Wolfgang Forstmeier

Conclusions beyond support: overconfident estimates in mixed models

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.

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 winners 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.

A novel song parameter correlates with extra-pair paternity and reflects male longevity

Although elaborate bird song provides one of the prime examples of a trait that evolved under sexual selection, it is still unclear whether females judge the quality of males by attributes of their song and whether these song features honestly signal a mals genetic quality. We measured the ability of male dusky warblers Phylloscopus fuscatus to maintain a high sound amplitude during singing, which probably reflects an individuas physiological limitations. This new measure of singing performance was correlated with male longevity and with extra–pair paternity, indicating that females who copulated with better singers obtained ‘good gene’ for their offspring. Our findings are consistent with the idea that females assess male quality by subtle differences in their performance during the production of notes, rather than by the quantity or versatility of song. In addition, observations on territorial conflicts indicate that attractive males invest less in competition over territories because they can reproduce via extra–pair paternity.

The recombination landscape of the zebra finch Taeniopygia guttata genome

Understanding the causes and consequences of variation in the rate of recombination is essential since this parameter is considered to affect levels of genetic variability, the efficacy of selection, and the design of association and linkage mapping studies. However, there is limited knowledge about the factors governing recombination rate variation. We genotyped 1920 single nucleotide polymorphisms in a multigeneration pedigree of more than 1000 zebra finches (Taeniopygia guttata) to develop a genetic linkage map, and then we used these map data together with the recently available draft genome sequence of the zebra finch to estimate recombination rates in 1 Mb intervals across the genome. The average zebra finch recombination rate (1.5 cM/Mb) is higher than in humans, but significantly lower than in chicken. The local rates of recombination in chicken and zebra finch were only weakly correlated, demonstrating evolutionary turnover of the recombination landscape in birds. The distribution of recombination events was heavily biased toward ends of chromosomes, with a stronger telomere effect than so far seen in any organism. In fact, the recombination rate was as low as 0.1 cM/Mb in intervals up to 100 Mb long in the middle of the larger chromosomes. We found a positive correlation between recombination rate and GC content, as well as GC-rich sequence motifs. Levels of linkage disequilibrium (LD) were significantly higher in regions of low recombination, showing that heterogeneity in recombination rates have left a footprint on the genomic landscape of LD in zebra finch populations.

Heterozygosity-fitness correlations in zebra finches: microsatellite markers can be better than their reputation

Numerous studies have reported associations between heterozygosity in microsatellite markers and fitness‐related traits (heterozygosity–fitness correlations, HFCs). However, it has often been questioned whether HFCs reflect general inbreeding depression, because a small panel of microsatellite markers does not reflect very well an individual’s inbreeding coefficient (F) as calculated from a pedigree. Here, we challenge this prevailing view. Because of chance events during Mendelian segregation, an individual’s realized proportion of the genome that is identical by descent (IBD) may substantially deviate from the pedigree‐based expectation (i.e. F). This Mendelian noise may result in a weak correlation between F and multi‐locus heterozygosity, but this does not imply that multi‐locus heterozygosity is a bad estimator of realized IBD. We examined correlations between 11 fitness‐related traits measured in up to 1192 captive zebra finches and three measures of inbreeding: (i) heterozygosity across 11 microsatellite markers, (ii) heterozygosity across 1359 single‐nucleotide polymorphism (SNP) markers and (iii) F, based on a 5th‐generation pedigree. All 11 phenotypic traits showed positive relationships with measures of heterozygosity, especially traits that are most closely related to fitness. Remarkably, the small panel of microsatellite markers produced equally strong HFCs as the large panel of SNP markers. Both marker‐based approaches produced stronger correlations with phenotypes than the pedigree‐based F, and this did not seem to result from the shortness of our pedigree. We argue that a small panel of microsatellites with high allelic richness may better reflect an individual’s realized IBD than previously appreciated, especially in species like the zebra finch, where much of the genome is inherited in large blocks that rarely experience cross‐over during meiosis.

Genetic variation and differentiation in captive and wild zebra finches (Taeniopygia guttata).

The zebra finch (Taeniopygia guttata) is a small Australian grassland songbird that has been domesticated over the past two centuries. Because it is easy to breed in captivity, it has become a widely used study organism, especially in behavioural research. Most work has been conducted on domesticated populations maintained at numerous laboratories in Europe and North America. However, little is known about the extent to which, during the process of domestication, captive populations have gone through bottlenecks in population size, leading to inbred and potentially genetically differentiated study populations. This is an important issue, because (i) behavioural studies on captive populations might suffer from artefacts arising from high levels of inbreeding or lack of genetic variation in such populations, and (ii) it may hamper the comparability of research findings. To address this issue, we genotyped 1000 zebra finches from 18 captive and two wild populations at 10 highly variable microsatellite loci. We found that all captive populations have lost some of the genetic variability present in the wild, but there is no evidence that they have gone through a severe bottleneck, as the average captive population still showed a mean of 11.7 alleles per locus, compared to a mean of 19.3 alleles/locus for wild zebra finches. We found significant differentiation between the captive populations (FST = 0.062). Patterns of genetic similarity closely match geographical relationships, so the most pronounced differences occur between the three continents: Australia, North America, and Europe. By providing a tree of the genetic similarity of the different captive populations, we hope to contribute to a better understanding of variation in research findings obtained by different laboratories.

Female extrapair mating behavior can evolve via indirect selection on males

In many species that form socially monogamous pair bonds, a considerable proportion of the offspring is sired by extrapair males. This observation has remained a puzzle for evolutionary biologists: although mating outside the pair bond can obviously increase the offspring production of males, the benefits of such behavior to females are less clear, yet females are known to actively solicit extrapair copulations. For more than two decades adaptionist explanations have dominated the discussions, yet remain controversial, and genetic constraint arguments have been dismissed without much consideration. An intriguing but still untested hypothesis states that extrapair mating behavior by females may be affected by the same genetic variants (alleles) as extrapair mating behavior by males, such that the female behavior could evolve through indirect selection on the male behavior. Here we show that in the socially monogamous zebra finch, individual differences in extrapair mating behavior have a hereditary component. Intriguingly, this genetic basis is shared between the sexes, as shown by a strong genetic correlation between male and female measurements of extrapair mating behavior. Hence, positive selection on males to sire extrapair young will lead to increased extrapair mating by females as a correlated evolutionary response. This behavior leads to a fundamentally different view of female extrapair mating: it may exist even if females obtain no net benefit from it, simply because the corresponding alleles were positively selected in the male ancestors.

Female extra-pair mating: adaptation or genetic constraint?

Why do females of so many socially monogamous species regularly engage in matings outside the pair bond? This question has puzzled behavioural ecologists for more than two decades. Until recently, an adaptionists point of view prevailed: if females actively seek extra-pair copulations, as has been observed in several species, they must somehow benefit from this behaviour. However, do they? In this review, we argue that adaptive scenarios have received disproportionate research attention, whereas nonadaptive phenomena, such as pathological polyspermy, de novo mutations, and genetic constraints, have been neglected by empiricists and theoreticians alike. We suggest that these topics deserve to be taken seriously and that future work would benefit from combining classical behavioural ecology with reproductive physiology and evolutionary genetics.

Quantitative genetics and behavioural correlates of digit ratio in the zebra finch

A recent study on a captive zebra finch population suggested that variation in digit ratio (i.e. the relative length of the second to the fourth toe) might be an indicator of the action of sex steroids during embryo development, as is widely assumed for human digits. Zebra finch digit ratio was found to vary with offspring sex, laying order of eggs within a clutch, and to predict aspects of female mating behaviour. Hence, it was proposed that the measurement of digit ratio would give insights into how an individuals behaviour is shaped by its maternal environment. Studying 500 individuals of a different zebra finch population I set out to: (1) determine the proximate causes of variation in digit ratio by means of quantitative genetics and (2) to search for phenotypic and genetic correlations between digit ratio, sexual behaviour and aspects of fitness. In contrast to the earlier study, I found no sexual dimorphism in digit ratio and no effect of either laying order or experimentally altered hatching order on digit ratio. Instead, I found that variation in digit ratio was almost entirely additive genetic, with heritability estimates ranging from 71 to 84%. The rearing environment (from egg deposition to independence) explained an additional 5–6% of the variation in digit ratio, but there was no indication of any maternal effects transmitted through the egg. I found highly significant phenotypic correlations (and genetic correlations of similar size) between digit ratio and male song rate (positive correlation) as well as between digit ratio and female hopping activity in a choice chamber (negative correlation). Rather surprisingly, the strength of these correlations differed significantly between subsequent generations of the same population, illustrating how quickly such correlations can appear and disappear probably due to genotype–environment interactions.

Inbreeding depression of sexually selected traits and attractiveness in the zebra finch

An underexploited approach to study condition dependence of sexually selected ornaments is to use inbreeding to manipulate individual genetic quality. Because of differences in genetic architecture, sexually selected traits are expected to suffer stronger inbreeding depression than morphological traits. We used full-sib mating to investigate the effects of inbreeding on viability, attractiveness, morphology and potentially secondary sexual traits in male and female zebra finches, Taeniopygia guttata. Unexpectedly, the genetic load from lethal alleles (leading to early mortality) was low. In males, we found strong negative effects of inbreeding on song rate, beak colour, body size and choice chamber attractiveness, whereas body condition, fat deposition, song structure and plumage ornaments were unaffected. In females, beak colour, body size, fat deposition and choice chamber behaviour showed significant inbreeding depression. These results indicate that some but not all adult phenotypes are affected by inbreeding, most probably because of the homozygous expression of slightly deleterious mutations. Our findings complement alternative approaches to study the condition dependence of traits that may be relevant in mate choice or competition.