ESTIMATING UNCERTAINTY IN MULTIVARIATE RESPONSES TO SELECTION

Predicting the responses to natural selection is one of the key goals of evolutionary biology. Two of the challenges in fulfilling this goal have been the realization that many estimates of natural selection might be highly biased by environmentally induced covariances between traits and fitness, and that many estimated responses to selection do not incorporate or report uncertainty in the estimates. Here we describe the application of a framework that blends the merits of the Robertson–Price Identity approach and the multivariate breeder's equation to address these challenges. The approach allows genetic covariance matrices, selection differentials, selection gradients, and responses to selection to be estimated without environmentally induced bias, direct and indirect selection and responses to selection to be distinguished, and if implemented in a Bayesian‐MCMC framework, statistically robust estimates of uncertainty on all of these parameters to be made. We illustrate our approach with a worked example of previously published data. More generally, we suggest that applying both the Robertson–Price Identity and the multivariate breeder's equation will facilitate hypothesis testing about natural selection, genetic constraints, and evolutionary responses.     

A General Approach to the Predictability Issue in Survival Analysis with Applications

Very often in survival analysis one has to study martingaleintegrals where the integrand is not predictable and where thecounting process theory of martingales is not directly applicable,as for example in nonparametric and semiparametric applicationswhere the integrand is based on a pilot estimate. We call thisthe predictability issue in survival analysis. The problem hasbeen resolved by approximations of the integrand by predictablefunctions which have been justified by ad hoc procedures. Wepresent a general approach to the solution of this problem.The usefulness of the approach is shown in three applications.In particular, we argue that earlier ad hoc procedures do notwork in higher-dimensional smoothing problems in survival analysis.     

The evolution of multiple mating: Costs and benefits of polyandry to females and of polygyny to males

Polyandry is a paradox: why do females mate multiple times when a single ejaculate often provides enough sperm for lifetime egg production? Gowaty et al. addressed explanations for polyandry in Drosophila pseudoobscura from the perspective of hypotheses based on sex differences in costs of reproduction (CoR). Contrary to CoR, Gowaty et al. showed that (1) a single ejaculate was inadequate for lifetime egg production; (2) polyandry provided fitness benefits to females beyond provision of adequate sperm and (3) fitness benefits of polyandry were not offset by costs. Here, I discuss predictions of the ad hoc hypotheses of CoR and three alternative hypotheses to CoR to facilitate a discussion and further development of a strong inference approach to experiments on the adaptive significance of polyandry for females. Each of the hypotheses makes testable predictions; simultaneous tests of the predictions will provide a strong inference approach to understanding the adaptive significance of multiple mating. I describe a sex-symmetric experiment meant to evaluate variation in fitness among lifelong virgins (V); monogamous females and males with one copulation (M_OC); monogamous females and males with multiple copulations (M_MC); P_AND, polyandrous females; and P_GYN, polygynous males. Last, I recommend the study of many different species, while taking care in choice of study species and attention to the assumptions of specific hypotheses. I particularly urge the study of many more Drosophila species both in laboratory and the wild to understand the “nature of flies in nature,” where opportunities and constraints mold evolutionary responses.     

Computational mate choice: theory and empirical evidence

The present review is based on the thesis that mate choice results from information-processing mechanisms governed by computational rules and that, to understand how females choose their mates, we should identify which are the sources of information and how they are used to make decisions. We describe mate choice as a three-step computational process and for each step we present theories and review empirical evidence. The first step is a perceptual process. It describes the acquisition of evidence, that is, how females use multiple cues and signals to assign an attractiveness value to prospective mates (the preference function hypothesis). The second step is a decisional process. It describes the construction of the decision variable (DV), which integrates evidence (private information by direct assessment), priors (public information), and value (perceived utility) of prospective mates into a quantity that is used by a decision rule (DR) to produce a choice. We make the assumption that females are optimal Bayesian decision makers and we derive a formal model of DV that can explain the effects of preference functions, mate copying, social context, and females' state and condition on the patterns of mate choice. The third step of mating decision is a deliberative process that depends on the DRs. We identify two main categories of DRs (absolute and comparative rules), and review the normative models of mate sampling tactics associated to them. We highlight the limits of the normative approach and present a class of computational models (sequential-sampling models) that are based on the assumption that DVs accumulate noisy evidence over time until a decision threshold is reached. These models force us to rethink the dichotomy between comparative and absolute decision rules, between discrimination and recognition, and even between rational and irrational choice. Since they have a robust biological basis, we think they may represent a useful theoretical tool for behavioural ecologist interested in integrating proximate and ultimate causes of mate choice.     

Animal navigation: general properties of directed walks

The ability to locomote is a defining characteristic of all animals. Yet, all but the most trivial forms of navigation are poorly understood. Here we report and discuss the analytical results of an in-depth study of a simple navigation problem. In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and to continually reorient with reference to it. The other is to monitor body rotations from internal sensory information only. We showed previously that, at least for simple representations of locomotion, the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, but the second strategy will not do so, even after an infinite number of steps. This paper extends and generalizes the earlier results by demonstrating that these findings are true even when a very general model of locomotion is used. In this general model, error components within individual steps are not independent, and directional errors may be biased. In the absence of a compass, the expected path of a directed walk in general approximates a logarithmic spiral. Some examples are given to illustrate potential applications of the quantitative results derived here. Motivated by the analytical results developed in this work, a nomenclature for directed walks is proposed and discussed. Issues related to path integration in mammals and robots, and measuring the curvature of a noisy path are also addressed using directed walk theory.     

Using pseudo amino acid composition to predict transmembrane regions in protein: cellular automata and Lempel-Ziv complexity

Summary. Transmembrane (TM) proteins represent about 20–30% of the protein sequences in higher eukaryotes, playing important roles across a range of cellular functions. Moreover, knowledge about topology of these proteins often provides crucial hints toward their function. Due to the difficulties in experimental structure determinations of TM protein, theoretical prediction methods are highly preferred in identifying the topology of newly found ones according to their primary sequences, useful in both basic research and drug discovery. In this paper, based on the concept of pseudo amino acid composition (PseAA) that can incorporate sequence-order information of a protein sequence so as to remarkably enhance the power of discrete models (Chou, K. C., Proteins: Structure, Function, and Genetics, 2001, 43: 246–255), cellular automata and Lempel-Ziv complexity are introduced to predict the TM regions of integral membrane proteins including both α-helical and β-barrel membrane proteins, validated by jackknife test. The result thus obtained is quite promising, which indicates that the current approach might be a quite potential high throughput tool in the post-genomic era. The source code and dataset are available for academic users at liml@scu.edu.cn. Authors’ address: Menglong Li, College of Chemistry, Sichuan University, Chengdu, Sichuan 610064, P.R. China     

Evolutionary potential of morphological traits across different life‐history stages

Despite accumulating examples of selection acting on heritable traits in the wild, predicted evolutionary responses are often different from observed phenotypic trends. Various explanations have been suggested for these mismatches. These include within‐individual changes across lifespan that can create important variation in genetic architecture of traits and selection acting on them, but also potential problems with the methodological approach used to predict evolutionary responses of traits. Here, we used an 8‐year data set on tree swallow (Tachycineta bicolor) to first assess the effects of differences among three nestling life‐history stages on the genetic (co)variances of two morphological traits (body mass and primary feather length) and the selection acting on them over three generations. We then estimated the evolutionary potential of these traits by predicting their evolutionary responses using the breeder's equation and the secondary theorem of selection approaches. Our results showed variation in strength and direction of selection and slight changes in trait variance across ages. Predicted evolutionary responses differed importantly between both approaches for half of the trait–age combinations we studied, suggesting the presence of environmentally induced correlations between focal traits and fitness possibly biasing breeder's equation predictions. Our results emphasize that predictions of evolutionary potential for morphological traits are likely to be highly variable, both in strength and direction, depending on the life stage and method used, thus mitigating our capacity to predict adaptation and persistence of wild populations.     

脉冲-扩散周期竞争系统解的渐近行为

研究了在周期变化环境中具有扩散及种群密度可能发生突变的两竞争种群动力系统的数学模型．模型由反应扩散方程组以及初边值及脉冲条件组成．文章建立了研究模型的上下解方法,获得了一些比较原理．利用脉冲常微分方程的比较定理以及利用相应的脉冲常微分方程的解控制和估计所讨论模型的解,研究了系统模型的解的渐近性质．