High-resolution analyses of associations between medications, microbiome, and mortality in cancer patients.

Discerning the effect of pharmacological exposures on intestinal bacterial communities in cancer patients is challenging. Here, we deconvoluted the relationship between drug exposures and changes in microbial composition by developing and applying a new computational method, PARADIGM (parameters associated with dynamics of gut microbiota), to a large set of longitudinal fecal microbiome profiles with detailed medication-administration records from patients undergoing allogeneic hematopoietic cell transplantation. We observed that several non-antibiotic drugs, including laxatives, antiemetics, and opioids, are associated with increased Enterococcus relative abundance and decreased alpha diversity. Shotgun metagenomic sequencing further demonstrated subspecies competition, leading to increased dominant-strain genetic convergence during allo-HCT that is significantly associated with antibiotic exposures. We integrated drug-microbiome associations to predict clinical outcomes in two validation cohorts on the basis of drug exposures alone, suggesting that this approach can generate biologically and clinically relevant insights into how pharmacological exposures can perturb or preserve microbiota composition. The application of a computational method called PARADIGM to a large dataset of cancer patients' longitudinal fecal specimens and detailed daily medication records reveals associations between drug exposures and the intestinal microbiota that recapitulate in vitro findings and are also predictive of clinical outcomes.

Fatty acid oxidation fuels natural killer cell responses against infection and cancer.

Natural killer (NK) cells are a vital part of the innate immune system capable of rapidly clearing mutated or infected cells from the body and promoting an immune response. Here, we find that NK cells activated by viral infection or tumor challenge increase uptake of fatty acids and their expression of carnitine palmitoyltransferase I (CPT1A), a critical enzyme for long-chain fatty acid oxidation. Using a mouse model with an NK cell-specific deletion of CPT1A, combined with stable 13C isotope tracing, we observe reduced mitochondrial function and fatty acid-derived aspartate production in CPT1A-deficient NK cells. Furthermore, CPT1A-deficient NK cells show reduced proliferation after viral infection and diminished protection against cancer due to impaired actin cytoskeleton rearrangement. Together, our findings highlight that fatty acid oxidation promotes NK cell metabolic resilience, processes that can be optimized in NK cell-based immunotherapies.

The gut microbiota is associated with immune cell dynamics in humans.

The gut microbiota influences development1-3 and homeostasis4-7 of the mammalian immune system, and is associated with human inflammatory8 and immune diseases9,10 as well as responses to immunotherapy11-14. Nevertheless, our understanding of how gut bacteria modulate the immune system remains limited, particularly in humans, where the difficulty of direct experimentation makes inference challenging. Here we study hundreds of hospitalized-and closely monitored-patients with cancer receiving haematopoietic cell transplantation as they recover from chemotherapy and stem-cell engraftment. This aggressive treatment causes large shifts in both circulatory immune cell and microbiota populations, enabling the relationships between the two to be studied simultaneously. Analysis of observed daily changes in circulating neutrophil, lymphocyte and monocyte counts and more than 10,000 longitudinal microbiota samples revealed consistent associations between gut bacteria and immune cell dynamics. High-resolution clinical metadata and Bayesian inference allowed us to compare the effects of bacterial genera in relation to those of immunomodulatory medications, revealing a considerable influence of the gut microbiota-together and over time-on systemic immune cell dynamics. Our analysis establishes and quantifies the link between the gut microbiota and the human immune system, with implications for microbiota-driven modulation of immunity.

The Ultimate Guide to Bacterial Swarming: An Experimental Model to Study the Evolution of Cooperative Behavior.

Cooperation has fascinated biologists since Darwin. How did cooperative behaviors evolve despite the fitness cost to the cooperator? Bacteria have cooperative behaviors that make excellent models to take on this age-old problem from both proximate (molecular) and ultimate (evolutionary) angles. We delve into Pseudomonas aeruginosa swarming, a phenomenon where billions of bacteria move cooperatively across distances of centimeters in a matter of a few hours. Experiments with swarming have unveiled a strategy called metabolic prudence that stabilizes cooperation, have showed the importance of spatial structure, and have revealed a regulatory network that integrates environmental stimuli and direct cooperative behavior, similar to a machine learning algorithm. The study of swarming elucidates more than proximate mechanisms: It exposes ultimate mechanisms valid to all scales, from cells in cancerous tumors to animals in large communities.

Imaging Nasal Obstruction: An Objective Evaluation for a Subjective Complaint.

Nasal obstruction (NO) is a common clinical symptom characterized by a subjective sensation of insufficient airflow through the nasal cavity and may result from various factors, including changes in nasal anatomy, inflammatory conditions, tumoral lesions, and other etiologies. While a thorough medical history and physical examination can often identify its cause, imaging is usually necessary to fully understand the problem. Computed tomography (CT) is the primary imaging modality used to evaluate the nasal cavity and paranasal sinuses, allowing for the identification of potential causes and structural abnormalities. However, when soft tissue characterization is required, magnetic resonance imaging (MRI) is also useful. Understanding the anatomical and pathological basis of NO is crucial for accurate diagnosis and appropriate management. Imaging techniques provide valuable information for identifying the underlying causes of NO and guiding treatment decisions. This article reviews the normal anatomy of the nasal cavity and adjacent paranasal sinuses as well as the several conditions that may affect breathing comfort (tumors, inflammatory diseases, bony and cartilaginous anatomical variants, and "nonobstructive" mucosal thickenings), showing their normal presentation on CT and MRI.

Microbiota as Predictor of Mortality in Allogeneic Hematopoietic-Cell Transplantation.

BACKGROUND: Relationships between microbiota composition and clinical outcomes after allogeneic hematopoietic-cell transplantation have been described in single-center studies. Geographic variations in the composition of human microbial communities and differences in clinical practices across institutions raise the question of whether these associations are generalizable. METHODS: The microbiota composition of fecal samples obtained from patients who were undergoing allogeneic hematopoietic-cell transplantation at four centers was profiled by means of 16S ribosomal RNA gene sequencing. In an observational study, we examined associations between microbiota diversity and mortality using Cox proportional-hazards analysis. For stratification of the cohorts into higher- and lower-diversity groups, the median diversity value that was observed at the study center in New York was used. In the analysis of independent cohorts, the New York center was cohort 1, and three centers in Germany, Japan, and North Carolina composed cohort 2. Cohort 1 and subgroups within it were analyzed for additional outcomes, including transplantation-related death. RESULTS: We profiled 8767 fecal samples obtained from 1362 patients undergoing allogeneic hematopoietic-cell transplantation at the four centers. We observed patterns of microbiota disruption characterized by loss of diversity and domination by single taxa. Higher diversity of intestinal microbiota was associated with a lower risk of death in independent cohorts (cohort 1: 104 deaths among 354 patients in the higher-diversity group vs. 136 deaths among 350 patients in the lower-diversity group; adjusted hazard ratio, 0.71; 95% confidence interval [CI], 0.55 to 0.92; cohort 2: 18 deaths among 87 patients in the higher-diversity group vs. 35 deaths among 92 patients in the lower-diversity group; adjusted hazard ratio, 0.49; 95% CI, 0.27 to 0.90). Subgroup analyses identified an association between lower intestinal diversity and higher risks of transplantation-related death and death attributable to graft-versus-host disease. Baseline samples obtained before transplantation already showed evidence of microbiome disruption, and lower diversity before transplantation was associated with poor survival. CONCLUSIONS: Patterns of microbiota disruption during allogeneic hematopoietic-cell transplantation were similar across transplantation centers and geographic locations; patterns were characterized by loss of diversity and domination by single taxa. Higher diversity of intestinal microbiota at the time of neutrophil engraftment was associated with lower mortality. (Funded by the National Cancer Institute and others.).

The microbe-derived short-chain fatty acids butyrate and propionate are associated with protection from chronic GVHD.

Studies of the relationship between the gastrointestinal microbiota and outcomes in allogeneic hematopoietic stem cell transplantation (allo-HCT) have thus far largely focused on early complications, predominantly infection and acute graft-versus-host disease (GVHD). We examined the potential relationship of the microbiome with chronic GVHD (cGVHD) by analyzing stool and plasma samples collected late after allo-HCT using a case-control study design. We found lower circulating concentrations of the microbe-derived short-chain fatty acids (SCFAs) propionate and butyrate in day 100 plasma samples from patients who developed cGVHD, compared with those who remained free of this complication, in the initial case-control cohort of transplant patients and in a further cross-sectional cohort from an independent transplant center. An additional cross-sectional patient cohort from a third transplant center was analyzed; however, serum (rather than plasma) was available, and the differences in SCFAs observed in the plasma samples were not recapitulated. In sum, our findings from the primary case-control cohort and 1 of 2 cross-sectional cohorts explored suggest that the gastrointestinal microbiome may exert immunomodulatory effects in allo-HCT patients at least in part due to control of systemic concentrations of microbe-derived SCFAs.

Posterior Circulation Stroke: Coma (More Than Time) is Brain.

BACKGROUND AND PURPOSE: Contrary to anterior circulation, the legitimacy of endovascular treatment in posterior circulation stroke is still being questioned. Finding reliable prognostic factors and determining how patient selection should be done has become top priority. METHODS: Observational and retrospective study from two Portuguese hospitals, including all consecutive patients with posterior circulation occlusions who underwent thrombectomy between January 1st 2015 and December 31st 2019. RESULTS: Out of a total of 126 patients, the median age was 74 (IQR 61-80) and 39.7% were female. A good clinical outcome (mRS ≤2) was associated with a lower incidence of coma (24,2% vs 66,7%, p < 0,001) and of sudden onset coma (3% vs 18%,=0,04), a lower NIHSS at admission (14 vs 19, p < 0,001), a higher pc-ASPECTS at admission (10 vs 9, p < 0,001) and at 24 h (8 vs 6, p < 0,001) and a higher BATMAN score (7 vs 6, p = 0,017). Differences in the times of symptom-onset-to-recanalization (496 vs 536, p = 0,19) and symptom-onset-to-coma (130 vs 195, p = 0,52) were not remarkable. When excluding NIHSS and pc-ASPECTS at 24 h, coma (p = 0,003; OR=0,22; 95% CI: 0,08-0,59) and the pc-ASPECTS at admission (p = 0,037; OR=1,63; 95% CI: 1,03-2,57) become independent predictors of good outcome. CONCLUSIONS: In strokes from the posterior circulation, coma, more than time, appears to be an important prognostic factor. The BATMAN and the pc-ASPECTS scores were also associated with clinical outcome and coma.

Integrated Structural and Environmental Form-Finding: A Teaching Experiment.

This paper presents a teaching experiment in which 3D digital computational models are explored as the representational base to integrate formal, structural, and environmental performance criteria in design. By describing the academic experience, the paper reflects on its methodologies and results, as well as on the relation between human and computer factors in the design process. This assessment is important to make the students aware of the increasingly intelligent design systems offered by digital technologies to support architectural design, as well as of their relationship with precedent digital and analog representational mediums.

Modeling microbial cross-feeding at intermediate scale portrays community dynamics and species coexistence.

Social interaction between microbes can be described at many levels of details: from the biochemistry of cell-cell interactions to the ecological dynamics of populations. Choosing an appropriate level to model microbial communities without losing generality remains a challenge. Here we show that modeling cross-feeding interactions at an intermediate level between genome-scale metabolic models of individual species and consumer-resource models of ecosystems is suitable to experimental data. We applied our modeling framework to three published examples of multi-strain Escherichia coli communities with increasing complexity: uni-, bi-, and multi-directional cross-feeding of either substitutable metabolic byproducts or essential nutrients. The intermediate-scale model accurately fit empirical data and quantified metabolic exchange rates that are hard to measure experimentally, even for a complex community of 14 amino acid auxotrophies. By studying the conditions of species coexistence, the ecological outcomes of cross-feeding interactions, and each community's robustness to perturbations, we extracted new quantitative insights from these three published experimental datasets. Our analysis provides a foundation to quantify cross-feeding interactions from experimental data, and highlights the importance of metabolic exchanges in the dynamics and stability of microbial communities.

Compositional Lotka-Volterra describes microbial dynamics in the simplex.

Dynamic changes in microbial communities play an important role in human health and disease. Specifically, deciphering how microbial species in a community interact with each other and their environment can elucidate mechanisms of disease, a problem typically investigated using tools from community ecology. Yet, such methods require measurements of absolute densities, whereas typical datasets only provide estimates of relative abundances. Here, we systematically investigate models of microbial dynamics in the simplex of relative abundances. We derive a new nonlinear dynamical system for microbial dynamics, termed "compositional" Lotka-Volterra (cLV), unifying approaches using generalized Lotka-Volterra (gLV) equations from community ecology and compositional data analysis. On three real datasets, we demonstrate that cLV recapitulates interactions between relative abundances implied by gLV. Moreover, we show that cLV is as accurate as gLV in forecasting microbial trajectories in terms of relative abundances. We further compare cLV to two other models of relative abundance dynamics motivated by common assumptions in the literature-a linear model in a log-ratio transformed space, and a linear model in the space of relative abundances-and provide evidence that cLV more accurately describes community trajectories over time. Finally, we investigate when information about direct effects can be recovered from relative data that naively provide information about only indirect effects. Our results suggest that strong effects may be recoverable from relative data, but more subtle effects are challenging to identify.

Precision microbiome reconstitution restores bile acid mediated resistance to Clostridium difficile.

The gastrointestinal tracts of mammals are colonized by hundreds of microbial species that contribute to health, including colonization resistance against intestinal pathogens. Many antibiotics destroy intestinal microbial communities and increase susceptibility to intestinal pathogens. Among these, Clostridium difficile, a major cause of antibiotic-induced diarrhoea, greatly increases morbidity and mortality in hospitalized patients. Which intestinal bacteria provide resistance to C. difficile infection and their in vivo inhibitory mechanisms remain unclear. Here we correlate loss of specific bacterial taxa with development of infection, by treating mice with different antibiotics that result in distinct microbiota changes and lead to varied susceptibility to C. difficile. Mathematical modelling augmented by analyses of the microbiota of hospitalized patients identifies resistance-associated bacteria common to mice and humans. Using these platforms, we determine that Clostridium scindens, a bile acid 7α-dehydroxylating intestinal bacterium, is associated with resistance to C. difficile infection and, upon administration, enhances resistance to infection in a secondary bile acid dependent fashion. Using a workflow involving mouse models, clinical studies, metagenomic analyses, and mathematical modelling, we identify a probiotic candidate that corrects a clinically relevant microbiome deficiency. These findings have implications for the rational design of targeted antimicrobials as well as microbiome-based diagnostics and therapeutics for individuals at risk of C. difficile infection.

The Vibrio cholerae type VI secretion system can modulate host intestinal mechanics to displace gut bacterial symbionts.

Host-associated microbiota help defend against bacterial pathogens; however, the mechanisms by which pathogens overcome this defense remain largely unknown. We developed a zebrafish model and used live imaging to directly study how the human pathogen Vibrio cholerae invades the intestine. The gut microbiota of fish monocolonized by symbiotic strain Aeromonas veronii was displaced by V. cholerae expressing its type VI secretion system (T6SS), a syringe-like apparatus that deploys effector proteins into target cells. Surprisingly, displacement was independent of T6SS-mediated killing of A. veronii, driven instead by T6SS-induced enhancement of zebrafish intestinal movements that led to expulsion of the resident microbiota by the host. Deleting an actin cross-linking domain from the T6SS apparatus returned intestinal motility to normal and thwarted expulsion, without weakening V. cholerae's ability to kill A. veronii in vitro. Our finding that bacteria can manipulate host physiology to influence intermicrobial competition has implications for both pathogenesis and microbiome engineering.

High Heterogeneity of Multidrug-Resistant Enterobacteriaceae Fecal Levels in Hospitalized Patients Is Partially Driven by Intravenous ß-Lactams.

Multidrug-resistant Enterobacteriaceae (MRE) colonize the intestine asymptomatically from where they can breach into the bloodstream and cause life-threatening infections, especially in heavily colonized patients. Despite the clinical relevance of MRE colonization levels, we know little about how they vary in hospitalized patients and the clinical factors that determine those levels. Here, we conducted one of the largest studies of MRE fecal levels by tracking longitudinally 133 acute leukemia patients and monitoring their MRE levels over time through extensive culturing. MRE were defined as Enterobacteriaceae species that acquired nonsusceptibility to ≥1 agent in ≥3 antimicrobial categories. In addition, due to the selective media used, the MRE had to be resistant to third-generation cephalosporins. MRE were detected in 60% of the patients, but their fecal levels varied considerably among patients and within the same patient (>6 and 4 orders of magnitude, respectively). Multivariate analysis of clinical metadata revealed an impact of intravenous beta-lactams (i.e., meropenem and piperacillin-tazobactam), which significantly diminished the fecal MRE levels in hospitalized patients. Consistent with a direct action of beta-lactams, we found an effect only when the patient was colonized with strains sensitive to the administered beta-lactam (P < 0.001) but not with nonsusceptible strains. We report previously unobserved inter- and intraindividual heterogeneity in MRE fecal levels, suggesting that quantitative surveillance is more informative than qualitative surveillance of hospitalized patients. In addition, our study highlights the relevance of incorporating antibiotic treatment and susceptibility data of gut-colonizing pathogens for future clinical studies and in clinical decision-making.

Systems-level analysis of NalD mutation, a recurrent driver of rapid drug resistance in acute Pseudomonas aeruginosa infection.

Pseudomonas aeruginosa, a main cause of human infection, can gain resistance to the antibiotic aztreonam through a mutation in NalD, a transcriptional repressor of cellular efflux. Here we combine computational analysis of clinical isolates, transcriptomics, metabolic modeling and experimental validation to find a strong association between NalD mutations and resistance to aztreonam-as well as resistance to other antibiotics-across P. aeruginosa isolated from different patients. A detailed analysis of one patient's timeline shows how this mutation can emerge in vivo and drive rapid evolution of resistance while the patient received cancer treatment, a bone marrow transplantation, and antibiotics up to the point of causing the patient's death. Transcriptomics analysis confirmed the primary mechanism of NalD action-a loss-of-function mutation that caused constitutive overexpression of the MexAB-OprM efflux system-which lead to aztreonam resistance but, surprisingly, had no fitness cost in the absence of the antibiotic. We constrained a genome-scale metabolic model using the transcriptomics data to investigate changes beyond the primary mechanism of resistance, including adaptations in major metabolic pathways and membrane transport concurrent with aztreonam resistance, which may explain the lack of a fitness cost. We propose that metabolic adaptations may allow resistance mutations to endure in the absence of antibiotics and could be targeted by future therapies against antibiotic resistant pathogens.

Enhanced inference of ecological networks by parameterizing ensembles of population dynamics models constrained with prior knowledge.

BACKGROUND: Accurate network models of species interaction could be used to predict population dynamics and be applied to manage real world ecosystems. Most relevant models are nonlinear, however, and data available from real world ecosystems are too noisy and sparsely sampled for common inference approaches. Here we improved the inference of generalized Lotka-Volterra (gLV) ecological networks by using a new optimization algorithm to constrain parameter signs with prior knowledge and a perturbation-based ensemble method. RESULTS: We applied the new inference to long-term species abundance data from the freshwater fish community in the Illinois River, United States. We constructed an ensemble of 668 gLV models that explained 79% of the data on average. The models indicated (at a 70% level of confidence) a strong positive interaction from emerald shiner (Notropis atherinoides) to channel catfish (Ictalurus punctatus), which we could validate using data from a nearby observation site, and predicted that the relative abundances of most fish species will continue to fluctuate temporally and concordantly in the near future. The network shows that the invasive silver carp (Hypophthalmichthys molitrix) has much stronger impacts on native predators than on prey, supporting the notion that the invader perturbs the native food chain by replacing the diets of predators. CONCLUSIONS: Ensemble approaches constrained by prior knowledge can improve inference and produce networks from noisy and sparsely sampled time series data to fill knowledge gaps on real world ecosystems. Such network models could aid efforts to conserve ecosystems such as the Illinois River, which is threatened by the invasion of the silver carp.

Metabolic origins of spatial organization in the tumor microenvironment.

The genetic and phenotypic diversity of cells within tumors is a major obstacle for cancer treatment. Because of the stochastic nature of genetic alterations, this intratumoral heterogeneity is often viewed as chaotic. Here we show that the altered metabolism of cancer cells creates predictable gradients of extracellular metabolites that orchestrate the phenotypic diversity of cells in the tumor microenvironment. Combining experiments and mathematical modeling, we show that metabolites consumed and secreted within the tumor microenvironment induce tumor-associated macrophages (TAMs) to differentiate into distinct subpopulations according to local levels of ischemia and their position relative to the vasculature. TAMs integrate levels of hypoxia and lactate into progressive activation of MAPK signaling that induce predictable spatial patterns of gene expression, such as stripes of macrophages expressing arginase 1 (ARG1) and mannose receptor, C type 1 (MRC1). These phenotypic changes are functionally relevant as ischemic macrophages triggered tube-like morphogenesis in neighboring endothelial cells that could restore blood perfusion in nutrient-deprived regions where angiogenic resources are most needed. We propose that gradients of extracellular metabolites act as tumor morphogens that impose order within the microenvironment, much like signaling molecules convey positional information to organize embryonic tissues. Unearthing embryology-like processes in tumors may allow us to control organ-like tumor features such as tissue repair and revascularization and treat intratumoral heterogeneity.

Diversification and Evolution of Vancomycin-Resistant Enterococcus faecium during Intestinal Domination.

Vancomycin-resistant Enterococcus faecium (VRE) is a leading cause of hospital-acquired infections. This is particularly true in immunocompromised patients, where the damage to the microbiota caused by antibiotics can lead to VRE domination of the intestine, increasing a patient's risk for bloodstream infection. In previous studies we observed that the intestinal domination by VRE of patients hospitalized to receive allogeneic bone marrow transplantation can persist for weeks, but little is known about subspecies diversification and evolution during prolonged domination. Here we combined a longitudinal analysis of patient data and in vivo experiments to reveal previously unappreciated subspecies dynamics during VRE domination that appeared to be stable from 16S rRNA microbiota analyses. Whole-genome sequencing of isolates obtained from sequential stool samples provided by VRE-dominated patients revealed an unanticipated level of VRE population complexity that evolved over time. In experiments with ampicillin-treated mice colonized with a single CFU, VRE rapidly diversified and expanded into distinct lineages that competed for dominance. Mathematical modeling shows that in vivo evolution follows mostly a parabolic fitness landscape, where each new mutation provides diminishing returns and, in the setting of continuous ampicillin treatment, reveals a fitness advantage for mutations in penicillin-binding protein 5 (pbp5) that increase resistance to ampicillin. Our results reveal the rapid diversification of host-colonizing VRE populations, with implications for epidemiologic tracking of in-hospital VRE transmission and susceptibility to antibiotic treatment.

Antibiotic-Induced Shifts in Fecal Microbiota Density and Composition during Hematopoietic Stem Cell Transplantation.

Dramatic microbiota changes and loss of commensal anaerobic bacteria are associated with adverse outcomes in hematopoietic cell transplantation (HCT) recipients. In this study, we demonstrate these dynamic changes at high resolution through daily stool sampling and assess the impact of individual antibiotics on those changes. We collected 272 longitudinal stool samples (with mostly daily frequency) from 18 patients undergoing HCT and determined their composition by multiparallel 16S rRNA gene sequencing as well as the density of bacteria in stool by quantitative PCR (qPCR). We calculated microbiota volatility to quantify rapid shifts and developed a new dynamic systems inference method to assess the specific impact of antibiotics. The greatest shifts in microbiota composition occurred between stem cell infusion and reconstitution of healthy immune cells. Piperacillin-tazobactam caused the most severe declines among obligate anaerobes. Our approach of daily sampling, bacterial density determination, and dynamic systems modeling allowed us to infer the independent effects of specific antibiotics on the microbiota of HCT patients.

Evolution at the Edge of Expanding Populations.

Predicting the evolution of expanding populations is critical to controlling biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of evolution where organisms pay a reproductive cost to disperse faster. When does selection favor this "survival of the fastest"? We searched for a simple rule, motivated by evolution experiments where swarming bacteria evolved into a hyperswarmer mutant that disperses ∼100% faster but pays a growth cost of ∼10% to make many copies of its flagellum. We analyzed a two-species model based on the Fisher equation to explain this observation: the population expansion rate (v) results from an interplay of growth (r) and dispersal (D) and is independent of the carrying capacity: v=2(rD)1/2 . A mutant can take over the edge only if its expansion rate (v2) exceeds the expansion rate of the established species (v1); this simple condition ( v2>v1 ) determines the maximum cost in slower growth that a faster mutant can pay and still be able to take over. Numerical simulations and time-course experiments where we tracked evolution by imaging bacteria suggest that our findings are general: less favorable conditions delay but do not entirely prevent the success of the fastest. Thus, the expansion rate defines a traveling wave fitness, which could be combined with trade-offs to predict evolution of expanding populations.