biostudies-literaturePande JIsrael Science Foundation1783-1794https://www.ebi.ac.uk/biostudies/studies/S-EPMC9543749biostudies-literatureUnknown25(8)Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases. Here we provide two novel formulae, based on the diffusion approximation and a large-deviations (Wentzel-Kramers-Brillouin) approach, for the chance of invasion given the mean growth and its variance. The first formula has the virtue of simplicity, while the second one holds over a wider parameter range. The efficacy of the formulae, includiEcology lettersQuantifying invasibility.PMC95437492669/17Shnerb NMPande JTsubery YfalseQuantifying invasibility.Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases. Here we provide two novel formulae, based on the diffusion approximation and a large-deviations (Wentzel-Kramers-Brillouin) approach, for the chance of invasion given the mean growth and its variance. The first formula has the virtue of simplicity, while the second one holds over a wider parameter range. The efficacy of the formulae, includi2022-01-01T00:00:00Z2022 Aug2025-04-04T20:04:18.249Z2025-04-04T20:04:18.249ZS-EPMC95437493571756110.1111/ele.14031