Conditional male dimorphism and alternative reproductive tactics in a Neotropical arachnid (Opiliones)

In arthropods, most cases of morphological dimorphism within males are the result of a conditional evolutionarily stable strategy (ESS) with status-dependent tactics. In conditionally male-dimorphic species, the status` distributions of male morphs often overlap, and the environmentally cued threshold model (ET) states that the degree of overlap depends on the genetic variation in the distribution of the switchpoints that determine which morph is expressed in each value of status. Here we describe male dimorphism and alternative mating behaviors in the harvestman Serracutisoma proximum. Majors express elongated second legs and use them in territorial fights; minors possess short second legs and do not fight, but rather sneak into majors` territories and copulate with egg-guarding females. The static allometry of second legs reveals that major phenotype expression depends on body size (status), and that the switchpoint underlying the dimorphism presents a large amount of genetic variation in the population, which probably results from weak selective pressure on this trait. With a mark-recapture study, we show that major phenotype expression does not result in survival costs, which is consistent with our hypothesis that there is weak selection on the switchpoint. Finally, we demonstrate that switchpoint is independent of status distribution. In conclusion, our data support the ET model prediction that the genetic correlation between status and switchpoint is low, allowing the status distribution to evolve or to fluctuate seasonally, without any effect on the position of the mean switchpoint.

Leverage analysis for linear mixed models

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.