publicly accessible at https://github.com/AralRalud/BASE.git.

Sexual Harassment, Sexual Violence, and Mental Health Outcomes: Causal Inference with Ambiguous Exposures.

Social exposures and their impact on mental health has proven hard to capture, partly owing to the complex and multifaceted nature of social reality. Sexual harassment and sexual violence (SHV) are no exceptions. SHV can be conceptualized as a continuum of negative sexual experiences whose severity vary depending on multiple determinants. Further, SHV can be conceptualized as either discrete events or as a generally hostile sexual environment represented by latent variables. With any of these conceptualizations, SHV constitutes a broad construct containing many kinds of negative experiences. This ambiguity poses challenges for determining the mental health consequences, as different forms of SHV may vary in terms of their mental health impact. We discuss different conceptualizations of SHV in relation to mental health outcomes through the lens of the potential outcomes framework, with a focus on the consistency condition. The multiple versions of treatment theory is presented to show how to provide formal interpretations of causal estimates under ambiguous exposures. Lastly, we provide suggestions on how the increase the clarity and interpretability of the effects of SHV on mental health, by increasing the precision of the causal questions and the use of more specific definitions of SHV.

Dataset factors associated with age-related changes in brain structure and function in neurodevelopmental conditions.

With brain structure and function undergoing complex changes throughout childhood and adolescence, age is a critical consideration in neuroimaging studies, particularly for those of individuals with neurodevelopmental conditions. However, despite the increasing use of large, consortium-based datasets to examine brain structure and function in neurotypical and neurodivergent populations, it is unclear whether age-related changes are consistent between datasets and whether inconsistencies related to differences in sample characteristics, such as demographics and phenotypic features, exist. To address this, we built models of age-related changes of brain structure (regional cortical thickness and regional surface area; N = 1218) and function (resting-state functional connectivity strength; N = 1254) in two neurodiverse datasets: the Province of Ontario Neurodevelopmental Network and the Healthy Brain Network. We examined whether deviations from these models differed between the datasets, and explored whether these deviations were associated with demographic and clinical variables. We found significant differences between the two datasets for measures of cortical surface area and functional connectivity strength throughout the brain. For regional measures of cortical surface area, the patterns of differences were associated with race/ethnicity, while for functional connectivity strength, positive associations were observed with head motion. Our findings highlight that patterns of age-related changes in the brain may be influenced by demographic and phenotypic characteristics, and thus future studies should consider these when examining or controlling for age effects in analyses.

Bayesian multiregional clinical trials using model averaging.

Multiregional clinical trials (MRCTs) provide the benefit of more rapidly introducing drugs to the global market; however, small regional sample sizes can lead to poor estimation quality of region-specific effects when using current statistical methods. With the publication of the International Conference for Harmonisation E17 guideline in 2017, the MRCT design is recognized as a viable strategy that can be accepted by regional regulatory authorities, necessitating new statistical methods that improve the quality of region-specific inference. In this article, we develop a novel methodology for estimating region-specific and global treatment effects for MRCTs using Bayesian model averaging. This approach can be used for trials that compare two treatment groups with respect to a continuous outcome, and it allows for the incorporation of patient characteristics through the inclusion of covariates. We propose an approach that uses posterior model probabilities to quantify evidence in favor of consistency of treatment effects across all regions, and this metric can be used by regulatory authorities for drug approval. We show through simulations that the proposed modeling approach results in lower MSE than a fixed-effects linear regression model and better control of type I error rates than a Bayesian hierarchical model.

Low awareness of the transitivity assumption in complex networks of interventions: a systematic survey from 721 network meta-analyses.

BACKGROUND: The transitivity assumption is the cornerstone of network meta-analysis (NMA). Violating transitivity compromises the credibility of the indirect estimates and, by extent, the estimated treatment effects of the comparisons in the network. The present study offers comprehensive empirical evidence on the completeness of reporting and evaluating transitivity in systematic reviews with multiple interventions. METHODS: We screened the datasets of two previous empirical studies, resulting in 361 systematic reviews with NMA published between January 2011 and April 2015. We updated our evidence base with an additional 360 systematic reviews with NMA published between 2016 and 2021, employing a pragmatic approach. We devised assessment criteria for reporting and evaluating transitivity using relevant methodological literature and compared their reporting frequency before and after the PRISMA-NMA statement. RESULTS: Systematic reviews published after PRISMA-NMA were more likely to provide a protocol (odds ratio (OR): 3.94, 95% CI: 2.79-5.64), pre-plan the transitivity evaluation (OR: 3.01, 95% CI: 1.54-6.23), and report the evaluation and results (OR: 2.10, 95% CI: 1.55-2.86) than those before PRISMA-NMA. However, systematic reviews after PRISMA-NMA were less likely to define transitivity (OR: 0.57, 95% CI: 0.42-0.79) and discuss the implications of transitivity (OR: 0.48, 95% CI: 0.27-0.85) than those published before PRISMA-NMA. Most systematic reviews evaluated transitivity statistically than conceptually (40% versus 12% before PRISMA-NMA, and 54% versus 11% after PRISMA-NMA), with consistency evaluation being the most preferred (34% before versus 47% after PRISMA-NMA). One in five reviews inferred the plausibility of the transitivity (22% before versus 18% after PRISMA-NMA), followed by 11% of reviews that found it difficult to judge transitivity due to insufficient data. In justifying their conclusions, reviews considered mostly the comparability of the trials (24% before versus 30% after PRISMA-NMA), followed by the consistency evaluation (23% before versus 16% after PRISMA-NMA). CONCLUSIONS: Overall, there has been a slight improvement in reporting and evaluating transitivity since releasing PRISMA-NMA, particularly in items related to the systematic review report. Nevertheless, there has been limited attention to pre-planning the transitivity evaluation and low awareness of the conceptual evaluation methods that align with the nature of the assumption.

Species-specific behavioural responses to environmental variation as a potential species coexistence mechanism in ants.

A fundamental question of ecology is why species coexist in the same habitat. Coexistence can be enabled through niche differentiation, mediated by trait differentiation. Here, behaviour constitutes an often-overlooked set of traits. However, behaviours such as aggression and exploration drive intra- and interspecific competition, especially so in ants, where community structure is usually shaped by aggressive interactions. We studied behavioural variation in three ant species, which often co-occur in close proximity and occupy similar dominance ranks. We analysed how intra- and allospecific aggression, exploration and foraging activity vary under field conditions, namely with temperature and over time. Behaviours were assessed for 12 colonies per species, and four times each during several months. All behavioural traits consistently differed among colonies, but also varied over time and with temperature. These temperature-dependent and seasonal responses were highly species-specific. For example, foraging activity decreased at high temperatures in Formica rufibarbis, but not in Lasius niger; over time, it declined strongly in L. niger but much less in F. rufibarbis. Our results suggest that, owing to these species-specific responses, no species is always competitively superior. Thus, environmental and temporal variation effects a dynamic dominance hierarchy among the species, facilitating coexistence via the storage effect.

ConSIG: consistent discovery of molecular signature from OMIC data.

The discovery of proper molecular signature from OMIC data is indispensable for determining biological state, physiological condition, disease etiology, and therapeutic response. However, the identified signature is reported to be highly inconsistent, and there is little overlap among the signatures identified from different biological datasets. Such inconsistency raises doubts about the reliability of reported signatures and significantly hampers its biological and clinical applications. Herein, an online tool, ConSIG, was constructed to realize consistent discovery of gene/protein signature from any uploaded transcriptomic/proteomic data. This tool is unique in a) integrating a novel strategy capable of significantly enhancing the consistency of signature discovery, b) determining the optimal signature by collective assessment, and c) confirming the biological relevance by enriching the disease/gene ontology. With the increasingly accumulated concerns about signature consistency and biological relevance, this online tool is expected to be used as an essential complement to other existing tools for OMIC-based signature discovery. ConSIG is freely accessible to all users without login requirement at https://idrblab.org/consig/.

Modulation of audiovisual integration in the left and right sides: effects of side and spatial coherency.

BACKGROUND: Using event-related potentials (ERPs), we aimed to investigate audiovisual integration neural mechanisms during a letter identification task in the left and right sides. Unimodal (A,V) and bimodal (AV) stimuli were presented on either side, with ERPs from unimodal (A,V) stimuli on the same side being compared to those from simultaneous bimodal stimuli (AV). Non-zero results of the AV-(A + V) difference waveforms indicated audiovisual integration on the left/right side. RESULTS: When spatially coherent AV stimuli were presented on the right side, two significant ERP components in the integrated differential wave were noted. The N134 and N262, present in the first 300 ms of the AV-(A + V) integration difference wave, indicated significant audiovisual integration effects. However, when these stimuli were presented on the left side, there were no significant integration components. This audiovisual integration difference may stem from left/right asymmetry of cerebral hemisphere language processing. CONCLUSIONS: Audiovisual letter information presented on the right side was easier to integrate, process, and represent. Additionally, only one significant integrative component peaked at 140 ms in the parietal cortex for spatially non-coherent AV stimuli and provided audiovisual multisensory integration, which could be attributed to some integrative neural processes that depend on the spatial congruity of the auditory and visual stimuli.

Artificial intelligence enhances whole-slide interpretation of PD-L1 CPS in triple-negative breast cancer: A multi-institutional ring study.

BACKGROUND AND AIMS: Evaluation of the programmed cell death ligand-1 (PD-L1) combined positive score (CPS) is vital to predict the efficacy of the immunotherapy in triple-negative breast cancer (TNBC), but pathologists show substantial variability in the consistency and accuracy of the interpretation. It is of great importance to establish an objective and effective method which is highly repeatable. METHODS: We proposed a model in a deep learning-based framework, which at the patch level incorporated cell analysis and tissue region analysis, followed by the whole-slide level fusion of patch results. Three rounds of ring studies (RSs) were conducted. Twenty-one pathologists of different levels from four institutions evaluated the PD-L1 CPS in TNBC specimens as continuous scores by visual assessment and our artificial intelligence (AI)-assisted method. RESULTS: In the visual assessment, the interpretation results of PD-L1 (Dako 22C3) CPS by different levels of pathologists have significant differences and showed weak consistency. Using AI-assisted interpretation, there were no significant differences between all pathologists (P = 0.43), and the intraclass correlation coefficient (ICC) value was increased from 0.618 [95% confidence interval (CI) = 0.524-0.719] to 0.931 (95% CI = 0.902-0.955). The accuracy of interpretation result is further improved to 0.919 (95% CI = 0.886-0.947). Acceptance of AI results by junior pathologists was the highest among all levels, and 80% of the AI results were accepted overall. CONCLUSION: With the help of the AI-assisted diagnostic method, different levels of pathologists achieved excellent consistency and repeatability in the interpretation of PD-L1 (Dako 22C3) CPS. Our AI-assisted diagnostic approach was proved to strengthen the consistency and repeatability in clinical practice.

On multi-type Cannings models and multi-type exchangeable coalescents.

A multi-type neutral Cannings population model with migration and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a multi-type coalescent sharing the exchangeability and consistency property. The proof gains from coalescent theory for single-type Cannings models and from decompositions of transition probabilities into parts concerning reproduction and migration respectively. The following section deals with a different but closely related multi-type Cannings model with mutation and fixed total population size but stochastically varying subpopulation sizes. The latter model is analyzed forward and backward in time with an emphasis on its behavior as the total population size tends to infinity. Forward in time, multi-type limiting branching processes arise for large population size. Its backward structure and related open problems are briefly discussed.

Gene Transfer-Based Phylogenetics: Analytical Expressions and Additivity via Birth-Death Theory.

The genomic era has opened up vast opportunities in molecular systematics, one of which is deciphering the evolutionary history in fine detail. Under this mass of data, analyzing the point mutations of standard markers is often too crude and slow for fine-scale phylogenetics. Nevertheless, genome dynamics (GD) events provide alternative, often richer information. The synteny index (SI) between a pair of genomes combines gene order and gene content information, allowing the comparison of genomes of unequal gene content, together with order considerations of their common genes. Recently, genome dynamics has been modeled as a continuous-time Markov process, and gene distance in the genome as a birth-death-immigration process. Nevertheless, due to complexities arising in this setting, no precise and provably consistent estimators could be derived, resulting in heuristic solutions. Here, we extend this modeling approach by using techniques from birth-death theory to derive explicit expressions of the system's probabilistic dynamics in the form of rational functions of the model parameters. This, in turn, allows us to infer analytically accurate distances between organisms based on their SI. Subsequently, we establish additivity of this estimated evolutionary distance (a desirable property yielding phylogenetic consistency). Applying the new measure in simulation studies shows that it provides accurate results in realistic settings and even under model extensions such as gene gain/loss or over a tree structure. In the real-data realm, we applied the new formulation to unique data structure that we constructed-the ordered orthology DB-based on a new version of the EggNOG database, to construct a tree with more than 4.5K taxa. To the best of our knowledge, this is the largest gene-order-based tree constructed and it overcomes shortcomings found in previous approaches. Constructing a GD-based tree allows to confirm and contrast findings based on other phylogenetic approaches, as we show.