On Indifference Zone Selection with a Preference Threshold

This paper discusses a selection criterion that generalizes the well-known concept of indifference zone selection through a preference threshold. A population is preferred to another population if the difference in the sums of observed values exceeds a given nonnegative threshold value. We present an argument for this selection rule by modelling preference by imprecise previsions. We aim at guidelines to design a selection experiment, which is characterized by two numbers: the number of necessary observations per population, and the preference threshold. Next to the probability of correct selection we also need a second specification. In this paper we consider a probability of false selection that is strongly related to the minimum probability of correct selection. Based on this model the outcome of an experiment may be ‘no selection’, at least not based on strong preference of a single population. The ideas are presented through a simple selection problem for normal populations with common known variance. Although the theory has a frequentist nature, the derivation and justification of the selection rule through imprecise previsions relies on Bayesian foundations, and via this route we gain more insight into the selection criterion.     

Variable selection for logistic regression using a prediction-focused information criterion

In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the focused information criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the mean squared error of the estimator of the quantity of interest in the selected model. In this article, we propose more general versions of the FIC, allowing other risk measures such as the one based on L(p) error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy.     

Bayesian Model Selection for Incomplete Data Using the Posterior Predictive Distribution

Summary We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998, Biometrika, 85 , 1–11) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.     

Cuckoos, cowbirds and hosts: adaptations, trade-offs and constraints

The interactions between brood parasitic birds and their host species provide one of the best model systems for coevolution. Despite being intensively studied, the parasite-host system provides ample opportunities to test new predictions from both coevolutionary theory as well as life-history theory in general. I identify four main areas that might be especially fruitful: cuckoo female gentes as alternative reproductive strategies, non-random and nonlinear risks of brood parasitism for host individuals, host parental quality and targeted brood parasitism, and differences and similarities between predation risk and parasitism risk. Rather than being a rare and intriguing system to study coevolutionary processes, I believe that avian brood parasites and their hosts are much more important as extreme cases in the evolution of life-history strategies. They provide unique examples of trade-offs and situations where constraints are either completely removed or particularly severe.     

PROMISCUITY,SEXUAL SELECTION,AND GENETIC DIVERSITY: A REPLY TO SPURGIN

We recently reported a positive association between female promiscuity and genetic diversity across passerine birds, and launched the hypothesis that female promiscuity acts as a balancing selection, pressure maintaining genetic diversity in populations (Gohli et al. 2013 ). Spurgin ( 2013 ) questions both our analyses and interpretations. While we agree that the hypothesis needs more comprehensive empirical testing, we find his specific points of criticism unjustified. In a more general perspective, we call for a more explicit recognition of female mating preferences as mechanisms of selection in population genetics theory.     

A new criterion for confounder selection

Summary We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, “Is the covariate a cause of the treatment?” and “Is the covariate a cause of the outcome?” If the answer to either question is “yes” then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion.     

Joint model selection of marginal mean regression and correlation structure for longitudinal data with missing outcome and covariates

This work develops a joint model selection criterion for simultaneously selecting the marginal mean regression and the correlation/covariance structure in longitudinal data analysis where both the outcome and the covariate variables may be subject to general intermittent patterns of missingness under the missing at random mechanism. The new proposal, termed “joint longitudinal information criterion” (JLIC), is based on the expected quadratic error for assessing model adequacy, and the second‐order weighted generalized estimating equation (WGEE) estimation for mean and covariance models. Simulation results reveal that JLIC outperforms existing methods performing model selection for the mean regression and the correlation structure in a two stage and hence separate manner. We apply the proposal to a longitudinal study to identify factors associated with life satisfaction in the elderly of Taiwan.     

Group selection, kin selection, altruism and cooperation: When inclusive fitness is right and when it can be wrong

Group selection theory has a history of controversy. After a period of being in disrepute, models of group selection have regained some ground, but not without a renewed debate over their importance as a theoretical tool. In this paper I offer a simple framework for models of the evolution of altruism and cooperation that allows us to see how and to what extent both a classification with and one without group selection terminology are insightful ways of looking at the same models. Apart from this dualistic view, this paper contains a result that states that inclusive fitness correctly predicts the direction of selection for one class of models, represented by linear public goods games. Equally important is that this result has a flip side: there is a more general, but still very realistic class of models, including models with synergies, for which it is not possible to summarize their predictions on the basis of an evaluation of inclusive fitness.     

A GENERAL MODEL FOR KIN SELECTION

Inclusive fitness theory is central to our understanding of the evolution of social behavior. By showing the importance of genetic transmission through nondescendent relatives, it helps to explain the evolution of reproductively altruistic behaviors, such as those observed in the social insects. Inclusive fitness thinking is quantified by Hamilton's rule, but Hamilton's rule has often been criticized for being inexact or insufficiently general. Here I show how adopting a genic perspective yields a very general version that remains pleasingly simple and transparent.     

Estimating and comparing thermal performance curves

I show how one can estimate the shape of a thermal performance curve using information theory. This approach ranks plausible models by their Akaike information criterion (AIC), which is a measure of a model's ability to describe the data discounted by the model's complexity. I analyze previously published data to demonstrate how one applies this approach to describe a thermal performance curve. This exemplary analysis produced two interesting results. First, a model with a very high r² (a modified Gaussian function) appeared to overfit the data. Second, the model favored by information theory (a Gaussian function) has been used widely in optimality studies of thermal performance curves. Finally, I discuss the choice between regression and ANOVA when comparing thermal performance curves and highlight a superior method called template mode of variation. Much progress can be made by abandoning traditional methods for a method that combines information theory with template mode of variation.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

Economic weights of fertility, prolificacy, milk yield and longevity in dairy sheep

Economic weights have been estimated in two breeds (Latxa and Manchega) using economic and technical data collected in 41 Latxa and 12 Manchega dairy sheep flocks. The traits considered were fertility (lambing per year), prolificacy (number of lambs), milk yield (litres) and longevity (as productive life, in years). A linear function was used, relating these traits to the different costs in the flock. The variable costs involved in the profit function were feed and labour. From this function, economic weights were obtained. Labour is considered in the Latxa breed to be a constraint. Moreover, farm profits are unusually high, which probably means that some costs were not included according to the economic theory. For that reason, a rescaling procedure was applied constraining total labour time at the farm. Genetic gains were estimated with the resulting economic weights to test if they give any practical difference. Milk yield only as selection criterion was also considered. The medians of the estimated economic weights for fertility, prolificacy, milk yield and longevity were 138.60 € per lambing, 40.00 € per lamb, 1.18 € per l, 1.66 € per year, and 137.66 € per lambing, 34.17 € per lamb, 0.73 € per l, 2.16 € per year under the linear approach in the Latxa and Manchega breeds respectively. Most differences between breeds can be related to differences in production systems. As for the genetic gains, they were very similar for all economic weights, except when only milk yield was considered, where a correlated decrease in fertility led to a strong decrease in profit. It is concluded that the estimates are robust for practical purposes and that breeding programmes should consider inclusion of fertility. More research is needed to include other traits such as somatic cell score, milk composition and udder traits.     

A reexamination of stability in randomly varying versus deterministic environments with comments on the stochastic theory of limiting similarity

The focus of this paper is a general relationship proposed by May (Amer. Natur. 107 (1973)) between the stability properties of stochastic models incorporating environmental variation and the stability properties of the deterministic models from which they are derived. The concepts of stochastic stability underlying this conjectured relationship are discussed and compared to the standard definitions of deterministic stability as well as alternative criteria for stability in stochastic models. It is shown by example that May's qualitative stability criterion does not ensure stability in any sense unless restrictive conditions on the form of the model are satisfied. Even under these conditions, the criterion, which is based on linearization, generally provides information only about the local dynamics of multispecies models. The applicability of such information to stochastic limiting similarity theory is discussed and alternative methods of analysis are proposed.     

Evaluation of the Kullback-Leibler Discrepancy for Model Selection in Open Population Capture-Recapture Models

The objective of this paper is to introduce the logical basis of AIC-based model selection to persons analyzing capture-recapture data and to explore the key theorettical aspect of AIC based model selection, for open-model capture-recapture, needed for AIC to perform well in this context. Almost all previous work on AIC assumes a Gaussian model; that assumption does not hold for capture-recapture models. Assuming the Cormack-Jolly-Seber model as the true model, we used numerical methods to evaluate the expectation of the log-likelihood relative to Akaike's target predictive log-likelihood. The use of this particular target criterion was motivated by the idea of using the Kullback-Leibler discrepancy for model selection, for which Akaike found the bias of the sample log-likelihood was asymptotically K, where K = the number of estimated (by MLE) parameters. In some sense, then, AIC is a bias-adjusted log-likelihood. For a set of 81 plausible cases, we evaluated this bias almost exactly. The ratio of this bias to the first order theory (bias of K) and to second order theory (K + a sample size adjustment) is essentially 1 for these 81 cases. Thus, AIC should be a suitable basis for model selection in open model capture-recapture.     

Spatial structure,host heterogeneity and parasite virulence: implications for vaccine‐driven evolution

Natural host‐parasite interactions exhibit considerable variation in host quality, with profound consequences for disease ecology and evolution. For instance, treatments (such as vaccination) may select for more transmissible or virulent strains. Previous theory has addressed the ecological and evolutionary impact of host heterogeneity under the assumption that hosts and parasites disperse globally. Here, we investigate the joint effects of host heterogeneity and local dispersal on the evolution of parasite life‐history traits. We first formalise a general theoretical framework combining variation in host quality and spatial structure. We then apply this model to the specific problem of parasite evolution following vaccination. We show that, depending on the type of vaccine, spatial structure may select for higher or lower virulence compared to the predictions of non‐spatial theory. We discuss the implications of our results for disease management, and their broader fundamental relevance for other causes of host heterogeneity in nature.     

SPATIAL VARIATION IN SELECTIVE REGIMES: SEXUAL SELECTION IN THE WATER STRIDER,GERRIS ODONTOGASTER

Studies of phenotypic selection in natural populations are often concerned with simply detecting selection. In adopting a more mechanistic approach, this study compares the sexual selection regimes in natural populations of the water strider Gerris odontogaster with a priori predictions of selection, based on a number of previous field and laboratory studies of the behavioral mechanisms of selection. In this species, a general reluctance of females to mate allows for intersexual selection for ability to subdue reluctant females in males. Female reluctance to mate has been shown to decrease with increasing population density, suggesting that sexual selection should be weaker in high density populations. Three different populations with large differences in population density were studied. A number of traits including parasite load, body mass, body size and male abdominal process length were found to experience significant sexual selection. The investigated populations differed considerably with regard to the total strength of selection on the measured traits and the form of selection on single traits. In general, males in the population with the highest density experienced the weakest selection for grasping ability. This pattern is ascribed to density-related alterations of female mating behavior. Selection for male grasping ability, as reflected by selection on male abdominal process length, is reduced in high-density populations where reluctant females are more easily subdued. Further, the studied populations differed significantly in mean phenotype and phenotypic variance for male abdominal process length. It is suggested that interpopulational differences in selective regimes may generate local adaptations with respect to male abdominal process length, and that gene flow may contribute to the maintenance of the high genetic variation in this trait. It is further suggested that more empirical effort should be made in quantifying and understanding spatial and temporal variation in selection in natural populations, since this may provide information on the prevalence of local adaptations in metric traits and on the mechanisms of selection.     

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.     

INTERACTION-INDEPENDENT SEXUAL SELECTION AND THE MECHANISMS OF SEXUAL SELECTION

Darwin identified explicitly two types of sexual selection, male contests (combat and displays) and female choice, and he devoted the overwhelming majority of his examples to traits that influence the outcome of these interactions. Subsequent treatments of sexual selection have emphasized the importance of intra- and intersexual interactions as sources of sexual selection. However, many traits that are important determinants of mating success influence mating success without necessarily affecting the outcome of intra- and intersexual interactions. Here, I argue that traits can be subject to sexual selection even if they do not affect the outcome of intra- and intersexual interactions. I distinguish two types of sexual selection, interaction-independent and interaction-dependent selection, based on whether variance in mating success is the result of trait-dependent outcomes of interactions between conspecifics. I then use this distinction to construct a framework for classifying types of sexual selection that unifies and expands previously proposed frameworks. Finally, I outline several implications that the concept of interaction-independent sexual selection has for the general theory of sexual selection.     

DIRECT SELECTION ON LIFE SPAN IN DROSOPHILA MELANOGASTER

An important issue in the study of the evolution of aging in Drosophila melanogaster is whether decreased early fecundity is inextricably coupled with increased life span in selection experiments on age at reproduction. Here, this problem has been tackled using an experimental design in which selection is applied directly to longevity. Selection appeared successful for short and long life, in females as well as males. Progeny production of females selected for long life was lower than for short-lived females throughout their whole life. No increase of late-life reproduction in long-lived females occurred, as has been found in selection experiments on age at reproduction. This discrepancy is explained in terms of the inadequacy of the latter design to separate selection on life span from selection on late-life fecundity. Moreover, starvation resistance and fat content were lower for adults selected for short life. In general, the data support the negative-pleiotropy–disposable-soma theory of aging, and it is hypothesized that the pleiotropic allocation of resources to maintenance versus to reproduction as implicated in the theory might involve lipid metabolism. It is argued that further research on this suggestion is urgent and should certainly comprise observations on male reproduction because these are for the greater part still lacking. In conclusion, the longevity of D. melanogaster can be genetically altered in a direct-selection design, and such an increase is accompanied by a decreased general reproduction and thus early reproduction.     

The experimental evolution of specialists,generalists, and the maintenance of diversity

Environmental heterogeneity may be a general explanation for both the quantity of genetic variation in populations and the ecological niche width of individuals. To evaluate this hypothesis, I review the literature on selection experiments in heterogeneous environments. The niche width usually – but not invariably – evolves to match the amount of environmental variation, specialists evolving in homogeneous environments and generalists evolving in heterogeneous environments. The genetics of niche width are more complex than has previously been recognized, particularly with respect to the magnitude of costs of adaptation and the putative constraints on the evolution of generalists. Genetic variation in fitness is more readily maintained in heterogeneous environments than in homogeneous environments and this diversity is often stably maintained through negative frequency‐dependent selection. Moreover environmental heterogeneity appears to be a plausible mechanism for at least two well‐known patterns of species diversity at the landscape scale. I conclude that environmental heterogeneity is a plausible and possibly very general explanation for diversity across the range of scales from individuals to landscapes.