Estimation of genetic (co)variances of Gompertz growth function parameters in pigs

Connecting mathematical models to genomes: joint estimation of model parameters and genome-wide marker effects on these parameters

MOTIVATION

Parameters of mathematical models used in biology may be genotype-specific and regarded as new traits. Therefore, an accurate estimation of these parameters and the association mapping on the estimated parameters can lead to important findings regarding the genetic architecture of biological processes. In this study, a statistical framework for a joint analysis (JA) of model parameters and genome-wide marker effects on these parameters was proposed and evaluated.

RESULTS

In the simulation analyses based on different types of mathematical models, the JA inferred the model parameters and identified the responsible genomic regions more accurately than the independent analysis (IA). The JA of real plant data provided interesting insights into photosensitivity, which were uncovered by the IA.

AVAILABILITY AND IMPLEMENTATION

The statistical framework is provided by the R package GenomeBasedModel available at https://github.com/Onogi/GenomeBasedModel. All R and C++ scripts used in this study are also available at the site.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Bayesian, Likelihood-Free Modelling of Phenotypic Plasticity and Variability in Individuals and Populations

There is a paradigm shift from the traditional focus on the “average” individual towards the definition and analysis of trait variation within individual life-history and among individuals in populations. This is a result of increasing availability of individual phenotypic data. The shift allows the use of genetic and environment-driven variations to assess robustness to challenge, gain greater understanding of organismal biological processes, or deliver individual-targeted treatments or genetic selection. These consequences apply, in particular, to variation in ontogenetic growth. We propose an approach to parameterise mathematical models of individual traits (e.g., reaction norms, growth curves) that address two challenges: 1) Estimation of individual traits while making minimal assumptions about data distribution and correlation, addressed via Approximate Bayesian Computation (a form of nonparametric inference). We are motivated by the fact that available information on distribution of biological data is often less precise than assumed by conventional likelihood functions. 2) Scaling-up to population phenotype distributions while facilitating unbiased use of individual data; this is addressed via a probabilistic framework where population distributions build on separately-inferred individual distributions and individual-trait interpretability is preserved. The approach is tested against Bayesian likelihood-based inference, by fitting weight and energy intake growth models to animal data and normal- and skewed-distributed simulated data. i) Individual inferences were accurate and robust to changes in data distribution and sample size; in particular, median-based predictions were more robust than maximum- likelihood-based curves. These results suggest that the approach gives reliable inferences using few observations and monitoring resources. ii) At the population level, each individual contributed via a specific data distribution, and population phenotype estimates were not disproportionally influenced by outlier individuals. Indices measuring population phenotype variation can be derived for study comparisons. The approach offers an alternative for estimating trait variability in biological systems that may be reliable for various applications, for example, in genetics, health, and individualised nutrition, while using fewer assumptions and fewer empirical observations. In livestock breeding, the potentially greater accuracy of trait estimation (without specification of multitrait variance-covariance parameters) could lead to improved selection and to more decisive estimates of trait heritability.

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

BACKGROUND

Growth curves have been widely used in genetic analyses to gain insights into the growth characteristics of both animals and plants. However, several questions remain unanswered, including how the initial phenotypes affect growth and what is the duration of any such impact. For beef cattle production in Japan, calves are procured from farms that specialize in reproduction and then moved to other farms where they are fattened to achieve their market/purchase value. However, the causal effect of growth, while calves are on the reproductive farms, on their growth during fattening remains unclear. To investigate this, we developed a model that combines a structural equation with a growth curve model. The causal effect was modeled with B-splines, which allows inference of the effect as a curve. We fitted the proposed structural growth curve model to repeated measures of body weight from a Japanese beef cattle population (n = 3831) to estimate the curve of the causal effect of the calves' initial weight on their trajectory of growth when they are on fattening farms.

RESULTS

Maternal and reproduction farm effects explained 26% of the phenotypic variance of initial weight at fattening farms. The structural growth curve model was fitted to remove the effects of these factors in growth curve analysis at fattening farms. The estimated curve of causal effects remained at approximately 0.8 for 200 d after the calves entered the fattening farms, which means that 64% of the phenotypic variance was explained by the initial weight. Then, the effect decreased linearly and disappeared approximately 620 d after entering the fattening farms, which corresponded to an average age of 871.5 d.

CONCLUSIONS

The proposed model is expected to provide more accurate estimates of genetic values for growth patterns because the confounding causal factors such as maternal and reproduction farm effects are removed. Moreover, examination of the inferred curve of the causal effect enabled us to estimate the effect of a calf's initial weight at arbitrary times during growth, which could provide suitable information for decision-making when shifting the time of slaughter, building models for genetic evaluation, and selecting calves for market.

Evaluation of feed efficiency traits for genetic improvement in Japanese Black cattle

We evaluated the genetic relationships (1) among feed efficiency traits with different fattening periods, (2) between feed efficiency traits and growth traits, and (3) between feed efficiency traits and carcass traits, to determine the influence of genetic factors on feed efficiency traits. In total, 4,578 Japanese Black cattle from a progeny testing program were used. Residual feed intake (RFI), residual BW gain (RG), and residual intake and BW gain (RIG) were defined as feed efficiency traits, and were measured for the first half (approximately 9 to 15 months of age), latter half (approximately 15 to 21 months of age), and total period of fattening (approximately 9 to 21 months of age). A single-trait animal model for estimating heritability and a two-trait animal model for estimating genetic and phenotypic correlations were used. The heritability estimates for RFI, RG, and RIG were different in each fattening period, ranging from 0.36 to 0.46, 0.19 to 0.28, and 0.28 to 0.34, respectively, and the heritability estimates for the total fattening period were greater than those for the first and latter halves separately. RIG showed the greatest preferred genetic correlation, with a greater feed conversion ratio than the other feed efficiency traits (ranging from -0.84 to -0.96). RG in the first and latter halves of the fattening period had different genetic correlations with the growth starting point (0.82 and -0.06, respectively) and maturity rate (0.49 and -0.51, respectively) of the Gompertz growth curve parameters, and is strongly dependent on the different fattening periods. Feed efficiency traits in different fattening periods had low genetic correlations with the carcass traits (from -0.05 to 0.19 for RFI; from 0.02 to 0.31 for RG; and from -0.11 to 0.20 for RIG). This study indicated the possibility for genetic improvement through the selection of high-RIG animals to decrease feed intake and increase BW gain without any unfavorable correlated responses affecting mature (asymptotic) weight and carcass grade.