Genomic analysis of feed efficiency traits in beef cattle using random regression models.

Feed efficiency plays a major role in the overall profitability and sustainability of the beef cattle industry, as it is directly related to the reduction of the animal demand for input and methane emissions. Traditionally, the average daily feed intake and weight gain are used to calculate feed efficiency traits. However, feed efficiency traits can be analysed longitudinally using random regression models (RRMs), which allow fitting random genetic and environmental effects over time by considering the covariance pattern between the daily records. Therefore, the objectives of this study were to: (1) propose genomic evaluations for dry matter intake (DMI), body weight gain (BWG), residual feed intake (RFI) and residual weight gain (RWG) data collected during an 84-day feedlot test period via RRMs; (2) compare the goodness-of-fit of RRM using Legendre polynomials (LP) and B-spline functions; (3) evaluate the genetic parameters behaviour for feed efficiency traits and their implication for new selection strategies. The datasets were provided by the EMBRAPA-GENEPLUS beef cattle breeding program and included 2920 records for DMI, 2696 records for BWG and 4675 genotyped animals. Genetic parameters and genomic breeding values (GEBVs) were estimated by RRMs under ssGBLUP for Nellore cattle using orthogonal LPs and B-spline. Models were compared based on the deviance information criterion (DIC). The ranking of the average GEBV of each test week and the overall GEBV average were compared by the percentage of individuals in common and the Spearman correlation coefficient (top 1%, 5%, 10% and 100%). The highest goodness-of-fit was obtained with linear B-Spline function considering heterogeneous residual variance. The heritability estimates across the test period for DMI, BWG, RFI and RWG ranged from 0.06 to 0.21, 0.11 to 0.30, 0.03 to 0.26 and 0.07 to 0.27, respectively. DMI and RFI presented within-trait genetic correlations ranging from low to high magnitude across different performance test-day. In contrast, BWG and RWG presented negative genetic correlations between the first 3 weeks and the other days of performance tests. DMI and RFI presented a high-ranking similarity between the GEBV average of week eight and the overall GEBV average, with Spearman correlations and percentages of individuals selected in common ranging from 0.95 to 1.00 and 93 to 100, respectively. Week 11 presented the highest Spearman correlations (ranging from 0.94 to 0.98) and percentages of individuals selected in common (ranging from 85 to 94) of BWG and RWG with the average GEBV of the entire period of the test. In conclusion, the RRM using linear B-splines is a feasible alternative for the genomic evaluation of feed efficiency. Heritability estimates of DMI, RFI, BWG and RWG indicate enough additive genetic variance to achieve a moderate response to selection. A new selection strategy can be adopted by reducing the performance test to 56 days for DMI and RFI selection and 77 days for BWG and RWG selection.

Genomic prediction and genetic correlations estimated for milk production and fatty acid traits in Walloon Holstein cattle using random regression models.

The aims of this study were to: (1) estimate genetic correlation for milk production traits (milk, fat and protein yields and fat and protein contents) and fatty acids (FA: C16:0, C18:1 cis-9, LCFA, SFA, and UFA) over days in milk, (2) investigate the performance of genomic predictions using single-step GBLUP (ssGBLUP) based on random regression models (RRM), and (3) identify the optimal scaling and weighting factors to be used in the construction of the H matrix. A total of 302 684 test-day records of 63.875 first lactation Walloon Holstein cows were used. Positive genetic correlations were found between milk yield and fat and protein yield (rg from 0.46 to 0.85) and between fat yield and milk FA (rg from 0.17 to 0.47). On the other hand, negative correlations were estimated between fat and protein contents (rg from -0.22 to -0.59), between milk yield and milk FA (rg from -0.22 to -0.62), and between protein yield and milk FA (rg from -0.11 to -0.19). The selection for high fat content increases milk FA throughout lactation (rg from 0.61 to 0.98). The test-day ssGBLUP approach showed considerably higher prediction reliability than the parent average for all milk production and FA traits, even when no scaling and weighting factors were used in the H matrix. The highest validation reliabilities (r2 from 0.09 to 0.38) and less biased predictions (b1 from 0.76 to 0.92) were obtained using the optimal parameters (i.e., ω = 0.7 and α = 0.6) for the genomic evaluation of milk production traits. For milk FA, the optimal parameters were ω = 0.6 and α = 0.6. However, biased predictions were still observed (b1 from 0.32 to 0.81). The findings suggest that using ssGBLUP based on RRM is feasible for the genomic prediction of daily milk production and FA traits in Walloon Holstein dairy cattle.

Is single-step genomic REML with the algorithm for proven and young more computationally efficient when less generations of data are present?

Efficient computing techniques allow the estimation of variance components for virtually any traditional dataset. When genomic information is available, variance components can be estimated using genomic REML (GREML). If only a portion of the animals have genotypes, single-step GREML (ssGREML) is the method of choice. The genomic relationship matrix (G) used in both cases is dense, limiting computations depending on the number of genotyped animals. The algorithm for proven and young (APY) can be used to create a sparse inverse of G (GAPY~-1) with close to linear memory and computing requirements. In ssGREML, the inverse of the realized relationship matrix (H-1) also includes the inverse of the pedigree relationship matrix, which can be dense with a long pedigree, but sparser with short. The main purpose of this study was to investigate whether costs of ssGREML can be reduced using APY with truncated pedigree and phenotypes. We also investigated the impact of truncation on variance components estimation when different numbers of core animals are used in APY. Simulations included 150K animals from 10 generations, with selection. Phenotypes (h2 = 0.3) were available for all animals in generations 1-9. A total of 30K animals in generations 8 and 9, and 15K validation animals in generation 10 were genotyped for 52,890 SNP. Average information REML and ssGREML with G-1 and GAPY~-1 using 1K, 5K, 9K, and 14K core animals were compared. Variance components are impacted when the core group in APY represents the number of eigenvalues explaining a small fraction of the total variation in G. The most time-consuming operation was the inversion of G, with more than 50% of the total time. Next, numerical factorization consumed nearly 30% of the total computing time. On average, a 7% decrease in the computing time for ordering was observed by removing each generation of data. APY can be successfully applied to create the inverse of the genomic relationship matrix used in ssGREML for estimating variance components. To ensure reliable variance component estimation, it is important to use a core size that corresponds to the number of largest eigenvalues explaining around 98% of total variation in G. When APY is used, pedigrees can be truncated to increase the sparsity of H and slightly reduce computing time for ordering and symbolic factorization, with no impact on the estimates.

The estimation of variance components is computationally expensive under large-scale genetic evaluations due to several inversions of the coefficient matrix. Variance components are used as parameters for estimating breeding values in mixed model equations (MME). However, resulting breeding values are not Best Linear Unbiased Predictions (BLUP) unless the variance components approach the true parameters. The increasing availability of genomic data requires the development of new methods for improving the efficiency of variance component estimations. Therefore, this study aimed to reduce the costs of single-step genomic REML (ssGREML) with the Algorithm for Proven and Young (APY) for estimating variance components with truncated pedigree and phenotypes using simulated data. In addition, we investigated the influence of truncation on variance components and genetic parameter estimates. Under APY, the size of the core group influences the similarity of breeding values and their reliability compared to the full genomic matrix. In this study, we found that to ensure reliable variance component estimation, it is required to consider a core size that corresponds to the number of largest eigenvalues explaining around 98% of the total variation in G to avoid biased parameters. In terms of costs, the use of APY slightly decreased the time for ordering and symbolic factorization with no impact on estimations.

Genetic study of quantitative traits supports the use of Guzerá as dual-purpose cattle.

OBJECTIVE: The aim of this study was to estimate genetic parameters for 305-day cumulative milk yield and components, growth, and reproductive traits in Guzerá cattle. METHODS: The evaluated traits were 305-day first-lactation cumulative yields (kg) of milk (MY305), fat (FY305), protein (PY305), lactose (LY305), and total solids (SY305); age at first calving (AFC) in days; adjusted scrotal perimeter (cm) at the ages of 365 (SP365) and 450 (SP450) days; and adjusted body weight (kg) at the ages of 210 (W210), 365 (W365), and 450 (W450) days. The (co)variance components were estimated using the restricted maximum likelihood method for single-trait, bi-trait and tri-trait analyses. Contemporary groups and additive genetic effects were included in the general mixed model. Maternal genetic and permanent environmental effects were also included for W210. RESULTS: The direct heritability estimates ranged from 0.16 (W210) to 0.32 (MY305). The maternal heritability estimate for W210 was 0.03. Genetic correlation estimates among milk production traits and growth traits ranged from 0.92 to 0.99 and from 0.92 to 0.99, respectively. For milk production and growth traits, the genetic correlations ranged from 0.33 to 0.56. The genetic correlations among AFC and all other traits were negative (-0.43 to -0.27). Scrotal perimeter traits and body weights showed genetic correlations ranging from 0.41 to 0.46, and scrotal perimeter and milk production traits showed genetic correlations ranging from 0.11 to 0.30. The phenotypic correlations were similar in direction (same sign) and lower than the corresponding genetic correlations. CONCLUSION: These results suggest the viability and potential of joint selection for dairy and beef traits in Guzerá cattle, taking into account reproductive traits.

Evaluation of Non-linear Models to Predict Potential Milk Yield of Beef Cows According to Parity Order Under Grazing.

This study aimed to evaluate the effect of parity order on milk yield (MY) and composition over time of grazing beef cows and to evaluate non-linear models to describe the lactation curve. Thirty-six pregnant Nellore cows (12 nulliparous, 2 years; 12 primiparous, 3 years; and 12 multiparous, 4-6 years) were included in the study. With calving day assigned as day 0, milking was performed using a milking machine to estimate MY on days 7, 14, 21, 42, 63, 91, 119, 154, and 203. Dummy variable analyses were applied to estimate its effects on MY, composition (kg and percentage), afternoon/morning, and afternoon/total proportions. Since multiparous cows had higher MY than nulliparous and primiparous cows, two different groups were used for lactation curve analysis: Mult (multiparous) and Null/Prim (nulliparous and primiparous). The MY estimated by the last edition of BR-Corte (Nutrient Requirements of Zebu and Crossbred Cattle) equation was compared with the observed values from this study. Five nonlinear models proposed by Wood (WD), Jenkins & Ferrell (JF), Wilmink (WK), Henriques (HR) and Cobby & Le Du (CL) were evaluated. Models were validated using an independent dataset of multiparous and primiparous cows. The estimates for parameters a, b, and c of the CL equation were compared between groups, and the BR-Corte equation used the model identity methodology. Nulliparous and primiparous cows displayed similar MY (P > 0.05); however, multiparous cows had an average MY that is 0.70 kg/day greater than that of nulliparous and primiparous cows (P < 0.05). Milk protein and total solids were higher for multiparous cows (P < 0.05). Effect of days in milking was found for milk fat, protein, and total solids (P < 0.05). The yield of all milk components was higher for multiparous cows than for nulliparous and primiparous cows. The afternoon/morning and afternoon/total proportions of milk production were not affected by parities and days in milking (P > 0.05), with an average of 0.76 and 0.42, respectively. The BR-Corte equation did not correctly estimate the MY (P < 0.05). The equations of WD, WK, and CL had the best estimate of MY for both Mult and Null/Prim datasets. The equations had a very similar Akaike's information criterion with correction and mean square error of prediction.

Assessment of digestible lysine requirements in lipopolysaccharide-challenged pigs.

To evaluate the effect of an Escherichia coli lipopolysaccharide (LPS) challenge on the digestible lysine (Lys) requirement for growing pigs, a nitrogen (N) balance assay was performed. Seventy-two castrated male pigs (19 ± 1.49 kg body weight [BW]) were allocated in a 2 × 6 factorial design composed of two immune activation states (control and LPS-challenged) and six dietary treatments with N levels of 0.94, 1.69, 2.09, 3.04, 3.23, and 3.97% N, as fed, where Lys was limiting, with six replicates and one pig per unit. The challenge consisted of an initial LPS dose of 30 µg/kg BW via intramuscular (IM) injection and a subsequent dose of 33.6 µg/kg BW after 48 h. The experimental period lasted 11 d and was composed of a 7-d adaptation and a subsequent 4-d sampling period in which N intake (NI), N excretion (NEX), and N deposition (ND) were evaluated. Inflammatory mediators and rectal temperature were assessed during the 4-d collection period. A three-way interaction (N levels × LPS challenge × time, P < 0.05) for IgG was observed. Additionally, two-way interactions (challenge × time, P < 0.05) were verified for IgA, ceruloplasmin, transferrin, haptoglobin, α-1-acid glycoprotein, total protein, and rectal temperature; and (N levels × time, P < 0.05) for transferrin, albumin, haptoglobin, total protein, and rectal temperature. LPS-challenged pigs showed lower (P < 0.05) feed intake. A two-way interaction (N levels × LPS challenge, P < 0.05) was observed for NI, NEX, and ND, with a clear dose-response (P < 0.05). LPS-challenged pigs showed lower NI and ND at 2.09% N and 1.69 to 3.97% N (P < 0.05), respectively, and higher NEX at 3.23% N (P < 0.05). The parameters obtained by a nonlinear model (N maintenance requirement, NMR and theoretical maximum N deposition, NDmaxT) were 152.9 and 197.1 mg/BWkg0.75/d for NMR, and 3,524.7 and 2,077.8 mg/BWkg0.75/d for NDmaxT, for control and LPS-challenged pigs, respectively. The estimated digestible Lys requirements were 1,994.83 and 949.16 mg/BWkg0.75/d for control and LPS-challenged pigs, respectively. The daily digestible Lys intakes required to achieve 0.68 and 0.54 times the NRmaxT value were 18.12 and 8.62 g/d, respectively, and the optimal dietary digestible Lys concentration may change depending on the feed intake levels. Based on the derived model parameters obtained in the N balance trial with lower cost and time, it was possible to differentiate the digestible Lys requirement for swine under challenging conditions.

Investigating pig survival in different production phases using genomic models.

Pig survival is an economically important trait with relevant social welfare implications, thus standing out as an important selection criterion for the current pig farming system. We aimed to estimate (co)variance components for survival in different production phases in a crossbred pig population as well as to investigate the benefit of including genomic information through single-step genomic best linear unbiased prediction (ssGBLUP) on the prediction accuracy of survival traits compared with results from traditional BLUP. Individual survival records on, at most, 64,894 crossbred piglets were evaluated under two multi-trait threshold models. The first model included farrowing, lactation, and combined postweaning survival, whereas the second model included nursery and finishing survival. Direct and maternal breeding values were estimated using BLUP and ssGBLUP methods. Furthermore, prediction accuracy, bias, and dispersion were accessed using the linear regression validation method. Direct heritability estimates for survival in all studied phases were low (from 0.02 to 0.08). Survival in preweaning phases (farrowing and lactation) was controlled by the dam and piglet additive genetic effects, although the maternal side was more important. Postweaning phases (nursery, finishing, and the combination of both) showed the same or higher direct heritabilities compared with preweaning phases. The genetic correlations between survival traits within preweaning and postweaning phases were favorable and strong, but correlations between preweaning and postweaning phases were moderate. The prediction accuracy of survival traits was low, although it increased by including genomic information through ssGBLUP compared with the prediction accuracy from BLUP. Direct and maternal breeding values were similarly accurate with BLUP, but direct breeding values benefited more from genomic information. Overall, a slight increase in bias was observed when genomic information was included, whereas dispersion of breeding values was greatly reduced. Combined postweaning survival presented higher direct heritability than in the preweaning phases and the highest prediction accuracy among all evaluated production phases, therefore standing out as a candidate trait for improving survival. Survival is a complex trait with low heritability; however, important genetic gains can still be obtained, especially under a genomic prediction framework.

Estimation of genetic parameters for body areas in Nile tilapia measured by digital image analysis.

Digital image analysis is a practical, non-invasive, and relatively low-cost tool that may assist in the evaluation of body traits in Nile tilapia, being particularly useful for assessing difficult-to-measure variables, such as body areas. In this study, we aimed to estimate variance components and genetic parameters for body areas of Nile tilapia obtained by digital images. The data set comprised body weight (BW) records of 1,917 pond-reared fish at 366 days of age. Of this total, 656 animals were photographed and subjected to image analysis of trunk area (TA), head area (HA), caudal fin area (CFA) and fillet area (FA). Heritabilities and genetic correlations were estimated through multiple-trait models based on Bayesian inference. Heritability estimates for BW, TA, HA, CFA and FA were 0.25, 0.23, 0.26, 0.21 and 0.25, respectively. Genetic correlations between the traits were high and positive, ranging from 0.70 to 0.98. We highlight the genetic correlation between BW and TA (rG  = 0.98) and FA (rG  = 0.97). In view of the observed results, it can be concluded that trunk and fillet areas obtained by digital image analysis can lead to indirect genetic gains in weight and other body areas. In addition, the areas studied have potential as a selection criterion and may assist in studies on changes in the body shape in Nile tilapia.

Progesterone and estrogen receptor expression by canine cutaneous soft tissue sarcomas / Expressão de receptores para progesterona e estrógeno em sarcomas de tecidos moles cutâneos em cães

Canine soft tissue sarcomas (STS) comprise a heterogeneous group of malignancies that share similar histopathological features, a low to moderate recurrence rate and low metastatic potential. In human medicine, the expression of estrogen receptors (ER) and progesterone receptors (PR) in sarcomas has been studied to search for prognostic factors and new treatment targets. Similar studies have yet to be conducted in veterinary medicine. The objective of this study was therefore to investigate by immunohistochemistry (IHC) the ER and PR expression in a series of 80 cutaneous and subcutaneous sarcomas in dogs with histopathological features of peripheral nerve sheath tumor (PNST) and perivascular wall tumor (PWT). All cases were positive for PR and negative for ER. Tumors of high malignancy grade (grade III) exhibited higher PR expression than low-grade tumors (grade I). Tumors with mitotic activity greater than 9 mitotic figures/10 high power fields also exhibited higher PR expression. In addition, there was a positive correlation between cell proliferation (Ki67) and PR expression. Therefore, it is possible that progesterone plays a greater role than estrogen in the pathogenesis of these tumors. Future studies should explore the potential for selective progesterone receptor modulators as therapeutic agents in canine STS, as well as evaluating PR expression as a predictor of prognosis.(AU)

Sarcomas de tecidos moles (STM) caninos compreendem um grupo heterogêneo de neoplasias malignas, que apresentam alterações histopatológicas similares, baixa a moderada taxa de recorrência e baixo potencial metastático. Em medicina humana, a expressão de receptor para estrógeno (RE) e receptor para progesterona (RP) nos sarcomas tem sido estudada, visando a busca por fatores prognósticos e novos alvos para tratamentos. Na medicina veterinária, ainda não foram realizados estudos similares. O objetivo deste trabalho foi investigar por imuno-histoquímica a expressão de RE e RP em uma série de 80 sarcomas cutâneos e subcutâneos de cães, com características histopatológicas de tumor de bainha de nervo periférico e tumor de parede perivascular. Todos os casos foram positivos para RP e negativos para RE. Tumores de alto grau de malignidade (grau III) exibiram maior expressão deste receptor que os tumores de baixo grau (grau I). Tumores com atividade mitótica maior que 9 figuras mitóticas/10 campos de grande aumento também exibiram maior expressão do RP. Em adição, houve correlação positiva entre o índice de proliferação celular (Ki67) e a expressão de RP. Assim, é possível que a progesterona desempenhe maior papel que o estrógeno na patogênese desses tumores. Futuros trabalhos poderão explorar o potencial dos moduladores seletivos de RP como agente terapêutico em STM caninos, bem como avaliar a expressão de RP como preditiva de prognóstico.(AU)

Applying the Metafounders Approach for Genomic Evaluation in a Multibreed Beef Cattle Population.

Pedigree information is incomplete by nature and commonly not well-established because many of the genetic ties are not known a priori or can be wrong. The genomic era brought new opportunities to assess relationships between individuals. However, when pedigree and genomic information are used simultaneously, which is the case of single-step genomic BLUP (ssGBLUP), defining the genetic base is still a challenge. One alternative to overcome this challenge is to use metafounders, which are pseudo-individuals that describe the genetic relationship between the base population individuals. The purpose of this study was to evaluate the impact of metafounders on the estimation of breeding values for tick resistance under ssGBLUP for a multibreed population composed by Hereford, Braford, and Zebu animals. Three different scenarios were studied: pedigree-based model (BLUP), ssGBLUP, and ssGBLUP with metafounders (ssGBLUPm). In ssGBLUPm, a total of four different metafounders based on breed of origin (i.e., Hereford, Braford, Zebu, and unknown) were included for the animals with missing parents. The relationship coefficient between metafounders was in average 0.54 (ranging from 0.34 to 0.96) suggesting an overlap between ancestor populations. The estimates of metafounder relationships indicate that Hereford and Zebu breeds have a possible common ancestral relationship. Inbreeding coefficients calculated following the metafounder approach had less negative values, suggesting that ancestral populations were large enough and that gametes inherited from the historical population were not identical. Variance components were estimated based on ssGBLUPm, ssGBLUP, and BLUP, but the values from ssGBLUPm were scaled to provide a fair comparison with estimates from the other two models. In general, additive, residual, and phenotypic variance components in the Hereford population were smaller than in Braford across different models. The addition of genomic information increased heritability for Hereford, possibly because of improved genetic relationships. As expected, genomic models had greater predictive ability, with an additional gain for ssGBLUPm over ssGBLUP. The increase in predictive ability was greater for Herefords. Our results show the potential of using metafounders to increase accuracy of GEBV, and therefore, the rate of genetic gain in beef cattle populations with partial levels of missing pedigree information.

Genetic parameters for fertility traits in Nellore bulls.

Nellore is the main cattle breed used in Brazil, being the largest commercial herd in the world. Beyond the importance of male reproductive efficiency for farm profit, the use of reproductive techniques, mainly artificial insemination, turns the evaluation of male reproductive traits even more important. Estimation of genetic parameters increases the knowledge on traits variances and allows envisaging the possibility of the inclusion of new traits as selection criterion. Genetic parameters for fifteen traits that can be classified as testicular biometry or physical and morphological semen traits were estimated for a Nellore bull population ranging from 18 to 36 months. Single-trait and bi-trait animal models were used for (co)variance components estimation. The contemporary group was considered as fixed effect and age at measurement as covariable. Scrotal circumference presented heritability of 0.47 ± 0.12. This value is similar to the heritabilities found for all testicular biometry traits (0.34-0.48). Sperm progressive motility, which has a direct effect on bull fertility, presented low heritability (0.07 ± 0.08). Major and total sperm defects presented moderate to high heritabilities (0.49 ± 0.18 and 0.39 ± 0.15, respectively), indicating that great genetic gain can be obtained through selection against sperm defects. High and positive genetic correlations were observed among testicular biometry traits, which also presented favourable genetic correlations with physical and morphological traits of the semen with magnitude ranging from high to low. Scrotal circumference presented moderate to high and favourable genetic correlations with sperm progressive motility, sperm turbulence, major sperm defects and total sperm defects. Thus, the selection for scrotal circumference results in favourable correlated genetic response for semen quality. The results show that the use of scrotal circumference as reference trait for bull fertility is appropriate, since it presents high heritability and favourable genetic correlation with semen quality.

Nonlinear quantile regression to describe the dry matter accumulation of garlic plants / Regressão quantílica não linear para descrever o acúmulo de matéria seca de alho

ABSTRACT: The objective of this study was to adjust nonlinear quantile regression models for the study of dry matter accumulation in garlic plants over time, and to compare them to models fitted by the ordinary least squares method. The total dry matter of nine garlic accessions belonging to the Vegetable Germplasm Bank of Universidade Federal de Viçosa (BGH/UFV) was measured in four stages (60, 90, 120 and 150 days after planting), and those values were used for the nonlinear regression models fitting. For each accession, there was an adjustment of one model of quantile regression (τ=0.5) and one based on the least squares method. The nonlinear regression model fitted was the Logistic. The Akaike Information Criterion was used to evaluate the goodness of fit of the models. Accessions were grouped using the UPGMA algorithm, with the estimates of the parameters with biological interpretation as variables. The nonlinear quantile regression is efficient for the adjustment of models for dry matter accumulation in garlic plants over time. The estimated parameters are more uniform and robust in the presence of asymmetry in the distribution of the data, heterogeneous variances, and outliers.

RESUMO: Este trabalho teve como objetivo ajustar modelos de regressão quantílica não linear para o estudo do acúmulo de matéria seca total em plantas de alho ao longo do tempo, e compará-los com modelos ajustados pelo método dos mínimos quadrados. A matéria seca total de nove acessos de alho pertencentes ao Banco de Germoplasma de Hortaliças da Universidade Federal de Viçosa (BGH/UFV) foi avaliada em quatro períodos (60, 90, 120 e 150 dias após plantio), e estes valores foram utilizados para o ajuste de modelos de regressão - não linear - logística. Para cada acesso, foram ajustados um modelo de regressão quantílica (τ=0,5) e um modelo pela metodologia dos mínimos quadrados. Para avaliar a qualidade de ajuste dos modelos foi utilizado o Critério de Informação de Akaike. Os acessos foram agrupados pelo algoritmo UPGMA, utilizando as estimativas dos parâmetros com interpretação biológica como variáveis. A regressão quantílica não linear foi eficiente no ajuste de modelos para descrição do acúmulo de matéria seca ao longo do tempo. As estimativas de parâmetros foram mais uniformes e robustas na presença de dados assimétricos, variâncias heterogêneas e de valores discrepantes.

Analysis of the adaptability of black bean cultivars by means of quantile regression / Análise da adaptabilidade de cultivares de feijão preto por meio de regressão quantílica

ABSTRACT: The aim of this study was to use quantile regression (QR) to characterize the effect of the adaptability parameter throughout the distribution of the productivity variable on black bean cultivars launched by different national research institutes (research centers) over the last 50 years. For this purpose, 40 cultivars developed by Brazilian genetic improvement programs between 1959 and 2013 were used. Initially, QR models were adjusted considering three quantiles (τ = 0.2, 0.5 and 0.8). Subsequently, with the confidence intervals, quantile models τ = 0.2 and 0.8 (QR0.2 and QR0.8) showed differences regarding the parameter of adaptability and average productivity. Finally, by grouping the cultivars into one of the two groups defined from QR0.2 and QR0.8, it was reported that the younger cultivars were associated to the quantile τ = 0.8, i.e., those with higher yields and more responsive conditions indicating that genetic improvement over the last 50 years resulted in an increase in both the productivity and the adaptability of cultivars.

RESUMO: Neste estudo objetivou-se utilizar a regressão quantílica (RQ) para caracterizar o efeito do parâmetro de adaptabilidade ao longo de toda a distribuição da variável produtividade em cultivares de feijão preto lançadas por diferentes instituições nacionais de pesquisa nos últimos 50 anos. Para tanto utilizou-se 40 cultivares desenvolvidas pelos programas brasileiros de melhoramento genético entre os anos de 1959 a 2013. Inicialmente foram ajustados modelos de RQ considerando três quantis (τ=0,2, 0,5, 0,8). Posteriormente, com os intervalos de confiança verificou-se que os modelos quantílicos τ=0,2 e 0,8 (RQ0,2 e RQ0,8) apresentaram diferenças quanto ao parâmetro de adaptabilidade e produtividade média. Finalmente, por meio do agrupamento das cultivares em um dos dois grupos definidos a partir de RQ0,2 e RQ0,8, constatou-se que as cultivares mais novas foram associadas ao quantil τ = 0,8, ou seja, aquelas com maiores produtividades e mais responsivas as condições ambientais indicando que o melhoramento ao longo dos últimos 50 anos possibilitou o incremento tanto na produtividade quanto na adaptabilidade das cultivares.

Combined index of genomic prediction methods applied to productivity / Índice combinado de métodos de predição genômica aplicado em características de produtividade em arroz

ABSTRACT: Rice cultivation has great national and global importance, being one of the most produced and consumed cereals in the world and the primary food for more than half of the world's population. Because of its importance as food, developing efficient methods to select and predict genetically superior individuals in reference to plant traits is of extreme importance for breeding programs. The objective of this research was to evaluate and compare the efficiency of the Delta-p, G-BLUP (Genomic Best Linear Unbiased Predictor), BayesCpi, BLASSO (Bayesian Least Absolute Shrinkage and Selection Operator), Delta-p/G-BLUP index, Delta-p/BayesCpi index, and Delta-p/BLASSO index in the estimation of genomic values and the effects of single nucleotide polymorphisms on phenotypic data associated with rice traits. Use of molecular markers allowed high selective efficiency and increased genetic gain per unit time. The Delta-p method uses the concept of change in allelic frequency caused by selection and the theoretical concept of genetic gain. The Index is based on the principle of combined selection, using the information regarding the additive genomic values predicted via G-BLUP, BayesCpi, BLASSO, or Delta-p. These methods were applied and compared for genomic prediction using nine rice traits: flag leaf length, flag leaf width, panicles number per plant, primary panicle branch number, seed length, seed width, amylose content, protein content, and blast resistance. Delta-p/G-BLUP index had higher predictive abilities for the traits studied, except for amylose content trait in which the method with the highest predictive ability was BayesCpi, being approximately 3% greater than that of the Delta-p/G-BLUP index.

RESUMO: A cultura do arroz tem grande importância nacional e mundial por ser um dos cereais mais produzidos e consumidos no mundo, caracterizando-se como o principal alimento de mais da metade da população mundial. Em função de sua importância alimentar, desenvolver métodos eficientes que visam a predição e a seleção de indivíduos geneticamente superiores, quanto a características da planta, é de extrema importância para os programas de melhoramento. Diante disso, o objetivo deste trabalho foi avaliar e comparar a eficiência do método Delta-p, G-BLUP, BayesCpi, BLASSO e o índice Delta-p/G-BLUP, índice Delta-p/BayesCpi e índice Delta-p/BLASSO, na estimação de valores genômicos e dos efeitos de marcadores SNPs (Single Nucleotide Polymorphisms) em dados fenotípicos associados a características de arroz. A utilização de marcadores moleculares permite alta eficiência seletiva e o aumento do ganho genético por unidade de tempo. O método Delta-p utiliza o conceito de mudança na frequência alélica devido à seleção e o conceito teórico de ganho genético. O Índice é baseado no princípio da seleção combinada, utiliza conjuntamente as informações dos valores genômicos aditivos preditos via G-BLUP, BayesCpi ou BLASSO e via Delta-p. Estes métodos foram aplicados e comparados quanto à predição genômica utilizando nove características de arroz (Oryza sativa), sendo elas: comprimento da folha bandeira, largura da folha bandeira; número de panículas por planta; número de ramos da panícula primária; comprimento de semente; largura de semente; teor de amilose; teor de proteína; resistência a bruzone. O índice Delta-p/G-BLUP obteve maiores capacidades preditivas para as características estudadas, exceto para a característica Conteúdo de amilose, em que o método que obteve maior capacidade preditiva foi o BayesCpi, sendo aproximadamente 3% superior ao índice Delta-p/G-BLUP.

Relationship of testicular biometry with semen variables in breeding soundness evaluation of Nellore bulls.

This study aimed to evaluate the correlation between testicular biometry and semen variables, as well as, to relate testicular variables to the probability of selecting Nellore bulls with desirable sperm morphology when conducting breeding soundness evaluations (BSE). A total of 2055 BSEs from 506 bulls comprised the dataset. Biometric variables evaluated were: scrotal circumference, testicular volume, width, length, ratio and eccentricity; and semen variables were sperm motility, major sperm defects, minor sperm defects and normal sperm. Data of testicular biometry were correlated with data for semen variables using the Pearson's correlation assessment. Effects of testicular variables in selecting for sperm morphology of bulls in the BSE were evaluated by logistic regression. Scrotal circumference, testicular volume, length and width were positively correlated to sperm motility (0.18 to 0.19) and normal sperm (0.24 to 0.27) and negatively correlated with values for major defects (-0.24 to -0.27), but for testicular ratio and eccentricity there were coefficients near zero for all semen traits. Testicular ratio and eccentricity were not suitable for predicting the probability of selecting a bull based on semen variables using the BSE, but scrotal circumference, testicular volume, length and width were highly significant (P < 0.0001) with moderate values of area under ROC (Receiver Operating Characteristics) curve (0.608 to 0.620).

Multi-trait multi-environment Bayesian model reveals G x E interaction for nitrogen use efficiency components in tropical maize.

Identifying maize inbred lines that are more efficient in nitrogen (N) use is an important strategy and a necessity in the context of environmental and economic impacts attributed to the excessive N fertilization. N-uptake efficiency (NUpE) and N-utilization efficiency (NUtE) are components of N-use efficiency (NUE). Despite the most maize breeding data have a multi-trait structure, they are often analyzed under a single-trait framework. We aimed to estimate the genetic parameters for NUpE and NUtE in contrasting N levels, in order to identify superior maize inbred lines, and to propose a Bayesian multi-trait multi-environment (MTME) model. Sixty-four tropical maize inbred lines were evaluated in two experiments: at high (HN) and low N (LN) levels. The MTME model was compared to single-trait multi-environment (STME) models. Based on deviance information criteria (DIC), both multi- and single-trait models revealed genotypes x environments (G x E) interaction. In the MTME model, NUpE was found to be weakly heritable with posterior modes of heritability of 0.016 and 0.023 under HN and LN, respectively. NUtE at HN was found to be highly heritable (0.490), whereas under LN condition it was moderately heritable (0.215). We adopted the MTME model, since combined analysis often presents more accurate breeding values than single models. Superior inbred lines for NUpE and NUtE were identified and this information can be used to plan crosses to obtain maize hybrids that have superior nitrogen use efficiency.

Can scrotal circumference-based selection discard bulls with good productive and reproductive potential?

Nonlinear mixed models were used to describe longitudinal scrotal circumference (SC) measurements of Nellore bulls. Models comparisons were based on Akaike's information criterion, Bayesian information criterion, error sum of squares, adjusted R2 and percentage of convergence. Sequentially, the best model was used to compare the SC growth curve in bulls divergently classified according to SC at 18-21 months of age. For this, bulls were classified into five groups: SC < 28cm; 28cm ≤ SC < 30cm, 30cm ≤ SC < 32cm, 32cm ≤ SC < 34cm and SC ≥ 34cm. Michaelis-Menten model showed the best fit according to the mentioned criteria. In this model, ß1 is the asymptotic SC value and ß2 represents the time to half-final growth and may be related to sexual precocity. Parameters of the individual estimated growth curves were used to create a new dataset to evaluate the effect of the classification, farms, and year of birth on ß1 and ß2 parameters. Bulls of the largest SC group presented a larger predicted SC along all analyzed periods; nevertheless, smaller SC group showed predicted SC similar to intermediate SC groups (28cm ≤ SC < 32cm), around 1200 days of age. In this context, bulls classified as improper for reproduction at 18-21 months old can reach a similar condition to those considered as good condition. In terms of classification at 18-21 months, asymptotic SC was similar among groups, farms and years; however, ß2 differed among groups indicating that differences in growth curves are related to sexual precocity. In summary, it seems that selection based on SC at too early ages may lead to discard bulls with suitable reproductive potential.

Quantile regression for genome-wide association study of flowering time-related traits in common bean.

Flowering is an important agronomic trait. Quantile regression (QR) can be used to fit models for all portions of a probability distribution. In Genome-wide association studies (GWAS), QR can estimate SNP (Single Nucleotide Polymorphism) effects on each quantile of interest. The objectives of this study were to estimate genetic parameters and to use QR to identify genomic regions for phenological traits (Days to first flower-DFF; Days for flowering-DTF; Days to end of flowering-DEF) in common bean. A total of 80 genotypes of common beans, with 3 replicates were raised at 4 locations and seasons. Plants were genotyped for 384 SNPs. Traditional single-SNP and 9 QR models, ranging from equally spaced quantiles (τ) 0.1 to 0.9, were used to associate SNPs to phenotype. Heritabilities were moderate high, ranging from 0.32 to 0.58. Genetic and phenotypic correlations were all high, averaging 0.66 and 0.98, respectively. Traditional single-SNP GWAS model was not able to find any SNP-trait association. On the other hand, when using QR methodology considering one extreme quantile (τ = 0.1) we found, respectively 1 and 7, significant SNPs associated for DFF and DTF. Significant SNPs were found on Pv01, Pv02, Pv03, Pv07, Pv10 and Pv11 chromosomes. We investigated potential candidate genes in the region around these significant SNPs. Three genes involved in the flowering pathways were identified, including Phvul.001G214500, Phvul.007G229300 and Phvul.010G142900.1 on Pv01, Pv07 and Pv10, respectively. These results indicate that GWAS-based QR was able to enhance the understanding on genetic architecture of phenological traits (DFF and DTF) in common bean.

Quantile regression of nonlinear models to describe different levels of dry matter accumulation in garlic plants / Regressão quantílica de um modelo não linear para descrição de diferentes níveis de acúmulo de matéria seca em plantas de alho

ABSTRACT: Plant growth analyses are important because they generate information on the demand and necessary care for each development stage of a plant. Nonlinear regression models are appropriate for the description of curves of growth, since they include parameters with practical biological interpretation. However, these models present information in terms of the conditional mean, and they are subject to problems in the adjustment caused by possible outliers or asymmetry in the distribution of the data. Quantile regression can solve these problems, and it allows the estimation of different quantiles, generating more complete and robust results. The objective of this research was to adjust a nonlinear quantile regression model for the study of dry matter accumulation in garlic plants (Allium sativum L.) over time, estimating parameters at three different quantiles and classifying each garlic accession according to its growth rate and asymptotic weight. The nonlinear regression model fitted was a Logistic model, and 30 garlic accessions were evaluated. These 30 accessions were divided based on the model with the closest quantile estimates; 12 accessions were classified as of lesser interest for planting, 6 were classified as intermediate, and 12 were classified as of greater interest for planting.

RESUMO: Análises de crescimento de plantas são importantes, pois geram informações sobre a demanda e os cuidados necessários para cada etapa de seu desenvolvimento. Modelos de regressão não linear são apropriados para descrever curvas de crescimento por apresentarem parâmetros com interpretação prática biológica. Entretanto, estes modelos apresentam informações em termos médios, e estão sujeitos a problemas no ajuste proporcionados por possíveis valores extremos ou assimetria na distribuição dos dados. A regressão quantílica pode contornar estes problemas, e ainda permite estimativas de diferentes quantis, gerando resultados mais completos e robustos. Assim, o objetivo deste trabalho foi ajustar um modelo de regressão quantílica não linear para o estudo do acúmulo de matéria seca em plantas de alho (Allium sativum L.) ao longo do tempo, estimando seus parâmetros em três diferentes quantis e classificando cada acesso de alho de acordo com sua taxa de crescimento e peso assintótico. O modelo de regressão não linear ajustado foi o Logístico, e foram utilizados 30 acessos de alho. Estes foram divididos de acordo com a curva do quantil de estimativas mais próximas, sendo classificados 12 acessos como de baixo interesse para o plantio, 6 de interesse intermediário e 12 como de alto interesse.

Genome prediction accuracy of common bean via Bayesian models / Acurácia de predição genômica em feijoeiro-comum via modelos Bayesianos

ABSTRACT: We aimed to apply genomic information based on SNP (single nucleotide polymorphism) markers for the genetic evaluation of the traits "stay-green" (SG), plant architecture (PA), grain aspect (GA) and grain yield (GY) in common bean through Bayesian models. These models were compared in terms of prediction accuracy and ability for heritability estimation for each one of the mentioned traits. A total of 80 cultivars were genotyped for 377 SNP markers, whose effects were estimated by five different Bayesian models: Bayes A (BA), B (BB), C (BC), LASSO (BL) e Ridge regression (BRR). Although, prediction accuracies calculated by means of cross-validation have been similar within each trait, the BB model stood out for the trait SG, whereas the BRR was indicated for the remaining traits. The heritability estimates for the traits SG, PA, GA and GY were 0.61, 0.28, 0.32 and 0.29, respectively. In summary, the Bayesian methods applied here were effective and ease to be implemented. The used SNP markers can help in the early selection of promising genotypes, since incorporating genomic information increase the prediction accuracy of the estimated genetic merit.

RESUMO: Objetivou-se incorporar informações genômicas de marcadores SNP ("single nucleotide polymorphism") na avaliação genética das características "stay-green" (SG), arquitetura de planta (AP), aspecto de grãos (AG) e produtividade de grãos (PG) em feijoeiro-comum via modelos Bayesianos. Estes modelos foram comparados quanto a acurácia de predição e habilidade de estimação da herdabilidade para cada característica. Utilizaram-se informações de 80 cultivares genotipadas para 377 marcadores SNP, cujos efeitos de substituição alélica foram estimados por meio de cinco diferentes modelos Bayesianos: Bayes A (BA), B (BB), C (BC), LASSO (BL) e regressão "ridge" (BRR). Embora as acurácias de predição calculadas por meio de análise de validação cruzada tenham sido similares dentro de cada característica, o modelo BB se destacou para a característica SG, enquanto o modelo BRR foi indicado para as demais. As herdabilidades estimadas para SG, AP, AG e PG foram, respectivamente, 0,61, 0,28, 0,32 e 0,29. Em resumo, os métodos contemplados mostraram-se efetivos e de fácil implementação. O conjunto de marcadores utilizado pode auxiliar na seleção precoce de genótipos promissores, uma vez que a incorporação de informações genômicas aumenta a acurácia de predição do mérito genético estimado.