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Department of Dairy Science, University of Wisconsin, Madison 53706
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Key Words: reproduction • fertility • genetic selection • dairy cattle
Abbreviation key: CI = calving interval, CR = conception rate, DFS = days to first service, DO = days open, DPPX = days until a positive pregnancy examination, DPR = daughter pregnancy rate, ERCR = estimated relative conception rate, NRR = nonreturn rate, SPC = services per conception, VCCR = veterinarian-confirmed conception rate
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Complications also arise in the statistical analysis of reproductive data. Traits such as conception rate (CR) and nonreturn rate (NRR), are recorded as binary observations (success or failure), and the application of Gaussian linear models to such data can lead to biases unless the probability of success is near 0.5 and variance components are homogeneous across management groups (Weller and Ron, 1992; Boichard and Manfredi, 1994; Weigel and Rekaya, 2000). Interval traits, such as calving interval (CI), days open (DO), or days to first service (DFS) and "count" traits, such as services per conception (SPC) pose other problems, namely skewness and censoring. Skewness might be addressed by transformation of the data, but censoring is a much greater challenge. Some cows never become pregnant, and others die or get culled prior to becoming pregnant. Discarding these records or considering them as complete can lead to serious biases in the resulting estimates of genetic parameters and animal breeding values. A final complication common to most genetic analyses of fertility traits, particularly those based on CI, DO, CR, NRR, or SPC, is that (i.e., service sire) and maternal (i.e., sire of the cow) effects exist.
A thorough review of the literature regarding genetic improvement of male and female fertility was recently provided by Weigel and Clay (2001). Therefore, the objective of this paper was to present 2 potential approaches to the genetic analysis of fertility that involve detailed reproductive data and advanced statistical methodology. In the first case, data regarding veterinarian-confirmed conception rate (VCCR) were used to evaluate male fertility in a threshold model that properly accounted for the binary nature of this trait. In the second case, data regarding the number of days from calving until first positive pregnancy examination (DPPX) were used to evaluate female fertility, as well as the impact of health and management traits on fertility, using a failure time (survival analysis) model that properly accounted for censoring among cows that were culled or failed to conceive.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The following threshold model was used for genetic evaluation of male fertility using the VCCR data described above:
 | ([1]) |
where:
| yijklmn | = | binary outcome (success or failure) of a particular insemination event;
| HYMi | = | fixed interaction of herd, year, and month of insemination;
| HTj | = | fixed interaction of herd and artificial insemination (AI) technician;
| HAk | = | fixed interaction of herd and age of service sire;
| HPMl | = | fixed interaction of herd, parity, and milk yield;
| HDk | = | fixed interaction of herd and days in milk (DIM);
| cl | = | random effect of cow, assumed multivariate normal with mean 0 and variance  ;
| ssm | = | random effect of service sire, assumed multivariate normal with mean 0 and variance  ;
| eijklmn | = | random residual, assumed multivariate normal with mean 0 and variance  .
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Age of service sire was divided into 2 categories, young sire or proven sire, depending on whether the insemination occurred when the service sire was <42 mo or 
42 mo of age, respectively. The interaction of parity and milk yield was based on the mean of DHI daily milk weights prior to 100 DIM and included 3 classes each for primiparous (<27, 27 to 36, or >36 kg/d) and multiparous (<36, 36 to 45, or >45 kg/d) cows. Four categories were created for DIM: 35 to 74, 75 to 114, 115 to 184, and 185 to 365.
Failure Time Analysis of Health and Management Influences on Fertility
Data for the failure time (survival) analysis included DPPX records for the most recent lactation of 50,252 Holstein cows in 51 Alta Genetics, Inc. (Watertown, WI) progeny test herds that used the DairyComp 305 management software (www.vas.com). These herds were located in 12 states, including: California (15), Wisconsin (11), and New York (10), and all herds appeared to have complete recording of reproductive health and management information. Completeness was ensured by applying the following edits to the data from each herd: 500 insemination events, 200 positive pregnancy examinations, 200 negative pregnancy examinations, 100 cows with either synchronization events (coded at "LUT" "GNRH", "PROST", or "SYNCH") or prebreeding heats (coded as "HEAT"), and 100 cows that were designated "do not breed" (coded as "DNB") or exposed to a natural service bull (coded as "BULLPEN"). The purpose of the latter 2 requirements was to identify cows that the producer had discontinued breeding by AI. Farmers that owned a natural service bull would often move these cows to a bullpen, while farmers that didn’t have a natural service bull would frequently code these cows as "do not breed".
Complete (uncensored) data occurred for cows that became pregnant and consisted of DPPX observations, i.e., DIM when the cow was first declared pregnant by a veterinarian. Incomplete (censored) data for cows that were not declared pregnant consisted of the maximum of the following variables: DIM at the last negative pregnancy examination, DIM at the last reported AI breeding (if no subsequent pregnancy examination), DIM at the time of culling or death (if not yet declared pregnant), DIM when designated "do not breed," or DIM when exposed to a natural service bull (if not yet declared pregnant). A total of 43% of the records were right-censored. The dependent variable, DPPX, was chosen instead of DO, because this eliminated the need to assign (with occasional errors) a particular previous AI breeding to each positive pregnancy examination. On the other hand, the DPPX value for a given cow depends on the number of days that elapse between her breeding and subsequent pregnancy examination, and this interval is known to vary between herds and examination methods (e.g., palpation vs. ultrasound). Through inclusion of a time-dependent herd-year-month effect (as described below), the present study can account for variation in the interval between breeding and pregnancy examination between herds or across time. However, selective application of ultrasound technology within a herd-year-month class (e.g., checking only the best animals by ultrasound) would introduce bias.
The hazard function, which reflects the instantaneous probability of a positive pregnancy examination for a given cow at "t" days postpartum, was modeled as follows:
 | ([2]) |
where
| hijk (t) | = | risk of a positive pregnancy examination for a specific cow at t days postpartum;
| h0 (t) | = | baseline risk of a positive pregnancy examination for an average cow at t days postpartum;
| HYMi (t) | = | time-dependent random effect of herd-year-month, assumed to follow a log-gamma distribution and modeled as a piecewise constant with change points on the first of each month;
| Pj | = | time-independent fixed effect of parity; and
| Ek | = | time-independent fixed effect of a particular health or management event, coded in a binary manner (presence or absence), that may or may not have occurred during the first 75 d postpartum.
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The impact of health and management effects could have been examined using time-dependent covariates with change points at the dates of onset and recovery from each illness or management practice. However, the duration of many events (e.g., mastitis, lameness) were unknown, and we therefore assigned a single, binary variable that represented the occurrence, or lack thereof, of each event prior to 75 DIM in the current lactation. Calving events included: twins, dystocia, and stillbirths (coded as remarks of "TWINS", "PULLED CALF", or "DEAD CALF", respectively, in the calving record). Reproductive health and management events included: metritis, retained placentas, "normal" palpation results (coded as "CHECKED OK"), prebreeding heats, and synchronization events. Other health and management events included: bST injections, displaced abomasums, hoof trimming, movements into the "hospital string," ketosis, lameness, and mastitis. Although previous studies (e.g., Buckley et al., 2000; Pryce et al., 2001) have indicated a relationship between BCS and reproductive performance, BSC data were routinely recorded for very few herds in this study.
Failure Time Analysis of Genetic Differences in Female Fertility
A subset of the DPPX data described above was subsequently used to evaluate genetic differences among dairy sires in female fertility. Records from cows that lacked valid sire identification and cows that were sired by natural service bulls were discarded, leaving data from 14,827 cows in 50 herds for the genetic analysis.
The hazard function, or risk of a positive pregnancy examination for a given cow at "t" days postpartum, was modeled as follows:
 | ([3]) |
where
| hijk (t) | = | risk of a positive pregnancy examination for a specific cow at t days postpartum;
| h0 (t) | = | baseline risk of a positive pregnancy examination for an average cow at t days postpartum;
| HYMi (t) | = | time-dependent random effect of herd-year-month, distributed as log-gamma and assumed piecewise constant with change points at the beginning of each month;
| Pj | = | time-independent fixed effect of parity;
| Sk | = | time-independent random effect of sire (of the cow), distributed as multivariate normal with (co)variance matrix  .
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The Survival Kit Version 3.12, a set of FORTRAN programs written by Ducrocq and Sölkner (1998), was used to apply models [2]
and [3] to the DPPX data described above. Details regarding the methodology are given by Ducrocq and Casella (1996).
Theoretical Extension to Discrete Failure Time Analysis for Evaluation of Male Fertility
Although model [3] provides a relatively straightforward assessment of female fertility, evaluation of male (service sire) fertility using failure time analysis offers an additional complication. In commercial dairy herds, the service sires used for first and subsequent (repeat) inseminations of a particular cow often differ. For example, a given cow might be mated to sire "A" at the first service, sire "B" at the second service, and sire "C" at the third service. Another cow might be mated to sire "B" for both the first and second services and sire "D" for the third and fourth services, and so on. Conceptually, this means that service sire should be modeled as a time-dependent covariate. Addition of service sire (as a function of time) to model [3] would require specification of beginning and ending points for the time period at which a given service sire is "responsible for " the fertility of his mate. For example, if a given cow is mated to sire "A" at 60 DIM and sire "B" at 80 DIM, we might assign time-dependent covariates "A" and "B" to her fertility record, accompanied by change points at 60 and 80 DIM, respectively. However, it is not obvious which service sire (if any) should be assigned prior to 60 DIM, nor is it clear that we should continue to "punish" sire "B" if, for example, this particular mate remains open at 250 DIM.
A more intuitive approach would be to apply failure time methodology on a discrete scale (Ducrocq and Sölkner, 1998). In this case, we can replace our variable, DPPX, with a "count" variable, such as SPC. For example, a given cow might conceive after 3 services, another might conceive after 6 services, while another might remain open after 5 services. Failure time analyses can properly handle censored observations from cows that are culled prior to achieving pregnancy and cows that remain open at the time of statistical analysis, so the limitation that plagues conventional analyses of SPC using linear or threshold models no longer applies. Furthermore, via inclusion of time-dependent covariates, failure time analyses can accommodate a different service sire for each insemination of a given cow, with change points modeled appropriately.
In the discrete case, the hazard function, or risk of pregnancy at service "t", can be modeled as follows:
 | ([4]) |
where
| hijkl (t) | = | risk of pregnancy for a specific cow at insemination t;
| h0 | = | baseline risk of pregnancy for an average cow at insemination t;
| HYMi (t) | = | time-dependent random effect of herd-year-month, distributed as log-gamma and assumed piecewise constant with change points at each insemination;
| Pj | = | time-independent fixed effect of parity;
| Sk | = | time-independent random effect of sire (of the cow), distributed as multivariate normal with (co)variance matrix A ;
| SSl (t) | = | time-dependent random effect of service sire, distributed as multivariate normal with (co)variance matrix and change points at each insemination.
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In this manner, male fertility can be modeled as well, and the resulting solutions can be interpreted as the tendency of each service sire to increase or decrease the number of services per conception of his mates.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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and 
comprising 6.6 and 0.3% of the total phenotypic variance in VCCR, respectively. The former contains both genetic and permanent environmental (i.e., repeatability) components of variance that are common to all observations from a specific cow. Among 59 AI technicians who had at least 1500 inseminations each, mean VCCR ranged from 15.8 to 41.1%. Five herds had 2 technicians that met this criterion, and the differences between these pairs of technicians within herd were 2.0, 0.9, 3.2, 6.6, and 3.7%, respectively.
Means for VCCR by month of insemination, age of service sire, and milk yield (by parity) are shown in Table 1
. As expected, mean VCCR was lowest (25.9%) in July and highest (34.1%) in February. Young sires tended to have lower VCCR (27.6%) than proven sires (30.5%), although this is probably a reflection of careless usage of inexpensive young sire semen (e.g., on cows that might not really be in heat) rather than a true indication of biological differences between bulls of different ages. Primiparous cows with daily milk yields > 36 kg/d and multiparous cows with daily yields > 45 kg/d tended to have slightly lower VCCR, by 1.8 and 1.6%, respectively, compared with other animals of the same age.
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shows the relationship between threshold model solutions for service sires and the corresponding estimated relative conception rate (ERCR) ratings (Clay and McDaniel, 2001) that are routinely published by Dairy Records Management Systems (Raleigh, NC) based on 70-d NRR after first service. The correlation between threshold model solutions and ERCR ratings was 0.57 for the 190 Holstein service sires that had at least 300 first services in the ERCR analysis and at least 10 inseminations in each of 10 herds in the threshold model analysis. This correlation indicates reasonably strong agreement between our results and ERCR values, given the size of our data set and the difference in trait definition (DPPX vs. NRR).
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, and the log-gamma distribution of herd-year-month effects, 
, were estimated as 2.66 and 2.71, respectively. The estimated sire variance, , was 0.013. Using the approximation of Ducrocq and Cassella (1996), this corresponds to a heritability estimate on the logarithmic scale of 2.5% and a heritability estimate on the original scale of 4.4%.
Table 2 shows the relative risk of a positive pregnancy examination at "t" days postpartum by parity and calving status. Compared with third-parity cows, for which the risk of pregnancy was constrained to unity, cows in first, second, fourth, and fifth or later parities were 8% more likely, 2% more likely, 5% less likely, and 12% less likely, respectively, to achieve pregnancy at a given time. Similarly, the risk of pregnancy decreased by 12% for cows that had twins, 26% for cows that had difficult calvings, and 20% for cows that gave birth to dead calves, relative to cows that had a normal calving.
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. Approximately 33.9% of the cows were "checked OK," reproductively speaking, prior to 75 DIM, and these animals were 3% more likely to become pregnant than cows that did not have a normal reproductive examination. Likewise, 21.3% of the cows came into (visible) heat prior to 75 DIM (although they weren’t bred at this time), and their risk of pregnancy was subsequently 20% higher than their counterparts that didn’t show heat before 75 DIM. Cows that were synchronized prior to 75 DIM, 37.9% of the total, were 4% more likely to become pregnant than unsynchronized cows. On the other hand, cows that had metritis and retained placentas were 20 and 18% less likely, respectively, to become pregnant than cows that had not experienced these disorders.
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. As shown in the table, cows that began receiving BST injections prior to 75 d postpartum were 4% more likely to become pregnant, although a cause-effect relationship cannot be proven, because this could reflect a tendency among producers to preselect candidates for BST based on health status or BCS. Cows that had ketosis early in lactation were 8% less likely to become pregnant than their healthy contemporaries, while the risk of pregnancy for cows that had displaced abomasums was reduced by 11%. Cows that had lameness or hoof trimming prior to 75 DIM were 10 or 15% less likely to achieve pregnancy, respectively, although hoof trimming data are difficult to interpret. Many producers routinely trim hooves at the time of dry-off, and this management practice can have beneficial effects on health, fertility, and survival. However, cows that were trimmed prior to 75 DIM in this study likely displayed moderate or severe lameness, thereby requiring "emergency" hoof trimming, rather than "preventative" hoof trimming. Cows that had clinical mastitis were 10% less likely to become pregnant than unaffected cows, and the risk of pregnancy for cows that entered the "hospital string" was reduced by 15%. The latter variable could easily be modeled as a time-dependent covariate in herds that routinely report both entry and exit dates for cows in the hospital string.
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. The correlation between DPR and relative risk of pregnancy for 144 sires with at least 25 daughters in the DPR analysis and at least 10 uncensored daughters in the failure time analysis was 0.32, indicating moderate agreement. However, one should not expect perfect agreement, due to the size of our data set (hence, low reliability of sire solutions) and the major differences in trait definition and model specification between the DPR and failure time analysis.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Given that many producers already report pregnancy examination results (either through the DHI system or a herd management software program), this trait should replace NRR, which is limited by the unrealistic assumption that all censored cows are actually pregnant. Given that dairy producers are keenly interested in both male and female fertility, analyses of traits such as VCCR with a threshold model can provide reliable, unbiased genetic information regarding the reproductive efficiency of both sexes.
A wealth of reproductive data exists on commercial dairy farms, and the availability of these data will lead to the development of "next-generation" models for analysis of reproductive traits. Failure time (survival analysis) models, in particular, are interesting due to their ability to provide a powerful, theoretically defensible analysis of interval traits that are subject to censoring, such as CI, DO, DFB, and DPPX. When applicable, both male and female fertility can be modeled in this manner, and each can be treated as a genetic effect or (permanent) environmental effect. However, extension of failure time methodology to the analysis of male fertility is complicated by the decision of many farmers to use different service sires for repeat inseminations on the same cow. An extension of this methodology to discrete or ‘count’ variables, such as SPC, will allow the inclusion of service sire as a time-dependent covariate, such that one can predict the tendency of a specific service sire to increase or decrease the SPC of his mates.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Received for publication July 7, 2003. Accepted for publication August 26, 2003.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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