Application of Bayesian causal inference and structural equation model to animal breeding

Optimized breeding goals and management practices for the improvement of target traits requires knowledge regarding any potential functional relationships between them. Fitting a structural equation model (SEM) allows for inferences about the magnitude of causal effects between traits to be made. In recent years, an adaptation of SEM was proposed in the context of quantitative genetics and mixed models. Several studies have since applied the SEM in the context of animal breeding. However, fitting the SEM requires choosing a causal structure with prior biological or temporal knowledge. The inductive causation (IC) algorithm can be used to recover an underlying causal structure from observed associations between traits. The results of the papers, which are introduced in this review, showed that using the IC algorithm to infer a causal structure is a helpful tool for detecting a causal structure without proper prior knowledge or with uncertain relationships between traits. The reports also presented that fitting the SEM could infer the effects of interventions, which are not given by correlations. Hence, information from the SEM provides more insights into and suggestions on breeding strategy than that from a multiple‐trait model, which is the conventional model used for multitrait analysis.     

Alternative animal models with maternal effects and foster dams

Effects of foster dams can be included in genetic evaluations using animal models with maternal effects in several ways. The alternatives discussed involve minor changes in computing strategies from strategies used with reduced animal models that predict breeding values for direct and maternal effects. The easiest alternative is to assign foster dams to groups by breed and time period and add equations for fixed effects of breed-period. Random and, assumed, independent effects of foster dams can be nested in breed-period groups. If foster dams do not repeat, then those effects can be absorbed into equations for other fixed effects, additive direct breeding value and breed-period effects by slightly modifying least squares contributions to coefficients of those equations. A third alternative for foster dams of the same breed is to add breeding values for foster dams for direct and maternal effects to solution vectors for breeding values. Equations are similar to those without foster dams, except that least squares contributions to coefficient matrix and right-hand sides are to equations for maternal breeding values and nongenetic maternal effects of foster dams rather than biological dams. Relationships and covariance between direct and maternal effects contribute mixed-model coefficients to direct and maternal breeding value equations of biological dams. This alternative basically requires only larger solution vectors for direct and maternal breeding values to accommodate foster dams that might not be included. The fourth alternative includes a vector of maternal breeding values for foster dams of each breed of foster dams and would require using rules of Westell to calculate coefficients due to relationships and fixed maternal genetic groups within each breed of foster dam. These alternatives do not require much additional computational effort compared with full or reduced animal model equations when the transformation to predict breeding values is used with Westell's rules to calculate coefficients due to relationships and genetic group effects due to prior genetic selection.     

Absorption of equations for non-parents for an animal model with maternal effects and genetic groups

Rules for forming the mixed-model equations for the reduced animal model with all relationships and including maternal effects have been set out by Quaas and Pollak. They also have shown how to simplify the mixed-model equations when genetic group effects are included in the model with what has become known as the Q-P transformation. Westell has given rules for calculating the coefficients for the Q-P transformed equations that are associated with the inverse of the numerator relationship matrix and genetic group effects. Those rules can be extended to include maternal effects and genetic groups for maternal as well as direct effects. As with the rules of Quaas and Pollak for the equations for the reduced animal model, a similar set of rules can be obtained for the genetic groups model after the Q-P transformation. The rules are derived easily by examining the algebraic results of absorbing the direct and maternal breeding value equations for non-parents into the parent breeding value, group and fixed effects equations. These rules involve Westell's rules and the inverse elements of the genetic (co)variance matrix for direct and maternal additive genetic effects. The rules make calculation of breeding values for parents for models including direct and maternal genetic group effects nearly as easy as for models without genetic group effects. Back solution for direct and maternal breeding values of non-parents similarly is as simple as when genetic group effects are not in the model.     

Variance components and breeding values for growth traits from different statistical models.

Estimates of genetic parameters resulting from various analytical models for birth weight (BWT, n = 4,155), 205-d weight (WWT, n = 3,884), and 365-d weight (YWT, n = 3,476) were compared. Data consisted of records for Line 1 Hereford cattle selected for postweaning growth from 1934 to 1989 at ARS-USDA, Miles City, MT. Twelve models were compared. Model 1 included fixed effects of year, sex, age of dam; covariates for birth day and inbreeding coefficients of animal and of dam; and random animal genetic and residual effects. Model 2 was the same as Model 1 but ignored inbreeding coefficients. Model 3 was the same as Model 1 and included random maternal genetic effects with covariance between direct and maternal genetic effects, and maternal permanent environmental effects. Model 4 was the same as Model 3 but ignored inbreeding. Model 5 was the same as Model 1 but with a random sire effect instead of animal genetic effect. Model 6 was the same as Model 5 but ignored inbreeding. Model 7 was a sire model that considered relationships among males. Model 8 was a sire model, assuming sires to be unrelated, but with dam effects as uncorrelated random effects to account for maternal effects. Model 9 was a sire and dam model but with relationships to account for direct and maternal genetic effects; dams also were included as uncorrelated random effects to account for maternal permanent environmental effects. Model 10 was a sire model with maternal grandsire and dam effects all as uncorrelated random effects. Model 11 was a sire and maternal grandsire model, with dams as uncorrelated random effects but with sires and maternal grandsires assumed to be related using male relationships. Model 12 was the same as Model 11 but with all pedigree relationships from the full animal model for sires and maternal grandsires. Rankings on predictions of breeding values were the same regardless of whether inbreeding coefficients for animal and dam were included in the models. Heritability estimates were similar regardless of whether inbreeding effects were in the model. Models 3 and 9 best fit the data for estimation of variances and covariances for direct, maternal genetic, and permanent environmental effects. Other models resulted in changes in ranking for predicted breeding values and for estimates of direct and maternal heritability. Heritability estimates of direct effects were smallest with sire and sire-maternal grandsire models.     

动物饲料国际贸易、养殖密度与环境氮磷平衡的关系

粮食和饲料的国际贸易促进了许多国家农业生产系统的专业化和集约化。专业化动物养殖越来越多地依赖进口大豆和玉米,虽然提高了动物生产力,但也促使作物和动物生产系统在空间上的分离。本文综述了几十年来全球范围内大豆和玉米的贸易变化,并将其与养殖密度和整个食品系统中营养平衡的变化联系起来。这一变化与不同的营养管理条例的差异和动物饲养密度的空间变化有关。深入解析这些变化有助于理解动物饲料国际贸易、养殖密度与氮磷平衡之间的复杂关系。     

Estimation of direct and correlated responses to selection using univariate animal models.

Analytic results obtained using simple models show that estimates of selection response of univariate experiments using animal models are completely dependent on the heritability used as prior when fixed effects are nested within generations, and both on the prior and on the true heritability parameter when fixed effects overlap across generations. Univariate animal model estimators of correlated changes of a trait not selected directly are usually biased. The absolute value of the estimate of the correlated response is smaller than the true value when the traits are only genetically correlated and larger than the expected value of zero when they are only environmentally correlated. The validity of the results derived from the analysis of simple models is confirmed using computer simulations, which illustrate the magnitude of the bias. It is emphasized that use of univariate animal models to estimate response in breeding programs whose breeding objectives include several correlated traits may lead to erroneous conclusions.     

Estimation of accuracies and expected genetic change from selection for selection indexes that use multiple‐trait predictions of breeding values

Procedures are described for estimating selection index accuracies for individual animals and expected genetic change from selection for the general case where indexes of EBVs predict an aggregate breeding objective of traits that may or may not have been measured. Index accuracies for the breeding objective are shown to take an important general form, being able to be expressed as the product of the accuracy of the index function of true breeding values and the accuracy with which that function predicts the breeding objective. When the accuracies of the individual EBVs of the index are known, prediction error variances (PEVs) and covariances (PECs) for the EBVs within animal are able to be well approximated, and index accuracies and expected genetic change from selection estimated with high accuracy. The procedures are suited to routine use in estimating index accuracies in genetic evaluation, and for providing important information, without additional modelling, on the directions in which a population will move under selection.     

数量遗传学和基因组学与未来的动物育种学

数量遗传学经过近 1 0 0年的发展 ,形成了一整套理论体系 ,其基本原理和方法已经发展成为动物育种学、植物育种学、人类遗传学和进化遗传学等四个相对独立的分支领域 ,然而这些领域之间的信息交流相当薄弱。在基因组学时代 ,随着对数量性状基因型的识别 ,人们通过对经典数量遗传学模型的修改 ,数量遗传学为分析表型信息和基因型信息提供了合理框架 ,数量遗传学将会比过去发挥更大的作用。讨论了一些在数量遗传学的各个分支领域发展起来的研究方法 ,动物育种工作者亟需广泛了解这些方法 ,为利用更加准确和复杂的模型来分析数量性状并指导动物育种创造条件     

Rearing conditions, morbidity and breeding performance in dairy heifers in southwest Sweden

We carried out a longitudinal study of 122 dairy herds in southwest Sweden to investigate relationships of rearing conditions and health with heifer breeding performance and to estimate the incidence of clinical diseases and survival until 1st calving. A total of 3081 animals born in 1998 (47% Swedish Red; 50% Swedish Holstein breed) were followed from birth until calving, culling or death. Information about housing, management, breeds and dates of birth, breeding and calving was obtained from farmers. Diseases were recorded by farmers and veterinarians; antibiotic treatment was used in <25% of all cases.Median time to breeding was 17.5 months, 64% of all heifers bred by AI conceived at 1st breeding, and median time to calving was 27.6 months. Age at 1st breeding (log-transformed), conception at 1st breeding (binary), and age at 1st calving (log-transformed) were analysed with three mixed models, accounting for clustering by considering random-intercept and random-slope effects at the herd level. Around 40 potential predictors or confounders were recorded and considered for modelling. Time to breeding and calving increase greatly with the time heifers spend grazing, although up to 5 months of grazing before 1st calving appears to be more favourable than no grazing at all. The effect of grazing differs depending on the season of birth. Zero-grazed heifers calve 20% later if exposed to indoor ammonia concentrations >10 ppm after start of breeding. There is considerable variation between herds in breeding performance, except for conception at 1st breeding—limiting the potential for improving conception by herd measures.Observed total disease incidence rate was 14 per 100 animal-years from 7 months of age to estimated conception and 4.7 per 100 animal-years from conception to calving, with great variation between herds. Infectious diseases were predominant, and diarrhoea, respiratory disease and ringworm were the most common diagnoses. Eight hundred and fifty-three heifers left the study before calving, due to herd exits (incidence risk 0.073%), selling off live (0.061%), spontaneous deaths (0.050%) or slaughter (0.092%).     

探索种养结合模式 发展生态循环农业

近年来,南阳市立足当地资源优势,不断探索出肉牛+甜玉米种植,北繁南育+农牧结合,奶牛饲养+苜蓿种植+生态观赏,奶山羊养殖+猕猴桃种植+产业扶贫等种养结合模式,同时不断探索出二季全株青贮+一季大麦三熟种植模式,实现了规模化种植业助力现代化养殖业、养殖业带动种殖业的发展新路子,对提升耕地质量,改善农业农村环境,发展生态循环农业具有重要的现实意义。     

Time to first calving and calving interval in bovine virus diarrhoea virus (BVDV) sero-converted dairy herds in Norway

Dairy herds in M?re and Romsdal County, Norway (regarded as initially free from the bovine virus diarrhoea virus (BVDV) infection) were studied retrospectively from 1992 to 1996. The herd reproductive performance (time to first calving, calving interval, and number of breeding services) was investigated for a potential effect of BVDV sero-conversion. The herd culling pattern--possibly affecting the above measurements--was included for investigation. Two different statistical models were used: the generalised estimating equation (GEE) method and multilevel modelling using Gibbs sampling. Though slightly different estimates resulted, both models agreed on an effect of BVDV in the second year after sero-conversion on the herd average time to first calving by--on an average-- 14-16 days. In subsets of case herds testing positive for BVDV antibodies among young stock, the impact on time to first calving tended to be more pronounced by an additional increase of 18 days. No effect on the number of breeding services for heifers or cows was observed (indicating a need to search for other determinants than reduced conception risk). There appeared to be no effect of BVDV on the herd average calving interval. There was a tendency for a higher risk for reporting animals lost/died in sero-converted herds, which we believe might be related to the occurrence of mucosal disease.     

Economic evaluation for conservation of farm animal genetic resources

The decline in biodiversity of farm animal genetic resources (AnGR) has come to the forefront of concern in the discussion of animal conservation and breeding programmes. To improve decision‐making regarding conservation and breeding programmes, a number of evaluation techniques of farm AnGR are available. This paper presents an overview of the different values associated to AnGR and of the techniques for their measurement being employed in the economic literature. Those include linear programming and farm simulation models, dynamic models estimating the value of research and development and econometric models estimating the demand for breed characteristics. While farm programming and simulation models are fairly well developed, they do have large data requirements. Alternatively, contingent valuation methods are available, in particular when the goal is to capture non‐market values embedded in breeds.     

Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model

We describe an approach to modelling the spatio-temporal spread of foot and mouth disease through feral animal and unfenced livestock populations. We used a susceptible-infected-recovered model, implemented in a cellular automata framework, to assess the spread of FMD across two regions of Queensland, Australia. Following a sensitivity analysis on the infectious states, scenario analyses were conducted using feral pigs only as the susceptible population, and then with the addition of livestock, and initiated in the wet season and in the dry season. The results indicate that, depending on the season the outbreak is initiated, and without the implementation of control measures, an outbreak of Foot and Mouth Disease around Winton could continue unchecked, while an outbreak around Cape York may die out naturally. The approach explicitly incorporates the spatial relationships between the populations through which the disease spreads and provides a framework by which the spread of disease outbreaks can be explored through varying the model parameters. It highlights the emergence and importance of spatio-temporal patterns, something that previous modelling of FMD in feral animal and unfenced livestock populations has lacked.     

Comparison of threshold vs linear and animal vs sire models for predicting direct and maternal genetic effects on calving difficulty in beef cattle

This study compared the accuracy of several models for obtaining genetic evaluations of calving difficulty. The models were univariate threshold animal (TAM), threshold sire-maternal grandsire (TSM), linear animal (LAM), and linear sire-maternal grandsire (LSM) models and bivariate threshold-linear animal (TLAM), threshold-linear sire-maternal grandsire (TLSM), linear-linear animal (LLAM), and linear-linear sire-maternal grandsire (LLSM) models for calving difficulty and birth weight. Data were obtained from the American Gelbvieh Association and included 84,420 first-parity records of both calving difficulty and birth weight. Calving difficulty scores were distributed as 73.4% in the first category (no assistance), 18.7% in the second, 6.3% in the third, and 1.6% in the fourth. Included in the animal models were fixed sex of calf by age of dam subclasses, random herd-year-season effects, and random animal direct and maternal breeding values. Sire-maternal grandsire models were similar to the animal models, with animal and maternal effects replaced by sire and maternal grandsire effects. Models were compared using a data splitting technique based on the correlation of estimated breeding values from two samples, with one-half of the calving difficulty records discarded randomly in the first sample and the remaining calving difficulty records discarded in the second sample. Reported correlations are averages of 10 replicates. The results obtained using animal models confirmed the slight advantage of TAM over LAM (0.69 vs 0.63) and TLAM over LLAM (0.90 vs 0.86). Bivariate analyses greatly improved the accuracy of genetic prediction of direct effects on calving difficulty relative to univariate analyses. Similar ranking of the models was found for maternal effects, but smaller correlations were obtained for bivariate models. For sire-maternal grandsire models, no differences between sire or maternal grandsire correlations were observed for TLSM compared to LLSM, and small differences were observed between TSM and LSM. The threshold model offered advantages over the linear model in animal models but not in sire-maternal grandsire models. For genetic evaluation of calving difficulty in beef cattle, the threshold-linear animal model seems to be the best choice for predicting both direct and maternal effects.     

Survey on housing,management and welfare of dairy cattle in tie-stalls in western Italian Alps

In the Alps, the traditional breeding system for dairy cattle is based on the alternation between a free-ranging period on mountain ranges during the summer, and an indoor period in tie-stalls in the winter. Several welfare issues may arise in tie-stall housing systems. We describe the situation in 47 farms in three villages in western Italy, trying to identify possible relationships among structural and management characteristics, animal health and behaviour traits. A long duration of the grazing period, associated with frequent manure removal during the housing period, are probably key factors for limiting the occurrence of lameness. Teat trauma is more common in narrower stalls. Getting-up behaviour is unnatural in most of the visited farms. Some lack in the farmers’ knowledge of animal behaviour was noted. Some structural and management characteristics are strictly related to geographical constraints. However, circumstances permitting, some expedients may be achieved for improving welfare levels.     

牛MHC(BoLA)基因的研究进展

牛MHC(BoLA)不仅与移植排斥反应和免疫反应有关,而且还与一些经济性状有关.该文简述了BoLA的分布、结构、功能和基本特征,并且介绍了BoLA基因与主要经济性状如生产性能和疾病的关系,并对其作为动物育种遗传标记的应用前景进行了展望.认为MHC作为遗传标记,通过标记辅助选择进行抗病育种可以培育出高产、抗病力强的家畜品种.     

Repeated-measure animal models to estimate genetic components of mature weight,hip height,and body condition score

Information on mature weight, hip height, and body condition score from Angus cows was analyzed to estimate variance components and compare prediction models. Observations from repeated measures were analyzed with animal models with or without condition score as a covariate and with or without an effect for permanent environment. Heritability (repeatability) estimates for mature weight, hip height, and condition score from Method R procedures were 0.40 (0.77), 0.62 (0.81), and 0.11 (0.38), respectively, from animal models containing a permanent environmental effect but without a covariate for condition score. Heritability estimates from animal models without a permanent environmental effect were similar to repeatability estimates from animal models with it, suggesting inflated estimates of genetic variance from models not containing a permanent environmental effect. Regressing mature weight on condition score reduced both additive genetic variance and permanent environmental variance, increasing the heritability estimate of mature weight to 0.54 and altering the biological interpretation of the trait. The covariate for condition score had little effect on hip height. Regressions of mature weight and hip height on condition score were 25.9 kg/unit of body condition score and 0.4 cm/unit, respectively. Least-squares means for mature weight and hip height tended to increase until 7 and 5 yr of age, respectively. Condition score tended to increase until 6 yr of age and decrease after 8 yr of age. Correlations between breeding value solutions for the same trait were high whether or not prediction models included a permanent environmental effect or a covariate for condition score, and whether or not the variance components used were derived from models containing a covariate for condition score. Results suggest the importance of including a permanent environmental effect in genetic prediction models for these traits. Whether mature weight should be adjusted for body condition is arguable, depending on availability of condition score predictions and tools for analyzing mature weight and condition score predictions in an environment-specific context.     

畜禽遗传资源的经济价值评估

畜禽遗传资源的生物多样性的减少正在成为动物保护和品种改良研究中最受关注的问题。为了提高动物保护和育种方案的决策制定能力,各国的学者提出了许多相关的经济价值评估方法。本文从经济学角度分析了畜禽遗传资源的经济价值及其范畴,对其相关的评估方法进行了回顾。其中包括线性规划与农场模拟模型、估计研究和发展价值的动态模型以及估计育种性状需求的计量经济学模型等内容。农场规划和模拟模型已经发展得很完善,但它们需要大量的数据信息。目前最可取的方法是假设价值评估方法,当目标为获取品种的非市场经济价值时尤其如此。     

Genomic selection in multi‐environment plant breeding trials using a factor analytic linear mixed model

Genomic selection (GS) is a statistical and breeding methodology designed to improve genetic gain. It has proven to be successful in animal breeding; however, key points of difference have not been fully considered in the transfer of GS from animal to plant breeding. In plant breeding, individuals (varieties) are typically evaluated across a number of locations in multiple years (environments) in formally designed comparative experiments, called multi‐environment trials (METs). The design structure of individual trials can be complex and needs to be modelled appropriately. Another key feature of MET data sets is the presence of variety by environment interaction (VEI), that is the differential response of varieties to a change in environment. In this paper, a single‐step factor analytic linear mixed model is developed for plant breeding MET data sets that incorporates molecular marker data, appropriately accommodates non‐genetic sources of variation within trials and models VEI. A recently developed set of selection tools, which are natural derivatives of factor analytic models, are used to facilitate GS for a motivating data set from an Australian plant breeding company. The power and versatility of these tools is demonstrated for the variety by environment and marker by environment effects.     

Considering relationships and genetic grouping in mixed model sire evaluation: A simulation study

In sire evaluation using the best linear unbiased prediction (BLUP) method a relationship matrix including only the relationships among sires can be used. The aim of the present study was to show properties of this method when models with or without grouping of sires are applied. The examination consisted of Monte-Carlo simulation of special situations occurring in dairy sire evaluation. Up to 20 repetitions were generated for each data set. Sire effects were equal for all repetitions of a particular set, cow and residual effects being sampled afresh. Thus, in addition to the correlation between true and estimated breeding value, the true standard deviation of estimated breeding value could be calculated from the results of repeated sire evaluation.With respect to these parameters, the results show that models which do not contain sire grouping but include relationships were superior to grouping models even when relationships are considered in addition. This superiority increases with decreasing number of daughters per sire.The hypothesis that a model without sire grouping but including a relationship matrix leads to a bias in the estimation of breeding values when dams of bulls are selected, could not be confirmed. On condition that the frequency of sires which are related to other sires is high, a model including a relationship matrix but without grouping can be recommended.