Summary 1.Researchers frequently take repeated measurements of individuals in a sample with the goal of quantifying the proportion of the total variation that can be attributed to variation among individuals vs. variation among measurements within individuals. The proportion of the variation attributed to variation among individuals is known as repeatability and is most frequently estimated as the intraclass correlation coefficient (ICC). The goal of our study is to provide guidelines for determining the sample size (number of individuals and number of measurements per individual) required to accurately estimate the ICC. 2. We report a range of ICCs from the literature and estimate 95% confidence intervals for these estimates. We introduce a predictive equation derived by Bonett (2002), and we test the assumptions of this equation through simulation. Finally, we create an R statistical package for the planning of experiments and estimation of ICCs. 3. Repeatability estimates were reported in 1AE5% of the articles published in the journals surveyed. Repeatabilities tended to be highest when the ICC was used to estimate measurement error and lowest when it was used to estimate repeatability of behavioural and physiological traits. Few authors report confidence intervals, but our estimated 95% confidence intervals for published ICCs generally indicated a low level of precision associated with these estimates. This survey demonstrates the need for a protocol to estimate repeatability. 4. Analysis of the predictions from Bonett's equation over a range of sample sizes, expected repeatabilities and desired confidence interval widths yields both analytical and intuitive guidelines for designing experiments to estimate repeatability. However, we find a tendency for the confidence interval to be underestimated by the equation when ICCs are high and overestimated when ICCs and the number of measurements per individual are low. 5. The sample size to use when estimating repeatability is a question pitting investigator effort against expected precision of the estimate. We offer guidelines that apply over a wide variety of ecological and evolutionary studies estimating repeatability, measurement error or heritability. Additionally, we provide the R package, icc, to facilitate analyses and determine the most economic use of resources when planning experiments to estimate repeatability.

Summary1. The Non-Additive InVerses (nadiv) R software package contains functions to create and use non-additive genetic relationship matrices in the animal model of quantitative genetics. 2. This study discusses the concepts relevant to non-additive genetic effects and introduces the package. 3. nadiv includes functions to create the inverse of the dominance and epistatic relatedness matrices from a pedigree, which are required for estimating these genetic variances in an animal model. The study focuses on three widely used software programs in ecology and in evolutionary biology (ASReml, MCMCglmm and WOMBAT) and how nadiv can be used in conjunction with each. Simple tutorials are provided in the Supporting Information.

The rate of evolution of population mean fitness informs how selection acting in contemporary populations can counteract environmental change and genetic degradation (mutation, gene flow, drift, recombination). This rate influences population increases (e.g., range expansion), population stability (e.g., cryptic eco-evolutionary dynamics), and population recovery (i.e., evolutionary rescue). We review approaches for estimating such rates, especially in wild populations. We then review empirical estimates derived from two approaches: mutation accumulation (MA) and additive genetic variance in fitness (IAw). MA studies inform how selection counters genetic degradation arising from deleterious mutations, typically generating estimates of <1% per generation. IAw studies provide an integrated prediction of proportional change per generation, nearly always generating estimates of <20% and, more typically, <10%. Overall, considerable, but not unlimited, evolutionary potential exists in populations facing detrimental environmental or genetic change. However, further studies with diverse methods and species are required for more robust and general insights.

Extra-pair reproduction is widely hypothesized to allow females to avoid inbreeding with related socially paired males. Consequently, numerous field studies have tested the key predictions that extra-pair offspring are less inbred than females’ alternative within-pair offspring, and that the probability of extra-pair reproduction increases with a female's relatedness to her socially paired male. However, such studies rarely measure inbreeding or relatedness sufficiently precisely to detect subtle effects, or consider biases stemming from failure to observe inbred offspring that die during early development. Analyses of multigenerational song sparrow (Melospiza melodia) pedigree data showed that most females had opportunity to increase or decrease the coefficient of inbreeding of their offspring through extra-pair reproduction with neighboring males. In practice, observed extra-pair offspring had lower inbreeding coefficients than females’ within-pair offspring on average, while the probability of extra-pair reproduction increased substantially with the coefficient of kinship between a female and her socially paired male. However, simulations showed that such effects could simply reflect bias stemming from inbreeding depression in early offspring survival. The null hypothesis that extra-pair reproduction is random with respect to kinship therefore cannot be definitively rejected in song sparrows, and existing general evidence that females avoid inbreeding through extra-pair reproduction requires reevaluation given such biases.