Multivariate analyses of genotype x environment interaction of popcorn

The objectives of this work were to evaluate the genotype x environment (GxE) interaction for popcorn and to compare two multivariate analyses methods. Nine popcorn cultivars were sown on four dates one month apart during each of the agricultural years 1998/1999 and 1999/2000. The experiments were carried out using randomized block designs, with four replicates. The cv. Zélia contributed the least to the GxE interaction. The cv. Viçosa performed similarly to cv. Rosa-claro. Optimization of GxE was obtained for cv. CMS 42 for a favorable mega-environment, and for cv. CMS 43 for an unfavorable environment. Multivariate analysis supported the results from the method of Eberhart & Russell. The graphic analysis of the Additive Main effects and Multiplicative Interaction (AMMI) model was simple, allowing conclusions to be made about stability, genotypic performance, genetic divergence between cultivars, and the environments that optimize cultivar performance. The graphic analysis of the Genotype main effects and Genotype x Environment interaction (GGE) method added to AMMI information on environmental stratification, defining mega-environments and the cultivars that optimized performance in those mega-environments. Both methods are adequate to explain the genotype x environment interactions.

Association between the PNPLA3 (rs738409 C>G) variant and hepatocellular carcinoma: Evidence from a meta-analysis of individual participant data.

The incidence of hepatocellular carcinoma (HCC) is increasing in Western countries. Although several clinical factors have been identified, many individuals never develop HCC, suggesting a genetic susceptibility. However, to date, only a few single-nucleotide polymorphisms have been reproducibly shown to be linked to HCC onset. A variant (rs738409 C>G, encoding for p.I148M) in the PNPLA3 gene is associated with liver damage in chronic liver diseases. Interestingly, several studies have reported that the minor rs738409[G] allele is more represented in HCC cases in chronic hepatitis C (CHC) and alcoholic liver disease (ALD). However, a significant association with HCC related to CHC has not been consistently observed, and the strength of the association between rs738409 and HCC remains unclear. We performed a meta-analysis of individual participant data including 2,503 European patients with cirrhosis to assess the association between rs738409 and HCC, particularly in ALD and CHC. We found that rs738409 was strongly associated with overall HCC (odds ratio [OR] per G allele, additive model=1.77; 95% confidence interval [CI]: 1.42-2.19; P=2.78 × 10(-7) ). This association was more pronounced in ALD (OR=2.20; 95% CI: 1.80-2.67; P=4.71 × 10(-15) ) than in CHC patients (OR=1.55; 95% CI: 1.03-2.34; P=3.52 × 10(-2) ). After adjustment for age, sex, and body mass index, the variant remained strongly associated with HCC. Conclusion: Overall, these results suggest that rs738409 exerts a marked influence on hepatocarcinogenesis in patients with cirrhosis of European descent and provide a strong argument for performing further mechanistic studies to better understand the role of PNPLA3 in HCC development.

Regulation of sodium transport in the cortical collecting duct : physiological role of GILZ in vitro and in vivo : characterisation of Na+ transport in the mCCDcl1 cell line

SUMMARY Regulation of sodium excretion by the kidney is a key mechanism in the long term regulation of blood pressure, and when altered it constitutes a risk factor for the appearance of arterial hypertension. Aldosterone, which secretion depends upon salt intake in the diet, is a steroid hormone that regulates sodium reabsorption in the distal part of the nephron (functional unit of the kidney) by modulating gene transcription. It has been shown that it can act synergistically with the peptidic hormone insulin through the interaction of their signalisation pathways. Our work consisted of two distinct parts: 1) the in vitro and in vivo characterisation of Glucocorticoid-Induced Leucine Zipper (GILZ) (an aldosterone-induced gene) mechanism of action; 2) the in vitro characterisation of insulin mechanism of action and its interaction with aldosterone. GILZ mRNA, coded by the TSC22D3 gene, is strongly induced by aldosterone in the cell line of principal cells of the cortical collecting duct (CCD) mpkCCDc14, suggesting that GILZ is a mediator of aldosterone response. Co-expression of GILZ and the amiloride-sensitive epithelial sodium channel ENaC in vitro in the Xenopus oocyte expression system showed that GILZ has no direct effect on the ENaC-mediated Na+ current in basal conditions. To define the role of GILZ in the kidney and in other organs (colon, heart, skin, etc.), a conditional knock-out mouse is being produced and will allow the in vivo study of its role. Previous data showed that insulin induced a transepithelial sodium transport at supraphysiological concentrations. Insulin and the insulin-like growth factor 1 (IGF-1) are able to bind to each other receptor with an affinity 50 to 100 times lower than to their cognate receptor. Our starting hypothesis was that the insulin effect observed at these supraphysiological concentrations is actually mediated by the IGF receptor type 1 (IGF-1R). In a new cell line that presents all the characteristics of the principal cells of the CCD (mCCDc11) we have shown that both insulin and IGF-1 induce a physiologically significant increase of Na+ transport through the activation of IGF-1R. Aldosterone and insulin/IGF-1 have an additive effect on Na+ transport, through the activation of the PI3-kinase (PI3-K) pathway and the phosphorylation of the serum- and glucocorticoid-induced kinase 1 (Sgk1) by the IGF-1R, and the induction of Sgk1 expression by aldosterone. Thus, Sgk1 integrates IGF-1/insulin and aldosterone effects. We suggest that IGF-1 is physiologically relevant in the modulation of sodium balance, while insulin can only regulate Na+ transport at supraphysiological conditions. Both hormones would bind to the IGF-1R and induce Na+ transport by activating the PI3-K PDK1/2 - Sgk1 pathway. We have shown for the first time that Sgk1 is expressed and phosphorylated in principal cells of the CCD in basal conditions, although the mechanism that maintains Sgk1 phosphorylation is not known. This new role for IGF-1 suggests that it could be a salt susceptibility gene. In effect, IGF-1 stimulates Na+ and water transport in the kidney in vivo. Moreover, 35 % of the acromegalic patients (overproduction of growth hormone and IGF-1) are hypertensives (higher proportion than in normal population), and genetic analysis suggest a link between the IGF-1 gene locus and blood pressure. RÉSUMÉ La régulation de l'excrétion rénale de sodium (Na+) joue un rôle principal dans le contrôle à long terme de la pression sanguine, et ses altérations constituent un facteur de risque de l'apparition d'une hypertension artérielle. L'aldosterone, dont la sécrétion dépend de l'apport en sel dans la diète, est une hormone stéroïdienne qui régule la réabsorption de Na+ dans la partie distale du nephron (unité fonctionnelle du rein) en contrôlant la transcription de gènes. Elle peut agir de façon synergistique avec l'hormone peptidique insuline, probablement via l'interaction de leurs voies de signalisation cellulaire. Le but de notre travail comportait deux volets: 1) caractériser in vitro et in vivo le mécanisme d'action du Glucocorticoid Induced Leucine Zipper (GILZ) (un gène induit par l'aldosterone); 2) caractériser in vitro le mécanisme d'action de l'insuline et son interaction avec l'aldosterone. L'ARNm de GILZ, codé par le gène TSC22D3, est induit par l'aldosterone dans la lignée cellulaire de cellules principales du tubule collecteur cortical (CCD) mpkCCDc14, suggérant que GILZ est un médiateur potentiel de la réponse à l'aldosterone. La co-expression in vitro de GILZ et du canal à Na+ sensible à l'amiloride ENaC dans le système d'expression de l'oocyte de Xénope a montré que GILZ n'a pas d'effet sur les courants sodiques véhiculées par ENaC en conditions basales. Une souris knock-out conditionnelle de GILZ est en train d'être produite et permettra l'étude in vivo de son rôle dans le rein et d'autres organes. Des expériences préliminaires ont montré que l'insuline induit un transport transépithelial de Na+ à des concentrations supraphysiologiques. L'insuline et l'insulin-like growth factor 1 (IGF-1) peuvent se lier à leurs récepteurs réciproques avec une affinité 50 à 100 fois moindre qu'à leur propre récepteur. Nous avons donc proposé que l'effet de l'insuline soit médié par le récepteur à l'IGF type 1 (IGF-1R). Dans une nouvelle lignée cellulaire qui présente toutes les caractéristiques des cellules principales du CCD (mCCDc11) nous avons montré que les deux hormones induisent une augmentation physiologiquement significative du transport du Na+ par l'activation des IGF-1 R. Aldosterone et insuline/IGF-1 ont un effet additif sur le transport de Na+, via l'activation de la voie de la PI3-kinase et la phosphorylation de la serum- and glucocorticoid-induced kinase 1 (Sgk1) par l'IGF-1R, dont l'expression est induite par l'aldosterone. Sgk1 intègre les effets de l'insuline et l'aldosterone. Nous proposons que l'IGF-1 joue un rôle dans la modulation physiologique de la balance sodique, tandis que l'insuline régule le transport de Na+ à des concentrations supraphysiologiques. Les deux hormones agissent en se liant à l'IGF-1R et induisent le transport de Na+ en activant la cascade de signalisation PI3-K - PDK1/2 - Sgk1. Nous avons montré pour la première fois que Sgk1 est exprimée et phosphorylée dans des conditions basales dans les cellules principales du CCD, mais le mécanisme qui maintient sa phosphorylation n'est pas connu. Ce nouveau rôle pour l'IGF-1 suggère qu'il pourrait être un gène impliqué de susceptibilité au sel. Aussi, l'IGF-1 stimule le transport rénal de Na+ in vivo. De plus, 35 % des patients atteints d'acromégalie (surproduction d'hormone de croissance et d'IGF-1) sont hypertensifs (prévalence plus élevée que la population normale), et des analyses génétiques suggèrent un lien entre le locus du gène de l'IGF-1 et la pression sanguine. RÉSUMÉ GRAND PUBLIC Nos ancêtres se sont génétiquement adaptés pendant des centaines de millénaires à un environnement pauvre en sel (chlorure de sodium) dans la savane équatoriale, où ils consommaient moins de 0,1 gramme de sel par jour. On a commencé à ajouter du sel aux aliments avec l'apparition de l'agriculture (il y a 5000 à 10000 années), et aujourd'hui une diète omnivore, qui inclut des plats préparés, contient plusieurs fois la quantité de sodium nécessaire pour notre fonction physiologique normale (environ 10 grammes par jour). Le corps garde sa concentration constante dans le sang en s'adaptant à une consommation très variable de sel. Pour ceci, il module son excrétion soit directement, soit en sécrétant des hormones régulatrices. Le rein joue un rôle principal dans cette régulation puisque l'excrétion urinaire de sel change selon la diète et peut aller d'une quantité dérisoire à plus de 36 grammes par jour. L'attention qu'on prête au sel est liée à sa relation avec l'hypertension essentielle. Ainsi, le contrôle rénal de l'excrétion de sodium et d'eau est le principal mécanisme dans la régulation de la pression sanguine, et une ingestion excessive de sel pourrait être l'un des facteurs-clé déclenchant l'apparition d'un phénotype hypertensif. L'hormone aldosterone diminue l'excrétion de sodium par le rein en modulant l'expression de gènes qui pourraient être impliqués dans la sensibilité au sel. Dans une lignée cellulaire de rein l'expression du gène TSC22D3, qui se traduit en la protéine Glucocorticoid Induced Leucine Zipper (GILZ), est fortement induite par l'aldosterone. Ceci suggère que GILZ est un médiateur potentiel de l'effet de l'aldosterone, et pourrait être impliqué dans la sensibilité au sel. Pour analyser la fonction de GILZ dans le rein plusieurs approches ont été utilisées. Par exemple, une souris dans laquelle GILZ est spécifiquement inactivé dans le rein est en train d'être produite et permettra l'étude du rôle de GILZ dans l'organisme. De plus, on a montré que GILZ, en conditions basales, n'a pas d'effet direct sur la protéine transportant le sodium à travers la membrane des cellules, le canal sodique épithélial ENaC. On a aussi essayé de trouver des protéines qui interagissent directement avec GILZ utilisant une technique appelée du « double-hybride dans la levure », mais aucun candidat n'a émergé. Des études ont montré que, à de hautes concentrations, l'insuline peut aussi diminuer l'excrétion de sodium. A ces concentrations, elle peut activer son récepteur spécifique, mais aussi le récepteur d'une autre hormone, l'Insulin-Like Growth Factor 1 (IGF-1). En plus, l'infusion d'IGF-1 augmente la rétention rénale de sodium et d'eau, et des mutations du gène codant pour l'IGF-1 sont liées aux différents niveaux de pression sanguine. On a utilisé une nouvelle lignée cellulaire de rein développée dans notre laboratoire, appelée mCCDc11, pour analyser l'importance relative des deux hormones dans l'induction du transport de sodium. On a montré que les deux hormones induisent une augmentation significative du transport de sodium par l'activation de récepteurs à l'IGF-1 et non du récepteur à l'insuline. On a montré qu'à l'intérieur de la cellule leur activation induit une augmentation du transport sodique par le biais du canal ENaC en modifiant la quantité de phosphates fixés sur la protéine Serumand Glucocorticoid-induced Kinase 1 (Sgk1). On a finalement montré que l'IGF-1 et l'aldosterone ont un effet additif sur le transport de sodium en agissant toutes les deux sur Sgk1, qui intègre leurs effets dans le contrôle du transport de sodium dans le rein.

Key locations for soybean genotype assessment in Central Brazil

The objective of this work was to identify key locations for the establishment of soybean (Glycine max) genetic breeding programs, in the Central Region of Brazil. Grain yield data of three maturity groups of soybean genotypes, from regional trials conducted over three years, at 18 locations in Brazilian Cerrado were used. A key location for the early phases of the breeding program was defined as the site that best classifies the winning genotypes in the region. Key locations for the final phases were defined as those sites that best represent each environmental stratum, in relation to the adaptability of the respective winning genotype. This adaptability was estimated by additive main effects and multiplicative interaction (AMMI) model analysis, using the distance between the score of each location in a stratum and the score of the winning genotype, which characterizes such stratum in an AMMI biplot. The locations that best classified the winning genotypes over space and time were Mineiros, Placas and Rio Verde. For the final phases of genotype selection, with data from the three maturity group, the recommended locations were: Buritis, Chapadão do Céu, Iraí, Pamplona, Placas, Planaltina, Rio Verde, Sacramento, Senador Canedo, Uberaba, and Uberlândia.

Interference of genotypes x environments interaction in the genetic control of resistance to Asian rust soybean

The objectives of this work were to identify parents resistant to Asian soybean rust using diallel crosses, obtain information on the genetic control of soybean resistance to the pathogen and verify whether the combining ability estimates interact with the environment (year or time of assessment). The F1 generation was obtained in a greenhouse from crosses between five contrasting parents for the trait resistance to soybean rust, in a complete diallel without reciprocals. Two rust-severity assessments were carried out on individual soybean plants of 25 treatments (parents and F2 and F3 populations) in 2006/2007 and 2007/2008, in an experimental field at Embrapa Soja, Londrina, PR, Brazil. Additive effects predominated in the genetic control of soybean resistance to Asian rust, and the interaction of the segregant populations with the environment, although significant, did not alter the genetic parameter's general combining ability (GCA) and specific combining ability estimates, indicating that estimates obtained in one year and one assessment can be extrapolated to others. BR01-18437 inbred line is resistant to Asian rust and showed high GCA effects. This line should be used as parent if the objective is the resistance to Phakopsora pachyrhizi.

Selection strategies of segregant soybean populations for resistance to Asian rust

The objective of this work was to identify the best selection strategies for the more promising parental combinations to obtain lines with good resistance to soybean Asian rust (Phakopsora pachyrhizi). Two experiments were carried out in the field during the 2006/2007 and 2007/2008 growing seasons, to determine the percentage of infected leaf area of individual plants of five parents and their segregant F2 and F3 populations. The data obtained indicates that additive genetic variance predominates in the control of soybean resistance to Asian rust, and that the year and time of assessment do not significantly influence the estimates of the genetic parameters obtained. The narrow-sense heritability (h²r) ranged from 23.12 to 55.83%, and indicates the possibility of successful selection of resistant individuals in the early generations of the breeding program. All the procedures used to select the most promising populations to generate superior inbred lines for resistance to P. pachyrhizi presented similar results and identified the BR01-18437 x BRS 232 population as the best for inbred line selection.

Interação entre genótipos e ambientes em diferentes tipos de híbridos de milho

O objetivo deste trabalho foi comparar o desempenho produtivo, a adaptabilidade e a estabilidade de híbridos simples, triplos e duplos de milho originados de um mesmo conjunto de linhagens. Foram avaliados 10 híbridos simples, 30 híbridos triplos e 15 híbridos duplos, além de nove híbridos comerciais utilizados como testemunhas. Utilizou-se o delineamento experimental látice triplo 8x8. Os experimentos foram avaliados em 12 ambientes. O caráter avaliado foi a produtividade de espigas corrigida para 13% de umidade. Realizaram-se as análises de variância individuais e conjunta e verificada a presença da interação genótipos x ambientes, procedeu-se à análise de estabilidade por meio da estimativa da ecovalência e do método AMMI (Additive Main Effects and Multiplicative Interaction). A produtividade média de híbridos simples, triplos e duplos, provenientes de um mesmo conjunto de linhagens, não diferiu estatisticamente, e a diferença de produtividade entre os melhores híbridos simples, duplos e triplos foi baixa (cerca de 10%), o que torna a análise de custo e benefício necessária para a escolha de cultivares para plantio comercial. Os híbridos duplos foram os que menos contribuíram para a interação genótipos x ambientes, seguidos pelos híbridos triplos e os simples. A metodologia utilizada permite identificar híbridos estáveis e produtivos em todos os tipos de milho avaliados

The role of cisplatin and NAMI-A plasma-protein interactions in relation to combination therapy

The aim of the study is to evaluate the differences of protein binding of NAMI-A, a new ruthenium drug endowed with selective antimetastatic properties, and of cisplatin and to ascertain the possibility to use two drugs based on heavy metals in combination to treat solid tumour metastases. For this purpose, we have developed a technique that allows the proteins, to which metal drugs bind, to be identified from real protein mixtures. Following incubation with the drugs, the bands containing platinum and/or ruthenium are separated by native PAGE, SDS-PAGE and 2D gel electrophoresis, and identified using laser ablation inductively coupled plasma mass spectrometry. Both drugs interact with essentially the same proteins which, characterised by proteomics, are human serum albumin precursor, macroglobulin alpha 2 and human serotransferrin precursor. The interactions of NAMI-A are largely reversible whereas cisplatin forms stronger interactions that are less reversible. These data correlate well with the MCa mammary carcinoma model on which full doses of NAMI-A combined with cisplatin show additive effects as compared to each treatment taken alone, independently of whether NAMI-A precedes or follows cisplatin. Furthermore, the implication from this study is that the significantly lower toxicity of NAMI-A, compared to cisplatin, could be a consequence of differences in the mode of binding to plasma proteins, involving weaker interactions compared to cisplatin.

Genotype by environment interaction for seed yield per plant in rapeseed using AMMI model

The objective of this study was to assess genotype by environment interaction for seed yield per plant in rapeseed cultivars grown in Northern Serbia by the AMMI (additive main effects and multiplicative interaction) model. The study comprised 19 rapeseed genotypes, analyzed in seven years through field trials arranged in a randomized complete block design, with three replicates. Seed yield per plant of the tested cultivars varied from 1.82 to 19.47 g throughout the seven seasons, with an average of 7.41 g. In the variance analysis, 72.49% of the total yield variation was explained by environment, 7.71% by differences between genotypes, and 19.09% by genotype by environment interaction. On the biplot, cultivars with high yield genetic potential had positive correlation with the seasons with optimal growing conditions, while the cultivars with lower yield potential were correlated to the years with unfavorable conditions. Seed yield per plant is highly influenced by environmental factors, which indicates the adaptability of specific genotypes to specific seasons.

Different methods to assess yield temporal stability in rubber

The objective of this work was to assess, during six years, the temporal stability of natural rubber yield of 25 superior Hevea brasiliensis genotypes, using the Wricke, Eberhart & Russell, Lin & Binns, additive main effect and multiplicative interaction (AMMI) analysis, and harmonic mean of the relative performance of the genetic values (HMRPGV) methods. The IAC 40 and IAC 300 genotypes were identified as stable and high yielding by the Eberhart & Russell, Lin & Binns, HMRPGV, and AMMI Biplot methods. The ranking of the other more stable genotypes identified by these analyses was altered. The observed results in the AMMI Biplot agreed with those observed in the Wricke method for identifying stable, but lower yielding genotypes. The simultaneous use of different methods allows a more accurate indication of stable genotypes. Stability analyses based on different principles show agreement in indicating stable genotypes.

Importance of abiotic stress as a range-limit determinant for European plants: insights from species' responses to climatic gradients

Aim We examined whether species occurrences are primarily limited by physiological tolerance in the abiotically more stressful end of climatic gradients (the asymmetric abiotic stress limitation (AASL) hypothesis) and the geographical predictions of this hypothesis: abiotic stress mainly determines upper-latitudinal and upper-altitudinal species range limits, and the importance of abiotic stress for these range limits increases the further northwards and upwards a species occurs. Location Europe and the Swiss Alps. Methods The AASL hypothesis predicts that species have skewed responses to climatic gradients, with a steep decline towards the more stressful conditions. Based on presence-absence data we examined the shape of plant species responses (measured as probability of occurrence) along three climatic gradients across latitudes in Europe (1577 species) and altitudes in the Swiss Alps (284 species) using Huisman-Olff-Fresco, generalized linear and generalized additive models. Results We found that almost half of the species from Europe and one-third from the Swiss Alps showed responses consistent with the predictions of the AASL hypothesis. Cold temperatures and a short growing season seemed to determine the upper-latitudinal and upper-altitudinal range limits of up to one-third of the species, while drought provided an important constraint at lower-latitudinal range limits for up to one-fifth of the species. We found a biome-dependent influence of abiotic stress and no clear support for abiotic stress as a stronger upper range-limit determinant for species with higher latitudinal and altitudinal distributions. However, the overall influence of climate as a range-limit determinant increased with latitude. Main conclusions Our results support the AASL hypothesis for almost half of the studied species, and suggest that temperature-related stress controls the upper-latitudinal and upper-altitudinal range limits of a large proportion of these species, while other factors including drought stress may be important at the lower range limits.

High capacity audio watermarking using the high frequency band of the wavelet domain

This paper proposes a novel high capacity robust audio watermarking algorithm by using the high frequency band of the wavelet decomposition at which the human auditory system (HAS) is not very sensitive to alteration. The main idea is to divide the high frequency band into frames and, for embedding, to change the wavelet samples depending on the average of relevant frame¿s samples. The experimental results show that the method has a very high capacity (about 11,000 bps), without significant perceptual distortion (ODG in [¿1 ,0] and SNR about 30dB), and provides robustness against common audio signal processing such as additive noise, filtering, echo and MPEG compression (MP3).

Análise AMMI da produtividade de grãos em linhagens de soja selecionadas para resistência à ferrugem asiática

O objetivo deste trabalho foi quantificar os efeitos da interação genótipo x ambiente (GxE) sobre a produtividade de grãos em progênies de soja pré-selecionadas para resistência à ferrugem asiática (Phakopsora pachyrhizi). Doze ensaios de avaliação de progênies (linhagens F6 e F7) foram conduzidos em diferentes ambientes (combinação de locais, anos e tratamentos fungicidas para controle de doenças de final de ciclo, incluindo ou não a ferrugem). A análise "additive main effects and multiplicative interaction" (AMMI) capturou, como padrão da interação GxE, 57% da variação associada aos resíduos de não aditividade, dos quais 44% foram retidos no primeiro componente principal de interação e o restante, no segundo. O primeiro componente associou-se a diferenças entre os anos de avaliação, o que denota imprevisibilidade na predição. O segundo componente, no entanto, associou-se ao manejo diferenciado do cultivo, no que se refere ao controle ou não das doenças. Entre os genótipos de ampla adaptabilidade produtiva, as linhagens USP 02-16.045 e USP 10-10 apresentaram desempenho destacado.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524) of test-day milk yield (TDMY) from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects), whereas the contemporary group, calving age (linear and quadratic effects) and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.