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1.  Correlates of male fitness in captive zebra finches - a comparison of methods to disentangle genetic and environmental effects 
It is a common observation in evolutionary studies that larger, more ornamented or earlier breeding individuals have higher fitness, but that body size, ornamentation or breeding time does not change despite of sometimes substantial heritability for these traits. A possible explanation for this is that these traits do not causally affect fitness, but rather happen to be indirectly correlated with fitness via unmeasured non-heritable aspects of condition (e.g. undernourished offspring grow small and have low fitness as adults due to poor health). Whether this explanation applies to a specific case can be examined by decomposing the covariance between trait and fitness into its genetic and environmental components using pedigree-based animal models. We here examine different methods of doing this for a captive zebra finch population where male fitness was measured in communal aviaries in relation to three phenotypic traits (tarsus length, beak colour and song rate).
Our case study illustrates how methods that regress fitness over breeding values for phenotypic traits yield biased estimates as well as anti-conservative standard errors. Hence, it is necessary to estimate the genetic and environmental covariances between trait and fitness directly from a bivariate model. This method, however, is very demanding in terms of sample sizes. In our study parameter estimates of selection gradients for tarsus were consistent with the hypothesis of environmentally induced bias (βA = 0.035 ± 0.25 (SE), βE = 0.57 ± 0.28 (SE)), yet this differences between genetic and environmental selection gradients falls short of statistical significance.
To examine the generality of the idea that phenotypic selection gradients for certain traits (like size) are consistently upwardly biased by environmental covariance a meta-analysis across study systems will be needed.
PMCID: PMC3229482  PMID: 22067225
2.  Cryptic multiple hypotheses testing in linear models: overestimated effect sizes and the winner's curse 
Fitting generalised linear models (GLMs) with more than one predictor has become the standard method of analysis in evolutionary and behavioural research. Often, GLMs are used for exploratory data analysis, where one starts with a complex full model including interaction terms and then simplifies by removing non-significant terms. While this approach can be useful, it is problematic if significant effects are interpreted as if they arose from a single a priori hypothesis test. This is because model selection involves cryptic multiple hypothesis testing, a fact that has only rarely been acknowledged or quantified. We show that the probability of finding at least one ‘significant’ effect is high, even if all null hypotheses are true (e.g. 40% when starting with four predictors and their two-way interactions). This probability is close to theoretical expectations when the sample size (N) is large relative to the number of predictors including interactions (k). In contrast, type I error rates strongly exceed even those expectations when model simplification is applied to models that are over-fitted before simplification (low N/k ratio). The increase in false-positive results arises primarily from an overestimation of effect sizes among significant predictors, leading to upward-biased effect sizes that often cannot be reproduced in follow-up studies (‘the winner's curse’). Despite having their own problems, full model tests and P value adjustments can be used as a guide to how frequently type I errors arise by sampling variation alone. We favour the presentation of full models, since they best reflect the range of predictors investigated and ensure a balanced representation also of non-significant results.
PMCID: PMC3015194  PMID: 21297852
Bonferroni correction; Effect size estimation; Generalised linear models; Model selection; Multiple regression; Multiple testing; Parameter estimation; Publication bias
3.  Molecular evolution of genes in avian genomes 
Genome Biology  2010;11(6):R68.
Obtaining a draft genome sequence of the zebra finch (Taeniopygia guttata), the second bird genome to be sequenced, provides the necessary resource for whole-genome comparative analysis of gene sequence evolution in a non-mammalian vertebrate lineage. To analyze basic molecular evolutionary processes during avian evolution, and to contrast these with the situation in mammals, we aligned the protein-coding sequences of 8,384 1:1 orthologs of chicken, zebra finch, a lizard and three mammalian species.
We found clear differences in the substitution rate at fourfold degenerate sites, being lowest in the ancestral bird lineage, intermediate in the chicken lineage and highest in the zebra finch lineage, possibly reflecting differences in generation time. We identified positively selected and/or rapidly evolving genes in avian lineages and found an over-representation of several functional classes, including anion transporter activity, calcium ion binding, cell adhesion and microtubule cytoskeleton.
Focusing specifically on genes of neurological interest and genes differentially expressed in the unique vocal control nuclei of the songbird brain, we find a number of positively selected genes, including synaptic receptors. We found no evidence that selection for beneficial alleles is more efficient in regions of high recombination; in fact, there was a weak yet significant negative correlation between ω and recombination rate, which is in the direction predicted by the Hill-Robertson effect if slightly deleterious mutations contribute to protein evolution. These findings set the stage for studies of functional genetics of avian genes.
PMCID: PMC2911116  PMID: 20573239
4.  Compensatory investment in zebra finches: females lay larger eggs when paired to sexually unattractive males 
The classical version of the differential allocation hypothesis states that, when females reproduce over their lifetime with partners that differ in their genetic quality, they should invest more in reproduction with high-quality males. However, in species with lifetime monogamy, such as the zebra finch, partner quality will typically remain the same. In this case, the compensatory investment (CI) hypothesis predicts higher investment for low-quality males, because low genetic quality offspring are more dependent on maternal resources. Here, we show that female zebra finches invested more resources, both in terms of egg volume and yolk carotenoid content, when paired to a low genetic quality male, as judged from his previous ability to obtain extra-pair paternity in aviary colonies. We also found that females deposited slightly larger amounts of testosterone into eggs when paired to a low parental quality male, as judging from his previous success in rearing offspring. This is, to our knowledge, the first experimental support for the CI hypothesis in a species with lifetime monogamy. We stress that in more promiscuous species, the benefits of classical differential allocation may partly be neutralized by the supposed benefits of CI.
PMCID: PMC2660937  PMID: 18986974
carotenoids; differential allocation hypothesis; egg resources; mate attractiveness; maternal effects; reproductive investment
5.  Conclusions beyond support: overconfident estimates in mixed models 
Behavioral Ecology  2008;20(2):416-420.
Mixed-effect models are frequently used to control for the nonindependence of data points, for example, when repeated measures from the same individuals are available. The aim of these models is often to estimate fixed effects and to test their significance. This is usually done by including random intercepts, that is, intercepts that are allowed to vary between individuals. The widespread belief is that this controls for all types of pseudoreplication within individuals. Here we show that this is not the case, if the aim is to estimate effects that vary within individuals and individuals differ in their response to these effects. In these cases, random intercept models give overconfident estimates leading to conclusions that are not supported by the data. By allowing individuals to differ in the slopes of their responses, it is possible to account for the nonindependence of data points that pseudoreplicate slope information. Such random slope models give appropriate standard errors and are easily implemented in standard statistical software. Because random slope models are not always used where they are essential, we suspect that many published findings have too narrow confidence intervals and a substantially inflated type I error rate. Besides reducing type I errors, random slope models have the potential to reduce residual variance by accounting for between-individual variation in slopes, which makes it easier to detect treatment effects that are applied between individuals, hence reducing type II errors as well.
PMCID: PMC2657178  PMID: 19461866
experimental design; maternal effects; mixed-effect models; random regression; repeated measures; type I error
Many species show substantial between-individual variation in mating preferences, but studying the causes of such variation remains a challenge. For example, the relative importance of heritable variation versus shared early environment effects (like sexual imprinting) on mating preferences has never been quantified in a population of animals. Here, we estimate the heritability of and early rearing effects on mate choice decisions in zebra finches based on the similarity of choices between pairs of genetic sisters raised apart and pairs of unrelated foster sisters. We found a low and nonsignificant heritability of preferences and no significant shared early rearing effects. A literature review shows that a low heritability of preferences is rather typical, whereas empirical tests for the relevance of sexual imprinting within populations are currently limited to very few studies. Although effects on preference functions (i.e., which male to prefer) were weak, we found strong individual consistency in choice behavior and part of this variation was heritable. It seems likely that variation in choice behavior (choosiness, responsiveness, sampling behavior) would produce patterns of nonrandom mating and this might be the more important source of between-individual differences in mating patterns.
PMCID: PMC2871178  PMID: 19895552
Heritability; mate choice; preference functions; quantitative genetics; sexual imprinting; zebra finch

Results 1-6 (6)