Are extra-pair males different from cuckolded males? A case study and a meta-analytic examination.

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Abstract

Traditional models for female extra-pair matings assume that females benefit indirectly from extra-pair mating behaviour. Under these so-called adaptive models, extra-pair males are hypothesized to have more compatible genotypes, larger body size, exaggerated ornaments or to be older than cuckolded males. Alternatively, ('nonadaptive') models that consider female extra-pair matings to be a by-product posit that female extra-pair mating can be maintained even if there is no benefit to females. This could happen if, for example, males gained fitness benefits from extra-pair mating, while female and male extra-pair mating behaviours were genetically correlated. Extra-pair males are also expected to be older and larger if this improves their ability to convince or coerce females to mate. We investigated whether a female's extra-pair mates differed from her cuckolded mate in both genetic and phenotypic traits by analysing data from an insular house sparrow population. We found that extra-pair males were older than cuckolded males, consistent with both models. However, in contrast to the expectations from from adaptive models, extra-pair and cuckolded males were of similar genetic relatedness, and hence expected compatibility, with the female, and had comparable body size and secondary sexual traits. We also updated previous meta-analyses examining differences between extra-pair and cuckolded males. The meta-analytic results matched results from our house sparrow case study. Although we cannot completely exclude indirect benefits for females, nonadaptive models may better explain female extra-pair matings. These neglected alternative models deserve more research attention, and this should improve our understanding of the evolution of mating systems.

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Effect size, confidence interval and statistical significance: a practical guide for biologists.

Shinichi Nakagawa, Innes Cuthill (2007)

Null hypothesis significance testing (NHST) is the dominant statistical approach in biology, although it has many, frequently unappreciated, problems. Most importantly, NHST does not provide us with two crucial pieces of information: (1) the magnitude of an effect of interest, and (2) the precision of the estimate of the magnitude of that effect. All biologists should be ultimately interested in biological importance, which may be assessed using the magnitude of an effect, but not its statistical significance. Therefore, we advocate presentation of measures of the magnitude of effects (i.e. effect size statistics) and their confidence intervals (CIs) in all biological journals. Combined use of an effect size and its CIs enables one to assess the relationships within data more effectively than the use of p values, regardless of statistical significance. In addition, routine presentation of effect sizes will encourage researchers to view their results in the context of previous research and facilitate the incorporation of results into future meta-analysis, which has been increasingly used as the standard method of quantitative review in biology. In this article, we extensively discuss two dimensionless (and thus standardised) classes of effect size statistics: d statistics (standardised mean difference) and r statistics (correlation coefficient), because these can be calculated from almost all study designs and also because their calculations are essential for meta-analysis. However, our focus on these standardised effect size statistics does not mean unstandardised effect size statistics (e.g. mean difference and regression coefficient) are less important. We provide potential solutions for four main technical problems researchers may encounter when calculating effect size and CIs: (1) when covariates exist, (2) when bias in estimating effect size is possible, (3) when data have non-normal error structure and/or variances, and (4) when data are non-independent. Although interpretations of effect sizes are often difficult, we provide some pointers to help researchers. This paper serves both as a beginner's instruction manual and a stimulus for changing statistical practice for the better in the biological sciences.

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Statistical confidence for likelihood-based paternity inference in natural populations.

T. C. Marshall, J Slate, L. E. B. Kruuk … (1998)

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.