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Genetic parameters of differential somatic cell count, milk composition, and cheese-making traits measured and predicted using spectral data in Holstein cows

  • S. Pegolo
    Correspondence
    Corresponding author
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • L.F.M. Mota
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • V. Bisutti
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • M. Martinez-Castillero
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • D. Giannuzzi
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • L. Gallo
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • S. Schiavon
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • F. Tagliapietra
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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  • A. Revello Chion
    Affiliations
    Associazione Regionale Allevatori del Piemonte, Via Torre Roa, 13, 12100 Cuneo, Italy
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  • E. Trevisi
    Affiliations
    Department of Animal Science, Food and Nutrition - DIANA, Università Cattolica del Sacro Cuore, 29122 Piacenza, Italy

    Romeo and Enrica Invernizzi Research Center for Sustainable Dairy Production of the Università Cattolica del Sacro Cuore (CREI), 29122 Piacenza, Italy
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  • R. Negrini
    Affiliations
    Department of Animal Science, Food and Nutrition - DIANA, Università Cattolica del Sacro Cuore, 29122 Piacenza, Italy

    Italian Association of Breeders (AIA), 00161 Rome, Italy
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  • P. Ajmone Marsan
    Affiliations
    Department of Animal Science, Food and Nutrition - DIANA, Università Cattolica del Sacro Cuore, 29122 Piacenza, Italy

    Nutrigenomics and Proteomics Research Center - PRONUTRIGEN, Università Cattolica del Sacro Cuore, 29122 Piacenza, Italy
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  • A. Cecchinato
    Affiliations
    Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE), University of Padova, Viale dell' Università 16, 35020 Legnaro PD, Italy
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Open ArchivePublished:July 09, 2021DOI:https://doi.org/10.3168/jds.2021-20395

      ABSTRACT

      Mastitis is one of the most prevalent diseases in dairy cattle and is the cause of considerable economic losses. Alongside somatic cell count (SCC), differential somatic cell count (DSCC) has been recently introduced as a new indicator of intramammary infection. The DSCC is expressed as a count or a proportion (%) of polymorphonuclear neutrophils plus lymphocytes (PMN-LYM) in milk somatic cells. These numbers are complemented to total somatic cell count or to 100 by macrophages (MAC). The aim of this study was to investigate the genetic variation and heritability of DSCC, and its correlation with milk composition, udder health indicators, milk composition, and technological traits in Holstein cattle. Data used in the analysis consisted in single test-day records from 2,488 Holstein cows reared in 36 herds located in northern Italy. Fourier-transform infrared (FTIR) spectroscopy was used to predict missing information for some milk coagulation and cheese-making traits, to increase sample size and improve estimation of the genetic parameters. Bayesian animal models were implemented via Gibbs sampling. Marginal posterior means of the heritability estimates were 0.13 for somatic cell score (SCS); 0.11 for DSCC, MAC proportion, and MAC count; and 0.10 for PMN-LYM count. Posterior means of additive genetic correlations between SCS and milk composition and udder health were low to moderate and unfavorable. All the relevant genetic correlations between the SCC traits considered and the milk traits (composition, coagulation, cheese yield and nutrients recovery) were unfavorable. The SCS showed genetic correlations of −0.30 with the milk protein proportion, −0.56 with the lactose proportion and −0.52 with the casein index. In the case of milk technological traits, SCS showed genetic correlations of 0.38 with curd firming rate (k20), 0.45 with rennet coagulation time estimated using the curd firming over time equation (RCTeq), −0.39 with asymptotic potential curd firmness, −0.26 with maximum curd firmness (CFmax), and of −0.31 with protein recovery in the curd. Differential somatic cell count expressed as proportion was correlated with SCS (0.60) but had only 2 moderate genetic correlations with milk traits: with lactose (−0.32) and CFmax (−0.33). The SCS was highly correlated with the log PMN-LYM count (0.79) and with the log MAC count (0.69). The 2 latter traits were correlated with several milk traits: fat (−0.38 and −0.43 with PMN-LYM and MAC counts, respectively), lactose percentage (−0.40 and −0.46), RCTeq (0.53 and 0.41), tmax (0.38 and 0.48). Log MAC count was correlated with k20 (+0.34), and log PMN-LYM count was correlated with CFmax (−0.26) and weight of water curd as percentage of weight of milk processed (−0.26). The results obtained offer new insights into the relationships between the indicators of udder health and the milk technological traits in Holstein cows.

      Key words

      INTRODUCTION

      Mastitis in its clinical and subclinical forms is the most common and economically damaging disease in dairy herds (
      • Ruegg P.L.
      New perspectives in udder health management.
      ), affecting production, milk quality and composition (
      • Bobbo T.
      • Ruegg P.L.
      • Stocco G.
      • Fiore E.
      • Gianesella M.
      • Morgante M.
      • Pasotto D.
      • Bittante G.
      • Cecchinato A.
      Associations between pathogen-specific cases of subclinical mastitis and milk yield, quality, protein composition, and cheese-making traits in dairy cows.
      ), animal welfare (
      • Halasa T.
      • Huijps K.
      • Østerås O.
      • Hogeveen H.
      Economic effects of bovine mastitis and mastitis management: A review.
      ), and antimicrobial resistance related to antibiotic therapy (
      • Trevisi E.
      • Zecconi A.
      • Cogrossi S.
      • Razzuoli E.
      • Grossi P.
      • Amadori M.
      Strategies for reduced antibiotic usage in dairy cattle farms.
      ). Udder health has therefore become of increasing importance in recent years, as have herd management strategies that should be continuously improved to increase milk production sustainability and efficiency (
      • Nørstebø H.
      • Dalen G.
      • Rachah A.
      • Heringstad B.
      • Whist A.C.
      • Nødtvedt A.
      • Reksen O.
      Factors associated with milking-to-milking variability in somatic cell counts from healthy cows in an automatic milking system.
      ).
      Somatic cell count is commonly used as proxy for udder health in dairy cattle (
      • Barkema H.W.
      • Van der Ploeg J.D.
      • Schukken Y.H.
      • Lam T.J.G.M.
      • Benedictus G.
      • Brand A.
      Management style and its association with bulk milk somatic cell count and incidence rate of clinical mastitis.
      ;
      • Guzzo N.
      • Sartori C.
      • Mantovani R.
      Genetic parameters of different measures of somatic cell counts in the Rendena breed.
      ). Given the positive correlation with mastitis and its higher heritability (
      • Koeck A.
      • Miglior F.
      • Kelton D.F.
      • Schenkel F.S.
      Alternative somatic cell count traits to improve mastitis resistance in Canadian Holsteins.
      ), SCC and especially SCS [log2(SCC/100,000) + 3)] are currently used for the genetic evaluation of udder health. The differential SCC (DSCC) has been recently proposed as a novel indicator of mammary gland inflammation status (
      • Damm M.
      • Holm C.
      • Blaabjerg M.
      • Bro M.N.
      • Schwarz D.
      Differential somatic cell count—A novel method for routine mastitis screening in the frame of Dairy Herd Improvement testing programs.
      ). This trait represents the proportion of PMN and lymphocytes (LYM) in milk total SCC. The SCC includes also macrophages (MAC), the proportion of which can be indirectly estimated subtracting DSCC from 100%. The DSCC, combined with SCS, may provide a more comprehensive picture of the inflammatory process in the mammary gland.
      When the udder is healthy, the milk has relatively high proportions of LYM and MAC and a small proportion of PMN (
      • Wickström E.
      • Persson-Waller K.
      • Lindmark-Månsson H.
      • Östensson K.
      • Sternesjö Å.
      Relationship between somatic cell count, polymorphonuclear leucocyte count and quality parameters in bovine bulk tank milk.
      ;
      • Schwarz D.
      • Diesterbeck U.S.
      • König S.
      • Brügemann K.
      • Schlez K.
      • Zschöck M.
      • Wolter W.
      • Czerny C.P.
      Flow cytometric differential cell counts in milk for the evaluation of inflammatory reactions in clinically healthy and subclinically infected bovine mammary glands.
      ). Several studies have shown that when an infection occurs, not only do the proportions of these immune cells change, but they also vary according to the infection stage. In acute inflammation, the proportion of PMN increases (
      • Pilla R.
      • Malvisi M.
      • Snel G.G.M.
      • Schwarz D.
      • König S.
      • Czerny C.P.
      • Piccinini R.
      Differential cell count as an alternative method to diagnose dairy cow mastitis.
      ) and may reach 95% (
      • Kehrli Jr., M.E.
      • Shuster D.E.
      Factors affecting milk somatic cells and their role in health of the bovine mammary gland.
      ), whereas in chronic conditions, LYM increase, with a consequent decrease in PMN (
      • Leitner G.
      • Eligulashvily R.
      • Krifucks O.
      • Perl S.
      • Saran A.
      Immune cell differentiation in mammary gland tissues and milk of cows chronically infected with Staphylococcus aureus.
      ).
      Recently, studies have started to investigate DSCC from a phenotypic point of view, including its potential role as trait proxy for udder health (
      • Zecconi A.
      • Vairani D.
      • Cipolla M.
      • Rizzi N.
      • Zanini L.
      Assessment of subclinical mastitis diagnostic accuracy by differential cell count in individual cow milk.
      ) and its relationships with SCC (
      • Damm M.
      • Holm C.
      • Blaabjerg M.
      • Bro M.N.
      • Schwarz D.
      Differential somatic cell count—A novel method for routine mastitis screening in the frame of Dairy Herd Improvement testing programs.
      ), milk yield and composition (
      • Stocco G.
      • Summer A.
      • Cipolat-Gotet C.
      • Zanini L.
      • Vairani D.
      • Dadousis C.
      • Zecconi A.
      Differential somatic cell count as a novel indicator of milk quality in dairy cows.
      ;
      • Zecconi A.
      • Dell'Orco F.
      • Vairani D.
      • Rizzi N.
      • Cipolla M.
      • Zanini L.
      Differential somatic cell count as a marker for changes of milk composition in cows with very low somatic cell count.
      ;
      • Pegolo S.
      • Giannuzzi D.
      • Bisutti V.
      • Tessari R.
      • Gelain M.E.
      • Gallo L.
      • Schiavon S.
      • Tagliapietra F.
      • Trevisi E.
      • Ajmone Marsan P.
      • Bittante G.
      • Cecchinato A.
      Associations between differential somatic cell count and milk yield, quality, and technological characteristics in Holstein cows.
      ), and cheese-making traits (
      • Pegolo S.
      • Giannuzzi D.
      • Bisutti V.
      • Tessari R.
      • Gelain M.E.
      • Gallo L.
      • Schiavon S.
      • Tagliapietra F.
      • Trevisi E.
      • Ajmone Marsan P.
      • Bittante G.
      • Cecchinato A.
      Associations between differential somatic cell count and milk yield, quality, and technological characteristics in Holstein cows.
      ). In addition, the genetic parameters of DSCC have been preliminarily investigated by
      • Bobbo T.
      • Penasa M.
      • Cassandro M.
      Short communication: Genetic aspects of milk differential somatic cell count in Holstein cows: A preliminary analysis.
      , who found DSCC to have a higher heritability than SCS (0.08 vs. 0.04).
      For genetic purposes, there is growing interest in methods that can routinely and accurately predict phenotypes at low cost. Fourier-transform infrared (FTIR) spectroscopy analysis of milk is one such method (
      • Tiplady K.M.
      • Lopdell T.J.
      • Littlejohn M.D.
      • Garrick D.J.
      The evolving role of Fourier-transform mid-infrared spectroscopy in genetic improvement of dairy cattle.
      ). It has proved to be an effective tool for large-scale phenotyping of several dairy cattle traits with good accuracy (
      • Cecchinato A.
      • Toledo-Alvarado H.
      • Pegolo S.
      • Rossoni A.
      • Santus E.
      • Maltecca C.
      • Bittante G.
      • Tiezzi F.
      Integration of wet-lab measures, milk infrared spectra, and genomics to improve difficult-to-measure traits in dairy cattle populations.
      ). Good prediction of phenotypes depends on the development of good calibration models.
      To date no studies have developed calibration equations for milk cheese-making traits assessed with the 9-MilCA procedure (
      • Cipolat-Gotet C.
      • Cecchinato A.
      • Stocco G.
      • Bittante G.
      The 9-MilCA method as a rapid, partly automated protocol for simultaneously recording milk coagulation, curd firming, syneresis, cheese yield, and curd nutrients recovery or whey loss.
      ) using FTIR spectra in the Holstein breed, or estimated genetic parameters for these traits using measured or predicted phenotypes. In addition, the genetic relationships between DSCC and cheese making have never been investigated despite this being a fundamental step before considering the potential inclusion of DSCC in dairy cattle breeding programs.
      We therefore exploited the integration of various databases assembled in other research projects with the aims of (1) developing specific FTIR calibration equations for milk coagulation properties (MCP) measured by lactodynamography, and for cheese-making traits obtained with the 9-MilCA nano-cheesemaking procedure; (2) applying these FTIR equations to spectral data where the aforementioned reference values were missing; and (3) inferring the genetic parameters of SCS, DSCC-related traits, 13 phenotypes related to milk composition and udder health, and 17 milk technological traits (measured and predicted) in a cohort of 2,488 Holstein cows.

      MATERIALS AND METHODS

      Field Data and Milk Collection

      The present study was part of LATSAN and BENELAT projects which aimed at developing new strategies and innovative tools for the improvement of animal welfare and milk quality in dairy cattle breeding. We took advantage of the integration of data from previous research projects which were generated with the same methodology within the same laboratory of our research group. Milk samples were collected once during the evening milking from 2,488 Holstein Friesian cows reared in herds located in different regions of northern Italy and characterized by semi-intensive management systems (Table 1). Cows were fed TMR based on silage, except for those reared in 2 herds located in the Parmigiano Reggiano Protected Denomination of Origin hard cheese-production area. Because regulations governing the production of this cheese do not allow the use of silages, the cows in these herds were fed a ration based on dry roughage, mainly alfalfa and meadow hay, and concentrates. Drinking water was available from automatic water bowls. Large herds were sampled more than once because the laboratory could only process a maximum of roughly 65 cheese-making procedures per day. Animals with clinical signs of disease or that had received medical treatment were not sampled.
      Table 1Schematic representation of different sources of information exploited in this study
      HerdLocationPhenotype
      Number of records available before editing.
      FTIR spectra
      FTIR = Fourier-transformed infrared spectroscopy spectral data available for this study.
      Milk compositionMCP-CF
      MCP-CF = milk coagulation properties and curd firming traits: rennet coagulation time; curd firming rate as the time to a curd firmness of 20 mm; curd firmness at 30 min from rennet addition; rennet coagulation time estimated using the equation; asymptotic potential curd firmness; curd firming instant rate constant; syneresis instant rate constant; maximum curd firmness achieved within 45 min; and time at achievement of CFmax.
      CY
      CY = cheese yield traits: weight of fresh curd as percentage of weight of milk processed; weight of curd solids as percentage of weight of milk processed; and weight of water curd as percentage of weight of milk processed.
      REC
      REC = recovery traits: protein of the curd as percentage of the protein of the milk processed; fat of the curd as percentage of the fat of the milk processed; solids of the curd as percentage of the solids of the milk processed; and energy of the curd as percentage of energy of the milk processed.
      SCC
      DSCC = differential SCC.
      DSCC
      DSCC = differential SCC.
      Herd 1Lombardy81816181
      Herd 2Emilia-Romagna964877940901962471964
      Herd 3Emilia-Romagna73737372733773
      Herd 4Emilia-Romagna195180182179194
      Herd 5Emilia-Romagna273269270269273
      Herd 6Veneto141141141141
      Herd 7Veneto58565653585874
      Herd 8Veneto236202020235235235
      Herd 9 to herd 36
      All these herds sampled in Trentino Alto Adige region were grouped together as there were no differences among them in providing phenotypic and FTIR spectra information.
      Trentino Alto Adige region467462379470
      Total (36 herds)2,4881,9371,5411,4942,3961,0032,038
      1 Number of records available before editing.
      2 MCP-CF = milk coagulation properties and curd firming traits: rennet coagulation time; curd firming rate as the time to a curd firmness of 20 mm; curd firmness at 30 min from rennet addition; rennet coagulation time estimated using the equation; asymptotic potential curd firmness; curd firming instant rate constant; syneresis instant rate constant; maximum curd firmness achieved within 45 min; and time at achievement of CFmax.
      3 CY = cheese yield traits: weight of fresh curd as percentage of weight of milk processed; weight of curd solids as percentage of weight of milk processed; and weight of water curd as percentage of weight of milk processed.
      4 REC = recovery traits: protein of the curd as percentage of the protein of the milk processed; fat of the curd as percentage of the fat of the milk processed; solids of the curd as percentage of the solids of the milk processed; and energy of the curd as percentage of energy of the milk processed.
      5 DSCC = differential SCC.
      6 FTIR = Fourier-transformed infrared spectroscopy spectral data available for this study.
      7 All these herds sampled in Trentino Alto Adige region were grouped together as there were no differences among them in providing phenotypic and FTIR spectra information.
      After collection, all the individual milk samples were kept at 4°C until analysis. The samples were divided into 2 aliquots. Preservative (bronopol) was added to one of these, which was then transferred to the laboratories of the Breeders Association of the Veneto and of the Breeders Federation of the Province of Trento (Trento, Italy) for milk quality and composition analyses. The other, without preservative, was transported to the cheese-making laboratory of the Department of Agronomy, Food, Natural Resources, Animals and Environment (DAFNAE) of the University of Padua (Legnaro, Padua, Italy) for assessment of milk technological traits. The analyses were carried out within 48 h of sample collection or within 24 h for the composition analysis. Pedigree information was provided by the Italian Holstein and Jersey Association (ANAFIJ, Cremona, Italy); only cows with phenotypic records and their ancestors were included in the study.

      Milk Composition Traits

      Analyses of milk quality and composition, including protein, casein, fat, and lactose percentages, urea (mg/100 g), and milk conductivity (mS/cm) were carried out with an FT6000 Milkoscan infrared analyzer (Foss A/S). Somatic cell count (cells/mL) and DSCC (proportion) were determined with a Fossomatic 7 DC analyzer (Foss A/S). To obtain a normal distribution, SCC was log-transformed to SCS according to the equation proposed by
      • Ali A.K.A.
      • Shook G.E.
      An optimum transformation for somatic cell concentration in milk.
      [SCS = log2(SCC/100,000) + 3]. The DSCC was also expressed as a quantitative variable taking into account the total SCC (
      • Pegolo S.
      • Giannuzzi D.
      • Bisutti V.
      • Tessari R.
      • Gelain M.E.
      • Gallo L.
      • Schiavon S.
      • Tagliapietra F.
      • Trevisi E.
      • Ajmone Marsan P.
      • Bittante G.
      • Cecchinato A.
      Associations between differential somatic cell count and milk yield, quality, and technological characteristics in Holstein cows.
      ):
      PMN-LYM count, 103/mL = DSCC × SCC (103/mL);


      MAC count, 103/mL = (1 – DSCC) × SCC (103/mL).


      As with SCC, the PMN-LYM and MAC counts were then log-transformed as log2 (PMN-LYM or MAC count/100,000) + 3.
      Milk pH values were determined with a Crison Basic electrode (Crison Instruments SA), whereas milk conductivity was measured by an online device installed in the milking parlor (Afimilk).

      Analysis of Milk Coagulation and Curd Firmness Properties

      Analysis of MCP was carried out in duplicate by the same operator on milk samples from 34 herds using 2 identical mechanical lactodynamographs (Formagraph; Foss A/S), according to
      • Stocco G.
      • Cipolat-Gotet C.
      • Bobbo T.
      • Cecchinato A.
      • Bittante G.
      Breed of cow and herd productivity affect milk composition and modeling of coagulation, curd firming, and syneresis.
      . In brief, the procedure consisted of adding 200 µL of rennet solution (Hansen Standard 215 with 80 ± 5% chymosin and 20 ± 5% pepsin; Pacovis Amrein AG) diluted to 1.2% (wt/vol) with fresh distilled water to every milk samples (10 mL), previously heated in a water bath at 35°C.
      For each traditional single-point MCP trait, we recorded rennet coagulation time (RCT, min), which is the time from rennet addition to the start of coagulation); curd firming time (k20, min), which is the time taken from rennet addition to reach a curd firmness of 20 mm); and curd firmness (a30, mm), measured at 30 min after rennet addition. The 240 recordings of the width of the coagulation curve (one every 15s, 1-h test length) extrapolated from the 2 Formagraph runs were modeled using the equation proposed by
      • Bittante G.
      • Contiero B.
      • Cecchinato A.
      Prolonged observation and modelling of milk coagulation, curd firming, and syneresis.
      to obtain estimates of the following curd firming and syneresis parameters: RCT, estimated from the curd firming equation (RCTeq, min); the curd firming instant rate constant (kCF,% min); the curd syneresis instant rate constant (kSR, % min); the maximum curve reached within 60 min (CFmax, mm); the asymptotic potential curd firmness (CFp, mm) and time needed to reach CFmax (tmax, min). Repeated measures were averaged before statistical analysis.

      Analysis of Cheese-Making Traits

      Cheese yield (CY) and nutrient recoveries were assessed in duplicate from milk samples from 20 herds using the 9-MilCA method proposed by
      • Cipolat-Gotet C.
      • Cecchinato A.
      • De Marchi M.
      • Bittante G.
      Genetic parameters of different measures of cheese yield and milk nutrient recovery from an individual model cheese-manufacturing process.
      . Briefly, 9 mL of each sample was poured into a glass tube and heated at 35°C for 15 min before adding 200 µL of rennet solution (Hansen Standard 215 with 80 ± 5% chymosin and 20 ± 5% pepsin; Pacovis Amrein AG) diluted to 1.2% (wt/vol) with fresh distilled water, then incubated for 30 min at 35°C. After incubation, a first cut was made manually with a stainless steel spatula, then the samples were cooked at 55°C for 30 min with a further manual cut in the middle of the cooking phase. At the end of the cooking phase, each curd was separated from the whey for 30 min at room temperature, then gently pressed to accelerate whey drainage. The curd and whey were weighed separately with precision scales. Whey composition traits (fat, protein, lactose, and total solids) were determined with a MilkoScan FT-2 infrared spectrophotometer (Foss A/S). With this procedure, we obtained 7 traits related to cheese making, with 3 related to CY: CYCURD, CYSOLIDS, and CYWATER (%), representing the weight of curd, of curd dry matter, and of water retained in the curd, respectively, in percentage of the weight of milk processed, and 4 traits relating to nutrient recoveries in the curd as percentage of the same nutrient in the milk processed (REC): RECPROTEIN, RECFAT, RECENERGY, RECSOLIDS, calculated as the differences in composition between curd and whey (
      • Cipolat-Gotet C.
      • Cecchinato A.
      • De Marchi M.
      • Bittante G.
      Genetic parameters of different measures of cheese yield and milk nutrient recovery from an individual model cheese-manufacturing process.
      ). Repeated measures were averaged before statistical analysis.

      FTIR Spectra

      Data.

      Individual milk samples were analyzed using a MilkoScan FT6000 (Foss A/S). The spectrum covered the wavenumbers 5,010 to 925 cm−1, from the short-wavelength infrared (SWIR), through the medium-wavelength infrared (MWIR), to the long-wavelength infrared (LWIR) regions. Spectra were expressed as absorbances calculated as log(1/transmittance) and standardized to mean zero and standard deviation equal to one. Two spectral acquisitions were carried out for each sample and averaged before data analysis (
      • Ferragina A.
      • de los Campos G.
      • Vazquez A.I.
      • Cecchinato A.
      • Bittante G.
      Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data.
      ). A preliminary analysis of the milk FTIR spectra was carried out to identify possible outliers in the data set. We performed a principal component analysis of the FTIR spectral wavelengths through the Mahalanobis distance, considering a significance level of 0.05 to identify animals with greater differences in their spectral information (
      • Shah N.K.
      • Gemperline P.J.
      A program for calculating Mahalanobis distances using principal component analysis.
      ). Phenotypic information more than 3 SD above or below the herd-date average were discarded from the FTIR predictions.

      Cross-Validation Scenarios.

      The predictive ability of each milk technological trait (traditional MCP, curd firming, CY, and REC traits) was assessed using 2 alternative cross-validation (CV) scenarios: random cross-validation and herd-date-out cross-validation. For the random cross-validation, the data set was randomly split into 10-folds approximately equal-sized. Nine of these folds were used as the training population, and one was assigned as validation population. The cross-validation process was repeated 10 times using each fold once as the validation population; the correlations were estimated for each run and then averaged to obtain the estimate of predictive ability. For the herd-date-out CV, samples were assigned to the calibration, and validation sets based on the herd-date of sampling. The herd-dates used for training population consisted of about 80% of the samples, and the other 20% was assigned as a validation set; the process was repeated 10 times, such that the samples from each herd were predicted on the validation set. We selected the gradient boosting machine (GBM) statistical method because previous results indicated that this method achieved the highest accuracy of FTIR-based prediction of different phenotypic traits (
      • Mota L.F.M.
      • Pegolo S.
      • Baba T.
      • Peñagaricano F.
      • Morota G.
      • Bittante G.
      • Cecchinato A.
      Evaluating the performance of machine learning methods and variable selection methods for predicting difficult-to-measure traits in Holstein dairy cattle using milk infrared spectral data.
      ). The predictive ability of GBM method across these 2 CV scenarios was assessed by the coefficient of determination (R2) between the observed and predicted phenotypes and RMSE.

      Calibration Equations.

      The target traits to be predicted by FTIR were traditional milk coagulation properties expressed in minutes (RCT, k20, and a30), curd firming traits (RCTeq, CFp, kCF, kSR, CFmax, and tmax), CY in percentages (CYCURD, CYSOLIDS, and CYWATER), and recoveries in percentages (RECPROTEIN, RECFAT, RECSOLIDS, and RECENERGY). We used GBM implemented in the h2o R package (https://github.com/h2oai/h2o-3) to predict the target phenotype at the ith individual (yi) given the standardized FTIR spectral information (xij, j = 1,060).
      The GBM is an ensemble method that builds regression trees sequentially with some shrinkage and variable selection in a fully distributed way, with each tree built-in parallel aiming to convert weak learners into strong learners to reduce both bias and variance in the final predictive model (
      • Friedman J.
      • Hastie T.
      • Tibshirani R.
      Additive logistic regression: A statistical view of boosting.
      ;
      • Friedman J.H.
      Stochastic gradient boosting.
      ;
      • Hastie T.
      • Tibshirani R.
      • Friedman J.
      The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.
      ). The GBM method can be represented as follows:
      y=m=1Mβmb(x,γm)+e,


      where M is the number of iterations (expansion coefficients), βm is the function increment, also known as the “boost,” and b(x, γm) is the base learner, a function of the multivariate argument x with a set of parameters γm={γ1,γ2,,γm}. Expansions of the coefficients {βm}1M and parameters {γm}1M are used to map the FTIR (predictor variable, x) to the target phenotype (y) considering the joint distribution of all values (y,x) that minimize the loss function L{γi,F(x)} given [y,Fm-1(xi)+h(yi;xi,pm)], where pm is the FTIR (only 1 FTIR spectrum is selected at each iteration), minimizing i=1nL[y,Fm-1(xi)+h(yi;xi,pm)], and e is the residual effect. The GBM follows the algorithm specified by
      • Hastie T.
      • Tibshirani R.
      • Friedman J.
      The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.
      .
      The tuning of hyperparameters for the GBM model was identified through random search using the h2o.grid function from R h2o package (https://cran.r-project.org/web/packages/h2o). The search grid was defined by specifying the main hyperparameters that minimize the predictive error for each trait and training data set from each CV scenario. The 4 parameters with the strongest effect on the model's predictive ability were used in a random grid search: number of trees (Ntree), learning rate, maximum tree depth, and minimum samples per leaf. The Ntree values were determined in the range of 10 to 10,000 by intervals of 10; the learning rate in the range of 0.01 to 1 by intervals of 0.005; maximum tree depth in the range of 2 to 80 by intervals of 2; and minimum samples per leaf in the range of 5 to 100 by intervals of 5. The best combination of these 4 parameters was selected for subsequent analyses, for this we bagged 80% of the training data at each boosting iteration, and the remaining 20% were used as out-of-bag samples. This procedure means optimizing the hyperparameters of the GBM accurately learns the mapping from the FTIR to target phenotype data and the validation is used to assess the learning process based on RMSE and R-square (R2). Thus, the trained model is applied in a disjoint validation set to final model evaluation.

      FTIR Imputation.

      The calibration equations were applied to the herds where the MCP/CF and the CY and REC traits had not been measured with the reference methodology, but for which FTIR spectra were available. The FTIR predictions of MCP and CF traits were obtained for all the cows reared in herds 1 and 6, and for some of the cows reared in herds 2, 7, and 8, where reference MCP and CF measures were available for only a small number of animals (Table 1). In the case of CY and REC phenotypes, FTIR predictions were obtained for all the cows reared in herds 1 and 2, all the herds in Trento province (herds 9 to 36), and some of the cows reared in herds 7 and 8. After data editing, we had 437 MCP and CF predictions and 904 CY and REC predictions.

      Data Editing.

      A summary of the records available for all traits is given in Table 1. All the investigated traits underwent data editing: those falling outside the interval of the mean ± 3 standard deviations were excluded from the analyses. Additionally, only herd-dates with a minimum of 5 animals were retained.

      Genetic Analyses

      Univariate Model.

      The genetic parameters for the traits related to milk yield (kg/d), milk composition, udder health, traditional MCP, CF, CY, and REC were estimated using the following single-trait animal model:
      y=Xβ+Wh+Za+e,


      where y is the vector of phenotypic observations, β is the vector of fixed effects defined by DIM (6 classes: <60; 60–120; 121–180; 181–240; 241–300; >300 d), and parity of the cow (4 classes: 1, 2, 3, ≥4), h is the random effect of herd-date, u is the vector of additive genetic effects; X, W, and Z are the incidence matrices relating y to effects β, h, and u, respectively, and e is the residual effect. The prior distributions were flat for the fixed effects and normal for the herd (h), additive genetic (u), and residual (e) random effects:
      u={u}N(0,Aσu2),


      h={h}N(0,Iσh2),and


      e={e}N(0,Iσe2),


      where σu2, σh2 and σe2 are the variance components for the additive genetic, herd, and residual effects, respectively; A represents the numerator relationship matrix between individuals (
      • Wright S.
      Coefficients of inbreeding and relationship.
      ; the pedigree file contained data on 6,031 animals), I is an identity matrix, and ⊗ is the Kronecker product.

      Bivariate Models.

      Bi-trait animal models were used to infer the genetic correlations between SCS and DSCC-related traits (DSCC, logPMN-LYM count, and logMAC count) and the traits related to milk composition, udder health (lactose, casein index, pH, and milk conductivity), and traditional MCP, CF, CY, and REC, as follows:
      [yudyy]=[xud00xy][βudβy]+[Wud00Wy][hudhy]+[Zud00Zy][auday]+[eudey],


      where yud is the udder health trait (SCS and DSCC, logPMN-LYM count, logMAC count) and yy are the other traits, β is the vector of fixed effects previously defined, h is the random effect of herd-date, a is the vector of additive genetic effects; X, W, and Z are the incidence matrices relating y to effects β, h, and a, respectively, and e is the residual effect. The prior distributions were flat for the fixed effects and multivariate normal (MVN) for the herd (h), additive genetic (u), and residual (e) random effects:
      a={a}MVN(0,Aa),


      h={h}MVN(0,Ih),and


      e={e}MVN(0,Ie).


      Here, the (co)variance matrix components for the additive genetic, herd, and residual effects, respectively, are
      a=[σaud2σaud,yσaud,yσay2],


      h=[σhud200σhy2],and


      e=[σeud200σey2];


      where A represents the numerator relationship matrix between individuals (
      • Wright S.
      Coefficients of inbreeding and relationship.
      ; the pedigree file contained data on 6,031 animals), I is an identity matrix, and ⊗ is the Kronecker product.

      Gibbs Sampling.

      Samples of the posterior distributions of the genetic parameters were obtained by Bayesian inference using the Gibbs sampling algorithm implemented in the GIBBSF90 software, part of the BLUPF90 family of programs (
      • Misztal I.
      • Tsuruta S.
      • Lourenco D.A.L.
      • Masuda Y.
      • Aguilar I.
      • Legarra A.
      • Vitezica Z.
      Manual for BLUPF90 Family of Programs.
      ). The Bayesian analysis consisted of a single chain of 1,000,000 samples, where the first 100,000 were discarded as burn-in, and 1 in every 10 samples was saved. The remaining 90,000 samples were used to obtain posterior parameter estimates. Convergence was evaluated through visual inspection and using the Bayesian output analysis (
      • Smith B.J.
      boa: An R package for MCMC output convergence assessment and posterior inference.
      ) and Geweke test (
      • Geweke J.
      Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (with discussion).
      ). We considered the posterior mean as a point estimate, and the lower and upper bounds of the 95% highest posterior probability density regions (HPD95) as a credible interval.
      The posterior estimates for intraherd heritability and the herd-date incidence of each trait were calculated as h2=σa2/(σa2+σe2), and hherd/batch=σhd2/(σa2+σhd2+σe2) respectively, where σa2 is the additive genetic variance, σhd2 is the herd-date variance, and σe2 is the residual variance. The terms σa2, σh2, and σe2 were obtained by averaging the posterior estimates from the chains for each analysis run.
      We calculated the posterior estimates of genetic (rg) and residual (re) correlations between each pair of traits from all the posterior chains obtained in the bivariate analyses, as well as the cumulative probabilities above (for positive estimates) and below (for negative estimates) 0.0 from all the chains, using 90% probability as the threshold for certainty.

      RESULTS

      Descriptive Statistics of Milk Yield, Composition and Udder Health Traits

      Descriptive statistics for milk yield, composition, and udder health indicator traits are reported in Table 2. The SCS averaged 2.65 (± 1.66, SD). The DSCC percentage averaged 67.36% (± 14), indicating a percentage of PMN + LYM higher than MAC (which is calculated as 100 − DSCC, therefore 32.64%) in the mammary glands of the dairy cows included in this study. When the 2 major somatic cell groups derived from DSCC% were expressed as log counts, PMN-LYM averaged 2.37 and MAC 1.56.
      Table 2Descriptive statistics of single test-day milk yield, composition, and udder health
      Trait
      SCS = log2 (SCC/100) + 3; logPMN-LYM count: PMN-lymphocytes count expressed as log2 [(PMN-LYM count)/100,000] + 3; logMAC count: macrophages count expressed as log2 (MAC count/100,000) + 3; casein index = (casein/protein) × 100.
      NMeanSDP1
      P1 = 1st percentile; P99 = 99th percentile.
      P99
      P1 = 1st percentile; P99 = 99th percentile.
      Milk yield, kg/d2,38032.078.8313.0851.7
      Milk composition
       Fat, %2,3683.740.781.985.55
       Protein, %2,3893.510.352.774.34
       Casein, %2,3852.750.282.163.42
       Fat:protein2,3701.050.210.561.54
       Urea, mg/100 g2,35125.516.5212.6937.95
      Udder health
       SCS2,3702.651.66−0.476.52
       DSCC, %96667.3614.1334.191.71
       Log PMN-LYM count9432.371.59−0.946.02
       Log MAC count9351.561.10−0.924.08
       Lactose, %2,3494.930.204.465.36
       Casein index, %2,24778.11.2675.0780.92
       pH2,2906.570.076.416.72
      Milk conductivity, mS/cm1,2648.900.627.5710.3
      1 SCS = log2 (SCC/100) + 3; logPMN-LYM count: PMN-lymphocytes count expressed as log2 [(PMN-LYM count)/100,000] + 3; logMAC count: macrophages count expressed as log2 (MAC count/100,000) + 3; casein index = (casein/protein) × 100.
      2 P1 = 1st percentile; P99 = 99th percentile.

      FTIR Predictions of Milk Coagulation and Cheese-Making Traits

      Descriptive statistics for the measured and predicted MCP and cheese-making traits, and the model fitting parameters for the FTIR predictions are summarized in Table 3. On the whole, we obtained a moderate agreement between the measured and predicted traits, with coefficients of determination in CV in the range 0.58 to 0.71 for the random CV scenario and 0.57 to 0.68 for the herd-date out scenario. There was a loss of variability in predicted phenotypes, as evidenced by the lower standard deviations for all the predicted traits compared with the measured traits. As Table 1 shows, the predicted traits were connected with their reference measures via the pedigree, as some sires and sires of sires had daughters with both laboratory measures and FTIR predictions. Descriptive statistics for MCP and cheese-making traits combining the measured (for animals with phenotypic values) and FTIR-based predicted (for animals without phenotypic information) are reported in Table 4.
      Table 3Descriptive statistics for laboratory measures, model fitting parameters of random and herd-date out cross-validations, and descriptive statistics of Fourier-transform infrared (FTIR) predictions for animals without information (Np) for the investigated traits
      R2 training = coefficient of determination for calibration equation; R2 val = coefficient of determination for validation data set; RMSE = root mean squared error in validation subset.
      Trait
      MCP = milk coagulation properties; RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.
      Pedigree informationMeasuredRandom cross-validationHerd-date out cross-validationFTIR predictions
      NMeanSDR2 trainingValidationR2 trainingValidationNpMeanSD
      R2 valRMSER2 valRMSE
      Traditional MCP
       RCT, min1,58421.998.070.900.694.250.900.664.6543724.635.69
       k20, min1,5767.2054.350.920.682.640.910.642.784378.802.70
       a30, min1,58828.1215.610.920.688.810.920.639.0343723.897.60
      Curd firming
      RCTeq, min1,58022.207.910.910.674.690.90.654.8143724.805.46
       CFp, mm1,58753.4918.260.930.718.780.940.678.9843742.188.36
       kCF, % × min−11,5877.984.490.870.683.010.880.623.754379.221.83
       kSR, % × min−11,5870.710.360.860.660.180.870.610.204370.780.19
       CFmax, min1,58739.2213.630.930.706.570.880.676.7243732.086.43
       tmax, min1,58051.268.590.920.635.750.910.605.8543750.285.83
      Cheese yields (CY), %
       %CYCURD1,12120.563.800.860.631.940.890.602.3490422.512.99
       %CYSOLIDS1,1186.691.490.850.680.820.830.630.969046.720.64
       %CYWATER1,11813.963.390.860.602.110.810.682.4590413.461.42
      Recoveries (REC), %
       RECPROTEIN1,11878.625.680.880.583.760.870.593.8290479.141.50
       RECFAT1,11879.1311.590.900.598.420.880.587.9690478.634.50
       RECSOLIDS1,11850.056.970.860.594.980.840.574.8390450.622.72
       RECENERGY1,11862.288.290.870.615.600.830.585.6690463.153.31
      Ancestors in the pedigree, n6,031
      Generations, n5
      Animals with sires in common,
      Number of animals with sires in common = number of animals with sires in common between set of traits laboratory measured and predicted with FTIR.
      n
      676
      Sires in common,
      Number of sires in common = number of sires in common between set of traits laboratory measured and predicted with FTIR.
      n
      41
      Sires of sires in common,
      Number of sires of sires in common = number of sires of sires in common between set of traits laboratory measured and predicted with FTIR.
      n
      27
      1 R2 training = coefficient of determination for calibration equation; R2 val = coefficient of determination for validation data set; RMSE = root mean squared error in validation subset.
      2 MCP = milk coagulation properties; RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.
      3 Number of animals with sires in common = number of animals with sires in common between set of traits laboratory measured and predicted with FTIR.
      4 Number of sires in common = number of sires in common between set of traits laboratory measured and predicted with FTIR.
      5 Number of sires of sires in common = number of sires of sires in common between set of traits laboratory measured and predicted with FTIR.
      Table 4Descriptive statistics of traditional milk coagulation properties (MCP), curd firming (CF), cheese yields (%CY) and curd nutrient recoveries (REC)
      Numbers include laboratory-measured and FTIR-predicted records.
      considering the laboratory measures (for measured animals) and FTIR-predicted values (for not measured animals)
      Trait
      RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.
      NMeanSDP1
      P1 = 1st percentile; P99 = 99th percentile.
      P99
      P1 = 1st percentile; P99 = 99th percentile.
      RCT, min2,02122.046.869.2339.23
      k20, min2,0136.993.422.0416.00
      a30, mm2,02527.1713.501.5257.91
      Curd firming
       RCTeq, min2,01722.326.709.3639.08
       CFp, mm2,02450.9616.3116.0389.05
       kCF, % × min−12,0248.742.674.7916.31
       kSR, % × min−12,0240.760.340.041.65
       CFmax, mim2,02437.6711.7412.0065.12
       tmax, min2,01750.668.0530.1359.22
      Cheese yields (CY), %
       %CYCURD2,02520.613.4613.4927.31
       %CYSOLIDS2,0226.440.904.258.49
       %CYWATER2,02213.731.889.3218.63
      Recoveries (REC), %
       RECPROTEIN2,02279.342.2872.9185.95
       RECFAT2,02276.6610.0947.7492.50
       RECSOLIDS2,02249.384.4438.0658.94
       RECENERGY2,02261.405.9746.2472.51
      1 Numbers include laboratory-measured and FTIR-predicted records.
      2 RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.
      3 P1 = 1st percentile; P99 = 99th percentile.

      Variance Components, Heritabilities, and Herd-Date Incidences

      Milk Yield and Composition, and Udder Health Indicators.

      Posterior means of the variance components, heritabilities, and herd-date incidences for milk yield and composition, and udder health indicators are reported in Table 5. Heritability was low for milk fat (0.13) and moderate for milk yield (0.27), urea (0.29), protein (0.33), and casein (0.31). Heritability was low for SCS (0.13), DSCC%, (0.11), and for logPMN-LYM (0.10) and logMAC (0.11) counts. Moderate heritabilities were found for the lactose percentage, casein index, pH, and milk conductivity (ranging from 0.23 for the casein index to 0.30 for milk conductivity).
      Table 5Estimates
      Estimates are expressed as mean of the marginal posterior density of the parameter; σa2 = additive genetic variance, σhd2 = herd-date variance, σe2 = residual variance, h2 = heritability computed as σa2/σa2(σa2+σe2)(σa2+σe2), herd incidence computed as hherd−date=σhd2/σhd2(σa2+σhd2+σe2)(σa2+σhd2+σe2).
      of variance components, heritability, and herd incidence for milk composition and udder health
      Trait
      SCS = log2 (SCC/100,000) + 3; logPMN-LYM count = PMN-lymphocytes count expressed as log2 (PMN-LYM count/100,000) + 3; logMAC count = macrophages count expressed as log2 (MAC count/100,000) + 3.
      Varianceh2hherd-date
      σa2σhd2σe2MeanHPD95
      HPD95 = lower and upper bound of the 95% highest posterior density region.
      MeanHPD95
      Milk yield, kg/d12.7721.0932.820.270.17–0.390.310.20–0.42
      Milk composition
       Fat, %0.070.060.450.130.03–0.210.110.06–0.17
       Protein, %0.030.0090.070.330.19–0.470.050.05–0.13
       Casein, %0.020.0090.040.310.18–0.440.130.06–0.18
       Fat:protein0.0080.0090.040.170.09–0.200.160.09–0.22
       Urea, mg/100g5.569.3913.390.290.15–0.440.330.20–0.59
      Udder health
       SCS0.420.142.760.130.03–0.230.040.01–0.08
       DSCC26.552.09208.570.110.01–0.240.010.00–0.03
       logPMN-LYM count0.320.052.810.100.03–0.210.020.00–0.04
       logMAC count0.150.021.250.110.01–0.230.010.00–0.04
       Lactose, %0.0080.0090.0240.250.11–0.320.220.12–0.38
       Casein index, %0.782.862.830.230.11–0.310.420.31–0.56
       pH0.00150.00270.00410.270.10–0.340.320.20–0.43
       Milk conductivity, mS0.0970.0910.2270.300.16–0.400.220.09–0.36
      1 Estimates are expressed as mean of the marginal posterior density of the parameter; σa2 = additive genetic variance, σhd2 = herd-date variance, σe2 = residual variance, h2 = heritability computed as σa2/σa2(σa2+σe2)(σa2+σe2), herd incidence computed as hherddate=σhd2/σhd2(σa2+σhd2+σe2)(σa2+σhd2+σe2).
      2 SCS = log2 (SCC/100,000) + 3; logPMN-LYM count = PMN-lymphocytes count expressed as log2 (PMN-LYM count/100,000) + 3; logMAC count = macrophages count expressed as log2 (MAC count/100,000) + 3.
      3 HPD95 = lower and upper bound of the 95% highest posterior density region.
      Herd-date incidences were generally low for milk components and udder health indicators, with the exception of milk yield, urea, the casein index, milk pH and milk conductivity, which were moderate (ranging from 0.22 for milk conductivity to 0.42 for the casein index).

      Milk Coagulation Properties and Cheese-Making Traits.

      Posterior means of variance components, heritabilities, and herd-date incidences for measured and predicted MCP, CF, and cheese-making traits are reported in Table 6. Traditional MCP and CF traits were characterized by moderate heritabilities ranging from 0.17 for kCF to 0.28 for CFp. CY and REC traits had moderate heritabilities, ranging from 0.18 for RECFAT to 0.31 for %CYSOLIDS. The herd-date incidences for these traits were low to moderate, ranging from 0.09 for %CYWATER to 0.38 for CFmax.
      Table 6Estimates
      Estimates are expressed as mean of the marginal posterior density of the parameter; σa2 = additive genetic variance, σhd2 = herd-date variance, σe2 = residual variance, h2 = heritability computed as σa2/σa2(σa2+σe2)(σa2+σe2), herd incidence computed as hherd−date=σhd2/σhd2(σa2+σhd2+σe2)(σa2+σhd2+σe2).
      of variance components, heritability and herd incidence for milk coagulation properties (MCP), curd firming (CF), cheese yields (%CY) and curd nutrient recoveries (REC)
      Estimates are expressed as mean of the marginal posterior density of the parameter; σa2 = additive genetic variance, σhd2 = herd-date variance, σe2 = residual variance, h2 = heritability computed as σa2/σa2(σa2+σe2)(σa2+σe2), herd incidence computed as hherd−date=σhd2/σhd2(σa2+σhd2+σe2)(σa2+σhd2+σe2).
      Trait
      RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.
      Varianceh2hherd-date
      σa2σhd2σe2MeanHPD95
      HPD95 = lower and upper bound of the 95% highest posterior density region, SD: posterior standard deviation.
      MeanHPD95
      HPD95 = lower and upper bound of the 95% highest posterior density region, SD: posterior standard deviation.
      Traditional MCP
       RCT, min8.479.0923.960.260.13–0.390.220.15–0.27
       k20, min1.732.237.180.200.08–0.310.200.13–0.28
       a30, min24.3935.00115.450.170.06–0.290.200.14–0.24
      Curd firming
       RCTeq, min7.698.7428.320.210.10–0.330.190.13–0.26
       CFp, mm42.4970.27108.960.280.16–0.390.310.23–0.38
       kCF, % × min−11.061.255.260.170.07–0.310.160.10–0.24
       kSR, % × min−10.0250.0220.0770.250.21–0.310.180.12–0.26
       CFmax, min21.6350.0960.390.260.16–0.380.380.30–0.43
       tmax, min15.2110.3045.540.240.11–0.380.240.09–0.19
      Cheese yields (CY), %
       %CYCURD1.432.784.290.250.18–0.340.320.24–0.40
       %CYSOLIDS0.170.110.370.310.19–0.450.160.11–0.22
       %CYWATER0.630.332.510.200.09–0.330.090.06–0.14
      Recoveries (REC), %
       RECPROTEIN1.271.213.020.290.23–0.380.220.16–0.28
       RECFAT10.2719.1347.720.180.11–0.260.240.18–0.31
       RECSOLIDS2.802.529.680.220.13–0.340.170.11–0.23
       RECENERGY4.047.5215.670.200.11–0.320.270.19–0.36
      1 Estimates are expressed as mean of the marginal posterior density of the parameter; σa2 = additive genetic variance, σhd2 = herd-date variance, σe2 = residual variance, h2 = heritability computed as σa2/σa2(σa2+σe2)(σa2+σe2), herd incidence computed as hherddate=σhd2/σhd2(σa2+σhd2+σe2)(σa2+σhd2+σe2).
      2 RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.
      3 HPD95 = lower and upper bound of the 95% highest posterior density region, SD: posterior standard deviation.

      Genetic and Residual Correlations Between SCS and Milk Composition and Udder Health

      Posterior means of the additive genetic and residual correlations between SCS and milk yield and composition and udder health indicators are reported in Table 7. Only relevant correlations will be described. Moderate negative genetic correlations (given a posterior probability threshold of 90% accumulated above or below zero) were found between SCS and protein % (−0.30). Moderate to strong negative genetic correlations were found between SCS and lactose (−0.56) and the casein index % (−0.52). Residual correlations between SCS and milk composition, and udder health, even when relevant, tended to be weak.
      Table 7Estimates
      Estimates are expressed as mean of the marginal posterior density of the parameter. Number in parentheses represent the probability for the estimate being above 0 for positive estimates, and below 0 for negative estimates; estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      of additive genetic and residual correlations between somatic cell related traits, milk yield (MY), milk composition, and udder health
      Trait
      MY = milk yield; SCS = log2 (SCC/100,000) + 3; DSCC = differential SCC, model without including SCS effect; DSCCSCS = differential SCC, model including SCS effect; logPMN-LYM count = PMN-lymphocytes count expressed as log2 (PMN-LYM count/100,000) + 3; logMAC count = macrophages count expressed as log2 (MAC count/100,000) + 3.
      SCSDSCC-related traits
      DSCClog PMN-LYM countlog MAC count
      rarerarerarerare
      MY, kg/d−0.37(87)−0.14(73)−0.29(76)0.45(96)−0.12(62)0.03(70)−0.30(81)−0.07(78)
      Milk components
       Fat, %−0.22(83)0.11(98)−0.19(77)0.09(90)−0.38(91)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.10(88)−0.43(91)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.09(93)
       Protein, %−0.30(96)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.12(97)−0.16(71)0.04(70)−0.21(76)0.08(88)−0.18(71)0.12(97)
       Casein, %−0.19(82)0.08(90)−0.36(90)0.06(84)−0.30(85)0.05(89)−0.21(74)0.13(94)
       Fat:protein−0.26(81)0.12(90)−0.12(68)−0.08(86)−0.15(77)−0.06(92)−0.26(84)0.02(71)
       Urea, mg/100g−0.23(81)−0.07(88)−0.25(76)−0.12(96)−0.19(83)−0.07(85)−0.19(75)0.09(84)
      Udder health
       SCS0.60(98)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.13(98)0.79(100)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.30(100)0.69(97)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.30(100)
       Lactose, %−0.56(99)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.29(100)−0.32(91)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.06(84)−0.40(90)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.19(100)−0.46(95)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.20(98)
       Casein index, %−0.52(99)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.20(100)−0.23(77)0.05(80)−0.33(84)0.01(69)−0.26(89)−0.03(66)
       pH0.20(80)0.07(94)0.44(81)−0.02(38)0.23(83)−0.05(79)0.20(76)−0.03(71)
       Milk conductivity, S/cm0.31(86)0.15(100)0.26(81)0.02(64)0.20(76)0.03(70)0.22(77)0.13(93)
      1 Estimates are expressed as mean of the marginal posterior density of the parameter. Number in parentheses represent the probability for the estimate being above 0 for positive estimates, and below 0 for negative estimates; estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      2 MY = milk yield; SCS = log2 (SCC/100,000) + 3; DSCC = differential SCC, model without including SCS effect; DSCCSCS = differential SCC, model including SCS effect; logPMN-LYM count = PMN-lymphocytes count expressed as log2 (PMN-LYM count/100,000) + 3; logMAC count = macrophages count expressed as log2 (MAC count/100,000) + 3.
      * Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      Posterior means of the genetic and residual correlations between SCS and MCP, CF, and cheese-making traits are reported in Table 8. There were moderate positive genetic correlations between SCS and k20 (0.38) and RCTeq (0.45), and moderate negative genetic correlations between SCS and CFp, kSR, Cmax, and RECPROTEIN (ranging from −0.26 to −0.39). The residual correlation between SCS and RCTeq was positive, but very weak (0.12).
      Table 8Estimates
      Estimates are expressed as mean of the marginal posterior density of the parameter. Number in parentheses represent the probability for the estimate being above 0 for positive estimates, and below 0 for negative estimates; estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      of additive genetic and residual correlations between somatic cell related traits, milk coagulation properties (MCP), curd firming (CF), cheese yields (%CY), and curd nutrient recoveries (REC)
      Estimates are expressed as mean of the marginal posterior density of the parameter. Number in parentheses represent the probability for the estimate being above 0 for positive estimates, and below 0 for negative estimates; estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      Trait
      RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed. 3 SCS = log2 (SCC/100,000) + 3.
      SCSDSCC-related traits
      DSCC = differential SCC, model without including SCS effect; DSCCSCS = differential SCC, model including SCS effect; logPMN-LYM count = PMN-lymphocytes count expressed as log2 (PMN-LYM count/100,000) + 3; logMAC count = macrophages count expressed as log2 (MAC count/100,000) + 3.
      DSCClogPMN-LYM countlogMAC count
      rarerarerarerare
      Traditional MCP
       RCT, min0.29(75)−0.05(76)0.20(76)−0.03(75)0.26(81)−0.10(94)0.28(82)0.02(62)
       k20, min0.38(92)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.07(76)0.10(64)0.04(76)0.24(81)0.05(85)0.34(90)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.03(73)
       a30, min−0.18(74)−0.05(86)−0.21(72)−0.03(70)−0.28(81)−0.05(76)−0.24(77)−0.03(70)
      Curd firming
       RCTeq, min0.45(96)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.12(100)0.22(77)−0.06(89)0.53(95)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.05(86)0.41(90)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.02(67)
       CFp, min−0.39(97)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.02(84)−0.29(87)0.05(73)−0.44(85)−0.10(88)−0.34(88)−0.09(91)
       kCF, % × min−1−0.20(75)0.00(53)−0.13(67)0.02(57)−0.16(70)0.08(93)−0.18(71)−0.02(66)
       kSR, % × min−1−0.31(86)0.00(54)−0.26(80)0.08(88)−0.32(83)0.05(92)−0.27(85)0.01(69)
       CFmax, min−0.26(90)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.04(81)−0.33(91)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.06(81)−0.26(94)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.04(72)−0.21(81)−0.07(88)
       tmax, min0.19(77)0.06(84)0.22(80)−0.06(73)0.38(91)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.09(100)0.48(99)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.02(71)
      Cheese yields (CY), %
       %CYCURD−0.13(76)0.02(64)−0.16(73)0.02(66)−0.19(76)−0.08(95)−0.21(75)−0.08(92)
       %CYSOLIDS0.10(70)−0.01(60)0.10(65)−0.05(74)0.11(66)0.04(79)0.25(81)−0.03(68)
       %CYWATER−0.24(86)0.04(79)−0.19(75)0.05(78)−0.26(93)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      0.05(79)−0.27(83)−0.03(68)
      Recoveries (REC), %
       RECPROTEIN−0.31(93)
      Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      −0.03(74)−0.14(67)0.04(70)−0.18(81)0.03(69)−0.20(75)−0.02(66)
       RECFAT−0.13(69)0.00(51)−0.19(70)0.00(50)−0.23(83)−0.05(78)−0.26(79)−0.09(80)
       RECSOLIDS−0.11(70)−0.02(68)−0.28(80)0.11(97)−0.26(76)0.10(90)−0.29(79)0.00(58)
       RECENERGY−0.14(76)0.00(51)−0.09(64)0.07(87)−0.16(67)0.03(71)−0.25(76)−0.01(68)
      1 Estimates are expressed as mean of the marginal posterior density of the parameter. Number in parentheses represent the probability for the estimate being above 0 for positive estimates, and below 0 for negative estimates; estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.
      2 RCT = rennet coagulation time; k20 = curd firming rate as the time to a curd firmness of 20 mm; a30 = curd firmness at 30 min from rennet addition; RCTeq = rennet coagulation time estimated using the equation; CFP = asymptotic potential curd firmness; kCF = curd firming instant rate constant; kSR = syneresis instant rate constant; CFmax = maximum curd firmness achieved within 45 min; tmax = time at achievement of CFmax; %CYCURD = weight of fresh curd as percentage of weight of milk processed; %CYSOLIDS = weight of curd solids as percentage of weight of milk processed; %CYWATER = weight of water curd as percentage of weight of milk processed; RECPROTEIN = protein of the curd as percentage of the protein of the milk processed; RECFAT = fat of the curd as percentage of the fat of the milk processed; RECSOLIDS = solids of the curd as percentage of the solids of the milk processed; RECENERGY = energy of the curd as percentage of energy of the milk processed.3 SCS = log2 (SCC/100,000) + 3.
      4 DSCC = differential SCC, model without including SCS effect; DSCCSCS = differential SCC, model including SCS effect; logPMN-LYM count = PMN-lymphocytes count expressed as log2 (PMN-LYM count/100,000) + 3; logMAC count = macrophages count expressed as log2 (MAC count/100,000) + 3.
      * Estimates with probabilities ≥90% (as a threshold of relevance) are considered relevant.

      Genetic and Residual Correlations Between DSCC and Milk Composition and Udder Health

      DSCC Percentage.

      Posterior means of the additive genetic and residual correlations between DSCC traits and milk yield and composition and other udder health indicators are reported in Table 7. There was a strong positive genetic correlation between SCS and DSCC% (0.60), whereas the residual correlation was trivial. A relevant moderate negative genetic correlation between DSCC% and the lactose proportion (−0.32) was found. As with SCS, the residual correlations between DSCC% and milk composition, and udder health, when relevant, tended to be weak.
      Posterior means of the genetic and residual correlations between DSCC% and MCP, CF and cheese-making traits are reported in Table 8. There was a moderate negative genetic correlation between DSCC and Cmax (−0.33), and a weak positive residual correlation between DSCC and RECSOLIDS (0.11).

      PMN-LYM and MAC Counts.

      Posterior means of the genetic and residual correlations between the count traits (logPMN-LYM and logMAC) and milk yield and composition, and udder health indicators are reported in Table 7. Strong positive genetic correlations were found between SCS and the logPMN-LYM (0.79) and logMAC counts (0.69). Residual correlations with SCS were not relevant for either count traits. We obtained moderate negative genetic correlations between the count traits and the lactose proportion (−0.40 for the logPMN-LYM count and −0.46 for the logMAC count). The residual correlations between the count traits and milk composition, and udder health, when relevant, were very weak.
      Posterior means of the genetic and residual correlations between DSCC expressed as counts and MCP and cheese-making traits are reported in Table 8. The logPMN-LYM had relevant positive genetic correlations with RCTeq (0.53) and Tmax (0.38) and negative with CFmax (−0.26), and CYWATER (−0.26). The logMAC count had positive genetic correlations with k20 (0.34), RCTeq (0.41) and Tmax (0.48). On the other hand, the residual correlations between counts traits and MCP and cheese-making traits, when relevant, were very weak.

      DISCUSSION

      In a previous work, we evaluated the phenotypic associations between DSCC traits and milk composition, udder health, and technological characteristics (
      • Pegolo S.
      • Giannuzzi D.
      • Bisutti V.
      • Tessari R.
      • Gelain M.E.
      • Gallo L.
      • Schiavon S.
      • Tagliapietra F.
      • Trevisi E.
      • Ajmone Marsan P.
      • Bittante G.
      • Cecchinato A.
      Associations between differential somatic cell count and milk yield, quality, and technological characteristics in Holstein cows.
      ). Here, we studied the genetic variation in these novel traits and estimated their genetic correlations with the aforementioned milk traits. Investigation of the genetic background of DSCC is an essential requirement before considering to include this trait in selection programs aimed at improving mastitis resistance, milk quality and cheese-making aptitude in dairy cattle.

      FTIR Predictions

      In this study, we exploited the availability of FTIR spectra to increase the sample size and improve our estimations of genetic parameters. Our results showed that the GBM machine learning method was able to build predictive models for MCP and cheese-making traits using FTIR spectra with enough degree of predictive ability to be exploited in breeding programs. Indeed, as demonstrated in previous works (
      • Rutten M.J.M.
      • Bovenhuis H.
      • van Arendonk J.A.M.
      The effect of the number of observations used for Fourier transform infrared model calibration for bovine milk fat composition on the estimated genetic parameters of the predicted data.
      ;
      • Cecchinato A.
      • Toledo-Alvarado H.
      • Pegolo S.
      • Rossoni A.
      • Santus E.
      • Maltecca C.
      • Bittante G.
      • Tiezzi F.
      Integration of wet-lab measures, milk infrared spectra, and genomics to improve difficult-to-measure traits in dairy cattle populations.
      ), even calibrations equations with moderate predictive ability might result in high additive genetic correlations between measured and predicted milk technological traits, which paves the way for the possible use of FTIR predictions as indicator traits in selective breeding (
      • Cecchinato A.
      • Toledo-Alvarado H.
      • Pegolo S.
      • Rossoni A.
      • Santus E.
      • Maltecca C.
      • Bittante G.
      • Tiezzi F.
      Integration of wet-lab measures, milk infrared spectra, and genomics to improve difficult-to-measure traits in dairy cattle populations.
      ). Machine learning techniques have been shown to improve prediction performances compared with the standard partial least squares approach using FTIR spectra in dairy cattle because of their ability to model complex relationships between variables, such as nonlinearities and interactions (
      • Gianola D.
      • Okut H.
      • Weigel K.A.
      • Rosa G.J.M.
      Predicting complex quantitative traits with Bayesian neural networks: A case study with Jersey cows and wheat.
      ;
      • Dórea J.R.R.
      • Rosa G.J.M.
      • Weld K.A.
      • Armentano L.E.
      Mining data from milk infrared spectroscopy to improve feed intake predictions in lactating dairy cows.
      ). The results of the random and herd-date out CV procedures showed that the former overestimates the ability of FTIR spectra to predict MCP and cheese-making traits, as previously reported for other traits in dairy cattle (
      • Wang Q.
      • Bovenhuis H.
      Validation strategy can result in an overoptimistic view of the ability of milk infrared spectra to predict methane emission of dairy cattle.
      ). These results suggest that using the herd-date out CV would result in a more reliable estimation of the prediction accuracy.

      Phenotypic and Genetic Variation of DSCC and Other Milk Traits

      The average phenotypic values obtained for udder health indicators suggest that the herds were kept in hygienic conditions and under good management practices. Average phenotypic values for milk yield and composition were comparable to previous studies on the Holstein breed (
      • Bastin C.
      • Gengler N.
      • Soyeurt H.
      Phenotypic and genetic variability of production traits and milk fatty acid contents across days in milk for Walloon Holstein first-parity cows.
      ;
      • Cecchinato A.
      • Penasa M.
      • De Marchi M.
      • Gallo L.
      • Bittante G.
      • Carnier P.
      Genetic parameters of coagulation properties, milk yield, quality, and acidity estimated using coagulating and noncoagulating milk information in Brown Swiss and Holstein-Friesian cows.
      ;
      • Saha S.
      • Amalfitano N.
      • Bittante G.
      • Gallo L.
      Milk coagulation traits and cheese yields of purebred Holsteins and 4 generations of 3-breed rotational crossbred cows from Viking Red, Montbéliarde, and Holstein bulls.
      ).
      Regarding DSCC%, our estimate (67%) was lower than that reported by
      • Damm M.
      • Holm C.
      • Blaabjerg M.
      • Bro M.N.
      • Schwarz D.
      Differential somatic cell count—A novel method for routine mastitis screening in the frame of Dairy Herd Improvement testing programs.
      , who analyzed 655 routine milk samples from different countries and reported average DSCC values ranging from 72.7 in Denmark to 76.1% in Canada; but it was higher than the value reported by
      • Bobbo T.
      • Penasa M.
      • Cassandro M.
      Short communication: Genetic aspects of milk differential somatic cell count in Holstein cows: A preliminary analysis.
      ; 62.1%). There were corresponding differences in the MAC proportions in these studies, and therefore likely different udder health statuses. We found that the heritabilities of DSCC traits (proportion and counts), were similar to that of SCS, in contrast to
      • Bobbo T.
      • Penasa M.
      • Cassandro M.
      Short communication: Genetic aspects of milk differential somatic cell count in Holstein cows: A preliminary analysis.
      , who reported higher values for DSCC% than for SCS. Moreover, the heritabilities we obtained for these traits were higher than those of
      • Bobbo T.
      • Penasa M.
      • Cassandro M.
      Short communication: Genetic aspects of milk differential somatic cell count in Holstein cows: A preliminary analysis.
      ; 0.11 vs. 0.08 for DSCC%, and 0.13 vs. 0.04 for SCS). However, other studies on Holstein cows reported SCS heritability estimates similar to ours (
      • Castillo-Juarez H.
      • Oltenacu P.A.
      • Cienfuegos-Rivas E.G.
      Genetic and phenotypic relationships among milk production and composition traits in primiparous Holstein cows in two different herd environments.
      ;
      • Carlén E.
      • Strandberg E.
      • Roth A.
      Genetic parameters for clinical mastitis, somatic cell score, and production in the first three lactations of Swedish Holstein cows.
      ).
      The average phenotypic values of RCT and k20, and CF traits were in the range of variability found in previous studies on Holstein cows (
      • Stocco G.
      • Cipolat-Gotet C.
      • Bobbo T.
      • Cecchinato A.
      • Bittante G.
      Breed of cow and herd productivity affect milk composition and modeling of coagulation, curd firming, and syneresis.
      ;
      • Saha S.
      • Amalfitano N.
      • Bittante G.
      • Gallo L.
      Milk coagulation traits and cheese yields of purebred Holsteins and 4 generations of 3-breed rotational crossbred cows from Viking Red, Montbéliarde, and Holstein bulls.
      ). Cheese yield traits were ~2% higher than the values obtained by
      • Saha S.
      • Amalfitano N.
      • Bittante G.
      • Gallo L.
      Milk coagulation traits and cheese yields of purebred Holsteins and 4 generations of 3-breed rotational crossbred cows from Viking Red, Montbéliarde, and Holstein bulls.
      using the same methodology (9-MilCA). Recovery traits were comparable in the case of RECPROTEIN, and ~20% higher in the case of RECFAT traits. The heritability of MCP was in line with previous studies on the same breed (
      • Cecchinato A.
      • Penasa M.
      • De Marchi M.
      • Gallo L.
      • Bittante G.
      • Carnier P.
      Genetic parameters of coagulation properties, milk yield, quality, and acidity estimated using coagulating and noncoagulating milk information in Brown Swiss and Holstein-Friesian cows.
      ). As this is the first time that heritability estimates have been reported for CF, CY, and REC traits obtained with the 9-MilCA methodology in Holstein cows, we cannot make any comparisons with previous data. However, when comparing our results with previous estimates obtained in another breed (Brown Swiss) or with a different methodology, we generally found a good agreement except for some traits (i.e., CFp and kSR;
      • Cecchinato A.
      • Bittante G.
      Genetic and environmental relationships of different measures of individual cheese yield and curd nutrients recovery with coagulation properties of bovine milk.
      ). It is also worth mentioning that the estimates of variance components and heritabilities reported here include both the measured and predicted records. By combining laboratory measures with FTIR predictions, it is possible to increase the degrees of freedom for estimating the variance components, provided that FTIR spectral data are available and the coefficient of determination of CV for the investigated traits is high enough. In this regard, calibration equations for cheese-making traits have been shown to be robust enough to be used for obtaining predictions exploitable for breeding purposes (
      • Cecchinato A.
      • Toledo-Alvarado H.
      • Pegolo S.
      • Rossoni A.
      • Santus E.
      • Maltecca C.
      • Bittante G.
      • Tiezzi F.
      Integration of wet-lab measures, milk infrared spectra, and genomics to improve difficult-to-measure traits in dairy cattle populations.
      ).

      Genetic Relationships Between SCS and Milk Traits

      As expected, SCS was unfavorably correlated with udder health traits. In particular, we found negative genetic correlations with the lactose percentage and casein index, in agreement with previous findings for Holstein cows (
      • Miglior F.
      • Sewalem A.
      • Jamrozik J.
      • Bohmanova J.
      • Lefebvre D.M.
      • Moore R.K.
      Genetic analysis of milk urea nitrogen and lactose and their relationships with other production traits in Canadian Holstein cattle.
      ;
      • Stoop W.M.
      • Bovenhuis H.
      • van Arendonk J.A.M.
      Genetic parameters for milk urea nitrogen in relation to milk production traits.
      ;
      • Samoré A.B.
      • Canavesi F.
      • Rossoni A.
      • Bagnato A.
      Genetics of casein content in Brown Swiss and Italian Holstein dairy cattle breeds.
      ). These results provide further demonstration of the usefulness of these indicators of udder health, which could be integrated into a multitrait selection index in dairy cattle breeding programs for improving mastitis resistance. On the other hand, we found positive, but not relevant, genetic correlations with milk conductivity and pH, in line with previous results (
      • Ikonen T.
      • Morri S.
      • Tyrisevä A.M.
      • Ruottinen O.
      • Ojala M.
      Genetic and phenotypic correlations between milk coagulation properties, milk production traits, somatic cell count, casein content, and pH of milk.
      ;
      • Norberg E.
      Electrical conductivity of milk as a phenotypic and genetic indicator of bovine mastitis: A review.
      ). The biological explanation for these relationships lies in the alteration in animal physiological mechanisms induced by mastitis infection. Intramammary inflammation causes a reduction in milk lactose due to both a reduced synthetic ability of mammary epithelial cells and an increased leakage of lactose from milk to blood (
      • Ogola H.
      • Shitandi A.
      • Nanua J.
      Effect of mastitis on raw milk compositional quality.
      ;
      • Pegolo S.
      • Momen M.
      • Morota G.
      • Rosa G.J.M.
      • Gianola D.
      • Bittante G.
      • Cecchinato A.
      Structural equation modeling for investigating multi-trait genetic architecture of udder health in dairy cattle.
      ). The changes in osmotic equilibrium affect mineral transport across mammary epithelial cells and increase milk conductivity (
      • Paudyal S.
      • Melendez P.
      • Manriquez D.
      • Velasquez-Munoz A.
      • Pena G.
      • Roman-Muniz I.N.
      • Pinedo P.J.
      Use of milk electrical conductivity for the differentiation of mastitis causing pathogens in Holstein cows.
      ) and milk pH (
      • Early R.
      The Technology of Dairy Products.
      ). Proteolytic activity, which increases with increasing SCC, is responsible for the degradation in milk casein and consequently, for the increase in whey proteins, with a reduction in the casein index (
      • Kelly A.L.
      • O'Flaherty F.
      • Fox P.F.
      Indigenous proteolytic enzymes in milk: A brief overview of the present state of knowledge.
      ;
      • Pegolo S.
      • Giannuzzi D.
      • Bisutti V.
      • Tessari R.
      • Gelain M.E.
      • Gallo L.
      • Schiavon S.
      • Tagliapietra F.
      • Trevisi E.
      • Ajmone Marsan P.
      • Bittante G.
      • Cecchinato A.
      Associations between differential somatic cell count and milk yield, quality, and technological characteristics in Holstein cows.
      ).
      The genetic correlations between SCS and traditional MCP, CF, CY, and REC traits confirms that selection for low SCS could lead to an improvement in milk coagulation and cheese-making aptitude. This effect is likely related to the negative relationship between SCS and the casein index, because milk casein content is strictly related to the cheese-making aptitude of milk (
      • Wedholm A.
      • Larsen L.B.
      • Lindmark-Månsson H.
      • Karlsson A.H.
      • Andrén A.
      Effect of protein composition on the cheese-making properties of milk from individual dairy cows.
      ). Unfavorable genetic correlations between SCS and RCT, and between SCS and cheese-making traits in Holstein cows have also been previously reported (
      • Cecchinato A.
      • Penasa M.
      • De Marchi M.
      • Gallo L.
      • Bittante G.
      • Carnier P.
      Genetic parameters of coagulation properties, milk yield, quality, and acidity estimated using coagulating and noncoagulating milk information in Brown Swiss and Holstein-Friesian cows.
      ,
      • Cecchinato A.
      • Albera A.
      • Cipolat-Gotet C.
      • Ferragina A.
      • Bittante G.
      Genetic parameters of cheese yield and curd nutrient recovery or whey loss traits predicted using Fourier-transform infrared spectroscopy of samples collected during milk recording on Holstein, Brown Swiss, and Simmental dairy cows.
      ).

      DSCC Traits as New Selection Targets to Improve Milk Quality, Technological Characteristics, and Udder Health

      We found that there is potential to exploit the genetic variation in DSCC traits in breeding programs. The genetic correlation between SCS and DSCC% was different from 1 (0.60), which confirmed that they are not the same trait, in agreement with
      • Bobbo T.
      • Penasa M.
      • Cassandro M.
      Short communication: Genetic aspects of milk differential somatic cell count in Holstein cows: A preliminary analysis.
      . The genetic correlations between DSCC% and milk yield and composition and udder health traits tended to be unfavorable, in line with previous findings (
      • Bobbo T.
      • Penasa M.
      • Cassandro M.
      Short communication: Genetic aspects of milk differential somatic cell count in Holstein cows: A preliminary analysis.
      ). A similar pattern was observed for milk technological characteristics, not studied in previous research, reflecting the negative relationships observed between DSCC% and the milk fat and casein proportions, which are associated with milk coagulation and cheese-making ability (
      • Huppertz T.
      • Kelly A.L.
      Physical Chemistry of Milk Fat Globules.
      ;
      • Amalfitano N.
      • Cipolat-Gotet C.
      • Cecchinato A.
      • Malacarne M.
      • Summer A.
      • Bittante G.
      Milk protein fractions strongly affect the patterns of coagulation, curd firming, and syneresis.
      ). The genetic correlations between DSCC% and milk traits were weaker than between SCS and milk traits. However, the magnitude of the genetic correlations increased moving from DSCC% to the count traits. In a previous phenotypic study, we hypothesized that the associations between DSCC traits and milk quality and technological characteristics are influenced by the relative proportions of PMN and LYM, which are combined in DSCC% and present different patterns according to the presence and stage of disease (
      • Pegolo S.
      • Giannuzzi D.
      • Bisutti V.
      • Tessari R.
      • Gelain M.E.
      • Gallo L.
      • Schiavon S.
      • Tagliapietra F.
      • Trevisi E.
      • Ajmone Marsan P.
      • Bittante G.
      • Cecchinato A.
      Associations between differential somatic cell count and milk yield, quality, and technological characteristics in Holstein cows.
      ). From a genetic perspective,
      • Denholm S.J.
      • McNeilly T.N.
      • Banos G.
      • Coffey M.P.
      • Russell G.C.
      • Bagnall A.
      • Mitchell M.C.
      • Wall E.
      Estimating genetic and phenotypic parameters of cellular immune-associated traits in dairy cows.
      showed that blood LYM had a positive and neutrophils a negative genetic correlation with the milk fat proportion; this opposing pattern was also evident for the milk protein proportion, although it was not significant. The possibility of separating individual milk leukocyte populations may, therefore, facilitate biological interpretation of the relationships between DSCC and milk traits.
      Regarding breeding, the associations found in the present study do not seem to provide any clear evidence that there is an advantage to be gained by including DSCC (combined with SCS) in selection programs aimed at improving milk quality, udder health and cheese-making traits.

      CONCLUSIONS

      We found unfavorable genetic correlations between DSCC traits and milk quality and composition, and cheese-making traits. The magnitude of these correlations was generally smaller than in the case of SCS. When DSCC is expressed as a PMN-LYM count, however, the unfavorable genetic correlations with milk traits become stronger. Before considering the inclusion of DSCC traits in selection programs aimed at improving milk quality and cheese-making aptitude, further research using a larger number of records and herds, and possibly other breeds, is needed.

      ACKNOWLEDGMENTS

      The research was part of the projects (1) LATSAN funded by the Ministero delle politiche agricole alimentari, forestali e del turismo (MIPAAF), Rome, Italy, and (2) BENELAT – Interventi a breve e lungo termine per il miglioramento del benessere, dell'efficienza e della qualità delle produzioni dei bovini da latte della Lombardia – Bando per il finanziamento di progetti di ricerca in campo agricolo e forestale 2018 (d.d.s. 28 marzo 2018, n. 4403). The authors are also grateful to the Italian Holstein-Friesian and Jersey Cattle Breeders Association (ANAFIJ, Cremona, Italy) for collaborating in the research activities and for providing pedigree information. We also thank Sofia Ton and Marco Franzoi from Breeders Association of Veneto Region (ARAV, Padova, Italy) for milk composition analyses. The authors declare that there is no conflict of interest.

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