Pub Date : 2022-12-01DOI: 10.1016/j.anopes.2022.100005
M.A. Nilforooshan
Bending is a method for transforming symmetric non-positive-definite matrices to positive-definite (PD) to guarantee the invertibility of the matrix. Most of the bending approaches are based on eigendecomposition and eigenvalue modification of the matrix. Genetic and residual covariance matrices among traits used in multivariate analyses are among those matrices. Due to computational limitations, variance components for many traits are often estimated for multiple subsets of traits. Collating smaller matrices into a larger matrix may result in a non-PD matrix. Although the estimated covariance matrix from a single variance component estimation procedure is PD, the variance component estimation procedure requires a starting PD matrix. Aiming to modify the existing bending methods to improve bending performance, several tests were performed on a sample non-PD covariance matrix. Replacing negative eigenvalues with small positive values in decreasing order did not improve the bending performance (average absolute deviation between the upper triangle elements of the original matrix and the bent matrix) compared to replacing eigenvalues smaller than a small positive value with that small positive value (ε = 1e−4). Bending increases the sum of eigenvalues. Keeping the sum of eigenvalues constant (equal to the trace of the original matrix) did not improve the bending performance. Bending performance deteriorated when large eigenvalues were reduced to keep the sum of eigenvalues constant. In another attempt, besides increasing eigenvalues smaller than ε to ε, the smallest eigenvalue greater than ε was reduced. Reducing that eigenvalue to a certain level improved the bending performance. Therefore, a controlled reduction of the smallest eigenvalue greater than ε while simultaneously monitoring the improvement in bending performance is recommended.
{"title":"Compensating for the increase in the sum of eigenvalues and monitoring the bending performance for conditioning covariance matrices in multi-trait livestock evaluations","authors":"M.A. Nilforooshan","doi":"10.1016/j.anopes.2022.100005","DOIUrl":"10.1016/j.anopes.2022.100005","url":null,"abstract":"<div><p>Bending is a method for transforming symmetric non-positive-definite matrices to positive-definite (<strong>PD</strong>) to guarantee the invertibility of the matrix. Most of the bending approaches are based on eigendecomposition and eigenvalue modification of the matrix. Genetic and residual covariance matrices among traits used in multivariate analyses are among those matrices. Due to computational limitations, variance components for many traits are often estimated for multiple subsets of traits. Collating smaller matrices into a larger matrix may result in a non-PD matrix. Although the estimated covariance matrix from a single variance component estimation procedure is PD, the variance component estimation procedure requires a starting PD matrix. Aiming to modify the existing bending methods to improve bending performance, several tests were performed on a sample non-PD covariance matrix. Replacing negative eigenvalues with small positive values in decreasing order did not improve the bending performance (average absolute deviation between the upper triangle elements of the original matrix and the bent matrix) compared to replacing eigenvalues smaller than a small positive value with that small positive value (<em>ε</em> = 1e−4). Bending increases the sum of eigenvalues. Keeping the sum of eigenvalues constant (equal to the trace of the original matrix) did not improve the bending performance. Bending performance deteriorated when large eigenvalues were reduced to keep the sum of eigenvalues constant. In another attempt, besides increasing eigenvalues smaller than <em>ε</em> to <em>ε</em>, the smallest eigenvalue greater than <em>ε</em> was reduced. Reducing that eigenvalue to a certain level improved the bending performance. Therefore, a controlled reduction of the smallest eigenvalue greater than ε while simultaneously monitoring the improvement in bending performance is recommended.</p></div>","PeriodicalId":100083,"journal":{"name":"Animal - Open Space","volume":"1 1","pages":"Article 100005"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772694022000024/pdfft?md5=b02266b56a32d24aaaf775904142dcf9&pid=1-s2.0-S2772694022000024-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80903604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.1016/j.anopes.2022.100010
A. Boudon , M. Karhapää , H. Siljander-Rasi , E. Cantaloube , L. Brossard , N. Le Floc'h , M.C. Meunier-Salaün
In pig farming, physical constraints and genetic selection for high production are risk factors for the development of leg disorders, such as degraded locomotor activity. Interactions between both factors need to be explored. The study was carried out on two replicates of 80 pure-bred Large White growing-finishing pigs from the 8th generation of two divergent lines selected for low and high residual feed intake (LRFI, HRFI). Each replicate included 40 LRFI pigs and 40 HRFI pigs, housed on partly slatted flooring in a room equipped with a sorter allowing access to electronic self-feeders during two replicates. Ear tags determined the side of the room to which the pigs were oriented after the sorter exit and the distance back to the sorter (short: spontaneous activity, long: forced activity (FA)). Lameness was assessed individually weekly using visual gait scoring. At slaughter (weight of 100 kg), postmortem quantification of osteochondrosis (OC) lesions was performed on both the proximal and distal extremities of the humerus and femur. Low RFI pigs showed a lower feed conversion ratio (P < 0.001). They also showed lower individual numbers of sorter crossings per day and a lower proportion of standing pigs, which confirmed their lower physical activity. Forced activity clearly increased the number of sorter crossings/d/pig (P < 0.001), and the magnitude of the effect of FA was clearly lower in LRFI pigs than in HRFI pigs. The occurrence of gait was low (less than 9% of recorded scores). The proportion of scores classified as stiffness was higher for LRFI pigs than in HRFI pigs (P < 0.0001). The average lameness score was also higher for LRFI pigs and lower with FA (P < 0.05). The pigs of the LRFI line showed higher OC scores on both the proximal humerus and femur (P < 0.001) and lower OC scores on the distal humerus with surface evaluation (P < 0.05). The carcasses of LRFI pigs were heavier with a higher lean meat percentage (P < 0.001). Most OC scores were unaffected by FA. Only the OC scores of the distal femur (slice method) were higher with increased activity in LRFI pigs, whereas they were lower in HRFI pigs (P < 0.05). Seric biomarkers of cartilage synthesis and degradation were higher for pigs from the LRFI line, but no correlation could be observed between individual OC scores and cartilage biomarker contents.
{"title":"Effect of moderate forced physical activity on behaviour, lameness and osteochondrosis in growing pigs from two divergent lines selected for feed efficiency","authors":"A. Boudon , M. Karhapää , H. Siljander-Rasi , E. Cantaloube , L. Brossard , N. Le Floc'h , M.C. Meunier-Salaün","doi":"10.1016/j.anopes.2022.100010","DOIUrl":"10.1016/j.anopes.2022.100010","url":null,"abstract":"<div><p>In pig farming, physical constraints and genetic selection for high production are risk factors for the development of leg disorders, such as degraded locomotor activity. Interactions between both factors need to be explored. The study was carried out on two replicates of 80 pure-bred Large White growing-finishing pigs from the 8th generation of two divergent lines selected for low and high residual feed intake (<strong>LRFI</strong>, <strong>HRFI</strong>). Each replicate included 40 LRFI pigs and 40 HRFI pigs, housed on partly slatted flooring in a room equipped with a sorter allowing access to electronic self-feeders during two replicates. Ear tags determined the side of the room to which the pigs were oriented after the sorter exit and the distance back to the sorter (short: spontaneous activity, long: forced activity (<strong>FA</strong>)). Lameness was assessed individually weekly using visual gait scoring. At slaughter (weight of 100 kg), <em>postmortem</em> quantification of osteochondrosis (<strong>OC</strong>) lesions was performed on both the proximal and distal extremities of the humerus and femur. Low RFI pigs showed a lower feed conversion ratio (<em>P</em> < 0.001). They also showed lower individual numbers of sorter crossings per day and a lower proportion of standing pigs, which confirmed their lower physical activity. Forced activity clearly increased the number of sorter crossings/d/pig (<em>P</em> < 0.001), and the magnitude of the effect of FA was clearly lower in LRFI pigs than in HRFI pigs. The occurrence of gait was low (less than 9% of recorded scores). The proportion of scores classified as stiffness was higher for LRFI pigs than in HRFI pigs (<em>P</em> < 0.0001). The average lameness score was also higher for LRFI pigs and lower with FA (<em>P</em> < 0.05). The pigs of the LRFI line showed higher OC scores on both the proximal humerus and femur (<em>P</em> < 0.001) and lower OC scores on the distal humerus with surface evaluation (<em>P</em> < 0.05). The carcasses of LRFI pigs were heavier with a higher lean meat percentage (<em>P</em> < 0.001). Most OC scores were unaffected by FA. Only the OC scores of the distal femur (slice method) were higher with increased activity in LRFI pigs, whereas they were lower in HRFI pigs (<em>P</em> < 0.05). Seric biomarkers of cartilage synthesis and degradation were higher for pigs from the LRFI line, but no correlation could be observed between individual OC scores and cartilage biomarker contents.</p></div>","PeriodicalId":100083,"journal":{"name":"Animal - Open Space","volume":"1 1","pages":"Article 100010"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772694022000073/pdfft?md5=aa2db87018221de06d918c763e656236&pid=1-s2.0-S2772694022000073-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88695746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.1016/j.anopes.2022.100007
J. van Milgen , F.A. Eugenio , N. Le Floc'h
Changes in the postprandial nutrient concentration in the plasma are the result of the combined effects of intake, digestion, absorption, and metabolism. The concentration typically follows an asymmetrical bell-shaped curve as a function of the time after the meal. Although differences between dietary treatments can be analysed using a pairwise comparison of the observed nutrient concentrations, this provides little insight in the possible underlying biological mechanisms. These mechanisms may be represented in a model that can be used in a regression analysis to summarise the observed data in a limited number of parameters. The objective of this study was to propose equations that can be used in the statistical analysis of postprandial nutrient concentrations. The equations were derived from the compartmental representation of the Erlang function in which the last of a series of compartments was assumed to represent the nutrient concentration in the plasma. The preceding compartments were used to represent the postprandial response provoked by ingestion of the meal. A homeostatic control mechanism was included based on a target nutrient concentration that the animal seeks to maintain. This target concentration may differ between the fasting state and after ingestion of a meal. The models were developed as differential equations, which were integrated analytically providing equations that can be used for data analysis. The fit of the equations was tested using the postprandial histidine concentration of a pig that received a diet that was either balanced or unbalanced in the amino acid supply. The unbalanced diet was also deficient in histidine. The observed data could be summarised in three or four parameters that describe the target histidine concentration after an overnight fast, the possible change in the target concentration due to ingestion of a meal, the area under curve of the postprandial response (i.e., the “metabolic exposure”), and a rate constant describing the dynamics of the response. The biological interpretation of these and derived parameters is discussed, including the potential pitfalls of interpreting nutrient concentrations as nutrient flows. In conclusion, the models developed here are based on biological concepts and allow to summarise time series of nutrient concentrations in a limited number of parameters. The concepts can be modified depending on how the biological mechanisms involved are perceived and on the type of available data.
{"title":"A model to analyse the postprandial nutrient concentration in the plasma of pigs","authors":"J. van Milgen , F.A. Eugenio , N. Le Floc'h","doi":"10.1016/j.anopes.2022.100007","DOIUrl":"10.1016/j.anopes.2022.100007","url":null,"abstract":"<div><p>Changes in the postprandial nutrient concentration in the plasma are the result of the combined effects of intake, digestion, absorption, and metabolism. The concentration typically follows an asymmetrical bell-shaped curve as a function of the time after the meal. Although differences between dietary treatments can be analysed using a pairwise comparison of the observed nutrient concentrations, this provides little insight in the possible underlying biological mechanisms. These mechanisms may be represented in a model that can be used in a regression analysis to summarise the observed data in a limited number of parameters. The objective of this study was to propose equations that can be used in the statistical analysis of postprandial nutrient concentrations. The equations were derived from the compartmental representation of the Erlang function in which the last of a series of compartments was assumed to represent the nutrient concentration in the plasma. The preceding compartments were used to represent the postprandial response provoked by ingestion of the meal. A homeostatic control mechanism was included based on a target nutrient concentration that the animal seeks to maintain. This target concentration may differ between the fasting state and after ingestion of a meal. The models were developed as differential equations, which were integrated analytically providing equations that can be used for data analysis. The fit of the equations was tested using the postprandial histidine concentration of a pig that received a diet that was either balanced or unbalanced in the amino acid supply. The unbalanced diet was also deficient in histidine. The observed data could be summarised in three or four parameters that describe the target histidine concentration after an overnight fast, the possible change in the target concentration due to ingestion of a meal, the area under curve of the postprandial response (i.e., the “metabolic exposure”), and a rate constant describing the dynamics of the response. The biological interpretation of these and derived parameters is discussed, including the potential pitfalls of interpreting nutrient concentrations as nutrient flows. In conclusion, the models developed here are based on biological concepts and allow to summarise time series of nutrient concentrations in a limited number of parameters. The concepts can be modified depending on how the biological mechanisms involved are perceived and on the type of available data.</p></div>","PeriodicalId":100083,"journal":{"name":"Animal - Open Space","volume":"1 1","pages":"Article 100007"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772694022000048/pdfft?md5=dfa94dd1524fcd7da04955a471a30791&pid=1-s2.0-S2772694022000048-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77009642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}