Topological Uncertainty Research Articles

Genomic incongruence accompanies the evolution of flower symmetry in Eudicots: a case study in the poppy family (Papaveraceae, Ranunculales).

Reconstructing evolutionary trajectories and transitions that have shaped floral diversity relies heavily on the phylogenetic framework on which traits are modelled. In this study, we focus on the angiosperm order Ranunculales, sister to all other eudicots, to unravel higher-level relationships, especially those tied to evolutionary transitions in flower symmetry within the family Papaveraceae. This family presents an astonishing array of floral diversity, with actinomorphic, disymmetric (two perpendicular symmetry axes), and zygomorphic flowers. We generated nuclear and plastid datasets using the Angiosperms353 universal probe set for target capture sequencing (of 353 single-copy nuclear ortholog genes), together with publicly available transcriptome and plastome data mined from open-access online repositories. We relied on the fossil record of the order Ranunculales to date our phylogenies and to establish a timeline of events. Our phylogenomic workflow shows that nuclear-plastid incongruence accompanies topological uncertainties in Ranunculales. A cocktail of incomplete lineage sorting, post-hybridization introgression, and extinction following rapid speciation most likely explain the observed knots in the topology. These knots coincide with major floral symmetry transitions and thus obscure the order of evolutionary events.

Topological Characterization and Uncertainty Visualization of Atmospheric Rivers

AbstractAtmospheric rivers (ARs) are long, narrow regions of water vapor in the Earth's atmosphere that transport heat and moisture from the tropics to the mid‐latitudes. ARs are often associated with extreme weather events in North America and contribute significantly to water supply and flood risk. However, characterizing ARs has been a major challenge due to the lack of a universal definition and their structural variations. Existing AR detection tools (ARDTs) produce distinct AR boundaries for the same event, making the risk assessment of ARs a difficult task. Understanding these uncertainties is crucial to improving the predictability of AR impacts, including their landfall areas and associated precipitation, which could cause catastrophic flooding and landslides over the coastal regions. In this work, we develop an uncertainty visualization framework that captures boundary and interior uncertainties, i.e., structural variations, of an ensemble of ARs that arise from a set of ARDTs. We first provide a statistical overview of the AR boundaries using the contour boxplots of Whitaker et al. that highlight the structural variations of AR boundaries based on their nesting relationships. We then introduce the topological skeletons of ARs based on Morse complexes that characterize the interior variation of an ensemble of ARs. We propose an uncertainty visualization of these topological skeletons, inspired by MetroSets of Jacobson et al. that emphasizes the agreements and disagreements across the ensemble members. Through case studies and expert feedback, we demonstrate that the two approaches complement each other, and together they could facilitate an effective comparative analysis process and provide a more confident outlook on an AR's shape, area, and onshore impact.

Adaptive parameter local consistency automatic outlier removal algorithm for area-based matching

Abstract. Due to the influence of image differences and matching methods, geometric calibration of remote sensing images often results in the extraction of control points with inevitable outliers. Moreover, it is susceptible to limitations imposed by locally constrained outlier rejection methods, making it challenging to automatically remove relatively small gross errors. This paper introduces an adaptive parameter local consistency automatic outlier removal algorithm, referred to as APLC. Initially, we construct k-nearest neighbors for each pair of matching points, deriving distance and topological uncertainty based on the accuracy of point matching. Subsequently, we conduct cross-validation on the uncertainty between the two pairs of vectors formed by points within the neighborhood, aiming for parameter adaptation. Finally, a cost-defined function is introduced to assess the consistency of local structures. Through a two-stage outlier removal strategy, matching points that do not maintain local structural consistency are eliminated. To assess the effectiveness of the proposed algorithm, we conduct experimental comparisons using region-based initial matching results from the FY-3D remote sensing dataset, demonstrating its superiority compared to three state-of-the-art methods.

Stability, Bifurcation and Dynamics in a Network with Delays

In real-world networks, due to complex topological structures and uncertainties such as time delays, uncontrolled systems may generate instability and complexity, thereby degrading network performance. This paper provides a detailed analysis of the stability, Hopf bifurcation, and complex dynamics of a networked system under delayed feedback control. Based on the linear stability method and Hopf bifurcation theorem, the stability of the equilibrium of the error system and the existence of Hopf bifurcation are studied. The stability of periodic solutions bifurcating from the trivial equilibrium is analyzed using normal form theory and central manifold theorem. Special focus is on the effects of the network topology and time delays on the stability and Hopf bifurcation. The theoretical results are also extended to the complex networks with asymmetric adjacent matrices. In addition, the controlled model exhibits complicated dynamical behavior via three types of codimension two bifurcations and period-doubling bifurcations that eventually lead to chaos. Numerical experiments have validated the theoretical results and indicated that delayed feedback control can effectively generate or annihilate the complicated behavior of complex networks.

Optimizing Network Reliability in Dynamic or Rapidly-Changing Topologies

With communication, power and transportation networks facing ever-greater dynamics, optimizing reliability poses significant modeling and computational challenges. Most existing reliability optimization research assumes static topologies with predefined failure probabilities and connectivity demands. This work puts forth a time-varying mathematical program to maximize expected network reliability under shifting topological uncertainties. Sets, parameters, decision variables and constraints are defined as functions of time to capture variability in links, capacities, risks and demands. The formulation adapts to detected changes through re-optimization triggered by model error thresholds. Approximation techniques based on constraint sampling and decomposition address solve efficiency for large fluid networks. Evaluations on simulated dynamic test cases demonstrate superior reliability versus periodic and static optimization approaches while fulfilling budget limits. Accuracy metrics assess model fidelity over increasing volatility levels. Implementation case studies exhibit optimized resilience in software-defined communication architectures, smart grid reconfiguration, and adaptive transportation maintenance scenarios. The mathematical programming foundation provides a pathway to achieve connectivity resilience for critical infrastructure networks facing intensifying dynamics. The integration of optimization, prediction and adaptive response provides a paradigm for decision making under modern uncertain conditions.

An Overview of DC Microgrid Protection Schemes and the Factors Involved

The development of a suitable scheme for protection of DC microgrids is still a major challenge. This is due to the shortage of practical experience in appropriate protection guidelines and standards related to the uncertainty in the network topology, absence of a natural current zero-crossing point in DC systems, and dependence of fault current shape and magnitude on various factors. These factors include network topology, type of converters used in the network, type of fault and its location, fault impedance, and type of system grounding. In this paper, these factors and their impacts on the development of a comprehensive protection plan for DC microgrids have been investigated. Various algorithms that have been proposed in previous studies for fault detection and location are reviewed, and the technical challenges associated with the use of communication links in smart protection systems are described. In addition, the advent of new technologies for development of DC circuit breakers are reported, which are different from the conventional AC circuit breakers due to the differences between the faults in DC and AC microgrids and their respective clearance times. This comprehensive review covers all aspects of the DC microgrid protection including topology, converters, configurations, and types of faults.

Confusion will be my epitaph: genome-scale discordance stifles phylogenetic resolution of Holothuroidea.

Sea cucumbers (Holothuroidea) are a diverse clade of echinoderms found from intertidal waters to the bottom of the deepest oceanic trenches. Their reduced skeletons and limited number of phylogenetically informative traits have long obfuscated morphological classifications. Sanger-sequenced molecular datasets have also failed to constrain the position of major lineages. Noteworthy, topological uncertainty has hindered a resolution for Neoholothuriida, a highly diverse clade of Permo-Triassic age. We perform the first phylogenomic analysis of Holothuroidea, combining existing datasets with 13 novel transcriptomes. Using a highly curated dataset of 1100 orthologues, our efforts recapitulate previous results, struggling to resolve interrelationships among neoholothuriid clades. Three approaches to phylogenetic reconstruction (concatenation under both site-homogeneous and site-heterogeneous models, and coalescent-aware inference) result in alternative resolutions, all of which are recovered with strong support and across a range of datasets filtered for phylogenetic usefulness. We explore this intriguing result using gene-wise log-likelihood scores and attempt to correlate these with a large set of gene properties. While presenting novel ways of exploring and visualizing support for alternative trees, we are unable to discover significant predictors of topological preference, and our efforts fail to favour one topology. Neoholothuriid genomes seem to retain an amalgam of signals derived from multiple phylogenetic histories.

An Insight on Optimization Techniques for Uncertain and Reliable Routing in Wireless Body Area Networks

In recent times, Wireless Body Area Networks a subsection of Wireless Sensor Network is a promising technology for future healthcare realm with cutting-edge technologies that can assist healthcare professionals like doctors, nurses and biomedical engineers. Machine Learning and Internet of Things enabled medical big data is the future of healthcare sector and Medical Technology-based industries leading to applications in other sectors such as fitness tracking for commercial purposes, Sportsperson health monitoring to track their day-to-day activities and wearable devices for critical and emergency care. This comprehensive review article addresses Wireless Body Area Network state-of-art and the dependence of Optimization Techniques and Meta-heuristic Algorithms for an efficient routing path between two sensor nodes: source node and destination node and it plays an effective role in optimizing the network parameters such as radio range, energy consumption, throughput, data aggregation, clustering and routing. Designing of energy-efficient routing for wireless body are network is such a challenging task due to uncertainty in dynamic network topology, energy constraints and limited power consumption. Optimization Techniques can help the researchers to achieve the drawbacks mentioned above and energy-efficiency of the network can be improved. In this article, we focus majorly on the efficiency of usage of optimization algorithms for Wireless Body Area Network routing mechanisms and a summary of its earlier studies during 2012-2023 epoch. Genetic Algorithm, Particle Swarm Optimization, Ant Colony Optimization, Artificial Bee Colony and Firefly Optimization algorithms were discussed on achieving local optima for better results through optimization. This article provides an insight into existing gaps and further modifications to the researchers in WBAN that can motivate them to propose new ideas for reliable solutions. Performance comparison and evaluation of different bio-inspired optimization algorithms has been discussed for further improvement in optimized routing algorithms.

Plastid phylogenomics and plastome evolution in the morning glory family (Convolvulaceae).

Convolvulaceae, the morning glories or bindweeds, is a large family containing species of economic value, including crops, traditional medicines, ornamentals, and vegetables. However, not only are the phylogenetic relationships within this group still debated at the intertribal and intergeneric levels, but also plastid genome (plastome) complexity within Convolvulaceae is not well surveyed. We gathered 78 plastomes representing 17 genera across nine of the 12 Convolvulaceae tribes. Our plastid phylogenomic trees confirm the monophyly of Convolvulaceae, place the genus Jacquemontia within the subfamily Dicranostyloideae, and suggest that the tribe Merremieae is paraphyletic. In contrast, positions of the two genera Cuscuta and Erycibe are uncertain as the bootstrap support of the branches leading to them is moderate to weak. We show that nucleotide substitution rates are extremely variable among Convolvulaceae taxa and likely responsible for the topological uncertainty. Numerous plastomic rearrangements are detected in Convolvulaceae, including inversions, duplications, contraction and expansion of inverted repeats (IRs), and losses of genes and introns. Moreover, integrated foreign DNA of mitochondrial origin was found in the Jacquemontia plastome, adding a rare example of gene transfer from mitochondria to plastids in angiosperms. In the IR of Dichondra, we discovered an extra copy of rpl16 containing a direct repeat of ca. 200 bp long. This repeat was experimentally demonstrated to trigger effective homologous recombination, resulting in the coexistence of intron-containing and -lacking rpl16 duplicates. Therefore, we propose a hypothetical model to interpret intron loss accompanied by invasion of direct repeats at appropriate positions. Our model complements the intron loss model driven by retroprocessing when genes have lost introns but contain abundant RNA editing sites adjacent to former splicing sites.

Frequency synchronization adaptive control for power grids under topological uncertainty

In this paper, an adaptive control strategy is proposed to address the synchronization issue for weakly damped generators under topological uncertainty. A singular perturbation analysis is then adopted for strongly damped generators and a compensation control scheme is subsequently given to maintain synchronization under topological changes. Theoretical proof is laid out for the validity of the proposed control scheme. Besides, a power sharing strategy is supplemented for strongly damped generators based on the designed controller. Finally, simulation studies are carried out to verify the effectiveness of the control strategies. Results show that synchronization can be swiftly restored even when the power grid suffers a fatal topological change. The power sharing property can be achieved under the given restriction with the proposed controller.

Phylogeny and classification of the Australasian and Indomalayan mimosoid legumes Archidendron and Archidendropsis (Leguminosae, subfamily Caesalpinioideae, mimosoid clade).

The morphologically variable genus Archidendron is the second largest mimosoid legume genus from the Indomalayan-Australasian region, yet it has not been well represented in phylogenetic studies. Phylogenies that have included multiple representatives of Archidendron suggest it may not be monophyletic, and the same applies to Archidendropsis, another understudied genus of the Archidendron clade. The most comprehensive phylogeny of Archidendron and Archidendropsis to date is presented, based on four nuclear markers (ITS, ETS, SHMT and RBPCO). Exemplars from all genera of the wider Archidendron clade are sampled, including representatives of all series within Archidendron and the two subgenera of Archidendropsis. Our results confirm that Archidendron and Archidendropsis are not monophyletic. Within Archidendron, only one series (ser. Ptenopae) is resolved as monophyletic and species of Archidendron are divided into two primarily geographic lineages. One clade is distributed in western Malesia and mainland Asia and includes most representatives of series Clypeariae, while the other is mostly restricted to eastern Malesia and Australia and includes representatives of the seven other series plus two samples of series Clypeariae. No taxonomic changes are made for Archidendron due to the high level of topological uncertainty and the lack of discrete macromorphological characters separating these two lineages. Each of the two subgenera of Archidendropsis is monophyletic but they are not closely related. A new genus endemic to Queensland (Australia), Heliodendron Gill.K. Br. & Bayly, gen. nov., is described for the former Archidendropsissubg.Basaltica, and combinations for its three species are proposed: Heliodendronbasalticum (F. Muell.) Gill.K. Br. & Bayly, comb. nov., Heliodendronthozetianum (F. Muell.) Gill.K. Br. & Bayly, comb. nov., and Heliodendronxanthoxylon (C.T. White & W.D. Francis) Gill.K. Br. & Bayly, comb. nov.

Nuclear ribosomal phylogeny of Brachystegia: new markers for new insights about rain forests and Miombo woodlands evolution

Background and aims – Brachystegia is a species-rich tree genus found in tropical Africa and a typical element of Miombo woodlands, a widely distributed subtype of the Zambezian savanna. Plastid DNA was shown to be largely uninformative to assess species phylogenetic relationships due to widespread chloroplast capture among species. Here, we aim to assess the capacity of nuclear ribosomal DNA (rDNA) to clarify the phylogeny of Brachystegia species while accounting for intra-individual site polymorphisms (2ISPs), which are often present in rDNA and potentially phylogenetically informative. Material and methods – Genome skimming sequencing on 47 samples representing 27 of the 29 currently recognized Brachystegia species, allowed us to retrieve complete nuclear ribosomal cistrons encoding for 18S, 5.8S, and 25S rRNA genes (35S rDNA). We reconstructed the Brachystegia phylogeny using Maximum Likelihood methods based on the standard substitution model or integrating 2ISPs (GENOTYPE implementation in RAxML-NG). We additionally tested the effect of partitioning the data (one partition for rDNA genes and one for the ITS1+ITS2). We also conducted network inferences (Neighbor-Net splits graph), as a strict bifurcative approach might not properly model topological uncertainty at shallow phylogenetic depth. Key results – 2ISPs-aware and standard phylogenetic reconstructions are largely congruent. We identified several well-supported main clades clarifying the species relationships, including two clades of Miombo woodlands species. Miombo Group A includes species with ovoid to globose axillary dormant buds, while Miombo Group B species have flattened ones. Two morphologically close Brachystegia species (B. kennedyi and B. leonensis) found in Guineo-Congolian rain forests form also a robustly supported clade. 2ISPs coding allowed to identify an additional Guineo-Congolian clade (B. eurycoma and B. nigerica). Ribosomal DNA therefore proves more useful to explore the generic phylogeny than plastid DNA but the species relationships within and among the main clades remain poorly resolved, probably due to recent diversification and/or recurrent hybridization, so that the diversification of Brachystegia remains to be more properly characterised. Conclusion – Nuclear and plastid phylogenetic reconstructions of Brachystegia species are discordant. Even if not well-resolved, rDNA phylograms and networks are characterized by taxonomic sorting, while we observe a strictly geographic sorting in the plastid dataset. Most of the species’ relationships remain to be characterized using additional nuclear markers combined with in-depth morphological investigations.

Fuzzy consensus of multi‐agent systems with granular fuzzy uncertainty in communication topology

AbstractIn this paper, the consensus problem in linear multi‐agent systems with uncertain topology is investigated. The uncertainty in the communication topology is represented by granular fuzzy numbers obtained from expert knowledge, and the required calculations are performed with multidimensional relative–distance–measurement interval arithmetic. The concept of granular fuzzy graph and fuzzy Gershgorin disc theorem is introduced. Then a fuzzy consensus protocol is proposed for the multi‐agent system with fuzzy granular uncertain topology. A two‐step algorithm is also proposed to build the consensus protocol. We also propose a theorem for calculating the final value of fuzzy consensus, which shows the final value of consensus as a fuzzy number. Simulation results show the efficiency of the suggested algorithm.

Efficient sampling of complex interdependent and multiplex networks

Abstract Efficient sampling of interdependent and multiplex infrastructure networks is critical for effectively applying failure and recovery algorithms in real-world settings, as well as to generate property-preserving reduced-order graph-based ensembles that address topological uncertainties. In this article, we first explore the performance, that is, the success in preserving graph properties, of graph sampling algorithms for interdependent and multiplex networks with synthetic and real-world graphs. We simulate sampling algorithms under different parameter settings. These settings include probabilistic graph generators, coupling patterns and various performance metrics. Our results show that while Random Node and Random Walk sampling algorithms perform best for interdependent networks, Random Edge and Forest Fire sampling algorithms perform best for multiplex networks. Second, we propose and implement a novel similarity-based sampling algorithm for multiplex networks that samples only ${\it log}(N)$ number of layers of an $N$-layer multiplex network while yielding computational savings with performance guarantees. Experimental results show that similarity-based sampling outperforms complete sampling of all layers while decreasing performance costs from a linear scale to a logarithmic one. Our results also indicate that similarity-based sampling outperforms complete sampling and random selection in nearly all scenarios when tested with real-world data.

Incorporating Topological and Age Uncertainty into Event-Based Biogeography of Sand Spiders Supports Paleo-Islands in Galapagos and Ancient Connections among Neotropical Dry Forests

Event-based biogeographic methods, such as dispersal-extinction-cladogenesis, have become increasingly popular for attempting to reconstruct the biogeographic history of organisms. Such methods employ distributional data of sampled species and a dated phylogenetic tree to estimate ancestral distribution ranges. Because the input tree is often a single consensus tree, uncertainty in topology and age estimates are rarely accounted for, even when they may affect the outcome of biogeographic estimates. Even when such uncertainties are taken into account for estimates of ancestral ranges, they are usually ignored when researchers compare competing biogeographic hypotheses. We explore the effect of incorporating this uncertainty in a biogeographic analysis of the 21 species of sand spiders (Sicariidae: Sicarius) from Neotropical xeric biomes, based on a total-evidence phylogeny including a complete sampling of the genus. Using a custom R script, we account for uncertainty in ages and topology by estimating ancestral ranges over a sample of trees from the posterior distribution of a Bayesian analysis, and for uncertainty in biogeographic estimates by using stochastic maps. This approach allows for counting biogeographic events such as dispersal among areas, counting lineages through time per area, and testing biogeographic hypotheses, while not overestimating the confidence in a single topology. Including uncertainty in ages indicates that Sicarius dispersed to the Galapagos Islands when the archipelago was formed by paleo-islands that are now submerged; model comparison strongly favors a scenario where dispersal took place before the current islands emerged. We also investigated past connections among currently disjunct Neotropical dry forests; failing to account for topological uncertainty underestimates possible connections among the Caatinga and Andean dry forests in favor of connections among Caatinga and Caribbean + Mesoamerican dry forests. Additionally, we find that biogeographic models including a founder-event speciation parameter (“+J”) are more prone to suffer from the overconfidence effects of estimating ancestral ranges using a single topology. This effect is alleviated by incorporating topological and age uncertainty while estimating stochastic maps, increasing the similarity in the inference of biogeographic events between models with or without a founder-event speciation parameter. We argue that incorporating phylogenetic uncertainty in biogeographic hypothesis-testing is valuable and should be a commonplace approach in the presence of rogue taxa or wide confidence intervals in age estimates, and especially when using models including founder-event speciation.

Boolink: a graphical interface for open access Boolean network simulations and use in guard cell CO2 signaling.

Signaling networks are at the heart of almost all biological processes. Most of these networks contain large number of components, and often either the connections between these components are not known or the rate equations that govern the dynamics of soluble signaling components are not quantified. This uncertainty in network topology and parameters can make it challenging to formulate detailed mathematical models. Boolean networks, in which all components are either on or off, have emerged as viable alternatives to detailed mathematical models that contain rate constants and other parameters. Therefore, open-source platforms of Boolean models for community use are desirable. Here, we present Boolink, a freely available graphical user interface that allows users to easily construct and analyze existing Boolean networks. Boolink can be applied to any Boolean network. We demonstrate its application using a previously published network for abscisic acid (ABA)-driven stomatal closure in Arabidopsis spp. (Arabidopsis thaliana). We also show how Boolink can be used to generate testable predictions by extending the network to include CO2 regulation of stomatal movements. Predictions of the model were experimentally tested, and the model was iteratively modified based on experiments showing that ABA effectively closes Arabidopsis stomata at near-zero CO2 concentrations (1.5-ppm CO2). Thus, Boolink enables public generation and the use of existing Boolean models, including the prior developed ABA signaling model with added CO2 signaling components.

Robust Coordinated Control of Nonlinear Heterogeneous Platoon Interacted by Uncertain Topology

To simultaneously deal with the uncertain interaction topology, parametric errors and external disturbances, this paper proposes a new coordinated control scheme for the platoon composed of nonlinear and heterogeneous automated vehicles (AVs). In this scheme, different perturbations are dealt with separately to reduce the contraction among them by using the sliding mode control theory. Considering the individual dynamics, a distributed coordinated controller including both lateral and longitudinal motions is designed for each AV with online estimation of the unknown parameters and disturbances. On the sliding surfaces of longitudinal motion, a decoupling approach using the eigenvalue decomposition of topological matrix and linear transformation is proposed to deal with the topological uncertainty. Then the dynamical system of platoon coupled by the information flow is decomposed into the subsystems with lower order. The relationship of the robust performance between the original and decoupled system is analyzed theoretically. Based on this theoretical conclusion, a numerical way is given based on linear matrix inequality (LMI) theory to design the parameters of sliding motion dynamics. By this way, the exact topological matrix is not necessary and only the bound of its eigenvalue is required. The effectiveness of the proposed strategy is validated by several comparative simulations under variety conditions.

Decentralized Adaptive Protection Coordination Based on Agents Social Activities for Microgrids With Topological and Operational Uncertainties

A decentralized adaptive scheme is proposed in this article for protection coordination for microgrids with topological and operational uncertainties. This protection coordination scheme is performed in two stages. In the first stage, a traditional fault protection is deployed to clear the fault. If the fault is isolated successfully, the protection system returns to the regular fault-free state. If the fault is not cleared due to operational uncertainties in the protection system, the second stage of protection coordination is initiated. In this stage, based on a federation structure, a set of agents around the fault location negotiate to reach the best protection coordination strategy upon the occurrence of a single or multiple fault(s). Considering the operational uncertainties of the respective circuit breakers and communication links, the best fault clearance strategy is determined by analyzing the probability of correct operation of all proposed strategies and considering the least number of probable load outages. Two major factors impacting the probability of correct operation are fault currents flowing through the respective circuit breakers and the latency of the communication links. The efficiency of the proposed scheme is demonstrated by comparing the simulation results with their experimental counterparts and those obtained using the conventional centralized and decentralized adaptive methods.

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. In this paper, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green's kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal $\epsilon^{-2}$ asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

Mammal Community Structure through the Paleocene-Eocene Thermal Maximum.

AbstractHuman-mediated species invasion and climate change are leading to global extinctions and are predicted to result in the loss of important axes of phylogenetic and functional diversity. However, the long-term robustness of modern communities to invasion is unknown, given the limited timescales over which they can be studied. Using the fossil record of the Paleocene-Eocene thermal maximum (PETM; ∼56 Ma) in North America, we evaluate mammalian community-level response to a rapid global warming event (5°-8°C) and invasion by three Eurasian mammalian orders and by species undergoing northward range shifts. We assembled a database of 144 species body sizes and created a time-scaled composite phylogeny. We calculated the phylogenetic and functional diversity of all communities before, during, and after the PETM. Despite increases in the phylogenetic diversity of the regional species pool, phylogenetic diversity of mammalian communities remained relatively unchanged, a pattern that is invariant to the tree dating method, uncertainty in tree topology, and resolution. Similarly, body size dispersion and the degree of spatial taxonomic turnover of communities remained similar across the PETM. We suggest that invasion by new taxa had little impact on Paleocene-Eocene mammal communities because niches were not saturated. Our findings are consistent with the numerous studies of modern communities that record little change in community-scale richness despite turnover in taxonomic composition during invasion. What remains unknown is whether long-term robustness to biotic and abiotic perturbation are retained by modern communities given global anthropogenic landscape modification.