RESUMEN
Planning for the protection of species often involves difficult choices about which species to prioritize, given constrained resources. One way of prioritizing species is to consider their "evolutionary distinctiveness," (ED) that is, their relative evolutionary isolation on a phylogenetic tree. Several evolutionary isolation metrics or phylogenetic diversity indices have been introduced in the literature, among them the so-called Fair Proportion (FP) index (also known as the ED score). This index apportions the total diversity of a tree among all leaves, thereby providing a simple prioritization criterion for conservation. Here, we focus on the prioritization order obtained from the FP index and analyze the effects of species extinction on this ranking. More precisely, we analyze the extent to which the ranking order may change when some species go extinct and the FP index is recomputed for the remaining taxa. We show that for each phylogenetic tree, there are edge lengths such that the extinction of one leaf per cherry completely reverses the ranking. Moreover, we show that even if only the lowest-ranked species goes extinct, the ranking order may drastically change. We end by analyzing the effects of these two extinction scenarios (extinction of the lowest-ranked species and extinction of one leaf per cherry) for a collection of empirical and simulated trees. In both cases, we can observe significant changes in the prioritization orders, highlighting the empirical relevance of our theoretical findings. [Biodiversity conservation; Fair Proportion index; phylogenetic diversity; species prioritization.].
Asunto(s)
Biodiversidad , Evolución Biológica , Filogenia , Extinción Biológica , Benchmarking , Conservación de los Recursos NaturalesRESUMEN
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.
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Algoritmos , Modelos Genéticos , Humanos , FilogeniaRESUMEN
BACKGROUND: Early detection of abdominal hemorrhage via ultrasound has life-saving implications for military and civilian trauma. However, strict adherence to light discipline may prohibit the use of ultrasound devices in the deployed setting. Additionally, current night vision devices remain noncompatible with ultrasound technology. This study sought to assess an innovative night vision device with ultrasound capable picture-in-picture display via a intraabdominal hemorrhage model to identify noncompressible truncal hemorrhage in blackout conditions. METHODS: 8 post mortem fetal porcine specimens were used and divided into 2 groups: intrabdominal hemorrhage (n = 4) vs no hemorrhage (n = 4). Intrabdominal hemorrhage was modeled via direct injection of 200 mL of normal saline into the peritoneal cavity. Under blackout conditions, 5 participants performed a focused assessment with sonography for trauma (FAST) exam on each model using the prototype ultrasound-capable night vision device. RESULTS: Of the 40 FAST exams performed, 95% (N = 38) resulted in the correct identification of intraabdominal hemorrhage. Of the incorrectly identified exams, both were false positives resulting in a 100% sensitivity, 90% specificity, 91% positive predictive value, and a 100% negative predictive value. All participants noted the novel device was easy to use and provided superior visualization for performing FAST exams under blackout conditions. CONCLUSION: The ultrasound-enabled night vision prototype demonstrated promising results in identifying noncompressible truncal hemorrhage while maintaining strict light discipline in blackout conditions. Further research efforts should be directed at assessing the ability of providers to perform procedures in blackout conditions using the ultrasound-enabled prototype night vision device.
Asunto(s)
Hemorragia , Ultrasonografía , Porcinos , Hemorragia/diagnóstico por imagen , Animales , Ultrasonografía/instrumentación , Humanos , Traumatismos Abdominales/diagnóstico por imagen , Servicios Médicos de Urgencia , Diseño de EquipoRESUMEN
Phylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations) and non-tree-like 'reticulate' processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper, we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of 'expanding covers' of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.
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Evolución Molecular , Modelos Biológicos , Filogenia , Modelos Genéticos , Conceptos Matemáticos , AlgoritmosRESUMEN
Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in bacterial genomes through the same biological mechanism as inversions, and hence a model that incorporates both is desirable. However, while inversion distances between genomes have been well studied, there has yet to be a model which accounts for the combination of both deletions and inversions. To account for both of these operations, we introduce an algebraic model that utilises partial permutations. This leads to an algorithm for calculating the minimum distance to the most recent common ancestor of two bacterial genomes evolving by inversions (of adjacent regions) and deletions. The algebraic model makes the existing short inversion models more complete and realistic by including deletions, and also introduces new algebraic tools into evolutionary distance problems.
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Algoritmos , Inversión Cromosómica , Humanos , Evolución Biológica , Filogenia , Genoma Bacteriano , Reordenamiento GénicoRESUMEN
ABSTRACT: Electroconvulsive therapy (ECT) is a highly therapeutic and cost-effective treatment for severe and/or treatment-resistant major depression. However, because of the varied clinical practices, there is a great deal of heterogeneity in how ECT is delivered and documented. This represents both an opportunity to study how differences in implementation influence clinical outcomes and a challenge for carrying out coordinated quality improvement and research efforts across multiple ECT centers. The National Network of Depression Centers, a consortium of 26+ US academic medical centers of excellence providing care for patients with mood disorders, formed a task group with the goals of promoting best clinical practices for the delivery of ECT and to facilitate large-scale, multisite quality improvement and research to advance more effective and safe use of this treatment modality. The National Network of Depression Centers Task Group on ECT set out to define best practices for harmonizing the clinical documentation of ECT across treatment centers to promote clinical interoperability and facilitate a nationwide collaboration that would enable multisite quality improvement and longitudinal research in real-world settings. This article reports on the work of this effort. It focuses on the use of ECT for major depressive disorder, which accounts for the majority of ECT referrals in most countries. However, most of the recommendations on clinical documentation proposed herein will be applicable to the use of ECT for any of its indications.
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Trastorno Depresivo Mayor , Trastorno Depresivo Resistente al Tratamiento , Terapia Electroconvulsiva , Depresión , Documentación , Humanos , Resultado del TratamientoRESUMEN
OBJECTIVE: Catatonia is widely underdiagnosed, in large part due to inaccurate recognition of its specific features. This study aimed to evaluate the effectiveness of an online educational module to improve theoretical and practical knowledge of the Bush-Francis Catatonia Rating Scale (BFCRS) across a broad range of clinicians and medical students. METHOD: A 1-h online module, including a training manual and videos, was disseminated to medical students, psychiatry residents and fellows, and psychiatrists through national Listservs and through the Academy of Consultation-Liaison Psychiatry. Participants completed pre- and post-module testing consisting of a 50-question multiple-choice test and a 3-min standardized patient video scored using the 23-item BFCRS. Participants accessed the module from October 1, 2020, to April 4, 2021. Immediate improvement and 3-month knowledge retention were assessed using quantitative and qualitative analyses. RESULTS: Study enrollment was high with moderate dropout (pre-testing: n = 482; post-testing: n = 236; 3-month testing: n = 105). Adjusting for demographics, large pre-post improvements were found in performance (multiple-choice: 11.3 points; standardized patient scoring: 4.2 points; both p < 0.001) and for nearly all individual BFCRS items. Knowledge attrition was modest, and improvements persisted at 3 months. CONCLUSIONS: This educational resource provides descriptive and demonstrative reference standards of the items on the BFCRS. This curriculum improved identification of catatonia's features on both multiple choice and standardized patient scoring across all ages and training levels with good overall knowledge retention.
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Catatonia , Psiquiatría , Estudiantes de Medicina , Catatonia/diagnóstico , Catatonia/psicología , HumanosRESUMEN
Rooted phylogenetic networks provide a way to describe species' relationships when evolution departs from the simple model of a tree. However, networks inferred from genomic data can be highly tangled, making it difficult to discern the main reticulation signals present. In this paper, we describe a natural way to transform any rooted phylogenetic network into a simpler canonical network, which has desirable mathematical and computational properties, and is based only on the 'visible' vertices in the original network. The method has been implemented and we demonstrate its application to some examples.
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Algoritmos , Modelos Genéticos , Evolución Molecular , Genoma , Genómica , FilogeniaRESUMEN
BACKGROUND: Tardive dyskinesia (TD) is an involuntary movement disorder most commonly involving the tongue, lips, and face and less commonly the trunk and limbs. Although TD is historically associated with conventional antipsychotics, it still occurs with newer agents. Covert dyskinesia (CD), a form of TD, occurs after the discontinuation of antipsychotics, and it differs from other withdrawal emergent dyskinesia by its persistence for more than 8 to 12 weeks after discontinuation of dopamine receptor-blocking agents. Although initially reported in the 1960s with conventional antipsychotics, multiple recent reports describe several cases in association with aripiprazole (APZ). METHODS: We used PubMed and the Google Scholar for CD reports during the past 20 years. We also report a recent case ofCD. RESULTS: We identified 11 case reports of CD. Six were related to APZ, 3 to risperidone, 1 to amisulpride, and 1 to haloperidol. Our patient was an 81-year-old woman with a history of major depressive disorder who was admitted for worsening depression. Before hospitalization, she had been on APZ 5 mg/d for 2 years, but it was discontinued 4 months prior, and then she developed repetitive involuntary movements in her tongue, lips, and jaw 2 months after APZ discontinuation. The Abnormal Involuntary Movement Scale score was 5. Reinstating APZ a few months later led to disappearance of movements. CONCLUSIONS: Literature to date suggests that APZ is the atypical antipsychotic most commonly reported with CD. A possible risk might be APZ's unique mechanism of action and its association with akathisia. Following up patients with serial Abnormal Involuntary Movement Scale after antipsychotic discontinuation is recommended.
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Antipsicóticos/efectos adversos , Aripiprazol/efectos adversos , Discinesia Tardía/inducido químicamente , Anciano de 80 o más Años , Trastorno Depresivo Mayor , Femenino , HumanosRESUMEN
ABSTRACT: There is very limited information regarding the effectiveness of electroconvulsive therapy (ECT) as a treatment for major depressive disorder in transgender patients. This population is also at risk for comorbid conditions, such as posttraumatic stress disorder and substance use that could impact the outcome of ECT. We report our experience with the use of ECT in this population. Clinical and response characteristics of 7 consecutive cases are described in this series. All patients had multiple psychiatric diagnoses and were refractory to pharmacologic intervention. Pretreatment Beck Depression Inventory-II scores were 45.5 ± 3.2 SEM and posttreatment scores were 21.2 ± 6.4 [P < 0.01]. Suicidality scores reduced by greater than 60%, whereas remission of depression was obtained for 2 of 7, and 4 of 7 showed greater than 50% reduction in depression scores. Treatments were tolerated well using conventional treatment procedures. This case series suggests that ECT can be effective for depressed transgender patients with multiple clinical comorbidities.
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Trastorno Depresivo Mayor/terapia , Terapia Electroconvulsiva/métodos , Personas Transgénero/psicología , Adolescente , Adulto , Comorbilidad , Femenino , Humanos , Masculino , Pennsylvania , Estudios RetrospectivosRESUMEN
Blood disorders, diseases, and infections often affect the shape, number, and content of red blood cells (RBCs) dramatically. To combat these pathologies, many therapies target RBCs and their contents directly. Mean corpuscular hemoglobin concentration (MCHC) is an important pathological metric in both identification and treatment. However, current methods for RBC analysis and MCHC quantification rely on bulk measurements. Single RBC measurements could provide necessary insight into the heterogeneity of RBC health and improve therapeutic efficacy. In this study, we present a novel multimodal multiphoton approach for quantifying hemoglobin concentration at single RBC resolution. We achieve this by collecting two images simultaneously that allows us to excite water with stimulated Raman scattering and hemoglobin with transient absorption. This multimodal imaging is enabled by a newly designed orthogonal modulation theme for dual-channel lock-in detection. By leveraging water as an internal standard, we quantify MCHC of healthy RBCs and RBCs infected with Plasmodium yoelii, a commonly studied rodent parasite model.
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Eritrocitos/química , Hemoglobinas/análisis , Microscopía de Fluorescencia por Excitación Multifotónica , Análisis de la Célula Individual , Animales , Eritrocitos/parasitología , Ratones , Ratones Endogámicos BALB CRESUMEN
Phylogenetic networks are generalizations of phylogenetic trees that allow the representation of reticulation events such as horizontal gene transfer or hybridization, and can also represent uncertainty in inference. A subclass of these, tree-based phylogenetic networks, have been introduced to capture the extent to which reticulate evolution nevertheless broadly follows tree-like patterns. Several important operations that change a general phylogenetic network have been developed in recent years and are important for allowing algorithms to move around spaces of networks; a vital ingredient in finding an optimal network given some biological data. A key such operation is the nearest neighbour interchange, or NNI. While it is already known that the space of unrooted phylogenetic networks is connected under NNI, it has been unclear whether this also holds for the subspace of tree-based networks. In this paper, we show that the space of unrooted tree-based phylogenetic networks is indeed connected under the NNI operation. We do so by explicitly showing how to get from one such network to another one without losing tree-basedness along the way. Moreover, we introduce some new concepts, for instance "shoat networks", and derive some interesting aspects concerning tree-basedness. Last, we use our results to derive an upper bound on the size of the space of tree-based networks.
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Evolución Biológica , Modelos Genéticos , Filogenia , Algoritmos , Análisis por Conglomerados , Biología Computacional , Evolución Molecular , Transferencia de Gen Horizontal , Hibridación Genética , Conceptos Matemáticos , Modelos BiológicosRESUMEN
Metrics on rooted phylogenetic trees are integral to a number of areas of phylogenetic analysis. Cluster-similarity metrics have recently been introduced in order to limit skew in the distribution of distances, and to ensure that trees in the neighbourhood of each other have similar hierarchies. In the present paper we introduce a new cluster-similarity metric on rooted phylogenetic tree space that has an associated local operation, allowing for easy calculation of neighbourhoods, a trait that is desirable for MCMC calculations. The metric is defined by the distance on the Hasse diagram induced by a partial order on the set of rooted phylogenetic trees, itself based on the notion of a hierarchy-preserving map between trees. The partial order we introduce is a refinement of the well-known refinement order on hierarchies. Both the partial order and the hierarchy-preserving maps may also be of independent interest.
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Algoritmos , Modelos Genéticos , Filogenia , Análisis por Conglomerados , Biología Computacional , Simulación por Computador , Cadenas de Markov , Conceptos Matemáticos , Método de MontecarloRESUMEN
This paper introduces a new way to define a genome rearrangement distance, using the concept of mean first passage time from probability theory. Crucially, this distance provides a genuine metric on genome space. We develop the theory and introduce a link to a graph-based zeta function. The approach is very general and can be applied to a wide variety of group-theoretic models of genome evolution.
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Evolución Molecular , Reordenamiento Génico , Modelos Genéticos , Filogenia , Bacterias/genética , Inversión Cromosómica , Genoma , Genoma Bacteriano , Funciones de Verosimilitud , Cadenas de Markov , Conceptos Matemáticos , Teoría de la Probabilidad , Factores de TiempoRESUMEN
Catatonia was buried within the confines of schizophrenia for over a century- deterring study, appropriate diagnosis and treatment for many years. With revised changes in the classification of this distinct neuropsychiatric syndrome, it is becoming more recognized clinically and in ongoing research. Catatonia occurs among various psychiatric, metabolic or neurologic conditions. It may present in many forms, including neuroleptic malignant syndrome. Treatment with benzodiazepines or electroconvulsive therapy usually produces dramatic and rapid response, although systematic, randomized trials are lacking. The role of antipsychotic agents in treatment is controversial as they may worsen the syndrome. An important unresolved clinical question is the diagnosis and treatment of catatonia in the setting of delirium.
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Catatonia , Antipsicóticos/efectos adversos , Antipsicóticos/uso terapéutico , Benzodiazepinas/uso terapéutico , Catatonia/complicaciones , Catatonia/diagnóstico , Catatonia/terapia , Diagnóstico Diferencial , Terapia Electroconvulsiva , Humanos , Síndrome Neuroléptico Maligno/complicaciones , Síndrome Neuroléptico Maligno/diagnóstico , Síndrome Neuroléptico Maligno/terapiaRESUMEN
The formation of cyclobutane rings is a promising strategy in the development of potential drugs and/or synthetic intermediates, typically challenging to obtain due to their constrained nature. In this work, the [2 + 2] photocycloaddition reaction of S,S-dioxobenzothiophene-2-methanol was explored in microcrystalline powders and its outcome was compared to that observed in solution. It was found that the molecular constraints inherited within the crystal lattice provide an optimal environment that leads to photodimer 4 as the major product in ca. 9.6:0.4 diastereomeric ratios with conversions >95%. The photoreaction was analyzed via X-ray, displaying a crystalline-to-amorphous transformation and showing that units of monomer 2 align to generate the corresponding dimer with a syn-head-to-tail regio- and diastereoselectivity. This result contrasted with that obtained in solution, where the diastereomeric ratio varied as a function of the excited state that is generated, to yield mixtures of dimers 4 and 5 (anti-head-to-tail), or exclusively 5 in the triplet-sensitized photoreaction, in the presence of benzophenone. Density functional theory was used to elucidate a plausible detailed mechanism for the phototransformation, which aided in justifying the results that led to the corresponding dimers. X-ray crystallography allowed us to establish the stereochemical assignment of the obtained cyclobutyl rings. Thus, the use of solid-state or solution photochemistry can be used to gain control of diastereo- and regioselectivities in the formation of this important moiety.
RESUMEN
BACKGROUND: The generalizability of data derived from patient-reported outcome measures (PROMs) depends largely on the proportion of the relevant population that completes PROM surveys. However, PROM survey responses remain low, despite efforts to increase participation. Social incentives, such as the offer to make a charitable donation on behalf of the survey respondent, have generally not been effective where online surveys are concerned, but this has not been extensively tested in medicine. QUESTIONS/PURPOSES: (1) Do personalized social incentives increase response rates or response completeness for postoperative PROM surveys in an orthopaedic population? (2) Are there demographic factors associated with response and nonresponse to postoperative PROM surveys? (3) Are some demographic factors associated with increased response to social incentive offers? METHODS: Participants were selected from an institutional orthopaedics database. Patients were older than 18 years, had an email address on file, and had undergone one of the following procedures 1 to 2 years ago: Achilles tendon repair, ACL reconstruction, meniscectomy, hip arthroscopy, TKA, or THA. Of 4685 eligible patients, 3000 (64%) were randomly selected for inclusion in the study. Participants were randomized to one of four groups: (1) control: no incentive (n = 750); (2) patient donation: offer of a USD 5 donation to provide medical supplies to a pediatric orthopaedic patient (n = 751); (3) research donation: offer of a USD 5 donation to a procedure-specific research program (n = 749); or (4) explanation: explanation that response supports quality improvement (n = 750). The four groups did not differ regarding patient age, gender, race, procedure type, or time since procedure. All patients were sent an email invitation with the same PROM survey link. The proportion of patients who responded (defined here as the response rate) was measured at 4 weeks and compared between intervention groups. We used a logistic regression analysis to identify demographic factors associated with response while controlling for confounding variables and performed subgroup analyses to determine any demographic factors associated with increased response to social incentives. RESULTS: There was no difference in the overall response rate (research donation: 49% [353 of 725], patient donation: 45% [333 of 734], control: 45% [322 of 723], explanation: 44% [314 of 719]; p = 0.239) or response completeness (research donation: 89% [315 of 353], patient donation: 90% [301 of 333], control: 89% [287 of 322], explanation: 87% [274 of 314]; p = 0.647) between the four groups. Women (odds ratio [OR], 1.175; p = 0.042), older patients (< 58 years: OR, 1.016 per 1-year increase; p = 0.001; 58-64 years: OR, 1.023 per 1-year increase; p < 0.001; > 64 years: OR, 1.021 per 1-year increase; p < 0.001), and white patients (OR 2.034 compared with black patients, p < 0.001) were slightly more likely to respond, after controlling for potential confounding variables such as gender, age, race, and procedure type. In subgroup analyses, men (research donation: 49% [155 of 316], patient donation: 45% [146 of 328], control: 40% [130 of 325], explanation: 39% [127 of 325]; p = 0.041) and patients younger than 58 years (research donation: 40% [140 of 351], control: 35% [130 of 371], patient donation: 32% [113 of 357], explanation: 27% [93 of 340]; p = 0.004) were slightly more likely to respond to the research donation than those with other interventions were. CONCLUSIONS: Despite small effects in specific subgroups, personalized social incentives did not increase the overall response to postoperative orthopaedic surveys. Novel and targeted strategies will be necessary to reach response thresholds that enable healthcare stakeholders to use PROMs effectively. LEVEL OF EVIDENCE: Level I, therapeutic study.
Asunto(s)
Motivación , Procedimientos Ortopédicos/psicología , Medición de Resultados Informados por el Paciente , Sujetos de Investigación/psicología , Encuestas y Cuestionarios/estadística & datos numéricos , Negro o Afroamericano/psicología , Anciano , Femenino , Humanos , Masculino , Persona de Mediana Edad , Participación del Paciente/psicología , Estudios Prospectivos , Factores Sexuales , Población Blanca/psicologíaRESUMEN
Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. As more taxa are added, the new source trees may begin to tell a different evolutionary story when restricted to the original set of taxa. However, if the new trees, restricted to the original set of taxa, were to agree exactly with the earlier trees, then we might hope that their consensus would either agree with or resolve the original consensus tree. In this article, we ask under what conditions consensus methods exist that are "future proof" in this sense. While we show that some methods (e.g., Adams consensus) have this property for specific types of input, we also establish a rather surprising "no-go" theorem: there is no "reasonable" consensus method that satisfies the future-proofing property in general. We then investigate a second notion of "future proofing" for consensus methods, in which trees (rather than taxa) are added, and establish some positive and negative results. We end with some questions for future work.
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Clasificación/métodos , Filogenia , Algoritmos , Evolución BiológicaRESUMEN
Localized drug delivery systems (DDSs) provide therapeutic levels of drug agent while mitigating side effects of systemic delivery. These systems offer controlled release over extended periods of time making them attractive therapies. Monitoring drug dissolution is vital for developing safe and effective means of drug delivery. Currently, dissolution characterization methods are limited to bulk analysis and cannot provide dissolution kinetics at high spatial resolution. However, dissolution rates of drug particles can be heterogeneous with influences from many factors. Insights into finer spatiotemporal dynamics of single particle dissolution could potentially improve pharmacokinetic modeling of dissolution for future drug development. In this work, we demonstrate high-resolution chemical mapping of entecavir, a hepatitis B antiviral drug, embedded in a slow release poly(d,l-lactic acid) formulation with stimulated Raman scattering (SRS) microscopy. By tracking the volume change of individual micron-sized drug particles within the polymer matrix, we establish an analytical protocol for quantitatively profiling dissolution of single crystalline particles in implant formulations in an in situ manner.
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Portadores de Fármacos/química , Implantes de Medicamentos/farmacocinética , Liberación de Fármacos , Guanina/análogos & derivados , Química Farmacéutica/métodos , Implantes de Medicamentos/administración & dosificación , Guanina/administración & dosificación , Guanina/farmacocinética , Microscopía/métodos , Tamaño de la Partícula , Poliésteres/química , Espectrometría Raman/métodosRESUMEN
Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is that of identifiability, which essentially asks under what circumstances can we reliably identify the phylogenetic network that gave rise to the observed data? Recently, identifiability results have appeared for networks relative to a model of sequence evolution that generalizes the standard Markov models used for phylogenetic trees. However, these results are quite limited in terms of the complexity of the networks that are considered. In this paper, by introducing an alternative probabilistic model for evolution along a network that is based on some ground-breaking work by Thatte for pedigrees, we are able to obtain an identifiability result for a much larger class of phylogenetic networks (essentially the class of so-called tree-child networks). To prove our main theorem, we derive some new results for identifying tree-child networks combinatorially, and then adapt some techniques developed by Thatte for pedigrees to show that our combinatorial results imply identifiability in the probabilistic setting. We hope that the introduction of our new model for networks could lead to new approaches to reliably construct phylogenetic networks.