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Study species and calculation of lifetime fitness: Collared flycatchers were studied on the island of Gotland in the Swedish Baltic sea from 1980 and onwards. These birds breed in nest boxes that were supplied in ample numbers in a series of forest patches (plots). Individuals were ringed either as nestlings or when trapped at the nest as adults in order to allow lifelong individual identification and assessment of yearly reproductive success. Lifetime fitness was estimated as Lifetime Reproductive Success (LRS), the sum of all recruits (offspring that recruited back into the breeding population) of both sexes produced during an individual's lifetime. We here only used data on individuals that bred in the core patches of the study area which have been intensively monitored, and which started to breed in 1981–1999 in order to collect lifetime data on recruitment. Parts of the population have been involved in life-history experiments where a component of their reproductive output was manipulated. However, exclusion of such data necessarily leads to exclusion of the complete records of an individual, and could produce a bias in the animals used to estimate LRS versus the complete population, because such experiments are typically performed on ‘average’ individuals. Furthermore, we wanted to maximise the sample size and hence the power in our calculations of, especially, the genetic correlation in lifetime fitness across the sexes. We therefore considered the sum of all recruits that were raised in an individual's nest (independently of their origin) summed up for all individuals, irrespective of whether the individual was involved in an experiment at one point during its lifetime.
Estimating genetic (co)variances in Lifetime Reproductive Success: We partitioned the variance in LRS using a REML linear mixed model that incorporates pedigree-based estimated of genetic relatedness across all individuals (animal model, [17], [23]), which was implemented in AsReml (VSN International). We included as fixed effects the year an individual bred for the first time in order to correct for differences in LRS across ‘cohorts’ experiencing different environmental conditions during their lifetime, and the study plot in which the individual bred. As random effects, we estimated the additive genetic variances for males and females and the covariance between them. The estimation of the additive genetic (co)variances was based on pedigree information of 3,557 individuals that recruited back into the breeding population and for whom at least one parent was known. All other individuals were considered as base individuals. The animal model estimates the additive genetic covariance across sexes as a function of the covariance between opposite-sex relatives. Residual errors were set to be uncorrelated (i.e. zero) across sexes, because these cannot be estimated since sex-specific traits are not measured on the same individual. We tested for the significance of the additive genetic covariance by a Likelihood Ratio Test (LRT) based on −2×difference in log-likelihood between the unconstrained model specified above and a model with the intersexual genetic correlation set to zero, which has one degree of freedom. In addition, we specifically tested whether the confidence intervals around the genetic correlation differed from 1, by performing a LRT between the full model and a model where the genetic correlation was set at unity. The direction of the animal-model's genetic correlation was verified by calculating the resemblance of the LRS of male and female offspring to the LRS of their male and female parent. Prior to each analysis, LRS values were corrected for differences between cohort years and areas, and standardized to zero mean and unit standard deviation. Values of multiple same-sex offspring were averaged. Resemblance was calculated as the slope of a linear regression between sex-specific offspring and parent values.
Accounting for extra-pair paternities in the pedigree: There will be misassigned paternal links in the collared flycatcher pedigree, because about 15% of offspring are not sired by their social father, i.e. the male that provides care for them during the nestling phase [20]. Such errors have been shown to have relatively minor effect on the estimation of animal-model derived variances for morphological traits [21]. However, a systematic investigation of the consequences of pedigree errors for the accuracy of genetic correlations has not been made. Furthermore, in terms of LRS, extra-pair paternities will not only affect the pedigree links, but also the trait values for the males, since each cuckolded recruit will reduce the social male's LRS, but increase the extra-pair father's LRS. Hence, simulation results based on morphology cannot necessarily be applied to estimates of individual fitness such as LRS. We carried out two different simulations. In the first simulation, we assumed that for a randomly chosen 15% of recruits paternity was misassigned, and set their fathers as ‘unknown’. We then recalculated the LRS of all males based on this simulated pedigree. Some males' LRS was thus reduced. In this approach, 15% fewer recruits were assigned to a male parent, thereby reducing the amount of information in the pedigree and thus the power of the animal model in describing additive genetic (co)variances. Our second approach recognized that social males were cuckolded by males with a broader forehead patch [20]. Consequently, extra-pair paternities (EPP) will affect the estimated LRS of males non-randomly. For a randomly chosen 15% of recruits, paternity was assigned to a local male (i.e. a male breeding in the same year in the same study plot) with a broader forehead patch than the social male. We assigned paternity to a random local male in case such assignment was not possible, either because the social male's forehead patch was not measured or because the social male's forehead patch was the broadest forehead patch of all local males. Hence, in this simulation, some males' LRS was reduced whereas others' was increased, and in this simulation approach the same number of recruits were assigned to fathers as in the social pedigree thereby keeping the amount of information approximately equal. Again, the calculations for LRS were adjusted for the simulated pedigree. We simulated LRS data and pedigree 500 times, and calculated the additive genetic variances of males and females and the intersexual genetic correlation for each of the simulations. The additive genetic covariance matrix was left unconstrained, because constraining this matrix to be general positive led to failure of model convergence in some iteration (see results). Correlations could therefore exceed the range of −1 to 1. Conditional on our assumptions, these distributions will be informative of the robustness of our estimates based on the social pedigree with respect to extra-pair paternities, and we compared our observed values with the simulated values in order to assess the direction and possible bias of extra-pair paternities. The simulation of the pedigree and recalculation of LRS data was implemented with a purpose-specific programme coded in MATLAB (MathWorks), with animal model analyses implemented in AsReml (VSN International) as described above.
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