Combining Threshold, Thurstonian and Classical Linear Models in Horse Genetic Evaluations for Endurance Competitions

The racing time and rank at finish traits are commonly used for endurance horse breeding programs as a measure of their performance. Even so, given the nature of endurance competitions, many horses do not finish the race. However, the exclusion of non placed horses from the dataset could have an influence on the prediction of individual breeding values. The objective of the present paper was to develop a multitrait model including race time (T), rank (R) and placing (P), with different methodologies, to improve the genetic evaluation in endurance competitions in Spain. The database contained 6135 records from 1419 horses, with 35% of the records not placed. Horse pedigree included 10868 animals, with 52% Arab Horses. All models included gender, age and race effect as systematic effects and combined different random effects beside the animal and residual effects: rider, permanent environmental effect, and interaction horse-rider. The kilometers per race was included as a covariate for T. Heritabilities were estimated as moderately low, ranging from 0.06 to 0.14 for T, 0.09 to 0.15 for P, and 0.07 to 0.17 for R, depending on the model. T and R appeared mostly as inverse measures of the same trait due to their high genetic correlation, suggesting that T can be ignored in future genetic evaluations. P was the most independent trait from the genetic correlations. The possibility of simultaneously processing the threshold, Thurstonian and continuous traits has opened new opportunities for genetic evaluation in horse populations, and much more practical genetic evaluations can be done to help a proper genetic selection.

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PSXII-33 The Effect of Log Transformation on Carcass Data Measured by Ultrasound

Journal of Animal Science ◽

10.1093/jas/skaa278.451 ◽

2020 ◽

Vol 98 (Supplement_4) ◽

pp. 249-249

Author(s):

Tae Jeong Choi ◽

Byoungho Park ◽

Hannah Oh ◽

Oh Sang-Hyon

Keyword(s):

Genetic Parameters ◽

Carcass Traits ◽

Genetic Correlations ◽

Fat Content ◽

Genetic Evaluation ◽

Muscle Area ◽

Log Transformation ◽

Significant Difference ◽

Native Cattle ◽

Genetic Evaluations

Abstract This study is to evaluate the effect of log transformation on ultrasound data records on the genetic evaluation of Hanwoo (Korean native cattle) proven bulls. Three different scenarios were established: genetic evaluations using (A) only yearling weights (YW; n = 15,665) and carcass traits (CT); (B) YW, CT and raw ultrasound data at 12 and 24 months of age; and (C) YW, CT and log transformed data of raw ultrasound data records in (B). Carcass traits include carcass weight (CW; n = 6,526), loin muscle area (LMA; n = 6,820), backfat thickness (BFT; n = 6,723), and intramuscular fat (IMF; n = 5,037). Ultrasound traits include LMA, BFT, and fat content (FC; %), which were measured with Aquila Vet (Pie Medical) between the 12th and 13th rib. REMLF90 was used to estimate genetic parameters such as heritability and genetic correlations. Rank correlations of breeding values were analyzed using SAS 9.2. The heritability of YW was the highest at (B) and reduced by 0.2% at (C). The heritability of CW was higher at (B) and (C) than at (A) by 0.6%. In the case of BFT and IMF, (B) and (C) was 0.5% and 0.6% higher than (A) and -1.0% and -0.8% lower than (A), respectively. The heritabilities regarding ultrasound traits at 12 months of age were higher for LMA and FC in (C) than (B), and higher for BFT in (B) than (C). In the case of 24 months of age, (C) was higher in all ultrasound traits than (B). The rank correlations of (B) and (C) at 12 months were 0.995 in ultrasound LMA and 0.991 in ultrasound BFT. For 24 months, the correlations were 0.989 and 0.986, respectively. In conclusion, the results didn’t provide us with evidence of a significant difference in genetic evaluations among different scenarios regarding log transformation on ultrasound data records of carcass traits.

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Prediction of meat quality traits in the abattoir using portable near-infrared spectrometers: heritability of predicted traits and genetic correlations with laboratory-measured traits

Journal of Animal Science and Biotechnology ◽

10.1186/s40104-021-00555-5 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Simone Savoia ◽

Andrea Albera ◽

Alberto Brugiapaglia ◽

Liliana Di Stasio ◽

Alessio Cecchinato ◽

...

Keyword(s):

Meat Quality ◽

Near Infrared ◽

External Validation ◽

Genetic Correlations ◽

Genetic Selection ◽

Quality Traits ◽

Eye Muscle ◽

Meat Quality Traits ◽

Color Traits ◽

Selection Of

Abstract Background The possibility of assessing meat quality traits over the meat chain is strongly limited, especially in the context of selective breeding which requires a large number of phenotypes. The main objective of this study was to investigate the suitability of portable infrared spectrometers for phenotyping beef cattle aiming to genetically improving the quality of their meat. Meat quality traits (pH, color, water holding capacity, tenderness) were appraised on rib eye muscle samples of 1,327 Piemontese young bulls using traditional (i.e., reference/gold standard) laboratory analyses; the same traits were also predicted from spectra acquired at the abattoir on the intact muscle surface of the same animals 1 d after slaughtering. Genetic parameters were estimated for both laboratory measures of meat quality traits and their spectra-based predictions. Results The prediction performances of the calibration equations, assessed through external validation, were satisfactory for color traits (R2 from 0.52 to 0.80), low for pH and purge losses (R2 around 0.30), and very poor for cooking losses and tenderness (R2 below 0.20). Except for lightness and purge losses, the heritability estimates of most of the predicted traits were lower than those of the measured traits while the genetic correlations between measured and predicted traits were high (average value 0.81). Conclusions Results showed that NIRS predictions of color traits, pH, and purge losses could be used as indicator traits for the indirect genetic selection of the reference quality phenotypes. Results for cooking losses were less effective, while the NIR predictions of tenderness were affected by a relatively high uncertainty of estimate. Overall, genetic selection of some meat quality traits, whose direct phenotyping is difficult, can benefit of the application of infrared spectrometers technology.

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Convolutional Neural Networks to Estimate Dry Matter Yield in a Guineagrass Breeding Program Using UAV Remote Sensing

Sensors ◽

10.3390/s21123971 ◽

2021 ◽

Vol 21 (12) ◽

pp. 3971

Author(s):

Gabriel Silva de Oliveira ◽

José Marcato Junior ◽

Caio Polidoro ◽

Lucas Prado Osco ◽

Henrique Siqueira ◽

...

Keyword(s):

Remote Sensing ◽

Dry Matter ◽

Pearson Correlation ◽

Genetic Correlations ◽

Remote Sensing Data ◽

Breeding Program ◽

Yield Traits ◽

Dry Matter Yield ◽

Breeding Programs ◽

Ground Truth Data

Forage dry matter is the main source of nutrients in the diet of ruminant animals. Thus, this trait is evaluated in most forage breeding programs with the objective of increasing the yield. Novel solutions combining unmanned aerial vehicles (UAVs) and computer vision are crucial to increase the efficiency of forage breeding programs, to support high-throughput phenotyping (HTP), aiming to estimate parameters correlated to important traits. The main goal of this study was to propose a convolutional neural network (CNN) approach using UAV-RGB imagery to estimate dry matter yield traits in a guineagrass breeding program. For this, an experiment composed of 330 plots of full-sib families and checks conducted at Embrapa Beef Cattle, Brazil, was used. The image dataset was composed of images obtained with an RGB sensor embedded in a Phantom 4 PRO. The traits leaf dry matter yield (LDMY) and total dry matter yield (TDMY) were obtained by conventional agronomic methodology and considered as the ground-truth data. Different CNN architectures were analyzed, such as AlexNet, ResNeXt50, DarkNet53, and two networks proposed recently for related tasks named MaCNN and LF-CNN. Pretrained AlexNet and ResNeXt50 architectures were also studied. Ten-fold cross-validation was used for training and testing the model. Estimates of DMY traits by each CNN architecture were considered as new HTP traits to compare with real traits. Pearson correlation coefficient r between real and HTP traits ranged from 0.62 to 0.79 for LDMY and from 0.60 to 0.76 for TDMY; root square mean error (RSME) ranged from 286.24 to 366.93 kg·ha−1 for LDMY and from 413.07 to 506.56 kg·ha−1 for TDMY. All the CNNs generated heritable HTP traits, except LF-CNN for LDMY and AlexNet for TDMY. Genetic correlations between real and HTP traits were high but varied according to the CNN architecture. HTP trait from ResNeXt50 pretrained achieved the best results for indirect selection regardless of the dry matter trait. This demonstrates that CNNs with remote sensing data are highly promising for HTP for dry matter yield traits in forage breeding programs.

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High Heritabilities for Antibiotic Usage Show Potential to Breed for Disease Resistance in Finishing Pigs

Antibiotics ◽

10.3390/antibiotics10070829 ◽

2021 ◽

Vol 10 (7) ◽

pp. 829

Author(s):

Wim Gorssen ◽

Dominiek Maes ◽

Roel Meyermans ◽

Jürgen Depuydt ◽

Steven Janssens ◽

...

Keyword(s):

Pathogenic Bacteria ◽

Animal Health ◽

Molecular Genetic ◽

Genetic Correlations ◽

Genetic Selection ◽

Antibiotic Usage ◽

Finishing Pigs ◽

Production Traits ◽

Parenteral Antibiotic ◽

On Farm

The use of antimicrobials in animal production is under public debate, mainly due to the risk of transfer of resistance to pathogenic bacteria in humans. Therefore, measures have been taken during the last few decades to reduce antibiotic usage in animals, for instance, by national monitoring programmes and by improving animal health management. Although some initiatives exist in molecular genetic selection, quantitative genetic selection of animals towards decreased antibiotic usage is an underexplored area to reduce antibiotic usage. However, this strategy could yield cumulative effects. In this study, we derived new phenotypes from on-farm parenteral antibiotic records from commercially grown crossbred finishing pigs used in the progeny test of Piétrain terminal sires to investigate the heritability of antibiotics usage. Parenteral antibiotic records, production parameters and pedigree records of 2238 full-sib pens from two experimental farms in Belgium between 2014 and 2020 were analysed. Heritability estimates were moderate (18–44%) for phenotypes derived from all antibiotic treatments, and low (1–15%) for phenotypes derived from treatments against respiratory diseases only. Moreover, genetic correlations between these new phenotypes and mortality were low to moderate (0.08–0.60) and no strong adverse genetic correlations with production traits were found. The high heritabilities and favourable genetic correlations suggest these new phenotypes, derived from on-farm antibiotics records, to be promising for inclusion in future pig breeding programs to breed for a decrease in antibiotics usage.

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Comparison of two live-animal ultrasound systems for genetic evaluation of carcass traits in Angus cattle

Translational Animal Science ◽

10.1093/tas/txab011 ◽

2021 ◽

Author(s):

C J Duff ◽

J H J van der Werf ◽

P F Parnell ◽

S A Clark

Keyword(s):

Carcass Traits ◽

Genetic Correlations ◽

Subcutaneous Fat ◽

Genetic Evaluation ◽

Ultrasound Scan ◽

Ultrasound Scanning ◽

Eye Muscle ◽

Angus Cattle ◽

Breeding Objective ◽

Two Systems

Abstract The improvement of carcass traits is an important breeding objective in beef cattle breeding programs. The most common way of selecting for improvement in carcass traits is via indirect selection using ultrasound scanning of selection candidates which are submitted to genetic evaluation programs. Two systems used to analyse ultrasound images to predict carcass traits are the Pie Medical Esaote Aquila (PIE) and Central Ultrasound Processing (CUP). This study compared the ability of the two systems to predict carcass traits for genetic evaluation in Australian Angus cattle. Genetic and phenotypic parameters were estimated using data from 1648 Angus steers which were ultrasound scanned twice with both systems, first at feedlot entry and then following 100 days in the feedlot. The traits interpreted from ultrasound scanning included eye muscle area (EMA), rib fat (RIB) rump fat (RUMP) and intramuscular fat (IMF). Abattoir carcass data were collected on all steers following the full feedlot feeding period of 285 days. For all ultrasound scan traits, CUP resulted in higher phenotypic and genetic variances compared to the PIE. For IMF, CUP had higher heritability at feedlot intake (0.51 for CUP compared to 0.37 for PIE) and after 100 days feeding (0.54 for CUP compared to 0.45 PIE). CUP predicted IMF also tended to have stronger correlations with the breeding objective traits of carcass IMF marbling traits, both genetically (ranging from 0.59 to 0.75 for CUP compared to 0.45 to 0.63 for PIE) and phenotypically (ranging from 0.27 to 0.43 for CUP compared to 0.19 to 0.28 for PIE). Ultrasound scan EMA were the only group of traits in which the heritabilities were higher for PIE (0.52 for PIE compared to 0.40 for CUP at feedlot intake and 0.46 for PIE compared to 0.43 for CUP at 100 days of feeding), however with similar relationships to the breeding objective carcass EMA observed. For subcutaneous fat traits of ultrasound RIB and RUMP, the heritabilites and genetic correlations to the related carcass traits were similar, with the exception being the higher heritability observed for CUP predicted RUMP at feedlot intake at 0.52 compared to 0.38 for PIE. The results from this study indicates that the CUP system, compared to PIE, provides an advantage for genetic evaluation of carcass traits in Angus cattle, particularly for the IMF and associated marbling traits.

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Genetic importance of fat and eye muscle depth in Merino breeding programs

Animal Production Science ◽

10.1071/an14645 ◽

2016 ◽

Vol 56 (4) ◽

pp. 690 ◽

Cited By ~ 15

Author(s):

D. J. Brown ◽

A. A. Swan

Keyword(s):

Carcass Traits ◽

Genetic Correlations ◽

Fibre Diameter ◽

Economic Index ◽

Parasite Resistance ◽

Eye Muscle ◽

Breeding Programs ◽

Dual Purpose ◽

Internal Parasite ◽

Reproduction Traits

Australian Merino breeders have traditionally selected animals for breeding predominately on the basis of wool characteristics. Over recent decades, an increasing proportion of Merino breeders are interested in producing a ewe that can be used for prime-lamb production, but that also performs well for wool characteristics. Correlations between ultrasound carcass traits and other traits such as wool, internal parasite resistance and reproduction traits, are not very well known. The aims of this study were three-fold: (1) to estimate the genetic relationships between ultrasound carcass traits and wool, internal parasite resistance and reproduction traits, (2) to determine the value of recording ultrasound carcass traits in Merino breeding programs, and (3) to evaluate the impact of improving ewe genetic merit for fatness on their reproduction performance. Ultrasound fat and eye muscle depth had small to moderate genetic correlations with most traits, with positive correlations observed for bodyweight, fibre diameter, fibre curvature and reproduction, and negative correlations observed for fleece weight, fibre diameter coefficient of variation, worm egg count and breech wrinkle. As expected on the basis of these genetic correlations, estimated breeding values for fat depth of ewes had a positive association with their observed reproduction performance, but the effect explained only minimal variation in reproductive performance, and was extremely variable among flocks and years. A range of measurement scenarios was investigated for three standard MERINOSELECT indexes. Measuring fat and eye muscle depth resulted in 3%, 4% and 21% additional economic index gain for the fine, medium and dual purpose indexes, respectively, whereas measuring reproduction traits directly resulted in 17%, 27% and 45% additional gain in the economic index. Dual purpose index gains benefited more from measuring ultrasound carcass traits as it is the only index with a direct economic value placed on carcass traits. Measuring fat and eye muscle depth also resulted in a greater reduction in worm egg count. The results indicated that desirable genetic progress can be made in wool, ultrasound carcass, internal parasite resistance and number of lambs born and weaned simultaneously using multiple trait selection to account for the mix of favourable and unfavourable correlations between these traits. These results also demonstrated that the best method to maximise economic gain is to measure as many traits (or closely correlated traits) in the breeding objective as possible.

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Corrigendum to: Consequences of genetic selection for environmental impact traits on economically important traits in dairy cows

Animal Production Science ◽

10.1071/an16592_co ◽

2018 ◽

Vol 58 (10) ◽

pp. 1966

Author(s):

Purna Kandel ◽

Sylvie Vanderick ◽

Marie-Laure Vanrobays ◽

Hélène Soyeurt ◽

Nicolas Gengler

Keyword(s):

Dairy Cows ◽

Body Condition Score ◽

Genetic Correlations ◽

Genetic Selection ◽

Selection Response ◽

Direct Selection ◽

Correlated Response ◽

Production Traits ◽

Ch4 Emissions ◽

Natural Logarithm

Methane (CH4) emission is an important environmental trait in dairy cows. Breeding aiming to mitigate CH4 emissions require the estimation of genetic correlations with other economically important traits and the prediction of their selection response. In this study, test-day CH4 emissions were predicted from milk mid-infrared spectra of Holstein cows. Predicted CH4 emissions (PME) and log-transformed CH4 intensity (LMI) computed as the natural logarithm of PME divided by milk yield (MY). Genetic correlations of PME and LMI with traits used currently were approximated from correlations between estimated breeding values of sires. Values were for PME with MY 0.06, fat yield (FY) 0.09, protein yield (PY) 0.13, fertility 0.17; body condition score (BCS) –0.02; udder health (UDH) 0.22; and longevity 0.22. As expected by its definition, values were negative for LMI with production traits (MY –0.61; FY –0.15 and PY –0.40) and positive with fertility (0.36); BCS (0.20); UDH (0.08) and longevity (0.06). The genetic correlations of 33 type traits with PME ranged from –0.12 to 0.25 and for LMI ranged from –0.22 to 0.18. Without selecting PME and LMI (status quo) the relative genetic change through correlated responses of other traits were in PME by 2% and in LMI by –15%, but only due to the correlated response to MY. Results showed for PME that direct selection of this environmental trait would reduce milk carbon foot print but would also affect negatively fertility. Therefore, more profound changes in current indexes will be required than simply adding environmental traits as these traits also affect the expected progress of other traits.

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Analysis of horse breeding and equestrian sports in the Republic of Croatia

Biotechnology in Animal Husbandry ◽

10.2298/bah1103415b ◽

2011 ◽

Vol 27 (3) ◽

pp. 415-429

Author(s):

M. Baban ◽

M. Sakac ◽

N. Korabi ◽

B. Antunovic ◽

P. Mijic ◽

...

Keyword(s):

Transitional Period ◽

Therapeutic Riding ◽

Breeding Programs ◽

Long Period ◽

Horse Breeding ◽

Equestrian Sports ◽

Central Register ◽

Total Proportion ◽

The Republic ◽

Show Jumping

Horse breeding in the Republic of Croatia, before its entrance into European Union, is in the transitional period. In the breeding sense, Croatian horse breeding is set according to the model of European countries and is trying to counteract with ?modern horse breeding countries?. Croatian Center for Horse Breeding - Djakovo and Lipik State Stud Farms (CCHB), with the Central register of equidae is, as the head national institution, responsible for running and maintaining national central equidae database (49 registers of horses and 27 registers of breeding types). Croatia has registered total of 21.796 equidae, from which 19.306 animals are horses. Registered horses according to groups make the total proportion of 37% warmblood horses, 59% coldblood horses and 4% ponies. Horse breeders are organized in breeders associations, which form federations of associations referring to separate horse breeds. Currently in Croatia there are four federations of breeders associations (with 43 associations and 11 private stud farms). Those verified breeding organizations are conducting independently breeding programs and fully maintain breeding and selection obligations for horse breeds for which they have approval of the Croatian Ministry. Native breeds in Croatia are Croatian Coldblood, Croatian Posavac and Medjimurje horse (Murinsulaner), while Lipizzan horse is considered as protected breed. Development of horse breeding is considerably supported with national subsidies. Internationally verified breeds which are bred in Croatia are Lipizzan horse, Pure Arabian horses, Thoroughbred, Haflinger and Gidran horses. The horse breeding in Croatia is developing in four different directions. Ecological breeding implies native horse breeds and is spread on the areas of protected nature resorts in Croatia. Croatians are through their history connected to horse breeding, which is even today irreplaceable in traditional cultural manifestations (Djakovacki vezovi, Vinkovacke jeseni, Sinjska alka, etc.), various horse shows and fairs and also in more ?modern? ways through recreation and entertainment. The third direction of development of horse breeding in Croatia is therapeutic riding, which includes 26 associations, over one hundred horses and over one thousand users organized under the Therapeutic Riding Association of Croatia. Sports horse breeding represents fourth direction in Croatian horse breeding. It is formed by four federations: Croatian Trotting Federation (trotting), Croatian Gallop Federation (gallop sport) and Croatian Equestrian Federation (endurance, dressage, military, show jumping, driving). Croatian Equestrian Federation includes 49 equestrian clubs. In the last four years between 455 and 582 competitors and between 495 and 581 horses (for show jumping 45%, dressage 31%, endurance 19%, driving 5% and military) were licensed annually. Croatia achieved noticeable results on the international scene in driving sports and in Paralympics. In all mentioned directions of Croatian horse breeding, the tendency should be directed to achieving higher breeding standards (nutrition, stabling, transport, training) and more rational using of horses. Such breeding and using of horses will lead to top bred horses and successful sport horses. This implies synchronized work through long period of time, respecting institutional and breeding rules.

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Phenotypic diversity of horse breeds used in sports activities, employing multivariate analysis

Spanish Journal of Agricultural Research ◽

10.5424/sjar/2021191-16576 ◽

2021 ◽

Vol 19 (1) ◽

pp. e0401

Author(s):

Marcos P. G. Rezende ◽

Julio C. Souza ◽

Carlos H. M. Malhado ◽

Paulo L. S. Carneiro ◽

Johnny I. M. Araujo ◽

...

Keyword(s):

Multivariate Analysis ◽

Principal Components ◽

Phenotypic Diversity ◽

The Body ◽

Breeding Programs ◽

Mato Grosso ◽

Canonical Variables ◽

Horse Breeding ◽

Quarter Horse ◽

Euclidean Distances

Aim of study: Sports involving horses have notable financial importance. Breeds are evaluated to find the best-suited ones for a specific sport category. Phenotypic diversity using biometric markers was evaluated for Quarter Horse (QH), Arabic (AR), English Thoroughbred (ET), and Brazilian Equestrian (BE) horse breeds.Area of study: Mato Grosso do Sul-Brazil.Material and methods: Lengths, widths, and circumference measures of 268 horses were collected. These measures were used to estimate conformation indexes. The size-free canonical discriminant analysis was used to remove the size effect on the animal's shape. The similarity among breeds (by sex) was evaluated employing multivariate analysis (canonical analysis, MANOVA, principal components, Euclidean distances, and grouping through complete linkage), considering all linear measures and conformation indexes (included in the analysis of principal components).Main results: Four canonical variables (CANs), each one representing an equation to interpret the morpho-functionality of breeds “sustentation”, “structure”, “frame”, and “equilibrium”, were retained. The breeds presented differences when the CANs were simultaneously considered. Differences mainly were the size and the thickness of the body as well as the ability of the animal to move. ET, QH, and BE demonstrate a well-defined biometric profile. These three breeds clustered separately from AR breed.Research highlights: Canonical variables allow to verify the functional aptitudes since the responses were close to conformation indices commonly used as horse skill estimators. The implementation of these variables as selection criteria in horse breeding programs require further studies in larger populations of horses for a confirmation of the present results.

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Genetic Evaluation of Reproductive and Metabolic Disorders and Displaced Abomasum in Czech Holstein Cows

Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis ◽

10.11118/actaun201967040939 ◽

2019 ◽

Vol 67 (4) ◽

pp. 939-946

Author(s):

Eva Kašná ◽

Petr Fleischer ◽

Ludmila Zavadilová ◽

Soňa Šlosárková

Keyword(s):

Metabolic Disorders ◽

Genetic Parameters ◽

Genetic Correlations ◽

Health Data ◽

Genetic Evaluation ◽

Holstein Cows ◽

Retained Placenta ◽

Cystic Ovary ◽

On Line ◽

Parturient Paresis

We estimated the genetic parameters of the most frequent reproductive and metabolic disorders as recorded on‑line by 55 milk producers in Czech Holstein cows in the Diary of Diseases and Treatments. The dataset covered the period from July 2015 to May 2019. The coefficients of heritability were estimated for retained placenta (h2 = 0.01), metritis (h2 = 0.04), endometritis (h2 = 0.03), cystic ovary disease (h2 = 0.03), parturient paresis (h2 = 0.01), ketosis (h2 = 0.01) and displaced abomasum (h2 = 0.03). Positive genetic correlations different from 0 were estimated between parturient paresis and displaced abomasum (rg1g2 = 0.75), retained placenta and metritis (rg1g2 = 0.61), displaced abomasum and endometritis (rg1g22 = 0.49), metritis and endometritis (rg1g2 = 0.45), and metritis and displaced abomasum (rg1g2 = 0.41). Because each farmer recorded a slightly different portfolio of health data, the genetic correlations with metabolic disorders couldn’t be estimated in most cases, since the number of observations was not sufficient.

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