Synergizing economic growth and carbon emission reduction in China: A path to coupling the MFLP and PLUS models for optimizing the territorial spatial functional pattern.

Carbon emissions caused by economic growth are the main cause of global warming, but controlling economic growth to reduce carbon emissions does not meet China's conditions. Therefore, how to synergize economic growth and carbon emission reduction is not only a sustainable development issue for China, but also significant for mitigating global warming. The territorial spatial functional pattern (TSFP) is the spatial carrier for coordinating economic development and carbon emissions, but how to establish the TSFP of synergizing economic growth and carbon emission reduction remains unresolved. We propose a decision framework for optimizing TSFP coupled with the multi-objective fuzzy linear programming and the patch-generating land use simulation model, to provide a new path to synergize economic growth and carbon emission reduction in China. To confirm the reliability, we took Qionglai City as the demonstration. The results found a significant spatiotemporal coupling between TSFP and the synergistic states between economic growth and carbon emission reduction (q ≥ 0.8220), which resolves the theoretical uncertainty about synergizing economic growth and carbon emission reduction through the path of TSFP optimization. The urban space of Qionglai City in 2025 and 2030 obtained by the decision framework was 6497.57 hm2 and 6628.72 hm2 respectively, distributed in the central and eastern regions; the rural space was 60,132.92 hm2 and 56,084.97 hm2, concentrated in the east, with a few located in the west; and the ecological space was 71,072.52 hm2 and 74,998.31 hm2, mainly located in the western and southeastern areas. Compared with the TSFP in 2020, the carbon emission intensity of the TSFP obtained by the decision framework was reduced by 0.7 and 4.7 tons/million yuan, respectively, and realized the synergy between economic growth and carbon emission reduction (decoupling index was 0.25 and 0.21). Further confirming that TSFP optimization is an effective way to synergize economic growth and carbon emission reduction, which can provide policy implications for coordinating economic growth and carbon emissions for China and even similar developing countries.

Gene Flow and Isolation in the Arid Nearctic Revealed by Genomic Analyses of Desert Spiny Lizards.

The opposing forces of gene flow and isolation are two major processes shaping genetic diversity. Understanding how these vary across space and time is necessary to identify the environmental features that promote diversification. The detection of considerable geographic structure in taxa from the arid Nearctic has prompted research into the drivers of isolation in the region. Several geographic features have been proposed as barriers to gene flow, including the Colorado River, Western Continental Divide, and a hypothetical Mid-Peninsular Seaway in Baja California. However, recent studies suggest that the role of barriers in genetic differentiation may have been overestimated when compared to other mechanisms of divergence. In this study, we infer historical and spatial patterns of connectivity and isolation in Desert Spiny Lizards (Sceloporus magister) and Baja Spiny Lizards (S. zosteromus), which together form a species complex composed of parapatric lineages with wide distributions in arid western North America. Our analyses incorporate mitochondrial sequences, genomic-scale data, and past and present climatic data to evaluate the nature and strength of barriers to gene flow in the region. Our approach relies on estimates of migration under the multispecies coalescent to understand the history of lineage divergence in the face of gene flow. Results show that the S. magister complex is geographically structured, but we also detect instances of gene flow. The Continental Divide is a strong barrier to gene flow, while the Colorado River is more permeable. Analyses yield conflicting results for the catalyst of differentiation of peninsular lineages in S. zosteromus. Our study shows how large-scale genomic data for thoroughly sampled species can shed new light on biogeography. Furthermore, our approach highlights the need for the combined analysis of multiple sources of evidence to adequately characterize the drivers of divergence.

Major patterns in the introgression history of Heliconius butterflies.

Gene flow between species, although usually deleterious, is an important evolutionary process that can facilitate adaptation and lead to species diversification. It also makes estimation of species relationships difficult. Here, we use the full-likelihood multispecies coalescent (MSC) approach to estimate species phylogeny and major introgression events in Heliconius butterflies from whole-genome sequence data. We obtain a robust estimate of species branching order among major clades in the genus, including the 'melpomene-silvaniform' group, which shows extensive historical and ongoing gene flow. We obtain chromosome-level estimates of key parameters in the species phylogeny, including species divergence times, present-day and ancestral population sizes, as well as the direction, timing, and intensity of gene flow. Our analysis leads to a phylogeny with introgression events that differ from those obtained in previous studies. We find that Heliconius aoede most likely represents the earliest-branching lineage of the genus and that 'silvaniform' species are paraphyletic within the melpomene-silvaniform group. Our phylogeny provides new, parsimonious histories for the origins of key traits in Heliconius, including pollen feeding and an inversion involved in wing pattern mimicry. Our results demonstrate the power and feasibility of the full-likelihood MSC approach for estimating species phylogeny and key population parameters despite extensive gene flow. The methods used here should be useful for analysis of other difficult species groups with high rates of introgression.

Brief Analysis on the Degradation of Sugar-Based Copolyesters.

Isosorbide can be used as a third monomer in the synthesis of aliphatic polyesters, and its V-shaped bridging ring structure can effectively improve the rigidity of the copolyester molecular chain. In this work, a series of degradable polyester materials were prepared by modifying polybutylene succinate and using isosorbide as the third monomer. The degradation tests in this paper were implemented through the hydrolysis of copolyesters in distilled water, degradation in natural water and degradation tests in simulated natural environments. The results showed that PBS and its copolyesters can degrade under natural conditions, and the introduction of isosorbide can accelerate the degradation of copolyesters, which could effectively reduce pollutants in nature.

Efficient Bayesian inference under the multispecies coalescent with migration.

Analyses of genome sequence data have revealed pervasive interspecific gene flow and enriched our understanding of the role of gene flow in speciation and adaptation. Inference of gene flow using genomic data requires powerful statistical methods. Yet current likelihood-based methods involve heavy computation and are feasible for small datasets only. Here, we implement the multispecies-coalescent-with-migration model in the Bayesian program bpp, which can be used to test for gene flow and estimate migration rates, as well as species divergence times and population sizes. We develop Markov chain Monte Carlo algorithms for efficient sampling from the posterior, enabling the analysis of genome-scale datasets with thousands of loci. Implementation of both introgression and migration models in the same program allows us to test whether gene flow occurred continuously over time or in pulses. Analyses of genomic data from Anopheles mosquitoes demonstrate rich information in typical genomic datasets about the mode and rate of gene flow.

Risk factors for the development of postoperative atrial fibrillation after esophagectomy for esophageal cancer.

Postoperative atrial fibrillation (POAF) is one of the most complications after esophagectomy. Thus, our study was conducted to explore risk factors that are associated with POAF following esophagectomy. In the current study, we retrospectively evaluated 511 patients with esophageal cancer who underwent esophagectomy at our center between May 2018 and December 2020. The incidence of POAF and clinical variables were collected and analyzed. POAF occurred in 62 (12.13%) of 511 patients. Increasing age (P = .004) and lower preoperative albumin level (P = .028) was significantly associated with POAF. The length of stay was significantly increased in patients with POAF when compared to patients without POAF (P = .003). Multivariate analysis suggested that age (odds ratio [OR] = 1.049, 95% confidence interval [CI] = 1.008-1.093, P = .020), hypertension (OR = 2.207, 95% CI = 1.221-3.987, P = .009), respiratory complications (OR = 2.015, 95% CI = 1.130-3.591, P = .018) and Ivor Lewis approach (OR = 3.001, 95% CI = 1.032-8.723, P = .044) were independent risk factors for POAF following esophagectomy. Increasing age, preoperative hypertension, respiratory complications and Ivor Lewis approach are independent risk factors for POAF after esophagectomy. POAF is associated with prolonged length of stay. This study suggests that older patients, patients with hypertension or patients underwent Ivor Lewis approach should be monitored more closely during the postoperative period.

Inferring the Direction of Introgression Using Genomic Sequence Data.

Genomic data are informative about the history of species divergence and interspecific gene flow, including the direction, timing, and strength of gene flow. However, gene flow in opposite directions generates similar patterns in multilocus sequence data, such as reduced sequence divergence between the hybridizing species. As a result, inference of the direction of gene flow is challenging. Here, we investigate the information about the direction of gene flow present in genomic sequence data using likelihood-based methods under the multispecies-coalescent-with-introgression model. We analyze the case of two species, and use simulation to examine cases with three or four species. We find that it is easier to infer gene flow from a small population to a large one than in the opposite direction, and easier to infer inflow (gene flow from outgroup species to an ingroup species) than outflow (gene flow from an ingroup species to an outgroup species). It is also easier to infer gene flow if there is a longer time of separate evolution between the initial divergence and subsequent introgression. When introgression is assumed to occur in the wrong direction, the time of introgression tends to be correctly estimated and the Bayesian test of gene flow is often significant, while estimates of introgression probability can be even greater than the true probability. We analyze genomic sequences from Heliconius butterflies to demonstrate that typical genomic datasets are informative about the direction of interspecific gene flow, as well as its timing and strength.

CNETML: maximum likelihood inference of phylogeny from copy number profiles of multiple samples.

Phylogenetic trees based on copy number profiles from multiple samples of a patient are helpful to understand cancer evolution. Here, we develop a new maximum likelihood method, CNETML, to infer phylogenies from such data. CNETML is the first program to jointly infer the tree topology, node ages, and mutation rates from total copy numbers of longitudinal samples. Our extensive simulations suggest CNETML performs well on copy numbers relative to ploidy and under slight violation of model assumptions. The application of CNETML to real data generates results consistent with previous discoveries and provides novel early copy number events for further investigation.

DNA Sequences Are as Useful as Protein Sequences for Inferring Deep Phylogenies.

Inference of deep phylogenies has almost exclusively used protein rather than DNA sequences based on the perception that protein sequences are less prone to homoplasy and saturation or to issues of compositional heterogeneity than DNA sequences. Here, we analyze a model of codon evolution under an idealized genetic code and demonstrate that those perceptions may be misconceptions. We conduct a simulation study to assess the utility of protein versus DNA sequences for inferring deep phylogenies, with protein-coding data generated under models of heterogeneous substitution processes across sites in the sequence and among lineages on the tree, and then analyzed using nucleotide, amino acid, and codon models. Analysis of DNA sequences under nucleotide-substitution models (possibly with the third codon positions excluded) recovered the correct tree at least as often as analysis of the corresponding protein sequences under modern amino acid models. We also applied the different data-analysis strategies to an empirical dataset to infer the metazoan phylogeny. Our results from both simulated and real data suggest that DNA sequences may be as useful as proteins for inferring deep phylogenies and should not be excluded from such analyses. Analysis of DNA data under nucleotide models has a major computational advantage over protein-data analysis, potentially making it feasible to use advanced models that account for among-site and among-lineage heterogeneity in the nucleotide-substitution process in inference of deep phylogenies.

Nb2C MXene self-assembled Au nanoparticles simultaneously based on electromagnetic enhancement and charge transfer for surface enhanced Raman scattering.

Recent years, two-dimensional transition metal carbonitrides (MXene) have attracted much attention in the field of surface-enhanced Raman scattering (SERS). However, the relatively low enhancement of MXene is a major challenge. Herein, Nb2C-Au NPs nanocomposites were prepared by electrostatic self-assembly method, which have a synergistically conjugated SERS effect. The EM hot spots of Nb2C-Au NPs are significantly enlarged and expanded, while the surface Fermi level is decreased. This synergistic effect could improve the SERS performance of the system. Consequently, for the dye molecules CV and MeB, the detection limits reach 10-10 M and 10-9 M, respectively, while for biomolecule adenine, the detection limit is as low as 5 × 10-8 M. The results also show the good concentration-dependent linearity, uniformity, reproducibility and stability of SERS substrate. Nb2C-Au NPs could be a fast, sensitive and stable SERS platform for label-free and non-destructive detection. This work may expand the application of MXene based materials in the field of SERS.

Beginner's Guide on the Use of PAML to Detect Positive Selection.

The CODEML program in the PAML package has been widely used to analyze protein-coding gene sequences to estimate the synonymous and nonsynonymous rates (dS and dN) and to detect positive Darwinian selection driving protein evolution. For users not familiar with molecular evolutionary analysis, the program is known to have a steep learning curve. Here, we provide a step-by-step protocol to illustrate the commonly used tests available in the program, including the branch models, the site models, and the branch-site models, which can be used to detect positive selection driving adaptive protein evolution affecting particular lineages of the species phylogeny, affecting a subset of amino acid residues in the protein, and affecting a subset of sites along prespecified lineages, respectively. A data set of the myxovirus (Mx) genes from ten mammal and two bird species is used as an example. We discuss a new feature in CODEML that allows users to perform positive selection tests for multiple genes for the same set of taxa, as is common in modern genome-sequencing projects. The PAML package is distributed at https://github.com/abacus-gene/paml under the GNU license, with support provided at its discussion site (https://groups.google.com/g/pamlsoftware). Data files used in this protocol are available at https://github.com/abacus-gene/paml-tutorial.

Integrative genomic profiling reveals characteristics of lymph node metastasis in small cell lung cancer.

Background: Small cell lung cancer (SCLC) is the most aggressive lung cancer subtype, with more than 70% of patients having metastatic disease and a poor prognosis. However, no integrated multi-omics analysis has been performed to explore novel differentially expressed genes (DEGs) or significantly mutated genes (SMGs) associated with lymph node metastasis (LNM) in SCLC. Methods: In this study, whole-exome sequencing (WES) and RNA-sequencing were performed on tumor specimens to investigate the association between genomic and transcriptome alterations and LNM in SCLC patients with (N+, n=15) or without (N0, n=11) LNM. Results: The results of WES revealed that the most common mutations occurred in TTN (85%) and TP53 (81%). The SMGs, including ZNF521, CDH10, ZNF429, POLE, and FAM135B, were associated with LNM. Cosmic signature analysis showed that mutation signatures 2, 4, and 7 were associated with LNM. Meanwhile, DEGs, including MAGEA4, FOXI3, RXFP2, and TRHDE, were found to be associated with LNM. Furthermore, we found that the messenger RNA (mRNA) levels of RB1 (P=0.0087), AFF3 (P=0.058), TDG (P=0.05), and ANKRD28 (P=0.042) were significantly correlated with copy number variants (CNVs), and ANKRD28 expression was consistently lower in N+ tumors than in N0 tumors. Further validation in cBioPortal revealed a significant correlation between LNM and poor prognosis in SCLC (P=0.014), although there was no significant correlation between LNM and overall survival (OS) in our cohort (P=0.75). Conclusions: To our knowledge, this is the first integrative genomics profiling of LNM in SCLC. Our findings are particularly important for early detection and the provision of reliable therapeutic targets.

Estimation of species divergence times in presence of cross-species gene flow.

Cross-species introgression can have significant impacts on phylogenomic reconstruction of species divergence events. Here, we used simulations to show how the presence of even a small amount of introgression can bias divergence time estimates when gene flow is ignored in the analysis. Using advances in analytical methods under the multispecies coalescent (MSC) model, we demonstrate that by accounting for incomplete lineage sorting and introgression using large phylogenomic data sets this problem can be avoided. The multispecies-coalescent-with-introgression (MSci) model is capable of accurately estimating both divergence times and ancestral effective population sizes, even when only a single diploid individual per species is sampled. We characterize some general expectations for biases in divergence time estimation under three different scenarios: 1) introgression between sister species, 2) introgression between non-sister species, and 3) introgression from an unsampled (i.e., ghost) outgroup lineage. We also conducted simulations under the isolation-with-migration (IM) model and found that the MSci model assuming episodic gene flow was able to accurately estimate species divergence times despite high levels of continuous gene flow. We estimated divergence times under the MSC and MSci models from two published empirical datasets with previous evidence of introgression, one of 372 target-enrichment loci from baobabs (Adansonia), and another of 1000 transcriptome loci from 14 species of the tomato relative, Jaltomata. The empirical analyses not only confirm our findings from simulations, demonstrating that the MSci model can reliably estimate divergence times but also show that divergence time estimation under the MSC can be robust to the presence of small amounts of introgression in empirical datasets with extensive taxon sampling. [divergence time; gene flow; hybridization; introgression; MSci model; multispecies coalescent].

Power of Bayesian and Heuristic Tests to Detect Cross-Species Introgression with Reference to Gene Flow in the Tamias quadrivittatus Group of North American Chipmunks.

In the past two decades, genomic data have been widely used to detect historical gene flow between species in a variety of plants and animals. The Tamias quadrivittatus group of North America chipmunks, which originated through a series of rapid speciation events, are known to undergo massive amounts of mitochondrial introgression. Yet in a recent analysis of targeted nuclear loci from the group, no evidence for cross-species introgression was detected, indicating widespread cytonuclear discordance. The study used the heuristic method HYDE to detect gene flow, which may suffer from low power. Here we use the Bayesian method implemented in the program BPP to re-analyze these data. We develop a Bayesian test of introgression, calculating the Bayes factor via the Savage-Dickey density ratio using the Markov chain Monte Carlo (MCMC) sample under the model of introgression. We take a stepwise approach to constructing an introgression model by adding introgression events onto a well-supported binary species tree. The analysis detected robust evidence for multiple ancient introgression events affecting the nuclear genome, with introgression probabilities reaching 63%. We estimate population parameters and highlight the fact that species divergence times may be seriously underestimated if ancient cross-species gene flow is ignored in the analysis. We examine the assumptions and performance of HYDE and demonstrate that it lacks power if gene flow occurs between sister lineages or if the mode of gene flow does not match the assumed hybrid-speciation model with symmetrical population sizes. Our analyses highlight the power of likelihood-based inference of cross-species gene flow using genomic sequence data. [Bayesian test; BPP; chipmunks; introgression; MSci; multispecies coalescent; Savage-Dickey density ratio.].

Self-Assembled MXene-Au Multifunctional Nanomaterials with Various Shapes for Label-free SERS Detection of Pathogenic Bacteria and Photothermal Sterilization.

Early diagnosis of pathogenic bacteria and treatment are essential to prevent further infection. Photothermal therapy (PTT) is a promising sterilization method with advantages of minimal invasiveness and high efficiency. The effect of PTT depends on the performance of photothermal materials. Herein, Ti3C2-Au nanomaterials were prepared by the electrostatic self-assembly method, and the absorption characteristics were modulated by changing the morphology of Ti3C2-Au to achieve high photothermal conversion efficiency and sensitive label-free SERS bacterial detection. The results showed that the prepared Ti3C2-Au had better SERS performance than Au and achieved direct and sensitive detection of Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus). Under 808 nm laser irradiation, the photothermal conversion efficiency of Ti3C2-Au nanobipyramids (NBPs) was increased to 50.41% compared with the other two composites. The bactericidal rates of Ti3C2-Au NBPs against E. coli and S. aureus were 95.11 and 99.80% in 8 min, respectively, and the killing rates of nine other bacteria were all above 95%, showing broad-spectrum antibacterial properties. Cell viability studies showed that the Ti3C2-Au NBP had significantly improved biocompatibility compared with the Au NBP and was suitable for biological applications. It can simultaneously realize sensitive bacterial detection and photothermal sterilization and is important for the detection and inhibition of pathogenic bacteria.

Inference of Gene Flow between Species under Misspecified Models.

Genomic sequence data provide a rich source of information about the history of species divergence and interspecific hybridization or introgression. Despite recent advances in genomics and statistical methods, it remains challenging to infer gene flow, and as a result, one may have to estimate introgression rates and times under misspecified models. Here we use mathematical analysis and computer simulation to examine estimation bias and issues of interpretation when the model of gene flow is misspecified in analysis of genomic datasets, for example, if introgression is assigned to the wrong lineages. In the case of two species, we establish a correspondence between the migration rate in the continuous migration model and the introgression probability in the introgression model. When gene flow occurs continuously through time but in the analysis is assumed to occur at a fixed time point, common evolutionary parameters such as species divergence times are surprisingly well estimated. However, the time of introgression tends to be estimated towards the recent end of the period of continuous gene flow. When introgression events are assigned incorrectly to the parental or daughter lineages, introgression times tend to collapse onto species divergence times, with introgression probabilities underestimated. Overall, our analyses suggest that the simple introgression model is useful for extracting information concerning between-specific gene flow and divergence even when the model may be misspecified. However, for reliable inference of gene flow it is important to include multiple samples per species, in particular, from hybridizing species.

RADseq data reveal a lack of admixture in a mouse lemur contact zone contrary to previous microsatellite results.

Microsatellites have been a workhorse of evolutionary genetic studies for decades and are still commonly in use for estimating signatures of genetic diversity at the population and species level across a multitude of taxa. Yet, the very high mutation rate of these loci is a double-edged sword, conferring great sensitivity at shallow levels of analysis (e.g. paternity analysis) but yielding considerable uncertainty for deeper evolutionary comparisons. For the present study, we used reduced representation genome-wide data (restriction site-associated DNA sequencing (RADseq)) to test for patterns of interspecific hybridization previously characterized using microsatellite data in a contact zone between two closely related mouse lemur species in Madagascar (Microcebus murinus and Microcebus griseorufus). We revisit this system by examining populations in, near, and far from the contact zone, including many of the same individuals that had previously been identified as hybrids with microsatellite data. Surprisingly, we find no evidence for admixed nuclear ancestry. Instead, re-analyses of microsatellite data and simulations suggest that previously inferred hybrids were false positives and that the program NewHybrids can be particularly sensitive to erroneously inferring hybrid ancestry. Combined with results from coalescent-based analyses and evidence for local syntopic co-occurrence, we conclude that the two mouse lemur species are in fact completely reproductively isolated, thus providing a new understanding of the evolutionary rate whereby reproductive isolation can be achieved in a primate.

Bayesian Phylogenetic Inference using Relaxed-clocks and the Multispecies Coalescent.

The multispecies coalescent (MSC) model accommodates both species divergences and within-species coalescent and provides a natural framework for phylogenetic analysis of genomic data when the gene trees vary across the genome. The MSC model implemented in the program bpp assumes a molecular clock and the Jukes-Cantor model, and is suitable for analyzing genomic data from closely related species. Here we extend our implementation to more general substitution models and relaxed clocks to allow the rate to vary among species. The MSC-with-relaxed-clock model allows the estimation of species divergence times and ancestral population sizes using genomic sequences sampled from contemporary species when the strict clock assumption is violated, and provides a simulation framework for evaluating species tree estimation methods. We conducted simulations and analyzed two real datasets to evaluate the utility of the new models. We confirm that the clock-JC model is adequate for inference of shallow trees with closely related species, but it is important to account for clock violation for distant species. Our simulation suggests that there is valuable phylogenetic information in the gene-tree branch lengths even if the molecular clock assumption is seriously violated, and the relaxed-clock models implemented in bpp are able to extract such information. Our Markov chain Monte Carlo algorithms suffer from mixing problems when used for species tree estimation under the relaxed clock and we discuss possible improvements. We conclude that the new models are currently most effective for estimating population parameters such as species divergence times when the species tree is fixed.

Efficacy and safety of thoracoscopic resection for early-stage non-small cell lung cancer.

OBJECTIVE: To explore the efficacy and safety of thoracoscopic resection for early-stage non-small cell lung cancer (NSCLC). METHODS: A total of 110 patients with early-stage NSCLC admitted to Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology between August 2017 and December 2019 were enrolled and retrospectively analysed. Among them, 60 patients receiving thoracoscopic resection for lung cancer (LC) were assigned to the research group (Res group) and another 50 patients treated with routine open radical resection for LC were included in the control group (Con group). The following items of the two groups were evaluated and compared: treatment efficacy, operation indexes, VAS score, lung function, lung capacity, complications, 2-year tumour-free survival rate, 2-year survival rate, and quality of life (QoL). RESULTS: The Res group showed significantly better efficacy, and lower incidence of complications and VAS score than the Con group. In addition, patients in the Res group experienced less intraoperative blood loss, earlier anal exhaust, shorter hospital stay and indwelling time of drainage tube as well as less drainage volume. Furthermore, better recovery in pulmonary function and lung capacity, and significantly higher 2-year tumour-free survival rate, 2-year survival rate as well as postoperative QoL were noted in the Res group compared with the Con group. CONCLUSION: Thoracoscopic resection for LC is effective in the treatment of patients with early-stage NSCLC. It can substantially shorten the hospital stay and indwelling time of drainage tube and reduce drainage volume and blood loss, with high safety.

Estimation of Cross-Species Introgression Rates Using Genomic Data Despite Model Unidentifiability.

Full-likelihood implementations of the multispecies coalescent with introgression (MSci) model treat genealogical fluctuations across the genome as a major source of information to infer the history of species divergence and gene flow using multilocus sequence data. However, MSci models are known to have unidentifiability issues, whereby different models or parameters make the same predictions about the data and cannot be distinguished by the data. Previous studies of unidentifiability have focused on heuristic methods based on gene trees and do not make an efficient use of the information in the data. Here we study the unidentifiability of MSci models under the full-likelihood methods. We characterize the unidentifiability of the bidirectional introgression (BDI) model, which assumes that gene flow occurs in both directions. We derive simple rules for arbitrary BDI models, which create unidentifiability of the label-switching type. In general, an MSci model with k BDI events has 2k unidentifiable modes or towers in the posterior, with each BDI event between sister species creating within-model parameter unidentifiability and each BDI event between nonsister species creating between-model unidentifiability. We develop novel algorithms for processing Markov chain Monte Carlo samples to remove label-switching problems and implement them in the bpp program. We analyze real and synthetic data to illustrate the utility of the BDI models and the new algorithms. We discuss the unidentifiability of heuristic methods and provide guidelines for the use of MSci models to infer gene flow using genomic data.