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Abstract The genetic effective size (Ne) is arguably one of the most important characteristics of a population as it impacts the rate of loss of genetic diversity. Methods that estimate Ne are important in population and conservation genetic studies as they quantify the risk of a population being inbred or lacking genetic diversity. Yet there are very few methods that can estimate the Ne from data from a single population and without extensive information about the genetics of the population, such as a linkage map, or a reference genome of the species of interest. We present ONeSAMP 3.0, an algorithm for estimating Ne from single nucleotide polymorphism data collected from a single population sample using approximate Bayesian computation and local linear regression. We demonstrate the utility of this approach using simulated Wright–Fisher populations, and empirical data from five endangered Channel Island fox (Urocyon littoralis) populations to evaluate the performance of ONeSAMP 3.0 compared to a commonly used Ne estimator. Our results show that ONeSAMP 3.0 is broadly applicable to natural populations and is flexible enough that future versions could easily include summary statistics appropriate for a suite of biological and sampling conditions. ONeSAMP 3.0 is publicly available under the GNU General Public License at https://github.com/AaronHong1024/ONeSAMP_3. 

Let [Formula: see text] be a group acting properly and by isometries on a metric space [Formula: see text]; it follows that the quotient or orbit space [Formula: see text] is also a metric space. We study the Vietoris–Rips and Čech complexes of [Formula: see text]. Whereas (co)homology theories for metric spaces let the scale parameter of a Vietoris–Rips or Čech complex go to zero, and whereas geometric group theory requires the scale parameter to be sufficiently large, we instead consider intermediate scale parameters (neither tending to zero nor to infinity). As a particular case, we study the Vietoris–Rips and Čech thickenings of projective spaces at the first scale parameter where the homotopy type changes.