Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.

Seleção de progênies de meios-irmãos do composto Isanão VF-1 de milho na safra e safrinha

O aumento significativo da produção de milho na segunda safra no Brasil, principalmente no centro-sul do país, têm estimulado os programas de melhoramento da cultura a selecionar genótipos que sejam adaptáveis às condições climáticas das diferentes épocas de semeadura. Nesse sentido, o objetivo do presente trabalho foi quantificar a interação progênies x épocas de semeadura e verificar seus reflexos no progresso genético com o uso de índice de seleção multivariado para seleção de progênies do Composto Isanão VF-1 de milho. As semeaduras foram realizadas na segunda safra em 2004 e na primeira safra do ano agrícola 2004/05. Foram utilizadas 71 progênies de meios irmãos avaliadas em blocos ao acaso, com três repetições. Os caracteres avaliados foram: altura de plantas, altura de espigas, tombamento, prolificidade e rendimento de grãos. Realizaram-se a decomposição da interação progênies x épocas e foram estimados os ganhos pelo índice de seleção descrito por Mulamba e Mock. Houve predomínio da interação do tipo simples para maioria dos caracteres, exceto para prolificidade, que revelou 86% de interação do tipo complexa. Pelo índice de Mulamba e Mock, os ganhos proporcionais mais adequados para o conjunto de caracteres avaliados foi obtido pelos pesos econômicos atribuídos por tentativas. Os ganhos preditos foram de 1,41, 0,86, -13,03, 9,54 e 16,12% para altura de planta, altura de espiga, tombamento, prolificidade e rendimento de grãos, respectivamente.

The stability of P in coral reef fishes

The constancy of phenotypic variation and covariation is an assumption that underlies most recent investigations of past selective regimes and attempts to predict future responses to selection. Few studies have tested this assumption of constancy despite good reasons to expect that the pattern of phenotypic variation and covariation may vary in space and time. We compared phenotypic variance-covariance matrices (P) estimated for Populations of six species of distantly related coral reef fishes sampled at two locations on Australia's Great Barrier Reef separated by more than 1000 km. The intraspecific similarity between these matrices was estimated using two methods: matrix correlation and common principal component analysis. Although there was no evidence of equality between pairs of P, both statistical approaches indicated a high degree of similarity in morphology between the two populations for each species. In general, the hierarchical decomposition of the variance-covariance structure of these populations indicated that all principal components of phenotypic variance-covariance were shared but that they differed in the degree of variation associated with each of these components. The consistency of this pattern is remarkable given the diversity of morphologies and life histories encompassed by these species. Although some phenotypic instability was indicated, these results were consistent with a generally conserved pattern of multivariate selection between populations.

Multivariate Analysis for Animal Selection in Experimental Research

Background: Several researchers seek methods for the selection of homogeneous groups of animals in experimental studies, a fact justified because homogeneity is an indispensable prerequisite for casualization of treatments. The lack of robust methods that comply with statistical and biological principles is the reason why researchers use empirical or subjective methods, influencing their results. Objective: To develop a multivariate statistical model for the selection of a homogeneous group of animals for experimental research and to elaborate a computational package to use it. Methods: The set of echocardiographic data of 115 male Wistar rats with supravalvular aortic stenosis (AoS) was used as an example of model development. Initially, the data were standardized, and became dimensionless. Then, the variance matrix of the set was submitted to principal components analysis (PCA), aiming at reducing the parametric space and at retaining the relevant variability. That technique established a new Cartesian system into which the animals were allocated, and finally the confidence region (ellipsoid) was built for the profile of the animals’ homogeneous responses. The animals located inside the ellipsoid were considered as belonging to the homogeneous batch; those outside the ellipsoid were considered spurious. Results: The PCA established eight descriptive axes that represented the accumulated variance of the data set in 88.71%. The allocation of the animals in the new system and the construction of the confidence region revealed six spurious animals as compared to the homogeneous batch of 109 animals. Conclusion: The biometric criterion presented proved to be effective, because it considers the animal as a whole, analyzing jointly all parameters measured, in addition to having a small discard rate.

Effects of selection and drift on G matrix evolution in a heterogeneous environment: a multivariate Qst-Fst Test with the freshwater snail Galba truncatula.

Unraveling the effect of selection vs. drift on the evolution of quantitative traits is commonly achieved by one of two methods. Either one contrasts population differentiation estimates for genetic markers and quantitative traits (the Q(st)-F(st) contrast) or multivariate methods are used to study the covariance between sets of traits. In particular, many studies have focused on the genetic variance-covariance matrix (the G matrix). However, both drift and selection can cause changes in G. To understand their joint effects, we recently combined the two methods into a single test (accompanying article by Martin et al.), which we apply here to a network of 16 natural populations of the freshwater snail Galba truncatula. Using this new neutrality test, extended to hierarchical population structures, we studied the multivariate equivalent of the Q(st)-F(st) contrast for several life-history traits of G. truncatula. We found strong evidence of selection acting on multivariate phenotypes. Selection was homogeneous among populations within each habitat and heterogeneous between habitats. We found that the G matrices were relatively stable within each habitat, with proportionality between the among-populations (D) and the within-populations (G) covariance matrices. The effect of habitat heterogeneity is to break this proportionality because of selection for habitat-dependent optima. Individual-based simulations mimicking our empirical system confirmed that these patterns are expected under the selective regime inferred. We show that homogenizing selection can mimic some effect of drift on the G matrix (G and D almost proportional), but that incorporating information from molecular markers (multivariate Q(st)-F(st)) allows disentangling the two effects.

Multivariate approach in the selection of superior soybean progeny which carry the RR gene

Efficiency in the use of genetic variability, whether existing or created, increases when properly explored and analysed. Incorporation of biotechnology into breeding programs has been the general practice. The challenge for the researcher is the constant development of new and improved cultivars. The aim of this experiment was to select progenies with superior characteristics, whether or not carriers of the RR gene, derived from bi-parental crosses in the soybean, with the help of multivariate techniques. The experiment was carried out in a family-type experimental design, including controls, during the agricultural year 2010/2011 and 2011/2012 in Jaboticabal in the Brazilian State of São Paulo. From the F3 generation, phenotypically superior plants were selected, which were evaluated for the following traits: number of days to flowering; number of days to maturity; height of first pod insertion; plant height at maturity; lodging; agronomic value; number of branches; number of pods per plant; 100-seed weight; number of seeds per plant; grain yield per plant. Given the results, it appears possible to select superior progeny by principal component analysis. Cluster analysis using the K-means method links progeny according to the most important characteristics in each group and identifies, by the Ward method and by means of a dendrogram, the structure of similarity and divergence between selected progeny. Both methods are effective in aiding progeny selection.

Multivariate analysis for animal selection in experimental research

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Experimental evidence for multivariate stabilizing sexual selection

Stabilizing selection is a fundamental concept in evolutionary biology. In the presence of a single intermediate optimum phenotype (fitness peak) on the fitness surface, stabilizing selection should cause the population to evolve toward such a peak. This prediction has seldom been tested, particularly for suites of correlated traits. The lack of tests for an evolutionary match between population means and adaptive peaks may be due, at least in part, to problems associated with empirically detecting multivariate stabilizing selection and with testing whether population means are at the peak of multivariate fitness surfaces. Here we show how canonical analysis of the fitness surface, combined with the estimation of confidence regions for stationary points on quadratic response surfaces, may be used to define multivariate stabilizing selection on a suite of traits and to establish whether natural populations reside on the multivariate peak. We manufactured artificial advertisement calls of the male cricket Teleogryllus commodus and played them back to females in laboratory phonotaxis trials to estimate the linear and nonlinear sexual selection that female phonotactic choice imposes on male call structure. Significant nonlinear selection on the major axes of the fitness surface was convex in nature and displayed an intermediate optimum, indicating multivariate stabilizing selection. The mean phenotypes of four independent samples of males, from the same population as the females used in phonotaxis trials, were within the 95% confidence region for the fitness peak. These experiments indicate that stabilizing sexual selection may play an important role in the evolution of male call properties in natural populations of T. commodus.

Selection of mango rosa genotypes in a breeding population using the multivariate-biplot method.

Mango (Mangifera indica L.) trees stand out among the main fruit trees cultivated in Brazil. The mango rosa fruit is a very popular local variety (landrace), especially because of their superior technological characteristics such as high contents of Vitamin C and soluble solids (SS), as well as attractive taste and color. The objective of this study was to select a breeding population of mango rosa (polyclonal variety; ≥5 individuals) that can simultaneously meet the fresh and processed fruit Vmarkets, using the multivariate method of principal components and the biplot graphic.

Selection indices and multivariate analysis show similar results in the evaluation of growth and carcass traits in beef cattle.

2016

Model selection and the vectorial misspecification-resistant information criterion in multivariate time series

The thesis deals with the problem of Model Selection (MS) motivated by information and prediction theory, focusing on parametric time series (TS) models. The main contribution of the thesis is the extension to the multivariate case of the Misspecification-Resistant Information Criterion (MRIC), a criterion introduced recently that solves Akaike’s original research problem posed 50 years ago, which led to the definition of the AIC. The importance of MS is witnessed by the huge amount of literature devoted to it and published in scientific journals of many different disciplines. Despite such a widespread treatment, the contributions that adopt a mathematically rigorous approach are not so numerous and one of the aims of this project is to review and assess them. Chapter 2 discusses methodological aspects of MS from information theory. Information criteria (IC) for the i.i.d. setting are surveyed along with their asymptotic properties; and the cases of small samples, misspecification, further estimators. Chapter 3 surveys criteria for TS. IC and prediction criteria are considered for: univariate models (AR, ARMA) in the time and frequency domain, parametric multivariate (VARMA, VAR); nonparametric nonlinear (NAR); and high-dimensional models. The MRIC answers Akaike’s original question on efficient criteria, for possibly-misspecified (PM) univariate TS models in multi-step prediction with high-dimensional data and nonlinear models. Chapter 4 extends the MRIC to PM multivariate TS models for multi-step prediction introducing the Vectorial MRIC (VMRIC). We show that the VMRIC is asymptotically efficient by proving the decomposition of the MSPE matrix and the consistency of its Method-of-Moments Estimator (MoME), for Least Squares multi-step prediction with univariate regressor. Chapter 5 extends the VMRIC to the general multiple regressor case, by showing that the MSPE matrix decomposition holds, obtaining consistency for its MoME, and proving its efficiency. The chapter concludes with a digression on the conditions for PM VARX models.

Comparison of univariate and multivariate calibration for the determination of micronutrients in pellets of plant materials by laser induced breakdown spectrometry

The application of laser induced breakdown spectrometry (LIBS) aiming the direct analysis of plant materials is a great challenge that still needs efforts for its development and validation. In this way, a series of experimental approaches has been carried out in order to show that LIBS can be used as an alternative method to wet acid digestions based methods for analysis of agricultural and environmental samples. The large amount of information provided by LIBS spectra for these complex samples increases the difficulties for selecting the most appropriated wavelengths for each analyte. Some applications have suggested that improvements in both accuracy and precision can be achieved by the application of multivariate calibration in LIBS data when compared to the univariate regression developed with line emission intensities. In the present work, the performance of univariate and multivariate calibration, based on partial least squares regression (PLSR), was compared for analysis of pellets of plant materials made from an appropriate mixture of cryogenically ground samples with cellulose as the binding agent. The development of a specific PLSR model for each analyte and the selection of spectral regions containing only lines of the analyte of interest were the best conditions for the analysis. In this particular application, these models showed a similar performance. but PLSR seemed to be more robust due to a lower occurrence of outliers in comparison to the univariate method. Data suggests that efforts dealing with sample presentation and fitness of standards for LIBS analysis must be done in order to fulfill the boundary conditions for matrix independent development and validation. (C) 2009 Elsevier B.V. All rights reserved.

Simultaneous selection in progenies of yellow passion fruit using selection indices

This study aimed to evaluate the efficiency of simultaneous selection (selection indices) using estimated genetic gains in yellow passion fruit and to make a comparison between the methodologies of Mulamba & Mock and Elston. The study was conducted with 26 sib progenies of yellow passion fruit for intrinsic production characteristics including fruit number, fruit mass, fruit length and diameter, and for the fruit characteristics skin thickness, soluble solids and acidity. Two methodologies were applied: first, in the joint analysis of fruit characteristics and of intrinsic production characteristics in a single phase of selection; and second, in the analysis in two phases, in which priority was given to the intrinsic production characteristics in the first phase, and later, in the second phase, the best fruit characteristics were chosen among the progenies of the first phase. The analysis of variance was applied to the data to detect genetic variability among progenies. The Elston's selection indice was unable to provide distribution of genetic gains consistent with the purposes of the study, as it selected a single progeny of passion fruit. However, the index based on the sum of ranks of Mulamba & Mock was more suitable, as it provided a balanced distribution of gains, selecting a larger number of progenies. The methodology of selection using indices is advantageous in passion fruit, since it contributes to higher genetic gains for all the traits evaluated, and the selection in a single phase was proved efficient for progeny selection.

Multivariate QST-FST comparisons: a neutrality test for the evolution of the g matrix in structured populations.

Neutrality tests in quantitative genetics provide a statistical framework for the detection of selection on polygenic traits in wild populations. However, the existing method based on comparisons of divergence at neutral markers and quantitative traits (Q(st)-F(st)) suffers from several limitations that hinder a clear interpretation of the results with typical empirical designs. In this article, we propose a multivariate extension of this neutrality test based on empirical estimates of the among-populations (D) and within-populations (G) covariance matrices by MANOVA. A simple pattern is expected under neutrality: D = 2F(st)/(1 - F(st))G, so that neutrality implies both proportionality of the two matrices and a specific value of the proportionality coefficient. This pattern is tested using Flury's framework for matrix comparison [common principal-component (CPC) analysis], a well-known tool in G matrix evolution studies. We show the importance of using a Bartlett adjustment of the test for the small sample sizes typically found in empirical studies. We propose a dual test: (i) that the proportionality coefficient is not different from its neutral expectation [2F(st)/(1 - F(st))] and (ii) that the MANOVA estimates of mean square matrices between and among populations are proportional. These two tests combined provide a more stringent test for neutrality than the classic Q(st)-F(st) comparison and avoid several statistical problems. Extensive simulations of realistic empirical designs suggest that these tests correctly detect the expected pattern under neutrality and have enough power to efficiently detect mild to strong selection (homogeneous, heterogeneous, or mixed) when it is occurring on a set of traits. This method also provides a rigorous and quantitative framework for disentangling the effects of different selection regimes and of drift on the evolution of the G matrix. We discuss practical requirements for the proper application of our test in empirical studies and potential extensions.

Liver Transplantation for Neuroendocrine Tumors in Europe-Results and Trends in Patient Selection: A 213-Case European Liver Transplant Registry Study.

OBJECTIVE:: The purpose of this study was to assess outcomes and indications in a large cohort of patients who underwent liver transplantation (LT) for liver metastases (LM) from neuroendocrine tumors (NET) over a 27-year period. BACKGROUND:: LT for NET remains controversial due to the absence of clear selection criteria and the scarcity and heterogeneity of reported cases. METHODS:: This retrospective multicentric study included 213 patients who underwent LT for NET performed in 35 centers in 11 European countries between 1982 and 2009. One hundred seven patients underwent transplantation before 2000 and 106 after 2000. Mean age at the time of LT was 46 years. Half of the patients presented hormone secretion and 55% had hepatomegaly. Before LT, 83% of patients had undergone surgical treatment of the primary tumor and/or LM and 76% had received chemotherapy. The median interval between diagnosis of LM and LT was 25 months (range, 1-149 months). In addition to LT, 24 patients underwent major resection procedures and 30 patients underwent minor resection procedures. RESULTS:: Three-month postoperative mortality was 10%. At 5 years after LT, overall survival (OS) was 52% and disease-free survival was 30%. At 5 years from diagnosis of LM, OS was 73%. Multivariate analysis identified 3 predictors of poor outcome, that is, major resection in addition to LT, poor tumor differentiation, and hepatomegaly. Since 2000, 5-year OS has increased to 59% in relation with fewer patients presenting poor prognostic factors. Multivariate analysis of the 106 cases treated since 2000 identified the following predictors of poor outcome: hepatomegaly, age more than 45 years, and any amount of resection concurrent with LT. CONCLUSIONS:: LT is an effective treatment of unresectable LM from NET. Patient selection based on the aforementioned predictors can achieve a 5-year OS between 60% and 80%. However, use of overly restrictive criteria may deny LT to some patients who could benefit. Optimal timing for LT in patients with stable versus progressive disease remains unclear.