title: Detecting non-binomial sex allocation when developmental mortality operates.
abstract: Optimal sex allocation theory is one of the most intricately developed areas of evolutionary ecology. Under a range of conditions, particularly under population sub-division, selection favours sex being allocated to offspring non-randomly, generating non-binomial variances of offspring group sex ratios. Detecting non-binomial sex allocation is complicated by stochastic developmental mortality, as offspring sex can often only be identified on maturity with the sex of non-maturing offspring remaining unknown. We show that current approaches for detecting non-binomiality have limited ability to detect non-binomial sex allocation when developmental mortality has occurred. We present a new procedure using an explicit model of sex allocation and mortality and develop a Bayesian model selection approach (available as an R package). We use the double and multiplicative binomial distributions to model over- and under-dispersed sex allocation and show how to calculate Bayes factors for comparing these alternative models to the null hypothesis of binomial sex allocation. The ability to detect non-binomial sex allocation is greatly increased, particularly in cases where mortality is common. The use of Bayesian methods allows for the quantification of the evidence in favour of each hypothesis, and our modelling approach provides an improved descriptive capability over existing approaches. We use a simulation study to demonstrate substantial improvements in power for detecting non-binomial sex allocation in situations where current methods fail, and we illustrate the approach in real scenarios using empirically obtained datasets on the sexual composition of groups of gregarious parasitoid wasps.
authors.affiliation: School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK. Electronic address: r.d.wilkinson@sheffield.ac.uk.
authors.forename: Richard D
authors.initials: RD
authors.lastname: Wilkinson
authors.affiliation: School of Biosciences, University of Nottingham, Sutton Bonington Campus, Loughborough LE12 5RD, UK; Laboratory for Fundamental and Applied Research in Chemical Ecology, University of Neuchtel, Neuchtel 2000, Switzerland.
authors.forename: Apostolos
authors.initials: A
authors.lastname: Kapranas
authors.affiliation: School of Biosciences, University of Nottingham, Sutton Bonington Campus, Loughborough LE12 5RD, UK.
authors.forename: Ian C W
authors.initials: ICW
authors.lastname: Hardy
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D005075:Biological Evolution; D003198:Computer Simulation; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D009026:Mortality; D012744:Sex Ratio; D014863:Wasps / Q000502:physiology
keywords: Bayes factor; Markov chain Monte Carlo; Sex ratio; Under-dispersion