Development of a structural growth curve model that considers the causal effect of initial phenotypes

Modeling soybean growth: A mixed model approach

The evaluation of plant and animal growth, separately for genetic and environmental effects, is necessary for genetic understanding and genetic improvement of environmental responses of plants and animals. We propose to extend an existing approach that combines nonlinear mixed-effects model (NLMEM) and the stochastic approximation of the Expectation-Maximization algorithm (SAEM) to analyze genetic and environmental effects on plant growth. These tools are widely used in many fields but very rarely in plant biology. During model formulation, a nonlinear function describes the shape of growth, and random effects describe genetic and environmental effects and their variability. Genetic relationships among the varieties were also integrated into the model using a genetic relationship matrix. The SAEM algorithm was chosen as an efficient alternative to MCMC methods, which are more commonly used in the domain. It was implemented to infer the expected growth patterns in the analyzed population and the expected curves for each variety through a maximum-likelihood and a maximum-a-posteriori approaches, respectively. The obtained estimates can be used to predict the growth curves for each variety. We illustrate the strengths of the proposed approach using simulated data and soybean plant growth data obtained from a soybean cultivation experiment conducted at the Arid Land Research Center, Tottori University. In this experiment, plant height was measured daily using drones, and the growth was monitored for approximately 200 soybean cultivars for which whole-genome sequence data were available. The NLMEM approach improved our understanding of the determinants of soybean growth and can be successfully used for the genomic prediction of growth pattern characteristics.

Development of an index that decreases birth weight, promotes postnatal growth and yet minimizes selection intensity in beef cattle

OBJECTIVE

The main goal of our current study was to improve the growth curve of meat animals by decreasing the birth weight while achieving a finishing weight that is the same as that before selection but at younger age.

METHODS

Random regression model was developed to derive various selection indices to achieve desired gains in body weight at target time points throughout the fattening process. We considered absolute and proportional gains at specific ages (in weeks) and for various stages (i.e., early, middle, late) during the fattening process.

RESULTS

The point gain index was particularly easy to use because breeders can assign a specific age (in weeks) as a time point and model either the actual weight gain desired or a scaled percentage gain in body weight.

CONCLUSION

The point gain index we developed can achieve the desired weight gain at any given postnatal week of the growing process and is an easy-to-use and practical option for improving the growth curve.

Early Growth and Development and Nonlinear Model Fitting Analysis of Ashidan Yak

Understanding animal growth plays an important role in improving animal genetics and breeding. In order to explore the early growth and development law of Ashidan yak, the body weight (BW), wither height (WH), body oblique length (BL) and chest girth (CG) of 260 female Ashidan yaks were measured. These individuals grew under grazing conditions, and growth traits were measured at 6, 12, 18 and 30 months of age. Then the absolute growth and relative growth of Ashidan yak were calculated, and five nonlinear models (Logistic model, Gompertz model, Brody model, von Bertalanffy model and Richards model) were used to fit the growth curve of Ashidan yak. The fitting effect of the model was evaluated according to MSE, AIC and BIC. The results showed that the growth rate of Ashidan yak was the fastest from 12 to 18 months old, and the growth was slow or even stagnant from 6 to 12 months old. The AIC and BIC values of the Richards model were the lowest among the five models, with an AIC value of 4543.98 and a BIC value of 4563.19. The Richards model estimated body weight at 155.642 kg. In summary, the growth rate of female Ashidan yak changes with the seasons, growing faster in warm seasons and slower in cold seasons. Richards model is the best model to describe the growth curve of female Ashidan yak in five nonlinear models.

Invited review: Recursive models in animal breeding: Interpretation, limitations, and extensions

Structural equation models allow causal effects between 2 or more variables to be considered and can postulate unidirectional (recursive models; RM) or bidirectional (simultaneous models) causality between variables. This review evaluated the properties of RM in animal breeding and how to interpret the genetic parameters and the corresponding estimated breeding values. In many cases, RM and mixed multitrait models (MTM) are statistically equivalent, although subject to the assumption of variance-covariance matrices and restrictions imposed for achieving model identification. Inference under RM requires imposing some restrictions on the (co)variance matrix or on the location parameters. The estimates of the variance components and the breeding values can be transformed from RM to MTM, although the biological interpretation differs. In the MTM, the breeding values predict the full influence of the additive genetic effects on the traits and should be used for breeding purposes. In contrast, the RM breeding values express the additive genetic effect while holding the causal traits constant. The differences between the additive genetic effect in RM and MTM can be used to identify the genomic regions that affect the additive genetic variation of traits directly or causally mediated for another trait or traits. Furthermore, we presented some extensions of the RM that are useful for modeling quantitative traits with alternative assumptions. The equivalence of RM and MTM can be used to infer causal effects on sequentially expressed traits by manipulating the residual (co)variance matrix under the MTM. Further, RM can be implemented to analyze causality between traits that might differ among subgroups or within the parametric space of the independent traits. In addition, RM can be expanded to create models that introduce some degree of regularization in the recursive structure that aims to estimate a large number of recursive parameters. Finally, RM can be used in some cases for operational reasons, although there is no causality between traits.

Pre-weaning performance and commercial growth curve in Dorper, Katahdin, and Romanov crossed lambs in a highland zone from central Mexico

The aim was to evaluate the pre-weaning productive performance and growth curve of Dorper*Katahdin (DPr; n = 46), Kathadin*Kathadin (KTn; n = 204) and Romanov*Kathadin (RMv; n = 40) of commercial crossed lambs from central Mexico. We considered 1450 data from 290 crossbred lambs. The variables contemplated in this study were cross (CR), lambing type (LT), sex, birth weight (BW), weaning weight (WW), test days (TD), and daily weight gain (DWG). Correlation analysis and adjustment of growth curve were performed. Differences in CR and sex were found only in BW (p < 0.05). No differences in DWG, WW, and TD (p > 0.05) by CR and sex were found. Single lambing had the highest (p < 0.05) BW, WW, and DWG. Phenotypic correlations differ among crosses. Lambs crossed with DPr presented the highest values in parameters a and b and the lowest in c. The productive behavior of DPr, KTn, and RMv cross with KTn lambs in central Mexico is similar in the pre-weaning period; however, the growth curve and parameters that characterize it suggest that DPr lambs show a tendency to enhance productive behavior in this period.

Genomic Prediction of Green Fraction Dynamics in Soybean Using Unmanned Aerial Vehicles Observations

With the widespread use of high-throughput phenotyping systems, growth process data are expected to become more easily available. By applying genomic prediction to growth data, it will be possible to predict the growth of untested genotypes. Predicting the growth process will be useful for crop breeding, as variability in the growth process has a significant impact on the management of plant cultivation. However, the integration of growth modeling and genomic prediction has yet to be studied in depth. In this study, we implemented new prediction models to propose a novel growth prediction scheme. Phenotype data of 198 soybean germplasm genotypes were acquired for 3 years in experimental fields in Tottori, Japan. The longitudinal changes in the green fractions were measured using UAV remote sensing. Then, a dynamic model was fitted to the green fraction to extract the dynamic characteristics of the green fraction as five parameters. Using the estimated growth parameters, we developed models for genomic prediction of the growth process and tested whether the inclusion of the dynamic model contributed to better prediction of growth. Our proposed models consist of two steps: first, predicting the parameters of the dynamics model with genomic prediction, and then substituting the predicted values for the parameters of the dynamics model. By evaluating the heritability of the growth parameters, the dynamic model was able to effectively extract genetic diversity in the growth characteristics of the green fraction. In addition, the proposed prediction model showed higher prediction accuracy than conventional genomic prediction models, especially when the future growth of the test population is a prediction target given the observed values in the first half of growth as training data. This indicates that our model was able to successfully combine information from the early growth period with phenotypic data from the training population for prediction. This prediction method could be applied to selection at an early growth stage in crop breeding, and could reduce the cost and time of field trials.

Genetic associations between reproductive traits for first calving and growth curve characteristics of Japanese Black cattle

The objective of this study was to estimate genetic parameters for first calving reproductive traits and growth curve characteristics in Japanese Black cattle. The Gompertz growth function was fitted to body weight-age data to obtain the mature weight (MWT) and rate of maturing (ROM) of cows. Data of reproductive traits including the first service conception rate (CR) for heifers, age at the first calving (AFC), and gestation length for the first calving were collected. Records of 3,204 animals were used for analysis. Genetic parameters were estimated using a linear uni- and bivariate animal model. The heritability estimates were moderate (0.29 for ROM) and high (0.57 for MWT) for growth curve parameters and low (0.03-0.11) for reproductive traits. There was a negative genetic correlation between MWT and ROM (-0.26), suggesting that an animal with a faster ROM would show a lower MWT. CR was negatively correlated with MWT (-0.42) but significantly and positively correlated with ROM (0.91). There was a negative genetic correlation between AFC and MWT (-0.49). These results suggest that a heifer with a faster ROM and lower MWT would show a higher CR. Meanwhile, a heifer with a lower MWT would show a higher AFC.