Linear mixed‐effects models are powerful tools for analysing complex datasets with repeated or clustered observations, a common data structure in ecology and evolution. Mixed‐effects models involve complex fitting procedures and make several assumptions, in particular about the distribution of residual and random effects. Violations of these assumptions are common in real datasets, yet it is not always clear how much these violations matter to accurate and unbiased estimation. Here we address the consequences of violations in distributional assumptions and the impact of missing random effect components on model estimates. In particular, we evaluate the effects of skewed, bimodal and heteroscedastic random effect and residual variances, of missing random effect terms and of correlated fixed effect predictors. We focus on bias and prediction error on estimates of fixed and random effects. Model estimates were usually robust to violations of assumptions, with the exception of slight upward biases in estimates of random effect variance if the generating distribution was bimodal but was modelled by Gaussian error distributions. Further, estimates for (random effect) components that violated distributional assumptions became less precise but remained unbiased. However, this particular problem did not affect other parameters of the model. The same pattern was found for strongly correlated fixed effects, which led to imprecise, but unbiased estimates, with uncertainty estimates reflecting imprecision. Unmodelled sources of random effect variance had predictable effects on variance component estimates. The pattern is best viewed as a cascade of hierarchical grouping factors. Variances trickle down the hierarchy such that missing higher‐level random effect variances pool at lower levels and missing lower‐level and crossed random effect variances manifest as residual variance. Overall, our results show remarkable robustness of mixed‐effects models that should allow researchers to use mixed‐effects models even if the distributional assumptions are objectively violated. However, this does not free researchers from careful evaluation of the model. Estimates that are based on data that show clear violations of key assumptions should be treated with caution because individual datasets might give highly imprecise estimates, even if they will be unbiased on average across datasets.

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Phenotypes vary hierarchically among taxa and populations, among genotypes within 2 populations, among individuals within genotypes, and also within individuals for repeatedly 3 expressed labile phenotypic traits. This hierarchy produces some fundamental challenges to 4 clearly defining biological phenomena and constructing a consistent explanatory framework. We

Parentage of nestlings in a North Carolina population of indigo buntings (Passerina cyanea) was analyzed using DNA fingerprinting. Three minisatellite DNA probes (wild type M13, Jeffreys' 33.15 and 33.6) were used to analyze nuclear DNA isolated from muscle biopsies of 63 nestlings, their parents, and other local adults. Each probe detected approximately 15 scorable fragments per individual, with 18%-39% overlap between probes. The proportion of bands shared (using all fragments over all three probes) between presumably unrelated adults averaged 0.23. Of the 63 offspring analyzed, 35 had at least one fragment not present in either putative parent. The distribution of offspring with novel fragments was distinctly bimodal. The lower mode (offspring with 0, 1, or 2 novel fragments, N=41) fit a Poisson distribution, a pattern expected if mutation (estimated rate per fragment = 0.01) were the source of the novel fragments. The remaining 22 offspring had more novel fragments than could be explained by mutation alone (minimum of four independent fragments across all three probes, J?=8.2). A low band-sharing proportion with the resident male (X'= 0.24) and high band-sharing with the resident female (37= 0.60) implicated extra-pair fertilizations as the source of all 22. Thus in this sample, 35% of all nestlings came from extra-pair fertilizations and none from intra-specific brood parasitism. Of 25 broods sampled, 12 (48%) had at least one excluded offspring. In 3 broods all of the offspring excluded the resident male. Band-sharing proportions between excluded nestlings within a brood could not distinguish between single and multiple extra-pair paternity. Although young males tended to be excluded less often than older males, wing length and weight were not associated with the frequency of exclusion. Weight and wing length of females also were not associated with involvement in EPCs. Six of the 22 excluded offspring (in 3 broods) shared a large proportion of bands and had fewer than four novel fragments when compared to the fingerprints of a neighboring territorial male, implicating those males as actual fathers. The parentage of the remaining 16 offspring (in 9 broods) could not be clearly assigned because (1) one or more neighbors were not sampled or (2) difficulties in scoring across gels prevented confident alignment of fingerprint bands, and insufficient DNA was obtained from muscle samples to allow reanalysis of potential actual fathers on the same gel as excluded nestlings.