Ground-Based Mobile Measurements to Track Urban Methane Emissions from Natural Gas in 12 Cities across Eight Countries

To mitigate methane emission from urban natural gas distribution systems, it is crucial to understand local leak rates and occurrence rates. To explore urban methane emissions in cities outside the U.S., where significant emissions were found previously, mobile measurements were performed in 12 cities across eight countries. The surveyed cities range from medium size, like Groningen, NL, to large size, like Toronto, CA, and London, UK. Furthermore, this survey spanned across European regions from Barcelona, ES, to Bucharest, RO. The joint analysis of all data allows us to focus on general emission behavior for cities with different infrastructure and environmental conditions. We find that all cities have a spectrum of small, medium, and large methane sources in their domain. The emission rates found follow a heavy-tailed distribution, and the top 10% of emitters account for 60-80% of total emissions, which implies that strategic repair planning could help reduce emissions quickly. Furthermore, we compare our findings with inventory estimates for urban natural gas-related methane emissions from this sector in Europe. While cities with larger reported emissions were found to generally also have larger observed emissions, we find clear discrepancies between observation-based and inventory-based emission estimates for our 12 cities.

A dynamic model to measure retention of solid and liquid digesta fractions in chickens fed diets with differing fibre sources

Dietary fibres impact multiple digestive processes, and insights into the effects of various types of fibre on digesta retention time are required to optimise current feed formulation systems. Therefore, the objective of this study was to apply a dynamic modelling approach to generate estimates for the retention time of solid and liquid digesta in broilers fed different fibre sources. A maize-wheat-soybean meal control diet was compared against three diets in which wheat was partially substituted with oat hulls, rice husks, or sugar beet pulp (3% w/w). Non-starch polysaccharide (NSP) digestibility was evaluated in broilers between 23 and 25 days of age (n = 60 birds/treatment) using titanium dioxide (TiO₂, 0.5 g/kg) as a marker, after feeding the experimental diets for 21 days. Digesta mean retention time (MRT) was measured in another 108 birds at 30 days of age by the administration of an oral pulse dose of chromium sesquioxide (Cr₂O₃) as solid marker and Cobalt-EDTA as liquid marker, and subsequent measurement of marker recovery in compartments of the digestive tract (n = 2 or 3 replicate birds/time point/treatment). Marker recovery models to estimate fractional passage rates for solid and liquid digesta in crop, gizzard, small intestine, and caeca compartments of the gastrointestinal tract were developed to predict MRT of solid and liquid digesta for each dietary treatment. The models were composed of a series of first-order differential equations, representing the variation of marker concentration in a compartment over time. Estimated MRT of solid and liquid digesta in the gizzard varied from 20 min for oat hulls and 34 min for rice husks diets to 14 min for sugar beet pulp and 12 min for control diets. In the caeca, liquid MRT was decreased compared to the control diet (989 min) for the sugar beet pulp diet (516 min), while it was increased for both the oat hulls and rice husks diets (≈1 500 min). Overall, these estimates are greater than those previously reported, suggesting that liquid digesta retention in the caeca previously has been underestimated. Digestibility of total NSP was increased by dietary fibre inclusion, regardless of the fibre type, although degradation of constituent sugars of NSP varied among diets. In conclusion, the inclusion of fibre sources at a low level (3% w/w) in the diet of broiler modulated retention time mainly in the gizzard and caeca, and increased digestibility of NSP.

Uncertain in the face of change: Lack of contingency shift awareness during extinction is associated with higher fear-potentiated startle and PTSD symptoms in children

Intolerance of uncertainty is a transdiagnostic risk factor for fear-related disorders and is associated with higher levels of anxiety in children and adolescents. It is unclear how uncertainty relates to development of psychopathology in children who have experienced trauma in early life. The present study used a fear-potentiated startle paradigm in children to examine associations between uncertainty (assessed as unawareness of a change in reinforcement during fear extinction) and symptoms of anxiety and posttraumatic stress disorder (PTSD), as well as startle potentiation to threat and safety cues. Results showed that unaware children had strong positive associations between trauma exposure and PTSD symptoms, whereas aware children did not. Uncertainty interacted with anxiety in that children who were both unaware and had higher anxiety displayed higher fear-potentiated startle to safety cues and did not show discrimination between threat and safety during fear conditioning. These results suggest that anxious children who persist in associating a threat cue with an aversive event during extinction, after repeated presentations of the no longer reinforced conditioned stimulus, may express psychophysiological phenotypes related to PTSD.

Antimethanogenic effects of nitrate supplementation in cattle: A meta-analysis

Supplementing a diet with nitrate is regarded as an effective and promising methane (CH₄) mitigation strategy by competing with methanogens for available hydrogen through its reduction of ammonia in the rumen. Studies have shown major reductions in CH₄ emissions with nitrate supplementation, but with large variation in response. The objective of this study was to quantitatively investigate the effect of dietary nitrate on enteric CH₄ production and yield and evaluate the variables with high potential to explain the heterogeneity of between-study variability using meta-analytical models. A data set containing 56 treatments from 24 studies was developed to conduct a meta-analysis. Dry matter (DM) intake, nitrate dose (g/kg of DM), animal body weight, roughage proportion of diet, dietary crude protein and neutral detergent fiber content, CH₄ measurement technique, and type of cattle (beef or dairy) were considered as explanatory variables. Average DM intake and CH₄ production for dairy cows (16.2 ± 2.93 kg/d; 311 ± 58.8 g/d) were much higher than for beef cattle (8.1 ± 1.57 kg/d; 146 ± 50.9 g/d). Therefore, a relative mean difference was calculated and used to conduct random-effect and mixed-effect model analysis to eliminate the large variations between types of animal due to intake. The final mixed-effect model for CH₄ production (g of CH₄/d) had 3 explanatory variables and included nitrate dose, type of cattle, and DM intake. The final mixed-effect model for CH₄ yield (g of CH₄/kg of DM intake) had 2 explanatory variables and included nitrate dose and type of cattle. Nitrate effect sizes on CH₄ production (dairy: -20.4 ± 1.89%; beef: -10.1 ± 1.52%) and yield (dairy: -15.5 ± 1.15%; beef: -8.95 ± 1.764%) were significantly different between the 2 types of cattle. When data from slow-release nitrate sources were removed from the analysis, there was no significant difference in type of cattle anymore for CH₄ production and yield. Nitrate dose enhanced the mitigating effect of nitrate on CH₄ production and yield by 0.911 ± 0.1407% and 0.728 ± 0.2034%, respectively, for every 1 g/kg of DM increase from its mean dietary inclusion (16.7 g/kg of DM). An increase of 1 kg of DM/d in DM intake from its mean dietary intake (11.1 kg of DM/d) decreased the effect of nitrate on CH₄ production by 0.691 ± 0.2944%. Overall, this meta-analysis demonstrated that nitrate supplementation reduces CH₄ production and yield in a dose-dependent manner, and that elevated DM intake decreases the effect of nitrate supplementation on CH₄ production. Furthermore, the stronger antimethanogenic effect on CH₄ production and yield in dairy cows than in beef steers could be related to use of slow-release nitrate in beef cattle.

Application of adaptive neuro-fuzzy inference systems to estimate digestible critical amino acid requirements in young broiler chicks

This study aimed to find the digestible lysine (d.Lys), digestible sulfur amino acids (d.SAA), and digestible threonine (d.Thr) requirements to optimize body weight gain (BWG) and feed conversion ratio (FCR) via adaptive neuro-fuzzy inference systems (ANFIS) using either the Genetic algorithm (ANFIS-GA) or Particle Swarm Optimization algorithm (ANFIS-PSO) in Cobb-500 chicks from 1 to 10 d of age. The range of amino acids was 90 to 115% of the recommendations for male Cobb-500 chicks. The estimated dietary d.Lys, d.SAA, and d.Thr requirements by ANFIS-GA and ANFIS-PSO to optimize BWG were the same and were 12.10, 8.98, and 7.89 g/kg, respectively. The optimum BWG predicted by ANFIS-GA and ANFIS-PSO were 270 and 266 g, respectively for the 1 to 10 d period. The estimated dietary requirements of d.Lys, d.SAA, and d.Thr to minimize FCR at 0.995 by ANFIS-GA were 12.10, 8.98, and 7.89 g/kg, respectively. Although the estimated d.Lys and d.SAA requirements by ANFIS-PSO and ANFIS-GA were identical, the predicted d.Thr requirement by ANFIS-PSO was 0.01 g/kg higher than by ANFIS-GA to minimize FCR at 0.963. Comparison of goodness of fit in term of root mean square error revealed that the ANFIS-GA prediction was more accurate than ANFIS-PSO. This study demonstrates that the hybrid methodology of ANFIS-GA is as an effective and accurate approach to modeling and optimizing nutrient requirements.

Modelling cumulative egg production in laying hens and parent stocks of broiler chickens using classical growth functions

1. The objective of the present study is to introduce fresh insight into modelling of egg production by applying classical growth functions to egg production records reported by Aviagen Management Guide to laying hens and the parent stock of broiler chickens. 2. The functions (monomolecular, logistic, Gompertz, Richards and Morgan) were fitted using nonlinear regression procedures of SAS software, and their performance was assessed using goodness-of-fit statistics (coefficient of determination, residual mean squares, Akaike information criterion and Bayesian information criterion). 3. Overall, except for the logistic and Gompertz, the growth functions evaluated gave an acceptable fit to the cumulative egg production curves, with the Morgan equation ranking first followed by the Richards equation. The Morgan and Richards equations provided satisfactory predictions of weekly egg yield at different egg production stages, from early to late production, whereas the least accurate estimates were obtained with the logistic equation. 4. In conclusion, classical growth functions proved feasible alternatives to fit cumulative egg production curves of laying hens and parent stock of broiler chickens, resulting in suitable statistical performance and accurate estimates of production.

Sinusoidal function to describe the growth curve of dairy heifers

The objective of the present study is to introduce a sinusoidal function into dairy research and production by applying it to bodyweight records (from 1 to 24 months) from six dairy cow breeds reported by the Dairy Heifer Evaluation Project of Penn State Extension (USA) from 1991 to 1992. The function was evaluated with regard to its ability to describe the relationship between bodyweight and age in dairy heifers, and then compared with seven standard growth functions, namely monomolecular, logistic, Gompertz, von Bertalanffy, Richards, Schumacher and Morgan. The models were fitted to monthly bodyweight records of dairy heifers using non-linear regression to derive estimates of the parameters of each function. The models were tested for goodness of fit by using adjusted coefficient of determination, root mean square error, Akaike’s information criterion and Bayesian information criterion. Values of adjusted coefficient of determination were generally high for all models, suggesting the generally appropriate fit of the models to the data. The sinusoidal function provided the best fit of the growth curves for Brown Swiss, Guernsey and Milking Shorthorn breeds due to the lowest values of root mean square error, Akaike’s information criterion and Bayesian information criterion. According to the chosen statistical criteria, the Richards function provided the best fit for Ayrshire heifers, and the monomolecular the best for Holstein and Jersey. The least accurate estimates were obtained with the logistic. In conclusion, the sinusoidal function introduced here can be considered as an appropriate alternative to standard growth functions when modelling growth patterns in dairy heifers.

An isotope dilution model for partitioning of phenylalanine and tyrosine uptake by the liver of lactating dairy cows

An isotope dilution model to describe the partitioning of phenylalanine and tyrosine in the bovine liver was developed. The model comprises four intracellular and six extracellular pools and various flows connecting these pools and external blood. Conservation of mass principles were applied to generate the fundamental equations describing the behaviour of the system in the steady state. The model was applied to datasets from multi-catheterised dairy cattle during a constant infusion of [1-¹³C]phenylalanine and [2,3,5,6-²H]tyrosine tracers. Model solutions described the extraction of phenylalanine and tyrosine from the liver via the portal vein and hepatic artery. In addition, the exchange of free phenylalanine and tyrosine between extracellular and intracellular pools was explained and the hydroxylation of phenylalanine to tyrosine was estimated. The model was effective in providing information about the fates of phenylalanine and tyrosine in the liver and could be used as part of a more complex system describing amino acid metabolism in the whole animal.

A sinusoidal function and the Nelder-Mead simplex algorithm applied to growth data from broiler chickens

There has been much recent interest in mathematical developments for the analysis of growth in poultry. In this paper, we present a sinusoidal function to describe the evolution of growth as a function of time based on real life experiments. The function was evaluated with regard to its ability to describe the relationship between body weight and age in broilers and was compared to 4 standard growth functions: Gompertz, logistic, Lopez, and Richards. In order to estimate the model parameters, we adopted a global optimization method based on a direct search method instead of using gradient-based techniques. The results of this study show that both the sinusoidal function and the direct search method precisely describe the growth dynamics of broiler chickens. Fitting the growth functions to different data profiles nearly always led to the same or less maximized log-likelihood values for the sinusoidal equation, which is an indication of its superiority in describing growth data from broiler chickens.

Dietary mannoheptulose does not alter glucose or lipid metabolism in adult Labrador Retrievers

Mannoheptulose (MH), a glycolytic inhibitor, has been preliminarily investigated as a novel functional food ingredient for dogs. This study aimed to determine the effects of dietary MH, delivered as an extract of un-ripened avocados, on fatty acid and glucose kinetics in healthy adult Labrador Retriever dogs (n = 12 dogs). The study was a double-blindcrossover with each dog receiving both dietary treatments, control (CON) and MH (400 mg/kg of diet), in random order. Glucose and glycerol plasma turnover (Ra) and oxidation (Ox) were measured in fasting and in response to repeated meal feeding ("fed") with stable isotope tracers (U-¹³ C-glucose, 1,1,2,3,3-D₅ -glycerol) and indirect calorimetry. Palmitate Ra and Ox were examined during repeated meal feeding only using an oral bolus of U-¹³ C-K₂ -palmitate and indirect calorimetry. MH had no discernible effect on fasting glucose Ra (677, 722 SEM 36 μmol/min, CON, MH) or Ox (107, 109 μmol/min, CON, MH SEM 10 μmol/min) or fed glucose Ra (2913, 3626 SEM 644 μmol/min, CON, MH) or Ox (951, 936 SEM 174 μmol/min, CON, MH). Glycerol Ra, an index of the rate of lipolysis, was not different between dietary treatments (Fast 162, 113 SEM 35 μmol/min CON, MH; Fed 172, 135 SEM 21 μmol/min, CON, MH). Similarly, palmitate oxidation was not impacted by MH feeding (1966, 2276 SEM 79 μmol/min, CON, MH). Together, these findings do not support MH as a novel functional food ingredient at least at the dietary dose tested.

Prediction of portal and hepatic blood flow from intake level data in cattle

Interest is growing in developing integrated postabsorptive metabolism models for dairy cattle. An integral part of linking a multi-organ postabsorptive model is the prediction of nutrient fluxes between organs, and thus blood flow. The purpose of this paper was to use a multivariate meta-analysis approach to model portal blood flow (PORBF) and hepatic venous blood flow (HEPBF) simultaneously, with evaluation of hepatic arterial blood flow (ARTBF; ARTBF=HEPBF - PORBF) and PORBF/HEPBF (%) as calculated values. The database used to develop equations consisted of 296 individual animal observations (lactating and dry dairy cows and beef cattle) and 55 treatments from 17 studies, and a separate evaluation database consisted of 34 treatment means (lactating dairy cows and beef cattle) from 9 studies obtained from the literature. Both databases had information on dry matter intake (DMI), metabolizable energy intake (MEI), body weight, and a basic description of the diet including crude protein intake and forage proportion of the diet (FP; %). Blood flow (L/h or L/kg of BW^0.75/h) and either DMI or MEI (g or MJ/d or g or MJ/kg of BW^0.75/d) were examined with linear and quadratic fits. Equations were developed using cow within experiment and experiment as random effects, and blood flow location as a repeated effect. Upon evaluation with the evaluation database, equations based on DMI typically resulted in lower root mean square prediction errors, expressed as a % of the observed mean (rMSPE%) and higher concordance correlation coefficient (CCC) values than equations based on MEI. Quadratic equation terms were frequently nonsignificant, and the quadratic equations did not outperform their linear counterparts. The best performing blood flow equations were PORBF (L/h)=202 (±45.6) + 83.6 (±3.11) × DMI (kg/d) and HEPBF (L/h)=186 (±45.4) + 103.8 (±3.10) × DMI (kg/d), with rMSPE% values of 17.5 and 16.6 and CCC values of 0.93 and 0.94, respectively. The residuals (predicted - observed) for PORBF/HEPBF were significantly related to the forage % of the diet, and thus equations for PORBF and HEPBF based on forage and concentrate DMI were developed: PORBF (L/h)=210 (±51.0) + 82.9 (±6.43) × forage (kg of DM/d) + 82.9 (±6.04) × concentrate (kg of DM/d), and HEPBF (L/h)=184 (±50.6) + 92.6 (±6.28) × forage (kg of DM/d) + 114.2 (±5.88) × concentrate (kg of DM/d), where rMSPE% values were 17.5 and 17.6 and CCC values were 0.93 and 0.94, respectively. Division of DMI into forage and concentrate fractions improved the joint Bayesian information criterion value for PORBF and HEPBF (Bayesian information criterion=6,512 vs. 7,303), as well as slightly improved the rMSPE and CCC for ARTBF and PORBF/HEPBF. This was despite minimal changes in PORBF and HEPBF predictions. Developed equations predicted blood flow well and can easily be used within a postabsorptive model of nutrient metabolism. Results also suggest different sensitivity of PORBF and HEPBF to the composition of DMI, and accounting for this difference resulted in improved ARTBF predictions.

Utilization of macrominerals and trace elements in pregnant heifers with distinct feed efficiencies

The objective of the study was to evaluate utilization of dietary minerals and trace elements in pregnant heifers with distinct residual feed intakes (RFI). Feed intake, body weight (BW), and body composition traits were recorded in 36 crossbred heifers over a period of 37 wk, starting shortly after weaning at 8.3 (0.10; standard deviation) mo of age with an average BW of 276 (7.8) kg. Both BW and body composition were monitored regularly throughout the study, whereas individual feed intake was assessed during the last 84 d of the trial. Data recorded were used to calculate RFI for each heifer. Heifers were ranked based on RFI and assigned to high (n=14) or low (n=10) RFI groups. After the RFI study, 24 selected heifers [age 18.2 (0.14) mo; 87.5 (4.74) d in gestation; 497 (8.5) kg of BW] were used in an indirect digestibility trial (lignin as internal marker). Heifers were fed a ration containing corn silage, haylage, and a mineral premix in which Ca, P, K, Na, Mg, S, Cu, Fe, Mn, Mo, Se, Zn, and Co were provided in the diet according to National Research Council requirements of pregnant replacement heifers. The digestibility trial lasted 1 wk, during which samples of feces were gathered twice daily, and blood and liver biopsy samples were collected on the last day. We noted no significant differences between low- and high-RFI heifers in dry matter digestibility. Apparent absorption of Cu, Zn, and Mn was increased in heifers with low RFI, and apparent absorption of Co tended to be greater for these animals. Concentrations of macrominerals and trace elements in serum of pregnant heifers were similar for both groups except for Se, which was increased in the serum of low-RFI heifers. Liver concentrations of Cu, Fe, Mn, Mo, Se, and Zn did not differ between low- and high-RFI heifers. In conclusion, whereas improved absorption of some trace elements (Cu, Zn, Mn, and Co) and increased Se serum concentration appear to be associated with superior feed efficiency in pregnant heifers, further studies are needed to investigate the causality of such relationships.

Broiler responses to digestible threonine at different ages: a neural networks approach

Three experiments were conducted with broiler chickens to evaluate the effects of digestible threonine (DThr) and crude protein (CP) on their performance at three different phases of age: 1-14, 15-28 and 29-42 days. The measured traits included the following: average daily gain (ADG), feed intake (FI), feed conversion ratio (FCR), carcass crude protein (CCP), body lipid (BL), feather weight gain (FWG), protein deposited in feather (FCP), carcass plus feather protein (CFCP), carcass Thr deposition (CDThr) and nitrogen excretion (NE). A dilution technique was used to create seven diets (with eight replicates) increasing the DThr content from 1.5 to 10 g/kg of diet for phase 1, 1.3-8.9 g/kg of diet for phase 2, and 1.2-8.2 g/kg of diet for phase 3. Data measured were imported into neural networks (NNs) to: (i) predict the measured traits in response to DThr and CP, (ii) rank the importance of DThr and CP on these traits through sensitivity analysis and (iii) find the optimal levels of DThr and CP that lead to the desired (maximum or minimum) responses. For each trait investigated, 50 different random groups of data were generated using a bootstrapping method. These 50 data groups were then used to develop 50 separate NNs which were subsequently combined to construct the final ensemble NN model. In general, accuracy of the models constructed was acceptable, although models of high (ADG, FCR, CFCP, BL, DThr and NE; 0.64 ≤ R(2)  ≤ 0.99) and low (CCP, FWG and FCP; 0.26 ≤ R(2)  ≤ 0.79) accuracy were obtained. All models developed showed the greatest sensitivity to DThr. This may be explained by the dilution technique diet preparation used in these experiments. Optimization results showed decreases in optimal values of DThr and CP with increasing age for all traits. The highest level of DThr was suggested for minimum BL, followed by minimum FCR, maximum ADG, maximum CFCP, minimum NE and maximum CCP respectively. Results showed that the optimal values of DThr for minimum FCR in phases 1-3 were 8.5, 7.4 and 6.4 g/kg of diet, while these values for maximum ADG were 8.2, 7.2 and 6.4 g/kg of diet respectively.

Some novel growth functions and their application with reference to growth in ostrich

Four novel growth functions, namely, Pareto, extreme value distribution (EVD), Lomolino, and cumulative β-P distribution (CBP), are derived, and their ability to describe ostrich growth curves is evaluated. The functions were compared with standard growth equations, namely, the monomolecular, Michaelis-Menten (MM), Gompertz, Richards, and generalized MM (gMM). For this purpose, 2 separate comparisons were conducted. In the first, all the functions were fitted to 40 individual growth curves (5 males and 35 females) of ostriches using nonlinear regression. In the second, performance of the functions was assessed when data from 71 individuals were composited (570 data points). This comparison was undertaken using nonlinear mixed models and considering 3 approaches: 1) models with no random effect, 2) random effect incorporated as the intercept, and 3) random effect incorporated into the asymptotic weight parameter (Wf). The results from the first comparison showed that the functions generally gave acceptable values of R2 and residual variance. On the basis of the Akaike information criterion (AIC), CBP gave the best fit, whereas the Gompertz and Lomolino equations were the preferred functions on the basis of corrected AIC (AICc). Bias, accuracy factor, the Durbin-Watson statistic, and the number of runs of sign were used to analyze the residuals. CBP gave the best distribution of residuals but also produced more residual autocorrelation (significant Durbin-Watson statistic). The functions were applied to sample data for a more conventional farm species (2 breeds of cattle) to verify the results of the comparison of fit among functions and their applicability across species. In the second comparison, analysis of mixed models showed that incorporation of a random effect into Wf gave the best fit, resulting in smaller AIC and AIC values compared with those in the other 2 approaches. On the basis of AICc, best fit was achieved with CBP, followed by gMM, Lomolino, and Richards functions, respectively. The exponential, MM, Pareto, and EVD equations produced negative values for initial weight (W0) if left unconstrained. The Gompertz equation, in spite of having a fixed inflection point and therefore being less flexible, gave accurate estimates of both W0 and Wf and an acceptable goodness of fit favored by having fewer parameters than the other sigmoidal functions. Nevertheless, all the sigmoidal functions appeared appropriate in describing the growth trajectory of male and female ostriches to a reasonable level of accuracy.

On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

Six classical growth functions (monomolecular, Schumacher, Gompertz, logistic, Richards, and Morgan) were fitted to individual and average (by parity) cumulative milk production curves of Canadian Holstein dairy cows. The data analyzed consisted of approximately 91,000 daily milk yield records corresponding to 122 first, 99 second, and 92 third parity individual lactation curves. The functions were fitted using nonlinear regression procedures, and their performance was assessed using goodness-of-fit statistics (coefficient of determination, residual mean squares, Akaike information criterion, and the correlation and concordance coefficients between observed and adjusted milk yields at several days in milk). Overall, all the growth functions evaluated showed an acceptable fit to the cumulative milk production curves, with the Richards equation ranking first (smallest Akaike information criterion) followed by the Morgan equation. Differences among the functions in their goodness-of-fit were enlarged when fitted to average curves by parity, where the sigmoidal functions with a variable point of inflection (Richards and Morgan) outperformed the other 4 equations. All the functions provided satisfactory predictions of milk yield (calculated from the first derivative of the functions) at different lactation stages, from early to late lactation. The Richards and Morgan equations provided the most accurate estimates of peak yield and total milk production per 305-d lactation, whereas the least accurate estimates were obtained with the logistic equation. In conclusion, classical growth functions (especially sigmoidal functions with a variable point of inflection) proved to be feasible alternatives to fit cumulative milk production curves of dairy cows, resulting in suitable statistical performance and accurate estimates of lactation traits.

Integrated animal and cropping systems in single and multi-objective frameworks for enhancing the livelihood security of farmers and agricultural sustainability in Northern India

Fast degrading and declining land, water availability, biodiversity, environment and other natural resources, together with shrinking farm returns and reduced crop productivity caused by continuous and intensive cultivation of rice-wheat systems, necessitate diversification of farming in Northern India. Integrated farming systems (IFS) involving animals (livestock, fish, etc.) and cropping (cereals, trees, etc.) are recognised as an alternative for preserving ecosystems and enhancing livelihood security. A study was therefore undertaken under Northern Indian conditions to develop IFS models for various sizes of farm and to compare these models with the existing rice-wheat system for sustainability and profitability. The IFS models were developed in single objective (using linear programming) and multi-objective (using compromise programming) frameworks. Multi-objective analysis provides deeper insight into the problem as it caters directly for the multi-faceted needs of the farmers. These parallel methodologies offer a novel approach to modelling IFS to draw different farming scenarios for comparison. The IFS strategies developed show the potential to generate a greater farm income than with existing rice-wheat cropping for all sizes of farm. The study revealed that IFS offer more perspectives for an economically viable and sustainable agriculture for typical farms in Northern India.

Quantifying body water kinetics and fecal and urinary water output from lactating Holstein dairy cows

Reliable estimates of fresh manure water output from dairy cows help to improve storage design, enhance efficiency of land application, quantify the water footprint, and predict nutrient transformations during manure storage. The objective of the study was to construct a mechanistic, dynamic, and deterministic mathematical model to quantify urinary and fecal water outputs (kg/d) from individual lactating dairy cows. The model contained 4 body water pools: reticulorumen (QRR), post-reticulorumen (QPR), extracellular (QEC), and intracellular (QIC). Dry matter (DM) intake, dietary forage, DM, crude protein, acid detergent fiber and ash contents, milk yield, and milk fat and protein contents, days in milk, and body weight were input variables to the model. A set of linear equations was constructed to determine drinking, feed, and saliva water inputs to QRR and fractional water passage from QRR to QPR. Water transfer via the rumen wall was subjected to changes in QEC and total water input to QRR. Post-reticulorumen water passage was adjusted for DM intake. Metabolic water production and respiratory cutaneous water losses were estimated with functions of heat production in the model. Water loss in urine was driven by absorbed N left after being removed via milk. Model parameters were estimated simultaneously using observed fecal and urinary water output data from lactating Holstein cows (n=670). The model was evaluated with data that were not used for model development and optimization (n=377). The observations in both data sets were related to thermoneutral conditions. The model predicted drinking water intake, fecal, urinary, and total fresh manure water output with root mean square prediction errors as a percentage of average values of 18.1, 15.6, 30.6, and 14.6%, respectively. In all cases, >97% of the prediction error was due to random variability of data. The model can also be used to determine saliva production, heat and metabolic water production, respiratory cutaneous water losses, and size of major body water pools in lactating Holstein cows under thermoneutral conditions.

A meta-analysis of the effects of dietary copper, molybdenum, and sulfur on plasma and liver copper, weight gain, and feed conversion in growing-finishing cattle

The minerals Cu, Mo, and S are essential for metabolic functions related to cattle health and performance. The interaction between Cu, Mo, and S can determine the utilization of each mineral, in particular Cu, by ruminants. A meta-analysis was performed to evaluate the effects of dietary Cu, Mo, and S and their interactions on plasma and liver Cu, ADG, and G:F in growing-finishing cattle. Data were collated from 12 published studies. The model with the best fit to data indicated plasma Cu was positively affected by dietary Cu (P < 0.01) and negatively affected by both dietary Mo (P < 0.01) and S (P < 0.01). Another model also indicated that plasma Cu concentration is positively related to Cu:Mo ratio in the diet (P < 0.01). Dietary Cu had a positive effect on liver Cu (P < 0.01), whereas Mo showed a negative effect (P < 0.05), and no effect of dietary S on liver Cu was observed (P > 0.05). Average daily gain was negatively affected by dietary Mo (P < 0.05) and S (P < 0.01) and positively affected by Cu:Mo ratio (P < 0.01), likely because an increased Cu:Mo ratio minimizes the antagonistic effect of Mo on Cu. The feed conversion ratio was negatively affected by Mo (P < 0.05) and S (P < 0.01), whereas effects of the Cu:Mo ratio and dietary Cu were not significant (P > 0.05). The interaction between S and Mo affected (P < 0.01) G:F, which was likely related to a positive response with the proper balance between these minerals. In conclusion, dietary Cu, Mo, and S and the Cu:Mo ratio caused changes in plasma Cu. Only dietary Mo and S led to a negative response in the performance of growing-finishing cattle, whereas the diet Cu:Mo ratio has a linear and quadratic effect on ADG. Nutritionists and producers need to consider with caution the supplementation of growing-finishing cattle diets with Mo and S because of their potentially adverse effects on animal performance. An appropriate Cu:Mo ratio is desirable to minimize the effects of an impaired supply of Mo on Cu metabolism and ADG.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of lactating dairy cows

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and phenylalanine hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant.

Alternative growth functions for predicting body, carcass, and breast weight in ducks: Lomolino equation and extreme value function

In this study, 2 alternative growth functions, the Lomolino and the extreme value function (EVF), are introduced and their ability to predict body, carcass, and breast weight in ducks evaluated. A comparative study was carried out of these equations with standard growth functions: Gompertz, exponential, Richards, and generalized Michaelis-Menten. Goodness of fit of the functions was evaluated using R(2), mean square error, Akaike information criterion, and Bayesian information criterion, whereas bias factor, accuracy factor, Durbin-Watson statistic, and number of runs of sign were the criteria used for analysis of residuals. Results showed that predictive performance of all functions was acceptable, though the Richards and exponential equations failed to converge in a few cases for both male and female ducks. Based on goodness-of-fit statistics, the Richards, Gompertz, and EVF were the best equations whereas the worst fits to the data were obtained with the exponential. Analysis of residuals indicated that, for the different traits investigated, the least biased and the most accurate equations were the Gompertz, EVF, Richards, and generalized Michaelis-Menten, whereas the exponential was the most biased and least accurate. Based on the Durbin-Watson statistic, all models generally behaved well and only the exponential showed evidence of autocorrelation for all 3 traits investigated. Results showed that with all functions, estimated final weights of males were higher than females for the body, carcass, and breast weight profiles. The alternative functions introduced here have desirable advantages including flexibility and a low number of parameters. However, because this is probably the first study to apply these functions to predict growth patterns in poultry or other animals, further analysis of these new models is suggested.

Bootstrapped neural network models for analyzing the responses of broiler chicks to dietary protein and branched chain amino acids

Faridi, A., Golian, A., Heravi Mousavi, A. and France, J. 2014. Bootstrapped neural network models for analyzing the responses of broiler chicks to dietary protein and branched chain amino acids. Can. J. Anim. Sci. 94: 79–85. Reliable prediction of avian responses to dietary nutrients is essential for planning, management, and optimization activities in poultry nutrition. In this study, two bootstrapped neural network (BNN) models, each containing 100 separated neural networks (SNN), were developed for predicting average daily gain (ADG) and feed efficiency (FE) of broiler chicks in response to intake of protein and branched chain amino acids (BCAA) in the starter period. Using a re-sampling method, 100 different batches of data were generated for both the ADG and FE sets. Starting with 270 data lines extracted from eight studies in the literature, SNN models were trained, tested, and validated with 136, 67, and 67 data lines, respectively. All 200 SNN models developed, along with their respective BNN ones, were subjected to optimization (to find the optimum dietary protein and BCAA levels that maximize ADG and FE). Statistical analysis indicated that based on R 2, the BNN models were more accurate in 76 and 56 cases (out of 100) compared with the SNN models developed for ADG and FE, respectively. Optimization of the BNN models showed protein, isoleucine, leucine, and valine requirements for maximum ADG were 231.80, 9.05, 14.03 and 10.90 g kg−1 of diet, respectively. Also, maximum FE was obtained when the diet contained 232.30, 9.07, 14.50, and 11.04 g kg−1 of protein, isoleucine, leucine, and valine, respectively. The results of this study suggest that in meta-analytic modelling, bootstrap re-sampling algorithms should be used to better analyze available data and thereby take full advantage of them. This issue is of importance in the animal sciences as producing reliable data is both expensive and time-consuming.

A dynamic mechanistic model of lactic acid metabolism in the rumen

Current feed evaluation systems for ruminants are too imprecise to describe diets in terms of their acidosis risk. The dynamic mechanistic model described herein arises from the integration of a lactic acid (La) metabolism module into an extant model of whole-rumen function. The model was evaluated using published data from cows and sheep fed a range of diets or infused with various doses of La. The model performed well in simulating peak rumen La concentrations (coefficient of determination = 0.96; root mean square prediction error = 16.96% of observed mean), although frequency of sampling for the published data prevented a comprehensive comparison of prediction of time to peak La accumulation. The model showed a tendency for increased La accumulation following feeding of diets rich in nonstructural carbohydrates, although less-soluble starch sources such as corn tended to limit rumen La concentration. Simulated La absorption from the rumen remained low throughout the feeding cycle. The competition between bacteria and protozoa for rumen La suggests a variable contribution of protozoa to total La utilization. However, the model was unable to simulate the effects of defaunation on rumen La metabolism, indicating a need for a more detailed description of protozoal metabolism. The model could form the basis of a feed evaluation system with regard to rumen La metabolism.

Development of mathematical models to predict volume and nutrient composition of fresh manure from lactating Holstein cows

Organic compounds in dairy manure undergo a series of reactions producing pollutants such as ammonia and methane. Because various organic compounds have different reaction rates, the emissions could be accurately determined if amounts and concentrations of individual nutrients in manure are known. A set of empirical models were developed for predicting faecal and urinary water, carbon (C), nitrogen (N), acid detergent fibre and neutral detergent fibre output (kg/day) from lactating Holstein cows. Dietary nutrient contents, milk yield and composition, bodyweight, age and days in milk were used with or without dry matter intake (DMI) as potential predictor variables. Multi-collinearity, goodness of fit, model complexity, and random study and animal effects were taken into account during model development, which used 742 measured faecal or urinary nutrient output observations (kg/day). The models were evaluated with an independent dataset (n = 364). When DMI was used as a predictor variable, the models predicted faecal and urinary nutrient outputs successfully with root mean square prediction error as a percentage of average observed values (RMSPE%) ranging from 9.1% to 20.7%. All the predictions except urine output had RMSPE% ranging from 18.3% to 24.6% when DMI was not used. The nutrient output predictions were in reasonable agreement with observed values throughout the data range (systematic bias <14% of total bias). Fresh manure C : N ratio predictions were acceptable (RMSPE% = 14.3–15.2%) although the systematic bias were notable (17.1–20.7% of total bias). The models could be integrated successfully with process-based manure or soil models to assess nutrient transformation in dairy production systems.

Bayesian analysis of energy balance data from growing cattle using parametric and non-parametric modelling

Linear and non-linear models have been extensively utilised for the estimation of net and metabolisable energy requirements and for the estimation of the efficiencies of utilising dietary energy for maintenance and tissue gain. In growing animals, biological principles imply that energy retention rate is non-linearly related to the energy intake level because successive increments in energy intake above maintenance result in diminishing returns for tissue energy accretion. Heat production in growing cattle has been traditionally described by logarithmic regression and exponential models. The objective of the present study was to develop Bayesian models of energy retention and heat production in growing cattle using parametric and non-parametric techniques. Parametric models were used to represent models traditionally employed to describe energy use in growing steers and heifers whereas the non-parametric approach was introduced to describe energy utilisation while accounting for non-linearities without specifying a particular functional form. The Bayesian framework was used to incorporate prior knowledge of bioenergetics on tissue retention and heat production and to estimate net and metabolisable energy requirements (NEM and MEM, respectively), and the partial efficiencies of utilising dietary metabolisable energy for maintenance (km) and tissue energy gain (kg). The database used for the study consisted of 719 records of indirect calorimetry on steers and non-pregnant, non-lactating heifers. The NEM was substantially larger in energy retention models (ranged from 0.40 to 0.50 MJ/kg BW0.75.day) than were NEM estimates from heat-production models (ranged from 0.29 to 0.49 MJ/kg BW0.75.day). Similarly, km was also larger in energy retention models than in heat production models. These differences are explained by the nature of y-intercepts (NEM) in these two models. Energy retention models estimate fasting catabolism as the y-intercept, while heat production models estimate fasting heat production. Conversely, MEM was virtually identical in all models and approximately equal to 0.53 MJ/kg BW0.75.day in this database.

Prediction of nitrogen use in dairy cattle: a multivariate Bayesian approach

Quantification of dairy cattle nitrogen (N) excretion and secretion is necessary to improve the efficiency with which feed N is converted to milk N (ENU). Faecal and urinary N excretion and milk N secretion are correlated with each other and thus are more accurately described by a multivariate model that can accommodate the covariance between the three observations than by three separate univariate models. Further, by simultaneously predicting the three routes of excretion and taking advantage of the mass balance relationships between them, covariate effects on N partitioning from feed to faeces and absorbed N and from absorbed N to milk and urine N and animal ENU can be estimated. A database containing 1094 lactating dairy cow observations collated from indirect calorimetry experiments was used for model development. Dietary metabolisable energy content (ME, MJ/kg DM) increased ENU at a decreasing rate, increased the efficiency with which feed N was converted to absorbed N and decreased the efficiency with which absorbed N was converted to milk N. However, the parameter estimate of the effect of ME on post-absorption efficiency was not different from zero when the model was fitted to a data subset in which net energy and metabolisable protein were at or above requirement. This suggests the effect of ME on post-absorption N use is dependent on the energy status of the animal.

Proceedings of the 2013 Meeting of the Animal Science Modelling Group

This group meets yearly for one-day meetings. The 2013 meeting was sponsored by Nutreco Canada, Inc., Guelph, ON, Canada; ADM, Decatur, IL, USA; Cargill Animal Nutrition, Elk River, MN, USA; Ajinomoto Heartland, Inc., Chicago, IL, USA; Adisseo, Alpharetta, GA, USA; Lallemand Specialties, Inc., Milwaukee, WI, USA and Evonik Industries AG, Hanau, Germany. It was held on July 7 at the Hyatt Regency Indianapolis, One South Capital Avenue, Indianapolis, Indiana, USA, prior to the ADSA/ASAS Joint Annual Meeting. Summaries of the papers presented follow. Each summary has been peer reviewed and edited for clarity. The person who presented the paper is identified with an e-mail address.

Interpreting experimental data on egg production--applications of dynamic differential equations

This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.

Study of broiler chicken responses to dietary protein and lysine using neural network and response surface models

1. In this study, neural network (NN) and response surface (RS) models were developed to investigate the response [average daily gain (ADG) and feed efficiency (FE)] of young broiler chickens to dietary protein and lysine. For this purpose, data on their responses to dietary protein and lysine were extracted from the literature and separate NN and RS models were constructed. 2. Comparison between the NN and RS models revealed higher accuracy of prediction with the NN models compared to the RS models. In terms of R (2) values, the NN models developed for both ADG (R (2) = 0.923) and FE (R (2) = 0.904) were far superior to the RS models (R (2) for ADG = 0.511; R (2) for FE = 0.67). This suggests that the NN models can serve as an alternative option to conventional regression approaches including use of RS models. 3. Optimisation of the NN models developed for response to protein and lysine showed that diets containing 220.7 (g/kg of diet) protein and 12.85 (g/kg of diet) lysine maximise ADG, whereas maximum FE is achieved with diets containing 241.3 and 13.12 (g/kg) protein and lysine, respectively. Based on the optimisation results, optimal dietary protein and lysine concentrations for maximum FE in broiler chickens during the starting period are higher than for ADG.

Anti-methanogenic effects of monensin in dairy and beef cattle: a meta-analysis

Monensin is a widely used feed additive with the potential to minimize methane (CH4) emissions from cattle. Several studies have investigated the effects of monensin on CH4, but findings have been inconsistent. The objective of the present study was to conduct meta-analyses to quantitatively summarize the effect of monensin on CH4 production (g/d) and the percentage of dietary gross energy lost as CH4 (Ym) in dairy cows and beef steers. Data from 22 controlled studies were used. Heterogeneity of the monensin effects were estimated using random effect models. Due to significant heterogeneity (>68%) in both dairy and beef studies, the random effect models were then extended to mixed effect models by including fixed effects of DMI, dietary nutrient contents, monensin dose, and length of monensin treatment period. Monensin reduced Ym from 5.97 to 5.43% and diets with greater neutral detergent fiber contents (g/kg of dry matter) tended to enhance the monensin effect on CH4 in beef steers. When adjusted for the neutral detergent fiber effect, monensin supplementation [average 32 mg/kg of dry matter intake (DMI)] reduced CH4 emissions from beef steers by 19±4 g/d. Dietary ether extract content and DMI had a positive and a negative effect on monensin in dairy cows, respectively. When adjusted for these 2 effects in the final mixed-effect model, monensin feeding (average 21 mg/kg of DMI) was associated with a 6±3 g/d reduction in CH4 emissions in dairy cows. When analyzed across dairy and beef cattle studies, DMI or monensin dose (mg/kg of DMI) tended to decrease or increase the effect of monensin in reducing methane emissions, respectively. Methane mitigation effects of monensin in dairy cows (-12±6 g/d) and beef steers (-14±6 g/d) became similar when adjusted for the monensin dose differences between dairy cow and beef steer studies. When adjusted for DMI differences, monensin reduced Ym in dairy cows (-0.23±0.14) and beef steers (-0.33±0.16). Monensin treatment period length did not significantly modify the monensin effects in dairy cow or beef steer studies. Overall, monensin had stronger antimethanogenic effects in beef steers than dairy cows, but the effects in dairy cows could potentially be improved by dietary composition modifications and increasing the monensin dose.

A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

PURPOSE

Few models have been developed specifically for the epidemiology of diabetes. Diabetes incidence is critical in predicting diabetes prevalence. However, reliable estimates of disease incidence rates are difficult to obtain. The aim of this study was to propose a mathematical framework for predicting diabetes prevalence using incidence rates estimated within the model using body mass index (BMI) data.

METHODS

A generic mechanistic model was proposed considering birth, death, migration, aging, and diabetes incidence dynamics. Diabetes incidence rates were determined within the model using their relationships with BMI represented by the Hill equation. The Hill equation parameters were estimated by fitting the model to National Health and Nutrition Examination Survey (NHANES) 1999-2010 data and used to predict diabetes prevalence pertaining to each NHANES survey year. The prevalences were also predicted using diabetes incidence rates calculated from the NHANES data themselves. The model was used to estimate death rate parameters and to quantify sensitivities of prevalence to each population dynamic.

RESULTS

The model using incidence rate estimates from the Hill equations successfully predicted diabetes prevalence of younger, middle-aged, and older adults (prediction error, 20.0%, 9.64%, and 7.58% respectively). Diabetes prevalence was positively associated with diabetes incidence in every age group, but the associations among younger adults were stronger. In contrast, diabetes prevalence was more sensitive to death rates in older adults than younger adults. Both diabetes incidence and prevalence were strongly sensitive to BMI at younger ages, but sensitivity gradually declined as age progressed. Younger and middle aged adults diagnosed with diabetes had at least a two-fold greater risk of death than their nondiabetic counterparts. Nondiabetic older adults were found to be under slightly higher death risk (0.079) than those diagnosed with diabetes (0.073).

CONCLUSIONS

The proposed model predicts diagnosed diabetes incidence and prevalence reasonably well using the link between BMI and diabetes development risk. Ethnic group and gender-specific model parameter estimates could further improve predictions. Model prediction accuracy and applicability need to be comprehensively evaluated with independent data sets.

Evaluating the egg production of broiler breeder hens in response to dietary nutrient intake from 31 to 60 weeks of age through neural network models

Faridi, A., Golian, A. and France, J. 2012. Evaluating the egg production of broiler breeder hens in response to dietary nutrient intake from 31 to 60 weeks of age through neural network models. Can. J. Anim. Sci. 92: 473–481. The aim of this study was to evaluate the response of broiler breeder hens in terms of egg production to dietary nutrient intake. Using neural network (NN) models and breaking down the collected data from 98 commercial broiler breeder houses into 3-wk intervals, 10 NN-based models were developed from 31 to 60 wk of age. The data lines were divided into two random subsets of training (n=64) and testing (n=34) sets. The variables of interest for developing the models were metabolizable energy (ME; kcal bird−1 d−1), and crude protein (CP), total sulphur amino acids (TSAA), lysine (Lys), calcium (Ca) and available phosphorus (AP), all in g bird−1 d−1. The random optimization algorithm was applied to the constructed models to find the optimal level of the input variables which maximized egg production during the different intervals. The high R 2 values in all the developed models for both the training and testing sets indicate the accuracy of NN-based models in estimating egg production. The optimization results revealed that breeder hens consuming 485, 473, 471, 466, 460, 452, 448, 442, 437 and 445 kcal of ME bird−1 d−1 showed the highest egg production during the 10 consecutive 3-wk intervals from 31 to 60 wk of age, respectively. Moreover, the optimal performance of hens required the following average intakes from 31 to 60 wk of age (g bird−1 d−1): CP: 23.7; TSAA: 1.05; Lys: 1.07; Ca: 4.91; and AP: 0.58. The results show that energy (kcal bird−1 d−1) and other nutrient requirements (g bird−1 d−1) of broiler breeder hens from 31 to 60 wk of age do not change in consort together with age; therefore using different diets with different dietary nutrient levels during the production cycle may help the nutritionists better meet the requirements of broiler breeder hens. Based on the present study, it appears that company guideline recommendations may underestimate the nutrient requirements of hens during these weeks when egg production is declining gradually.