The development of eccentric waveform models enables us to explore the growing catalog of gravitational-wave events with measurable eccentricity. This opens new opportunities to gain insight into the formation channels and evolutionary pathways of compact binary systems using eccentricity. However, most recent population analyses have been limited to quasicircular binaries, primarily due to constraints in waveform modeling and sensitivity estimates. We are now entering an era where both of these limitations are being addressed, allowing for a more comprehensive investigation of eccentric binary populations. In this work, we perform a very first population analysis that simultaneously fits the mass, spin, redshift, and eccentricity distribution. Specifically, we use source-parameter estimation on 153 binary black holes in GWTC-4 catalog provided by the rapid iterative fitting framework using the SEOBNRv5EHM waveform model. We extend the default O4a population model to include orbital eccentricity. We find that inferred population properties are broadly consistent with conclusions obtained in previous analyses assuming quasicircular binaries. To assess sensitivity of our results to the most eccentric sources, we repeat our analysis excluding GW200129_065458. Consistent with our conclusions about each event and using the nonoverlapping mixture eccentricity model, we bound the branching ratio for eccentric events to be below 0.051890 and 0.022011 at 90% confidence with and without GW200129_065458, respectively. Using four different parametric population models for eccentricity, we argue that the rate of eccentric events is weakly constrained by observations and highly model dependent.

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• Gravitation
• Gravitational waves