A population's effective size (Ne ) is a key parameter that shapes rates of inbreeding and loss of genetic diversity, thereby influencing evolutionary processes and population viability. However, estimating Ne , and identifying key demographic mechanisms that underlie the Ne to census population size (N) ratio, remains challenging, especially for small populations with overlapping generations and substantial environmental and demographic stochasticity and hence dynamic age-structure. A sophisticated demographic method of estimating Ne /N, which uses Fisher's reproductive value to account for dynamic age-structure, has been formulated. However, this method requires detailed individual- and population-level data on sex- and age-specific reproduction and survival, and has rarely been implemented. Here, we use the reproductive value method and detailed demographic data to estimate Ne /N for a small and apparently isolated red-billed chough (Pyrrhocorax pyrrhocorax) population of high conservation concern. We additionally calculated two single-sample molecular genetic estimates of Ne to corroborate the demographic estimate and examine evidence for unobserved immigration and gene flow. The demographic estimate of Ne /N was 0.21, reflecting a high total demographic variance (σ2dg) of 0.71. Females and males made similar overall contributions to σ2dg. However, contributions varied among sex-age classes, with greater contributions from 3year-old females than males, but greater contributions from ≥5year-old males than females. The demographic estimate of Ne was ~30, suggesting that rates of increase of inbreeding and loss of genetic variation per generation will be relatively high. Molecular genetic estimates of Ne computed from linkage disequilibrium and approximate Bayesian computation were approximately 50 and 30, respectively, providing no evidence of substantial unobserved immigration which could bias demographic estimates of Ne . Our analyses identify key sex-age classes contributing to demographic variance and thus decreasing Ne /N in a small age-structured population inhabiting a variable environment. They thereby demonstrate how assessments of Ne can incorporate stochastic sex- and age-specific demography and elucidate key demographic processes affecting a population's evolutionary trajectory and viability. Furthermore, our analyses show that Ne for the focal chough population is critically small, implying that management to re-establish genetic connectivity may be required to ensure population viability.

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