Bivariate Linear Models Research Articles

Bayesian Bivariate Linear Mixed-Effects Models with Skew-Normal/Independent Distributions, with Application to AIDS Clinical Studies

Bivariate correlated (clustered) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed-effected (LME) model with normality assumptions for the random-effects and within-subject errors. However, those analyses might not provide robust inference when the normality assumptions are questionable if the data set particularly exhibits skewness and heavy tails. In this article, we develop a Bayesian approach to bivariate linear mixed-effects (BLME) models replacing the Gaussian assumptions for the random terms with skew-normal/independent (SNI) distributions. The SNI distribution is an attractive class of asymmetric heavy-tailed parametric structure which includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. We assume that the random-effects and the within-subject (random) errors, respectively, follow multivariate SNI and normal/independent (NI) distributions, which provide an appealing robust alternative to the symmetric normal distribution in a BLME model framework. The method is exemplified through an application to an AIDS clinical data set to compare potential models with different distribution specifications, and clinically important findings are reported.

The impact of a cardiovascular health awareness program (CHAP) on reducing blood pressure: a prospective cohort study

BackgroundHypertension is an important and modifiable cardiovascular risk factor that remains under-detected and under-treated, especially in the older individuals. Community-led interventions that integrate primary health care and local resources are promising approaches to improve awareness and management of hypertension and other cardiovascular risk factors. We aimed to evaluate the effect of a community-based Cardiovascular Health Awareness Program (CHAP) on participants’ blood pressure.MethodsThis study followed a cohort of community residents that participated in CHAP across 22 mid-sized Ontario communities over an 18-month period. The participants’ baseline risk factors, including blood pressure, and subsequent measures of blood pressure were recorded. We employed a bivariate linear mixed-effect model to estimate the change of systolic and diastolic blood pressure over time among the participants who attended more than two CHAP sessions.ResultsOf 13,596 participants, 2498 attended more than two CHAP sessions. For those repeated participants (attending more than two sessions) initially identified with high blood pressure, the average reduction of systolic blood pressure was from 142 to 123 mmHg over an 18-month period, a monthly rate ratio of 0.992 (95% CI: 0.991,0.994; p < 0.01). Similarly, the average reduction of diastolic blood pressure was from 78 to 69 mmHg, a monthly rate ratio of 0.993 (95% CI: 0.991,0.994; p < 0.01). The average blood pressure of the participants with normal baseline blood pressure remained controlled and unchanged. We also found that older adult participants who lived alone, were diagnosed with hypertension, reported healthier eating habits, and presented with a higher baseline systolic blood pressure had significantly greater odds of attending more than one session.ConclusionsCHAP was associated with a reduction in systolic and diastolic blood pressure for those participants who attended more than one session. The magnitude of blood pressure reductions was significant clinically and statistically.

Spontaneous theta rhythm and working memory co-variation during child development

The present study examines possible relationships between changes in electroencephalogram (EEG) power and in working memory (WM) due to brain maturation. Scores on the phonological loop, visuospatial sketchpad and executive components of WM, measured by the Working Memory Test Battery for Children (WMTB-C), were correlated with the power spectral density (PSD) values on the spontaneous EEG from 1 to 46Hz. In order to control for non-specific processes of visuomotor abilities, the reaction time (RT) variable was measured with an Oddball task. One hundred and sixty seven subjects (82 males and 85 females) between 6 and 26 years old participated in the study. Three minutes of spontaneous EEG were recorded. The WMTB-C and the Oddball task were also administered. The scores on each WM component increased and the RT in the Oddball decreased with age, while PSD values in the different frequencies decreased with age. Significant negative correlations between each of the components and the PSD were obtained. The maximal negative correlations were obtained in the theta (4–7Hz) range. A bivariate linear model including theta PSD and RT explained most of the WM variance due to age. The results suggest that spontaneous EEG maturation is closely related to WM maturation, particularly in the theta range.

Transformations of summary statistics as input in meta-analysis for linear dose-response models on a logarithmic scale: a methodology developed within EURRECA

BackgroundTo derive micronutrient recommendations in a scientifically sound way, it is important to obtain and analyse all published information on the association between micronutrient intake and biochemical proxies for micronutrient status using a systematic approach. Therefore, it is important to incorporate information from randomized controlled trials as well as observational studies as both of these provide information on the association. However, original research papers present their data in various ways.MethodsThis paper presents a methodology to obtain an estimate of the dose–response curve, assuming a bivariate normal linear model on the logarithmic scale, incorporating a range of transformations of the original reported data.ResultsThe simulation study, conducted to validate the methodology, shows that there is no bias in the transformations. Furthermore, it is shown that when the original studies report the mean and standard deviation or the geometric mean and confidence interval the results are less variable compared to when the median with IQR or range is reported in the original study.ConclusionsThe presented methodology with transformations for various reported data provides a valid way to estimate the dose–response curve for micronutrient intake and status using both randomized controlled trials and observational studies.

Heritability and Genetic Correlations Explained by Common SNPs for Metabolic Syndrome Traits

We used a bivariate (multivariate) linear mixed-effects model to estimate the narrow-sense heritability (h2) and heritability explained by the common SNPs (hg2) for several metabolic syndrome (MetS) traits and the genetic correlation between pairs of traits for the Atherosclerosis Risk in Communities (ARIC) genome-wide association study (GWAS) population. MetS traits included body-mass index (BMI), waist-to-hip ratio (WHR), systolic blood pressure (SBP), fasting glucose (GLU), fasting insulin (INS), fasting trigylcerides (TG), and fasting high-density lipoprotein (HDL). We found the percentage of h2 accounted for by common SNPs to be 58% of h2 for height, 41% for BMI, 46% for WHR, 30% for GLU, 39% for INS, 34% for TG, 25% for HDL, and 80% for SBP. We confirmed prior reports for height and BMI using the ARIC population and independently in the Framingham Heart Study (FHS) population. We demonstrated that the multivariate model supported large genetic correlations between BMI and WHR and between TG and HDL. We also showed that the genetic correlations between the MetS traits are directly proportional to the phenotypic correlations.

Genetic analysis of fertility in the Italian Brown Swiss population using different models and trait definitions

The aim of this study was to estimate genetic parameters for fertility and production traits in the Brown Swiss population reared in the Alps (Bolzano-Bozen province, Italy). Fertility indicators were interval from parturition to first service, interval from first service to conception (iFC), and interval from parturition to conception, either expressed as days and as number of potential 21-d estrus cycles (cPF, cFC, and cPC, respectively); number of inseminations to conception; conception rate at first service; and non-return rate at 56 d post-first service. Production traits were peak milk yield, lactation milk yield, lactation length, average lactation protein percentage, and average lactation fat percentage. Data included 71,556 lactations (parities 1 to 9) from 29,582 cows reared in 1,835 herds. Animals calved from 1999 to 2007 and were progeny of 491 artificial insemination bulls. Gibbs sampling and Metropolis algorithms were implemented to obtain (co)variance components using both univariate and bivariate censored threshold and linear sire models. All of the analyses accounted for parity and year-month of calving as fixed effects, and herd, permanent environmental cow, additive genetic sire, and residual as random effects. Heritability estimates for fertility traits ranged from 0.030 (iFC) to 0.071 (cPC). Strong genetic correlations were estimated between interval from parturition to first service and cPF (0.97), and interval from parturition to conception and cPC (0.96). The estimate of heritability for cFC (0.055) was approximately double compared with iFC (0.030), suggesting that measuring the elapsed time between first service and conception in days or potential cycles is not equivalent; this was also confirmed by the genetic correlation between iFC and cFC, which was strong (0.85), but more distant from unity than the other 2 pairs of fertility traits. Genetic correlations between number of inseminations to conception, conception rate at first service, non-return rate at 56 d post-first service, cPF, cFC, and cPC ranged from 0.07 to 0.82 as absolute value. Fertility was unfavorably correlated with production; estimates ranged from −0.26 (cPC with protein percentage) to 0.76 (cPC with lactation length), confirming the genetic antagonism between reproductive efficiency and milk production. Although heritability for fertility is low, the contemporary inclusion of several reproductive traits in a merit index would help to improve performance of dairy cows.

Estimating genomic breeding values and detecting QTL using univariate and bivariate models

BackgroundGenomic selection is particularly beneficial for difficult or expensive to measure traits. Since multi-trait selection is an important tool to deal with such cases, an important question is what the added value is of multi-trait genomic selection.MethodsThe simulated dataset, including a quantitative and binary trait, was analyzed with four univariate and bivariate linear models to predict breeding values for juvenile animals. Two models estimated variance components with REML using a numerator (A), or SNP based relationship matrix (G). Two SNP based Bayesian models included one (BayesA) or two distributions (BayesC) for estimated SNP effects. The bivariate BayesC model sampled QTL probabilities for each SNP conditional on both traits. Genotypes were permuted 2,000 times against phenotypes and pedigree, to obtain significance thresholds for posterior QTL probabilities. Genotypes were permuted rather than phenotypes, to retain relationships between pedigree and phenotypes, such that polygenic effects could still be estimated.ResultsCorrelations between estimated breeding values (EBV) of different SNP based models, for juvenile animals, were greater than 0.93 (0.87) for the quantitative (binary) trait. Estimated genetic correlation was 0.71 (0.66) for model G (A). Accuracies of breeding values of SNP based models were for both traits highest for BayesC and lowest for G. Accuracies of breeding values of bivariate models were up to 0.08 higher than for univariate models.The bivariate BayesC model detected 14 out of 32 QTL for the quantitative trait, and 8 out of 22 for the binary trait.ConclusionsAccuracy of EBV clearly improved for both traits using bivariate compared to univariate models. BayesC achieved highest accuracies of EBV and was also one of the methods that found most QTL. Permuting genotypes against phenotypes and pedigree in BayesC provided an effective way to derive significance thresholds for posterior QTL probabilities.

Estimation of genetic and phenotypic relationships between age at first calving and productive performance in Iranian Holsteins

Calving records from the Animal Breeding Center of Iran collected from January 1990 to December 2007 and comprising 207,106 first calving events of Holsteins from 2,506 herds were analysed using univariate and bivariate linear sire models to estimate heritabilities and genetic correlations between age at first calving (AFC) and productive performance. Average AFC was 26.48months in this study. The peak in the frequency distribution of AFC clearly exists coinciding with cows calving for the first time at approximately 25months of age. Heritability estimate for AFC was 0.34 which was greater than the corresponding values for productive traits. The heritability estimates were low to medium for productive traits which ranged from 0.17 to 0.26 for cows in their first calvings. Except for fat and protein percentages of milk, phenotypic and genetic correlations between AFC and productive performance traits were low to moderately negative. Range of genetic correlations between productive traits was -0.53 to 0.99. Reduction of age at first calving appeared to have a negative effect on first lactation protein and fat percentages; however, it had positive effects on milk yield, fat yield, protein yield and their mature equivalents. It seems that reducing age at first calving to 24-25months is probably more profitable than reducing age at first calving to an earlier time in Iranian conditions.

Correlation between per se and Testcross Performance in Rye (Secale cereale L.) Introgression Lines Estimated with a Bivariate Mixed Linear Model

ABSTRACTIn hybrid breeding a high correlation between per se performance of parental lines and hybrid performance can help to reduce the efforts for testcross trials. Our objectives were (i) to investigate the correlation between per se and testcross performance of rye (Secale cereale L.) candidate introgression lines (pre‐ILs) for thousand‐kernel weight, test weight, falling number, starch, pentosan, and protein content; and (ii) to investigate the consistency of quantitative trait loci (QTL) determined in pre‐ILs and their testcross progenies. Eighty pre‐ILs carrying donor chromosome segments (DCS) from the Iranian primitive rye Altevogt 14160 in the genetic background of elite line L2053‐N, were evaluated at four locations over 2 yr. Genetic correlations between per se and testcross performance were estimated with a bivariate mixed linear model. Putative QTL regions were detected by comparing the performance of pre‐ILs carrying certain DCS with the performance of the recurrent parent. Genotypic variances and heritabilities were higher for per se than for testcross performance. Genetic correlations between per se and testcross performance were mostly intermediate. Common QTL regions were observed for test weight, starch, pentosan, and protein content. Our results revealed that a superior per se performance of rye pre‐ILs is not indicative for a superior hybrid performance. Consequently, using rye pre‐ILs in hybrid breeding programs requires testcross trials.

Correlates of persistent smoking in bars subject to smokefree workplace policy.

This study’s goal was to characterize physical and social environments of stand-alone bars associated with indoor smoking despite California’s smokefree workplace law. In a random sample of 121 stand-alone bars in San Francisco, trained observers collected data on patrons, staff, neighborhood, indoor settings and smoking behaviors. Using bivariate (chi-square) and hierarchical linear modeling analyses, we identified four correlates of patrons’ indoor smoking: 1) bars serving predominantly Asian or Irish patrons, 2) ashtrays, 3) bartender smoking, and 4) female bartenders. Public health officials charged with enforcement of smokefree bar policies may need to attend to social practices within bars, and heighten perceptions of consistent enforcement of smokefree workplace laws.

Genetic parameters for claw and leg health, foot and leg conformation, and locomotion in Danish Holsteins

The purpose of this study was to estimate the genetic correlations among claw and leg health and potential indicator traits. Claw health was defined as absence of heel horn erosion, interdigital dermatitis, interdigital phlegmon, interdigital hyperplasia, laminitis, and sole ulcer. Leg health was defined as absence of hock infection, swollen hock, and bruising. The potential indicators were locomotion and foot and leg conformation, represented by rear leg side view, rear leg rear view, foot angle, and apparent hock quality and bone structure. The study was conducted using records from 429,877 Danish Holstein cows in first lactation. Binary health traits were divided into 3 subcategories: claw health, leg health, and absence of all claw and leg disorders. Genetic (rg) and phenotypic correlations were estimated using a bivariate linear sire model and REML. Estimated heritabilities were 0.01 for all 3 combined claw and leg health traits (on the observed binary scale), 0.09 for locomotion, 0.14 for rear leg rear view, 0.19 for rear leg side view, 0.13 for foot angle, 0.22 for apparent hock quality, and 0.27 for apparent bone structure. Heritabilities were 0.06 and 0.01 for claw health and leg health, respectively, when transformed to the underlying continuous scale. Claw and leg disorders are an increasing problem for Danish Holsteins, but genetic improvement of claw and leg health is challenging because the traits have low heritabilities. Claw and leg health were separate but correlated traits (rg=0.35). Locomotion and rear leg rear view were useful indicator traits for claw health (rg=0.46 and rg=0.21, respectively), whereas hock quality and bone structure were useful indicators for leg health (rg=0.42 and 0.26, respectively). Claw and leg health should be considered as separate traits in genetic evaluations that also include the useful indicator traits to compensate for low heritability of the health traits.

Linear mixed models for longitudinal shape data with applications to facial modeling

We present a novel application of methods for analysis of high-dimensional longitudinal data to a comparison of facial shape over time between babies with cleft lip and palate and similarly aged controls. A pairwise methodology is used that was introduced in Fieuws and Verbeke (2006) in order to apply a linear mixed-effects model to data of high dimensions, such as describe facial shape. The approach involves fitting bivariate linear mixed-effects models to all the pairwise combinations of responses, where the latter result from the individual coordinate positions, and aggregating the results across repeated parameter estimates (such as the random-effects variance for a particular coordinate). We describe one example using landmarks and another using facial curves from the cleft lip study, the latter using B-splines to provide an efficient parameterization. The results are presented in 2 dimensions, both in the profile and in the frontal views, with bivariate confidence intervals for the mean position of each landmark or curve, allowing objective assessment of significant differences in particular areas of the face between the 2 groups. Model comparison is performed using Wald and pseudolikelihood ratio tests.

Association of Obesity With Prostate Specific Antigen and Prostate Specific Antigen Velocity in Healthy Young Men

We examined whether the body mass index and change of weight are associated with the prostate specific antigen level as well as the rate of prostate specific antigen velocity in healthy young Korean men. We enrolled in this study 8,176 men who were younger than 51 years and in whom prostate specific antigen was evaluated at least 3 times. Bivariate and multivariate general linear models were used to assess the independent contributions of age, body mass index and prostate specific antigen. Mean prostate specific antigen velocity was compared in the men for different prostate specific antigen ranges, ages, body mass indexes and weight changes using ANOVA tests. Linear logistic regression analysis was used to determine the independent variables related to prostate specific antigen velocity greater than 0 ng/ml per year. Initial prostate specific antigen decreased in monotonic fashion according to the body mass index category. In the adjusted model the body mass index was a statistically significant variable. The number of men presenting with prostate specific antigen velocity greater than 0 ng/ml per year was significantly higher in those who were older and lower in those who had a greater weight gain (p <0.05 and <0.001, respectively). On multivariate analysis age more than 40 years and a weight gain of more than 5 kg were independent predictive variables that affected prostate specific antigen velocity more than 0 ng/ml per year. The results of this study show that age and weight changes are associated with substantial differences in prostate specific antigen velocity. Therefore, clinical interpretation of prostate specific antigen velocity may be biased by these factors.

REML Estimation of Genetic Correlations between Sexes on Beef Carcass Traits Using a Procedure of the Average Information Algorithm

In animal breeding and genetics applications, one topic is the evaluation of sexual dimorphism and genetic correlation between sexes. Also, in some cases, variances may be heterogeneous between levels of factors such as breed and herd as well as sex. Researches about these topics need the method for estimating relevant components of (co)variances. The objectives of this study are to derive a computational procedure of the average information algorithm for the restricted maximum likelihood estimation of the relevant (co)variances, and to estimate genetic correlations between sexes on beef carcass traits. In the current computational procedure, a derived expression for the average information matrix is used, whose elements are expressed using the solutions to the mixed model equations in a bivariate mixed linear model with heterogeneous variance and nil covariance of residuals assumed. For the current procedure, replacing the Hessian matrix by the derived average information matrix, a quasi-Newton type procedure is defined for the iterative estimation. Using simulated datasets, computing performance of the current procedure is investigated comparing with the expectation-maximization algorithm, the current procedure is applied to beef carcass traits data to estimate heritability for each sex and genetic correlation between sexes, and then the characteristics of the current procedure is concisely discussed.

Analysis of litter size and days to lambing in the Ripollesa ewe. I. Comparison of models with linear and threshold approaches1

The analysis focused on model fitting of 2 ewe reproductive traits, litter size, and days to lambing (interval between the introduction of the ram into the flock and the subsequent parturition of the ewes). The experimental data set of the Universitat Autònoma of Barcelona flock was used, including 1,598 records of litter size and 1,699 records of days to lambing from 376 Ripollesa ewes between 1986 and 2005. Univariate and bivariate models were considered as beginning points with linear or threshold approximation for litter size. Model fitting was evaluated in terms of goodness-of-fit and predictive ability, using the mean square error and the correlation between phenotypic and predicted records (rho(y,ŷ)) as reference parameters. The bivariate model was preferable for both variables, minimizing mean square error and maximizing rho(y,ŷ). A threshold approximation for litter size was preferable over a linear approximation. Models were also compared with a simulation study, comparing the correlation coefficient between simulated and predicted breeding values (rho(a,â)). The bivariate threshold model was favored, with a rho(y,ŷ) of 0.677 and 0.834 for litter size and days to lambing, respectively. Correlation coefficients between simulated and predicted breeding values in the bivariate linear model were reduced slightly to 0.651 and 0.831, respectively, and they were lowest with linear univariate models (0.642 and 0.802). Although the bivariate models for ewe litter size and days to lambing were more accurate than the univariate models, the threshold approaches showed a greater advantage under the bivariate model. For the purpose of genetic evaluation of litter size in sheep, use of the threshold-linear model seems justified. In the Ripollesa breed, the evaluation of litter size can benefit from recording birth weight.

Genetic Analysis of Number of Mastitis Cases and Number of Services to Conception Using a Censored Threshold Model

The objective of this study was to infer genetic parameters and genetic change for number of clinical mastitis cases (NCM) and number of services to conception (STC) in first-lactation Norwegian Red (NRF) cows. Records on 620,492 daughters of 3,064 NRF sires, with first calving from 1980 through 2004, were analyzed with a bivariate threshold liability model that takes censoring into account. Posterior mean (SD) of heritability of liability was 0.08 (0.004) for NCM and 0.03 (0.002) for STC. The mean (SD) of the posterior distribution of the genetic correlation between the 2 traits was 0.21 (0.04). Posterior means of the correlation between herd-5-yr effects, and between residuals for NCM and STC were 0.17 and 0.05, respectively. To evaluate effects of taking censoring into account, the data were also analyzed with a bivariate ordered threshold model ignoring censoring. The genetic correlation between NCM and STC was lower than in the censored threshold model (0.09 vs. 0.21). Heritability of liability to NCM and STC from this model was also slightly lower, whereas the point estimates of herd-5-yr and residual correlations were 0.15, and −0.01, respectively. These results suggest that genetic (co)variance may be understated in models ignoring censoring. For comparison purposes, the data were analyzed with a bivariate linear sire model and standard REML-BLUP procedures. The correlation (rank correlation) between sire evaluations from the censored threshold model and sire predicted transmitting abilities from the linear model was 0.90 (0.90) for NCM and 0.87 (0.86) for STC. The evolution of average sire posterior means by birth year of daughters was used to assess genetic change, and results indicated genetic reduction (i.e., genetic improvement) of NCM and little or no genetic change for STC in the NRF population.

Genetic Associations Between Clinical Mastitis and Somatic Cell Score in Early First-Lactation Cows

The objectives of this study were to examine genetic associations between clinical mastitis and somatic cell score (SCS) in early first-lactation cows, to estimate genetic correlations between SCS of cows with and without clinical mastitis, and to compare genetic evaluations of sires based on SCS or clinical mastitis. Clinical mastitis records from 15 d before to 30 d after calving and first test-day SCS records (from 6 to 30 d after calving) from 499,878 first-lactation daughters of 2,043 sires were analyzed. Results from a bivariate linear sire model analysis of SCS in cows with and without clinical mastitis suggest that SCS is a heterogeneous trait. Heritability of SCS was 0.03 for mastitic cows and 0.08 for healthy cows, and the genetic correlation between the 2 traits was 0.78. The difference in rank between sire evaluations based on SCS of cows with and without clinical mastitis varied from −994 to 1,125, with mean 0. A bivariate analysis with a threshold-liability model for clinical mastitis and a linear Gaussian model for SCS indicated that heritability of liability to clinical mastitis is at least as large as that of SCS in early lactation. The mean (standard deviation) of the posterior distribution of heritability was 0.085 (0.006) for liability to clinical mastitis and 0.070 (0.003) for SCS. The posterior mean (standard deviation) of the genetic correlation between liability to clinical mastitis and SCS was 0.62 (0.03). A comparison of sire evaluations showed that genetic evaluation based on SCS was not able to identify the best sires for liability to clinical mastitis. The association between sire posterior means for liability to clinical mastitis and sire predicted transmitting ability for SCS was far from perfect.

Predicting Nursing Facility Residents' Quality of Life Using External Indicators

A newly developed brief measure of nursing facility (NF) resident self-reported quality of life (QOL) has been proposed for inclusion in a modified version of the minimum data set (MDS). There is considerable interest in determining whether it is possible to develop indicators of QOL that are more convenient and less expensive than direct, in-person interviews with residents. QOL interview data from 2,829 residents living in 101 NFs using a 14-item version of a longer instrument were merged with data from the MDS and the Online Survey and Certification Automated Record (OSCAR). Bivariate and multivariate hierarchical linear modeling were used to assess the association of QOL with potential resident and facility level indicators. Resident and facility level indicators were associated with self-reported QOL in the expected direction. At the individual resident level, QOL is negatively associated with physical function, visual acuity, continence, being bedfast, depression, conflict in relationships, and positively associated with social engagement. At the facility level, QOL is negatively associated with citations for failing to accommodate resident needs or providing a clean, safe environment. The ratio of activities staff to residents is positively associated with QOL. This study did not find an association between QOL and either use of restraints or nurse staff levels. Approximately 9 percent of the total variance in self-reported QOL can be attributed to differences among facilities; 91 percent can be attributed to differences among residents. Resident level indicators explained about 4 percent of the variance attributable to differences among residents, and facility factors explained 49 percent of the variance attributable to differences among NFs. However, the different variables explained only 10 percent of the variance in self-reported QOL. A brief self-report measure of NF resident QOL is consistently associated with measures that can be constructed from extant data sources. However, the level of prediction possible from these data sources does not justify reliance on external indicators of resident QOL for policy purposes.

Growth rate of growing pigs is weakly correlated genetically with litter size, while the amount of genetic variation for growth rate changes with litter size

We reasoned that if we assessed pigs for litter size and growth rate during the grow-out stage of production (25–100 kg body weight) we would find: 1) an unfavourable genetic correlation between litter size and growth rate; and 2) that the amount of additive genetic variation expressed for growth rate varies with litter size. We tested these premises by assessing 2212 litters from the Yorkshire breed for litter size, while 3038 growing pigs from 550 of these litters were assessed for growth rate during the grow-out stage of production. Genetic correlations were estimated using the additive genetic (co)variances obtained from a bivariate linear animal model fitted to litter size and growth rate. The amount of additive genetic variation expressed for growth rate as a function of litter size was estimated by fitting a univariate linear animal model with random regression on litter size. Our findings did not support the first of our premises as we found that the genetic correlation between litter size and growth rate was favourable (0.28±0.27), albeit not significantly different from zero. However, we were able to support our second premise as we found that the relationship between amount of additive genetic variation for growth rate and litter size was quadratic; the amount of additive genetic variation was highest in small and large litters (h2=0.60 and 0.65), and lowest in intermediate litter sizes (h2=0.29). These findings indicate that: 1) breeding for litter size would not reduce the growth rate of growing pigs; and 2) the amount of genetic variation for growth rate changes with litter size.

Political Microcultures: Linking Civic Life and Democratic Discourse

At the core of democratic citizenship is deliberation: citizens' tendency and capacity for debating issues of common importance. This study considers civic organizations — often found to be political mobilizers — as political microcultures: environments for political discourse that structure participants' understanding of the practice of citizenship. The study consists of 20 focus groups, each composed of members of one of five kinds of civic organizations. The transcripts are analyzed using bivariate and hierarchical linear modeling techniques. The group context in which political discussions take place is found to have a significant impact on the structure and logic of those discussions, even after accounting for individual-level variations in the demographic characteristics and civic experiences of group participants. A significant portion of civic life and its contribution to democratic citizenship is in social environments that vary in the richness of their political discourse. Elements of political microcultures may explain part of the often-observed differences among civic organizations' degree and type of political mobilization.