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

In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.

Evolution and the Theory of Games

Rapid improvements in sequencing and array-based platforms are resulting in a flood of diverse genome-wide data, including data from exome and whole-genome sequencing, epigenetic surveys, expression profiling of coding and noncoding RNAs, single nucleotide polymorphism (SNP) and copy number profiling, and functional assays. Analysis of these large, diverse data sets holds the promise of a more comprehensive understanding of the genome and its relation to human disease. Experienced and knowledgeable human review is an essential component of this process, complementing computational approaches. This calls for efficient and intuitive visualization tools able to scale to very large data sets and to flexibly integrate multiple data types, including clinical data. However, the sheer volume and scope of data pose a significant challenge to the development of such tools.

Integrative Genomics Viewer

The arcsine square root transformation has long been standard procedure when analyzing proportional data in ecology, with applications in data sets containing binomial and non-binomial response variables. Here, we argue that the arcsine transform should not be used in either circumstance. For binomial data, logistic regression has greater interpretability and higher power than analyses of transformed data. However, it is important to check the data for additional unexplained variation, i.e., overdispersion, and to account for it via the inclusion of random effects in the model if found. For non-binomial data, the arcsine transform is undesirable on the grounds of interpretability, and because it can produce nonsensical predictions. The logit transformation is proposed as an alternative approach to address these issues. Examples are presented in both cases to illustrate these advantages, comparing various methods of analyzing proportions including untransformed, arcsine- and logit-transformed linear models and logistic regression (with or without random effects). Simulations demonstrate that logistic regression usually provides a gain in power over other methods.

/pdf/the-arcsine-is-asinine-the-analysis-of-proportions-in-ozlamgq3we.pdf

The arcsine is asinine: the analysis of proportions in ecology

The aim of this review is to consider the potential benefits that females may gain from mating more than once in a single reproductive cycle. The relationship between non-genetic and genetic benefits is briefly explored. We suggest that multiple mating for purely non-genetic benefits is unlikely as it invariably leads to the possibility of genetic benefits as well. We begin by briefly reviewing the main models for genetic benefits to mate choice, and the supporting evidence that choice can increase offspring performance and the sexual attractiveness of sons. We then explain how multiple mating can elevate offspring fitness by increasing the number of potential sires that compete, when this occurs in conjunction with mechanisms of paternity biasing that function in copula or post-copulation. We begin by identifying cases where females use pre-copulatory cues to identify mates prior to remating. In the simplest case, females remate because they identify a superior mate and 'trade up' genetically. The main evidence for this process comes from extra-pair copulation in birds. Second, we note other cases where pre-copulatory cues may be less reliable and females mate with several males to promote post-copulatory mechanisms that bias paternity. Although a distinction is drawn between sperm competition and cryptic female choice, we point out that the genetic benefits to polyandry in terms of producing more viable or sexually attractive offspring do not depend on the exact mechanism that leads to biased paternity. Post-copulatory mechanisms of paternity biasing may: (1) reduce genetic incompatibility between male and female genetic contributions to offspring; (2) increase offspring viability if there is a positive correlation between traits favoured post-copulation and those that improve performance under natural selection; (3) increase the ability of sons to gain paternity when they mate with polyandrous females. A third possibility is that genetic diversity among offspring is directly favoured. This can be due to bet-hedging (due to mate assessment errors or temporal fluctuations in the environment), beneficial interactions between less related siblings or the opportunity to preferentially fertilise eggs with sperm of a specific genotype drawn from a range of stored sperm depending on prevailing environmental conditions. We use case studies from the social insects to provide some concrete examples of the role of genetic diversity among progeny in elevating fitness. We conclude that post-copulatory mechanisms provide a more reliable way of selecting a genetically compatible mate than pre-copulatory mate choice. Some of the best evidence for cryptic female choice by sperm selection is due to selection of more compatible sperm. Two future areas of research seem likely to be profitable. First, more experimental evidence is needed demonstrating that multiple mating increases offspring fitness via genetic gains. Second, the role of multiple mating in promoting assortative fertilization and increasing reproductive isolation between populations may help us to understand sympatric speciation.

Why do females mate multiply? A review of the genetic benefits.

Preface and acknowledgements Part I. Sex Ratio Theory: 1. Models of sex ratio evolution Jon Seger and J. William Stubblefield 2. Optimal sex allocation: steps towards a mechanistic theory Ido R. Pen and Franz J. Weissing Part II. Statistical Analysis of Sex Ratio Data: 3. Statistical analysis of sex ratios: an introduction Kenneth Wilson and Ian C. W. Hardy 4. Analysis of sex ratios in social insects J. J. (Koos) Boomsma and Gosta Nachman 5. Analysis of sex ratio variances and consequences of sex allocation Sven Krackow, Evert Meelis and Ian C. W. Hardy 6. Comparative analysis of sex ratios Peter J. Mayhew and Ido R. Pen Part III. Genetics of Sex Ratio and Sex Determination: 7. Sex determining mechanisms in vertebrates Sarah B. M. Kraak and Ido R. Pen 8. Sex determination in invertebrates James M. Cook 9. Sex ratio distorters and their detection Richard Stouthamer, Gregory D. D. Hurst and J. A . J. (Hans) Breeuwer Part IV. Animal Sex Ratios Under Different Life-Histories: 10. Sex ratios of parasitic Hymenoptera with unusual life-histories Paul J. Ode and Martha S. Hunter 11. Sex ratio control in arrhenotkous and pseudo-arrhenotokous mites Maurice W. Sabelis, C. J. (Kees) Nagelkerke and J. A. J. (Hans) Breeuwer 12. Aphid sex ratios William A. Foster 13. Sex ratios in birds and mammals: can the hypotheses be disentangled Andrew Cockburn, Sarah Legge and Michael C. Double 14. Human sex ratios: adaptations and mechanisms, problems and prospects John Lazarus Part V. Sex ratios in other kingdoms: 15. Sex ratios of malaria parasites and related protozoa Andrew Read, Todd G. Smith , Sean Nee and Stuart A. West 16. Sex allocation in hermaphroditic plants Peter G. L. Klinkhamer and Tom J. de Jong 17. Sex ratios in dioecious plants Tom J. de Jong and Peter G. L. Klinkhamer Part VI. Applications of sex ratios: 18. Operational sex ratios and mating competition Charlotta Kvarnemo and Ingrid Ahnestjo 19. Using sex ratios: the past and the future Steven Hecht Orzack 20. Using sex ratios: why bother? Stuart A. West and Edward Allen Herre.

Sex ratios : concepts and research methods

Summary In this chapter we discuss how to make best use of sex ratio data. We identify three basic questions that such data can be used to answer: does the sex ratio differ from some theoretically expected mean value, does it differ from an expected distribution and is variation in sex ratio associated with some measured explanatory terms ? Our main focus is on the latter question. We discuss analytical methods in order of ‘sophistication’, starting with nonparametric methods (which make few assumptions about underlying statistical distributions), then classical parametric methods (which assume that data conform to a normal distribution of deviations from a statistical model) and finally generalized linear models ( GLMs ). GLMs are semi-parametric methods that encompass models assuming a normal distribution but may also assume other distributions. This is an important advantage as sex ratio data are best expressed as proportions (sex ratio = males/(males + females)) and deviations are expected to conform to a binomial distribution. GLMs assuming binomial distributions are often termed logistic regression models . Distributions may not conform to the normal or binomial assumptions of classical parametric analyses or logistic GLMs, and we discuss how these problems can be overcome. The statistical approaches we discuss are illustrated with worked examples and case histories from recent sex ratio literature. We also perform simulations to evaluate the relative performances of nonparametric, classical parametric and logistic GLM analyses: GLMs win.

Statistical analysis of sex ratios : an introduction.

Clutch size in a parasitoid wasp : a manipulation experiment

Assumptions about mating structure have been important in the development of sex ratio theory. Fisher's theory of frequency dependent selection for sex ratio equality, and Charnov's theory of sex allocation when host quality varies, assume panmixis, whereas Hamilton's theory of local mate competition assumes mating occurs only at the natal patch. An important group of organisms in stimulating the development of sex ratio theory, and in its empirical testing, have been the parasitoid Hymenoptera. These exhibit many life history variations and possess a mechanism by which females can adaptively control their progeny sex ratio. Although many parasitoid species may conform closely to both the assumptions and predictions of the above models, others do not

http://www.jstor.org/stable/pdfplus/3545278.pdf

Sex ratio and mating structure in the parasitoid Hymenoptera.

http://aerg.canberra.edu.au/library/sex_general/1997_Hardy_review_sex_allocation.pdf

Ian C.W. Hardy

Papers

Sex ratios : concepts and research methods

Statistical analysis of sex ratios : an introduction.

Clutch size in a parasitoid wasp : a manipulation experiment

Sex ratio and mating structure in the parasitoid Hymenoptera.

Possible factors influencing vertebrate sex ratios: an introductory overview