Genetic parameters for functional traits in dairy cattle from daily random regression models

Estimation of genetic parameters for feed efficiency traits using random regression models in dairy cattle

Feed efficiency has become an increasingly important research topic in recent years. As feed costs rise and the environmental impacts of agriculture become more apparent, improving the efficiency with which dairy cows convert feed to milk is increasingly important. However, feed intake is expensive to measure accurately on large populations, making the inclusion of this trait in breeding programs difficult. Understanding how the genetic parameters of feed efficiency and traits related to feed efficiency vary throughout the lactation period is valuable to gain understanding into the genetic nature of feed efficiency. This study used 121,226 dry matter intake (DMI) records, 120,500 energy-corrected milk (ECM) records, and 98,975 metabolic body weight (MBW) records, collected on 7,440 first-lactation Holstein cows from 6 countries (Canada, Denmark, Germany, Spain, Switzerland, and the United States), from January 2003 to February 2022. Genetic parameters were estimated using a multiple-trait random regression model with a fourth-order Legendre polynomial for all traits. Weekly phenotypes for DMI were re-parameterized using linear regressions of DMI on ECM and MBW, creating a measure of feed efficiency that was genetically corrected for ECM and MBW, referred to as genomic residual feed intake (gRFI). Heritability (SE) estimates varied from 0.15 (0.03) to 0.29 (0.02) for DMI, 0.24 (0.01) to 0.29 (0.03) for ECM, 0.55 (0.03) to 0.83 (0.05) for MBW, and 0.12 (0.03) to 0.22 (0.06) for gRFI. In general, heritability estimates were lower in the first stage of lactation compared with the later stages of lactation. Additive genetic correlations between weeks of lactation varied, with stronger correlations between weeks of lactation that were close together. The results of this study contribute to a better understanding of the change in genetic parameters across the first lactation, providing insight into potential selection strategies to include feed efficiency in breeding programs.

Invited Review: Increasing Milk Yield and Negative Energy Balance: A Gordian Knot for Dairy Cows?

The continued increase in milk production during the last century has not been accompanied by an adequate dry matter intake (DMI) by cows, which therefore experience a negative energy balance (NEB). NEB is low and of minor importance at low milk yield (MY), such as for the nutrition of one calf, and under these circumstances is considered "natural". MY and low DMI around parturition are correlated and are the reason for the genetic correlation between increasing MY and increasing NEB up to 2000 MJ or more for 2-3 months postpartum in high-genetic-merit dairy cows. The extension and duration of NEB in high-producing cows cannot be judged as "natural" and are compensated by the mobilization of nutrients, particularly of fat. The released non-esterified fatty acids (NEFAs) overwhelm the metabolic capacity of the cow and lead to the ectopic deposition of NEFAs as triglycerides (TGs) in the liver. The subsequent lipidosis and the concomitant hampered liver functions cause subclinical and clinical ketosis, both of which are associated with "production diseases", including oxidative and endoplasmatic stress, inflammation and immunosuppression. These metabolic alterations are regulated by homeorhesis, with the priority of the physiological function of milk production. The prioritization of one function, namely, milk yield, possibly results in restrictions in other physiological (health) functions under conditions of limited resources (NEB). The hormonal framework for this metabolic environment is the high concentration of growth hormone (GH), the low concentration of insulin in connection with GH-dependent insulin resistance and the low concentration of IGF-1, the so-called GH-IGF-1 axis. The fine tuning of the GH-IGF-1 axis is uncoupled because the expression of the growth hormone receptor (GHR-1A) in the liver is reduced with increasing MY. The uncoupled GH-IGF-1 axis is a serious impairment for the GH-dependent stimulation of gluconeogenesis in the liver with continued increased lipolysis in fat tissue. It facilitates the pathogenesis of lipidosis with ketosis and, secondarily, "production diseases". Unfortunately, MY is still increasing at inadequate DMI with increasing NEB and elevated NEFA and beta-hydroxybutyric acid concentrations under conditions of low glucose, thereby adding health risks. The high incidences of diseases and of early culling and mortality in dairy cows are well documented and cause severe economic problems with a waste of resources and a challenge to the environment. Moreover, the growing public concerns about such production conditions in agriculture can no longer be ignored.

[The lipidosis of the liver of dairy cows: Part 1 - Role of insulin and the Growth Hormone-IGF-1 axis]

Lipidosis of the liver of dairy cows is a metabolic disease known since many years and is caused by an uptake of nonesterified fatty acids (NEFA) into the liver cells, limited metabolism of NEFA (oxidation and production of β-hydroxybutyrate), and resynthesis in relation to a low efflux as triglyceride (TG). The pathogenesis of lipidosis includes a) an augmented release of NEFA by mobilisation of adipose tissue, b) uptake of NEFA into the liver cells, c) metabolism of NEFA and d) re-synthesis of triglyceride and e) an efflux of TG as very low density lipoprotein (VLDL). The steps a-e are postpartum modified by hormones as an increase of growth hormone, a pronounced insulin resistance in combination with a decreased insulin and of IGF-1 concentrations. These hormonal changes are related to an uncoupling of the growth hormone-IGF-1-axis with enhanced lipolysis and consequences mentioned above. These alterations are associated with inflammation, oxidative and endoplasmatic stress. The metabolic and hormonal alterations are the result of the selection of dairy cows primarily for milk production without adequate food intake with the consequence of lipidosis, ketosis and further health risks (production diseases).

Selection Response Due to Different Combination of Antagonistic Milk, Beef, and Morphological Traits in the Alpine Grey Cattle Breed

Selection in local dual-purpose breeds requires great carefulness because of the need to preserve peculiar traits and also guarantee the positive genetic progress for milk and beef production to maintain economic competitiveness. A specific breeding plan accounting for milk, beef, and functional traits is required by breeders of the Alpine Grey cattle (AG), a local dual-purpose breed of the Italian Alps. Hereditability and genetic correlations among all traits have been analyzed for this purpose. After that, different selection indexes were proposed to identify the most suitable for this breed. Firstly, a genetic parameters analysis was carried out with different datasets. The milk dataset contained 406,918 test day records of milk, protein, and fat yields and somatic cells (expressed as SCS). The beef dataset included performance test data conducted on 749 young bulls. Average daily gain, in vivo estimated carcass yields, and carcass conformation (SEUROP) were the phenotypes obtained from the performance tests. The morphological dataset included 21 linear type evaluations of 11,320 first party cows. Linear type traits were aggregated through factor analysis and three factors were retained, while head typicality (HT) and rear muscularity (RM) were analyzed as single traits. Heritability estimates (h2) for milk traits ranged from 0.125 to 0.219. Analysis of beef traits showed h2 greater than milk traits, ranging from 0.282 to 0.501. Type traits showed a medium value of h2 ranging from 0.238 to 0.374. Regarding genetic correlation, SCS and milk traits were strongly positively correlated. Milk traits had a negative genetic correlation with the factor accounting for udder conformations (-0.40) and with all performance test traits and RM. These latter traits showed also a negative genetic correlation with udder volume (-0.28). The HT and the factor accounting for rear legs traits were not correlated with milk traits, but negatively correlated with beef traits (-0.32 with RM). We argue that the consequence of these results is that the use of the current selection index, which is mainly focused on milk attitude, will lead to a deterioration of all other traits. In this study, we propose more appropriate selection indexes that account for genetic relationships among traits, including functional traits.

Genetic parameters of forage dry matter intake and milk produced from forage in Swedish Red and Holstein dairy cows

High-yielding dairy cows are often fed high proportions of cereal grain and pulses. For several reasons, it would be desirable to replace these feed sources with forage, which is not suitable for human consumption. Feeding large amounts of forage to dairy cows could also make dairy production more publicly acceptable in the future. In this study, we estimated genetic parameters for total dry matter intake (DMI), DMI from forage (DMI_For), energy-corrected milk (ECM), and ECM produced from forage (ECM_For). A total of 1,177 lactations from 575 cows of Swedish Red (SR) and Holstein (HOL) dairy breeds were included in the study. Mixed linear animal random regression models were used, with fixed effect of calving season and lactation week nested within parity 1 and 2+, fixed effect of calving year, and random regression coefficients for breeding value (up to linear) and permanent environmental effect (up to quadratic) of the cow. Heritability for DMI and DMI_For was generally higher for HOL than for SR in all-parity data and in later parities; however, the opposite was true for first parity. Heritability for DMI and DMI_For during the first 8 wk averaged 0.11 and 0.15, respectively, in all-parity data for the 2 breeds. Corresponding values for ECM_For and ECM were 0.21 and 0.29, respectively. In first parity, values were 0.32, 0.36, 0.28, and 0.51, respectively. The genetic correlation between DMI and DMI_For was high, above 0.83, and fairly constant across the lactation. The genetic correlation between ECM_For and ECM was close to unity in the later part of lactation for both breeds, but was around 0.8 in the early lactation for both breeds; it decreased for HOL to 0.54 in wk 17. The genetic correlations between DMI and ECM_For and between DMI_For and ECM_For were low and negative for HOL (absolute value ∼0.2-0.3), but changed for SR from weakly positive in early lactation to negative values and back to positive toward the end of lactation. For most traits, the correlation between wk 1 and wk 8 into the lactation was very high; the lowest value was for DMI in HOL at 0.81. The genetic correlation between parities was rather high in the first part of the lactation. During the first 8 wk, the correlation was lower for HOL than for SR, except for ECM. We found that DMI_For and ECM_For showed reasonably large heritability, and future work should explore the possibility of genomic evaluations.

A new method to estimate residual feed intake in dairy cattle using time series data

In dairy, the usual way to measure feed efficiency is through the residual feed intake (RFI) method. However, this method is, in its classical form, a linear regression, which, by construction, does not take into account the evolution of the RFI components across time, inducing approximations in the results. We present here a new approach that incorporates the dynamic dimension of the data. Using a multitrait random regression model, the correlations between milk, live weight, DM intake (DMI) and body condition score (BCS) were investigated across the lactation. In addition, at each time point, by a matrix regression on the variance-covariance matrix and on the animal effects from the three predictor traits, a predicted animal effect for intake was estimated, which, by difference with the actual animal effect for intake, gave a RFI estimation. This model was tested on historical data from the Aarhus University experimental farm (1 469 lactations out of 740 cows). Correlations between animal effects were positive and high for milk and DMI and for weight and DMI, with a maximum mid-lactation, stable across time at around 0.4 for weight and BCS, and slowly decreasing along the lactation for milk and weight, DMI and BCS, and milk and BCS. At the Legendre polynomial coefficient scale, the correlations were estimated with a high accuracy (averaged SE of 0.04, min = 0.02, max = 0.05). The predicted animal effect for intake was always extremely highly correlated with the milk production and highly correlated with BW for the most part of the lactation, but only slightly correlated with BCS, with the correlation becoming negative in the second half of the lactation. The estimated RFI possessed all the characteristics of a classical RFI, with a mean at zero at each time point and a phenotypic independence from its predictors. The correlation between the averaged RFI over the lactation and RFI at each time point was always positive and above 0.5, and maximum mid-lactation (>0.9). The model performed reasonably well in the presence of missing data. This approach allows a dynamic estimation of the traits, free from all time-related issues inherent to the traditional RFI methodology, and can easily be adapted and used in a genetic or genomic selection context.

Reliability of breeding values for feed intake and feed efficiency traits in dairy cattle: When dry matter intake recordings are sparse under different scenarios

Currently, routine recordings of dry matter intake (DMI) in commercial herds are practically nonexistent. Recording DMI from commercial herds is a prerequisite for the inclusion of feed efficiency (FE) traits in dairy cattle breeding goals. To develop future on-farm phenotyping strategies, recording strategies that are low cost and less demanding logistically and that give relatively accurate estimates of the animal's genetic merit are therefore needed. The objectives of this study were (1) to estimate genetic parameters for daily DMI and FE traits and use the estimated parameters to simulate daily DMI phenotypes under different DMI recording scenarios (SCN) and (2) to use the simulated data to estimate for different scenarios the associated reliability of estimated breeding value and accuracies of genomic prediction for varying sizes of reference populations. Five on-farm daily DMI recording scenarios were simulated: once weekly (SCN1), once monthly (SCN2), every 2 mo (SCN3), every 3 mo (SCN4), and every 4 mo (SCN5). To estimate reliability of estimated breeding values, DMI and FE observations and true breeding values were simulated based on variance components estimated for daily observations of Nordic Red cows. To emulate realistic on-farm recording, 5 data set replicates, each with 36,037 DMI and FE records, were simulated for real pedigree and data structure of 789 Holstein cows. Observations for the 5 DMI recording scenarios were generated by discarding data in a step-wise manner from the full simulated data per the scenario's definitions. For each of these scenarios, reliabilities were calculated as correlation between the true and estimated breeding values. Variance components and genetic parameters were estimated for daily DMI, residual feed intake (RFI), and energy conversion efficiency (ECE) fitting the random regression model. Data for variance components were from 227 primiparous Nordic Red dairy cows covering 8 to 280 d in milk. Lactation-wise heritability for DMI, RFI, and ECE was 0.33, 0.12, and 0.32, respectively, and daily heritability estimates during lactation ranged from 0.18 to 0.45, 0.08 to 0.32, and 0.08 to 0.45 for DMI, RFI, and ECE, respectively. Genetic correlations for DMI between different stages of lactation ranged from -0.50 to 0.99. The comparison of different on-farm DMI recording scenarios indicated that adopting a less-frequent recording scenario (SCN3) gave a similar level of accuracy as SCN1 when 17 more daughters are recorded per sire over the 46 needed for SCN1. Such a strategy is less demanding logistically and is low cost because fewer observations need to be collected per animal. The accuracy of genomic predictions associated with the 5 recording scenarios indicated that setting up a relatively larger reference population and adopting a less-frequent DMI sampling scenario (e.g., SCN3) is promising. When the same reference population size was considered, the genomic prediction accuracy of SCN3 was only 5.0 to 7.0 percentage points lower than that for the most expensive DMI recording strategy (SCN1). We concluded that DMI recording strategies that are sparse in terms of records per cow but with slightly more cows recorded per sire are advantageous both in genomic selection and in traditional progeny testing schemes when accuracy, logistics, and cost implications are considered.

Influence of milking frequency on genetic parameters associated with the milk production in the first and second lactations of Iranian Holstein dairy cows using random regression test day models

BACKGROUND

The milk yield can be affected by the frequency of milking per day, in dairy cows. Previous studies have shown that the milk yield is increased by 6-25 % per lactation when the milking frequency is increased from 2 to 3 times per day while the somatic cell count is decreased. To investigate the effect of milking frequency (3X vs. 4X) on milk yield and it's genetic parameters in the first and second lactations of the Iranian Holstein dairy cows, a total of 142,604 test day (TD) records of milk yield were measured on 20,762 cows.

RESULTS

Heritability estimates of milk yield were 0.25 and 0.19 for 3X milking frequency and 0.34 and 0.26 for 4X milking frequency throughout the first and second lactations, respectively. Repeatability estimates of milk yield were 0.70 and 0.71 for 3X milking frequency and 0.76 and 0.77 for 4X milking frequency, respectively. In comparison with 3X milking frequency, the milk yield of the first and second lactations was increased by 11.6 and 12.2 %, respectively when 4X was used (p < 0.01).

CONCLUSIONS

Results of this research demonstrated that increasing milking frequency led to an increase in heritability and repeatability of milk yield. The current investigation provided clear evidences for the benefits of using 4X milking frequency instead of 3X in Iranian Holstein dairy cows.

Alternative strategies for genetic analyses of milk flow in dairy cattle

Measurements for average milk flow (AMF) in kilograms of milk per minute of milking time from 629,161 Holstein cows from calving years 1990 to 2008 were used to estimate genetic covariance components using a variety of statistical models. For bivariate linear-threshold model applications, Gaussian-distributed AMF (linear sire model) was categorized into 2 distinct classes (threshold sire model) by setting arbitrary thresholds for extremely slow or extremely fast milking cows. In different bivariate runs with the 2 traits, Gaussian AMF and binary AMF, within a Bayesian framework, thresholds for the binary trait were 1.2, 1.6, 2.6, and 2.8 kg/min. Posterior heritabilities for AMF from the linear and the threshold models in all runs were in a narrow range and close to 0.26, and the posterior genetic correlation between AMF, defined as either a Gaussian or binary trait, was 0.99. A data subset was used to infer genetic and phenotypic relationships between AMF with test-day traits milk yield, fat percentage, protein percentage, somatic cell score (SCS), fat-to-protein ratio, and energy-corrected milk using recursive linear sire models, standard multiple trait linear sire models, and multiple trait linear sire models accounting for the effect of a trait 1 on a trait 2, and of trait 2 on trait 3, via linear regressions. The time-lagged 3-trait system focused on the first test-day trait after calving (trait 1), on AMF (trait 2), and on the test-day trait (trait 3) after the AMF measurement. Posterior means for heritabilities for AMF from linear and recursive linear models used for the reduced data set ranged between 0.29 and 0.38, and were slightly higher than heritabilities from the threshold models applied to the full data set. Genetic correlations from the recursive linear model and the linear model were similar for identical trait combinations including AMF and test-day traits 1 and 3. The largest difference was found for the genetic correlation between AMF and fat percentage from the first test day (i.e., -0.31 from the recursive linear model vs. -0.26 from the linear model). Genetic correlations from the linear model, including an additional regression coefficient, partly differed, especially when comparing correlations between AMF and SCS and between AMF and fat-to-protein ratio recorded after the AMF measurement data. Structural equation coefficients from the recursive linear model and corresponding regression coefficients from the linear model with additional regression, both depicting associations on the phenotypic scale, were quite similar. From a physiological perspective, all models confirmed the antagonistic relationship between SCS with AMF on genetic and phenotypic scales. A pronounced recursive relationship was also noted between productivity (milk yield and energy-corrected milk) and AMF, suggesting further research using physiological parameters as indicators for cow stress response (e.g., level of hormones) should be conducted.

Genetic parameters for energy balance, feed efficiency, and related traits in Holstein cattle

Objectives of the current study were to estimate genetic parameters in Holstein cows for energy balance (EB) and related traits including dry matter intake (DMI), body weight (BW), body condition score (BCS), energy-corrected milk (ECM) production, and gross feed efficiency (GFE), defined as the ratio of total ECM yield to total DMI over the first 150 d of lactation. Data were recorded for the first half of lactation on 227 and 175 cows in their first or later lactation, respectively. Random regression models were fitted to longitudinal data. Also, each trait was averaged over monthly intervals and analyzed by single and multivariate animal models. Heritability estimates ranged from 0.27 to 0.63, 0.12 to 0.62, 0.12 to 0.49, 0.63 to 0.72, and 0.49 to 0.53 for DMI, ECM yield, EB, BW, and BCS, respectively, averaged over monthly intervals. Daily heritability estimates ranged from 0.18 to 0.30, 0.10 to 0.26, 0.07 to 0.22, 0.43 to 0.67, and 0.25 to 0.38 for DMI, ECM yield, EB, BW, and BCS, respectively. Estimated heritability for GFE was 0.32. The genetic correlation of EB at 10d in milk (DIM) with EB at 150 DIM was -0.19, suggesting the genetic regulation of this trait differs by stage of lactation. Positive genetic correlations were found among DMI, ECM yield, and BW averaged over monthly intervals, whereas correlations of these traits with BCS depended upon stage of lactation. Total ECM yield for the lactation was positively correlated with DMI, but a negative genetic correlation between total ECM yield and EB was found. However, the genetic correlation between total ECM yield and EB in the first month of lactation was -0.02, indicating that total production is not genetically correlated with EB during the first month of lactation, when negative EB is most closely associated with diminished fitness. The genetic correlation between GFE and EB ranged from -0.73 to -0.99, indicating that selection for more efficient cows would favor a lower energy status. However, the genetic correlation between EB in the first month of lactation and GFE calculated from 75 to 150 DIM was not significant, indicating that the unfavorable correlation between GFE and EB in early lactation may be minimized with alternative definitions of efficiency. Thus, EB, GFE and related traits will likely respond to genetic selection in Holstein cows. However, the impact of selection for improved feed efficiency on EB must be carefully considered to avoid potential negative consequences of further reductions in EB at the onset of lactation.

Genetic parameters for serial, automatically recorded milkability and its relationship to udder health in dairy cattle

Serial measurements of three milkability traits from two commercial dairy farms in Germany were used to estimate heritabilities and breeding values (BVs). Overall, 6352 cows in first, second and third lactations supplied 2 188 810 records based on daily values recorded from 1998 to 2003. Only the records between day 8 and day 305 after calving were considered. The estimated genetic correlations between different parities within the three milkability traits ranged from rg = 0.88 to 0.98, i.e. they were sufficiently high to warrant a repeatability model. The resulting estimated heritability coefficients were h2 = 0.42 for average milk flow, h2 = 0.56 for maximum milk flow and h2 = 0.38 for milking time. We analysed the genetic correlation between milkability and somatic cell score (SCS) and between milkability and the liability to mastitis, respectively, as the optimum milk flow for udder health is not well defined. There were 66 146 records with information on somatic cell count. Furthermore, 23 488 days of medical treatment for udder diseases were available, resulting in 2 600 302 days of observation in total. Heritabilities for the liability to mastitis, estimated with a test-day threshold model, were h2 = 0.19 and h2 = 0.13, depending on the data-recording period (first 50 days of lactation and first 305 days of lactation, respectively). With respect to the relationship between milkability and udder health, the results indicated a slight and linear correlation insofar as one can assume: the higher the milk flow, the worse the udder health. For this reason, bulls and cows with high BVs for milk flow should be excluded from breeding to avoid a deterioration of udder health. The establishment of a special data-recording scheme for functional traits such as milkability and mastitis on commercial dairy farms may be possible according to these results.

Across-environment genetic correlations and the frequency of selective environments shape the evolutionary dynamics of growth rate in Impatiens capensis

Trade-offs can exist within and across environments, and constrain evolutionary trajectories. To examine the effects of competition and resource availability on trade-offs, we grew individuals of recombinant inbred lines of Impatiens capensis in a factorial combination of five densities with two light environments (full light and neutral shade) and used a Bayesian logistic growth analysis to estimate intrinsic growth rates. To estimate across-environment constraints, we developed a variance decomposition approach to principal components analysis, which accounted for sample size, model-fitting, and within-RIL variation prior to eigenanalysis. We detected negative across-environment genetic covariances in intrinsic growth rates, although only under full-light. To evaluate the potential importance of these covariances, we surveyed natural populations of I. capensis to measure the frequency of different density environments across space and time. We combined our empirical estimates of across-environment genetic variance-covariance matrices and frequency of selective environments with hypothetical (yet realistic) selection gradients to project evolutionary responses in multiple density environments. Selection in common environments can lead to correlated responses to selection in rare environments that oppose and counteract direct selection in those rare environments. Our results highlight the importance of considering both the frequency of selective environments and the across-environment genetic covariances in traits simultaneously.

Estimation of genetic parameters for monthly egg production in laying hens based on random regression models

Heritability and genetic correlations of monthly egg production under random regression models were estimated. Three layer lines (A22, A88, K66) in six consecutive generations were analysed. A22 (13,770 recorded hens) and A88 (13,950 recorded hens) are maternal lines of Rhode Island White birds selected on egg production and shell colour; K66 (9,351 recorded birds) is a paternal line of Rhode Island Red birds selected on egg weight. Eight models with different orders of Legendre polynomials were applied. Adequacy of the models was checked by the Akaike Information Criterion. According to the most adequate model including second order Legendre polynomials for fixed effects and third order for additive genetic and permanent environmental effects, relatively high heritabilities were estimated in the first (h2=0.3) and final (h2 above 0.3) periods of production with a substantial decrease in heritability during the egg production peak. Methodology based on random regression animal models can be recommended for genetic evaluation of laying hens.

Investigation of major gene for milk yield, milking speed, dry matter intake, and body weight in dairy cattle

The main aim of this study was to determine if there exist any major gene for milk yield (MY), milking speed (MS), dry matter intake (DMI), and body weight (BW) recorded at various stages of lactation in first-lactation dairy cows (2543 observations from 320 cows) kept at the research farm of the Swiss Federal Institute of Technology between April 1994 and April 2004. Data were modelled based a simple repeatability covariance structure and analysed by using Bayesian segregation analyses. Gibbs sampling was used to make statistical inferences on posterior distributions; inferences were based on a single run of the Markov chain for each trait with 500,000 samples, with each 10th sample collected because of the high correlation among the samples. The posterior mean (+/-SD) of major gene variance was 2.61 (+/-2.46) for MY, 0.83 (+/-1.26) for MS, 4.37 (+/-2.34) for DMI, and 2056.43 (+/-665.67) for BW. Highest posterior density regions for 3 of the 4 traits did not include 0 (except MS), which supported the evidence for major gene. With additional tests for agreement with Mendelian transmission probabilities, we could only confirm the existence of a major gene for MY, but not for MS, DMI, and BW. Expected Mendelian transmission probabilities and their model fits were also compared.