Estimating abundance and population size is essential for many ecological and conservation studies of parrots. Achieving these goals requires methods that yield reliable estimates, but parrot traits can make them difficult to detect, count, and capture. We review established and emergent sampling and analytical methods used to estimate parrot abundance and population size, focusing on their assumptions, requirements, and limitations. Roost surveys are cost-effective if all roost locations in a region are known and stable, which is uncommon. Capture-recapture methods incorporate detection probability, but capturing, marking and resighting parrots can be difficult. Distance sampling estimates detection probability and surveys multiple species simultaneously, but is sensitive to the spatial distribution of individuals and excludes birds in flight. Roadside transects can cover large areas and survey multiple species, but habitats near roads may differ from the surrounding areas, biasing abundance estimates. Occupancy surveys and hierarchical models usually require spatially and temporally replicated datasets. Both allow estimation of detection probability; the former dispenses with count data, while the latter is a versatile set of methods that can incorporate multiple processes influencing detection and abundance. Finally, passive acoustic surveys can sample multiple species simultaneously, but identification of vocalisations can be difficult and time-consuming.

Adult sex ratio (ASR, the proportion of males in the adult population) is a central concept in population and evolutionary biology, and is also emerging as a major factor influencing mate choice, pair bonding and parental cooperation in both human and non-human societies. However, estimating ASR is fraught with difficulties stemming from the effects of spatial and temporal variation in the numbers of males and females, and detection/capture probabilities that differ between the sexes. Here, we critically evaluate methods for estimating ASR in wild animal populations, reviewing how recent statistical advances can be applied to handle some of these challenges. We review methods that directly account for detection differences between the sexes using counts of unmarked individuals (observed, trapped or killed) and counts of marked individuals using mark-recapture models. We review a third class of methods that do not directly sample the number of males and females, but instead estimate the sex ratio indirectly using relationships that emerge from demographic measures, such as survival, age structure, reproduction and assumed dynamics. We recommend that detection-based methods be used for estimating ASR in most situations, and point out that studies are needed that compare different ASR estimation methods and control for sex differences in dispersal.This article is part of the themed issue 'Adult sex ratios and reproductive decisions: a critical re-examination of sex differences in human and animal societies'.