Paternity inference using highly polymorphic codominant markers is becoming common in the study of natural populations. However, multiple males are often found to be genetically compatible with each offspring tested, even when the probability of excluding an unrelated male is high. While various methods exist for evaluating the likelihood of paternity of each nonexcluded male, interpreting these likelihoods has hitherto been difficult, and no method takes account of the incomplete sampling and error-prone genetic data typical of large-scale studies of natural systems. We derive likelihood ratios for paternity inference with codominant markers taking account of typing error, and define a statistic delta for resolving paternity. Using allele frequencies from the study population in question, a simulation program generates criteria for delta that permit assignment of paternity to the most likely male with a known level of statistical confidence. The simulation takes account of the number of candidate males, the proportion of males that are sampled and gaps and errors in genetic data. We explore the potentially confounding effect of relatives and show that the method is robust to their presence under commonly encountered conditions. The method is demonstrated using genetic data from the intensively studied red deer (Cervus elaphus) population on the island of Rum, Scotland. The Windows-based computer program, CERVUS, described in this study is available from the authors. CERVUS can be used to calculate allele frequencies, run simulations and perform parentage analysis using data from all types of codominant markers.

Genotypes are frequently used to identify parentage. Such analysis is notoriously vulnerable to genotyping error, and there is ongoing debate regarding how to solve this problem. Many scientists have used the computer program CERVUS to estimate parentage, and have taken advantage of its option to allow for genotyping error. In this study, we show that the likelihood equations used by versions 1.0 and 2.0 of CERVUS to accommodate genotyping error miscalculate the probability of observing an erroneous genotype. Computer simulation and reanalysis of paternity in Rum red deer show that correcting this error increases success in paternity assignment, and that there is a clear benefit to accommodating genotyping errors when errors are present. A new version of CERVUS (3.0) implementing the corrected likelihood equations is available at http://www.fieldgenetics.com.

The ¢tness consequences of inbreeding and outbreeding are poorly understood in natural populations. We explore two microsatellite-based variables, individual heterozygosity (likely to correlate with recent inbreeding) and a new individual-speci¢c internal distance measure, mean d 2 (focusing on events deeper in the pedigree), in relation to two measures of ¢tness expressed early in life, birth weight and neonatal survival, in 670 red deer calves (Cervus elaphus) born on the Isle of Rum between 1982 and 1996. For comparison, we also analyse inbreeding coe¤cients derived from pedigrees in which paternity was inferred by molecular methods.Only 14 out of 231 calves (6.1%) had non-zero inbreeding coe¤cients, and neither inbreeding coe¤cient nor individual heterozygosity was consistently related to birth weight or neonatal survival. However, mean d 2 was consistently related to both ¢tness measures. Low mean d 2 was associated with low birth weight, especially following cold Aprils, in which foetal growth is reduced. Low mean d 2 was also associated with low neonatal survival, but this e¡ect was probably mediated by birth weight because ¢tting birth weight to the neonatal survival model displaced mean d 2 as an explanatory variable. We conclude that in the deer population ¢tness measures expressed early in life do not show evidence of inbreeding depression, but they do show evidence of heterosis, possibly as a result of population mixing. We also demonstrate the practical problems of estimating inbreeding via pedigrees compared with a direct marker-based estimate of individual heterozygosity. We suggest that, together, individual heterozygosity and mean d 2 , estimated using microsatellites, are useful tools for exploring inbreeding and outbreeding in natural populations.

Evolutionary and conservation biologists have a long-standing interest in the consequences of inbreeding. It is generally recognized that inbred individuals may experience reduced fitness or inbreeding depression. By the same token, relatively outbred individuals can have greater than average fitness, i.e. heterosis. However, nearly all of the empirical evidence for inbreeding depression comes from laboratory or domestic species. Inbreeding depression and heterosis are difficult to detect in natural populations due to the difficulties in establishing pedigrees. An alternative method is to correlate heterozygosity, which is measured using genetic markers, with a trait related to fitness. The typically studied traits, such as juvenile survival and growth rates, either cover only early life or are weakly correlated with lifetime breeding success (LBS). In this paper we show that heterozygosity is positively associated with male and female adult LBS in a wild population of red deer (Cervus elaphus) on the Isle of Rum, Scotland. To the authors' knowledge, this is the first time that inbreeding depression and/or heterosis have been detected for a trait highly correlated with overall fitness in both sexes in a wild population.

CERVUS is a Windows-based software package written to infer paternity in natural populations. It offers advantages over exclusionary-based methods of paternity inference in that multiple nonexcluded males can be statistically distinguished, laboratory typing error is considered and statistical confidence is determined for assigned paternities through simulation. In this study we use a panel of 84 microsatellite markers to retrospectively determine the accuracy of statistical confidence when CERVUS was used to infer paternity in a population of red deer (Cervus elaphus). The actual confidence of CERVUS-assigned paternities was not significantly different from that predicted by simulation.