Estimating Repeatability of Egg Size

—Measures of repeatability have long been used to assess patterns of variation in egg size within and among females. We compared different analytical approaches for estimating repeatability of egg size of Black Brant. Separate estimates of repeatability for eggs of each clutch size and laying sequence number varied from 0.49 to 0.64. We suggest that using the averaging egg size within clutches results in underestimation of variation within females and thereby overestimates repeatability. We recommend a nested design that partitions egg-size variation within clutches, among clutches within females, and among females. We demonstrate little variation in estimates of repeatability resulting from a nested model controlling for egg laying sequence and a nested model in which we assumed laying sequence was unknown. Egg size represents the unit of investment in a reproductive attempt for birds. Accordingly, researchers have long been interested in variation in egg size and its adaptive significance. Repeatability is a measure of the proportion of variation in a trait that is due to differences among individuals. Therefore, estimates of repeatability of egg size split the total phenotypic variation in egg size into within-individual and among-individual components. Falconer (1989) describes that partitioning of the phenotypic variance in terms of the origin of the different variance components. Variation in egg size among individuals is caused by a combination of genetic and environmental differences. Variation in egg size within an individual among years is caused by temporary environmental differences between reproductive attempts. Falconer (1989) goes on to demonstrate that estimates of repeatability are useful in the context of quantitative genetics because they set upper limits to levels of heritable variation. Falconer (1989) states that estimates of repeatability can be based on measures of a characteristic that are 4 E-mail: [email protected] repeated in either time or space. Following Falconer’s (1989) descriptions, egg size is repeated in both time and space—where time refers to different nesting attempts and space refers to eggs within a specific nesting attempt (i.e. clutch). In many cases researchers estimating repeatability of egg size use the average egg size within clutches (e.g. Lessells et al. 1989, Flint and Sedinger 1992, Flint and Grand 1996). However, that approach ignores some of the phenotypic variation in egg size within individuals (e.g. within clutches) and may have been used because researchers were uncertain how to deal with multiple measurements within clutches statistically. Other researchers have used a nested design to partition variance among females, within females among years, and within females within years (i.e. clutches) (LeBlanc 1987, Erikstad et al. 1998, Flint and Grand 1999). In this paper, we compare those two approaches in terms of estimates of repeatability. We decompose each estimate into its variance components and discuss each estimate in the context of quantitative genetics. We also discuss those estimates relative to the assumptions of repeatability analyses. Finally, we recommend approaches for estimating repeatability of egg size given specific data sets. Methods. This study was conducted at the Tutakoke River Black Brant (Branta bernicla nigricans) colony along the outer coastal fringe of the Yukon-Kuskokwim Delta from 1987–1997. Breeding Black Brant have been banded at that site since 1986, providing a large sample of identifiable females on which to measure repeatability. Methods of nest searching, measuring of eggs, and estimation of egg volume have been described by Flint and Sedinger (1992). Estimation of repeatability requires multiple measurements of individuals among years, and that large data set allowed partitioning to many different levels (i.e. specific clutch size and egg sequence numbers). In each analyses, we deleted individuals for which we did not have multiple measurements; therefore, sample sizes vary for each analyses. Further, we restricted our analyses to clutches of 3, 4, April 2001] 501 Short Communications TABLE 1. Estimated repeatability of egg size by clutch size and egg sequence number for Black Brant nesting on the Yukon-Kuskokwim Delta, Alaska. Clutch size Egg-sequence number