Estimation of maternal variance components considering cow-calf contacts under extensive pastoral systems

Traditional methods of variance component estimation for traits under maternal influence consist of partitioning the variance into direct additive genetic, maternal additive genetic, permanent maternal environmental, and error variance components. This partitioning is based on the assumption that each calf is nurtured and fed exclusively by its own dam. However, under extensive pastoral systems, voluntary cross-suckling may occur and could be quantified by using contact loggers recording cow-calf affiliations. A simulation study was conducted to test several variance


INTRODUCTION
The importance of maternal environment in domestic livestock is well recognized.Several studies have outlined the estimation of direct genetic, maternal genetic, and permanent maternal environmental effects for weaning weight in beef cattle (Robinson, 1996;Meyer, 1997).The rationale for these estimates is that traits such as weaning weight are influenced by the direct additive genetic effect, the direct effect of the genes for growth that the calf received from its sire and dam, and the growth environment provided by the calf's own dam (Quaas and Pollack, 1980;Henderson, 1988).The maternal environment provided by the dam is partly genetic and partly environmental.The basic assumption is that each calf is reared by its own mother and no systematic voluntary cross-suckling occurs with other cows in the herd.
Cross-suckling is known to occur, although information on its frequency and the effects of sex of the calf or 1081 models for partitioning maternal variation by including information on cow-calf contacts.The results indicated that weighting maternal genetic and permanent maternal environmental effects by the relative time calves spent with particular cows, including their own mothers, is feasible and significantly increased the log-likelihood of the models.However, the interpretation of the variance components in terms of traditional direct and maternal heritability is no longer straightforward.The need for further research and implications for the industry are discussed.lactation status of the dam is scanty.Le Neindre (1989) reported breed differences in the likelihood of cross-suckling in cattle suggesting that Friesians suckled more alien calves than the Salers.In general, cross-suckling events are not recorded and incorporated into the analysis of growth data.If information on cross-suckling were available, its use could lead to better estimates of maternal genetic and maternal environmental components for traits under maternal influence.With the advances in electronics, there is an opportunity to record animal-toanimal contacts that can be used to quantify animal behavior, allowing, in this case, measurement of the time a calf spends with its mother and with other cows.
In this paper, we describe a method of analysis for such data and apply it to simulated data to model the partitioning of maternal genetic variance by using the information on cow-calf contacts available through contact logging.The possibility of defining certain new traits based on the contact logging information is also discussed.

Contact Loggers
Contact loggers provide data on the proportion of time individual animals spend in close association with other animals and have been used to study cow-calf affiliations.Contact-logging collars are fitted to all cows and calves in a group, and social interactions are reported through an ultra high frequency transceiver that transmits and receives a unique code identifying all collars within a predefined proximity range (Swain and Bishop-Hurley, 2007).Sheep researchers in Australia are also using stationery loggers to identify ewe-lamb associations to establish maternal pedigree of the lamb (Atkins et al., 2006).This study simulated data that represent cow-calf contacts based on the type of data that are collected by using contact loggers.We assumed that contact data accurately represent the time each calf is spending with each cow and that contacts are highly correlated with cross-suckling events.

Simulation
A beef cattle population with records on weaning weight was simulated in 2 stages, as shown below.

Stage 1.
A population was simulated with 6 uncorrelated traits.Three calf traits (appetite, food conversion, and shyness) and 2 dam traits (milk and generosity) controlled the milk supply to the calf and the resulting growth rate.Shyness of a calf represents the relative disinclination of a calf to approach other cows (other than its own mother) in the vicinity, and the generosity of a cow represents the relative willingness of a cow to allow a calf other than its own to suckle.The 2 dam traits each had a direct genetic component, a permanent environmental component, and a year-specific error component.The sixth trait, with a heritability of 0.3, was used to select the animals retained in the herd; this trait was included solely to ensure that the population structure of the simulated herd was consistent with the population structure of a herd under selection.
The simulation commenced with a population of unrelated cattle comprising 20 males and 400 females in yr 1.The breeding program ran from yr 3 to 20, with assumptions of sexual maturity at 2 yr of age and all cows producing one calf per year.Each year, the 10 best bulls between 2 and 3 yr of age and the 200 best cows between 2 and 5 yr of age were selected and randomly mated to the bulls, at a rate of 20 cows per each bull.From this simulation, a population of 4,020 animals (420 base + 3,600 generated) with phenotypes on the 5 milk supply traits was available for the second stage of simulation.
Stage 2. This second stage used the phenotypes of the 5 milk supply traits to derive the weaning weight for all 4,020 animals.The weaning weight for each calf was derived by using 1,000 rounds of an agent-based simulation of feeding behavior.The basic logic of this simulation is that if hungry, a calf approaches cows based on the availability of milk, the generosity of a cow to let the calf suckle, and the interaction between calf shyness and the cow being a stranger, as opposed to its own mother.Calves were limited to suckling no more than 6 cows (including their own dam), and for simplicity of the simulation, it was assumed that there was no learning of which cows among the 6 were more likely to supply milk.Suckling events and total BW were recorded for each calf, and made available for further analyses.Pseudocode for the agent-based simulation appears in the Appendix.
The stochastic decisions in the agent-based simulation are made by comparing the phenotype record to a random number drawn from a uniform (0, 1) distribution.This requires that the phenotypes produced in the first stage of the simulation be converted from their normal distributions to probability values between zero and one.Rather than using an inverse Normal function, this was done by adding a trait-specific offset to adjust the mean and then moving trait values outside the interval [0.1, 0.9] to the interval boundary.The adjusted mean was chosen to give a plausible average incidence and distribution of values.
Tuning.To ensure that the weight and contact records produced by the agent-based model were realistic, an initial study was conducted to tune the input parameters for the final study to find a set of input parameters that produced plausible distributions of weaning weight and contacts based on the targeted variance components (Prayaga and Henshall, 2005) and earlier contact information (Swain and Bishop-Hurley, 2007).The input parameters identified have no intrinsic meaning, but simply produce a sufficiently realistic distribution of weaning weights to allow the study of methods of estimating genetic parameters when cow-calf contacts are recorded.
Both stages of the simulation were run with a variety of sets of input parameters.Input parameters to the data simulation were the 12 variance components (2 for each calf trait: direct additive and maternal additive; and 3 for each cow trait: direct additive, maternal additive, and maternal environment) used in the first stage of the simulation and the 5 trait-specific offsets used in the second stage.Variance components were estimated from the simulated data obtained from each run by using ASReml (Gilmour et al., 2006) and an objective function was evaluated.The objective function included variance components for weaning weight based on values derived from a study conducted at Belmont Research Station under extensive pastoral systems in tropical conditions (Prayaga and Henshall, 2005).The variance components were h 2 (heritability) = 0.23, m 2 (maternal heritability) = 0.12, and c 2 (permanent environmental variance of the dam, expressed as a proportion of the phenotypic variance) = 0.19.Covariance between direct and maternal genetic effects was assumed to be zero for the purpose of this simulation.The objective function also included targets for minimum and maximum weaning weights of 80 and 400 kg, respectively, and an arbitrary target of a mean of 60% (with a minimum of 30%) of suckling events occurring with the calf's own dam.

Models and Statistical Analyses
The simulation described above generated data on the weaning weight of the calf and the contacts between cows and calves.Each contact was assumed to last for a similar period so that the number of contacts between a cow and calf was proportional to the amount of time a calf spent with that particular cow.Consequently, dividing the number of contacts between a cow and calf by the sum of all cow contacts for that calf was used to represent the proportional time spent by the calf with its own dam (t 0 ) and with up to 5 other cows in the paddock (t 1 to t 5 ), ordered by frequency of contact.Thus, the total of all these proportions (t 0 , t 1 , t 2 , t 3 , t 4 , t 5 ) was 1.Some of these proportions (t 1 to t 5 ) were zero (coded as missing) for calves that suckled fewer than 5 extra cows; the corresponding superfluous dam identity fields were assigned missing values.The first few lines of a sample data set after combining the information from BW and contacts is given in Table 1.
The descriptive statistics for the data generated from the simulation are presented in Table 2.The correlations between the proportional time spent by the calves with their own dams (t 0 ) and other dams (t 1 to t 5 ) and weaning weight are presented in Table 3.
Weaning Weight.The weaning weight of the calves was analyzed under various animal models by using ASReml (Gilmour et al., 2006).The traditional animal model (model [1]) can be written as where y is an n × 1 vector of n observations on weaning weight; b is a p × 1 vector of p fixed effects; u a and u m are q × 1 vectors of direct additive and maternal additive genetic effects, respectively, where q is the number of animals in the pedigree; c is a c × 1 vector of maternal permanent environment effects, where c is the number of dams of recorded animals; X is a design matrix of order n × p relating the observations in y to the fixed effects in b; Z a and Z m are the design matrices of the order n × q relating observations in y to the random effects in u a and u m ; Z c is a design matrix of the order n × c relating observations to the maternal permanent environmental effects; and e is a vector of random residual effects.
The variance structure for the model can be described as where σ 2 a is the direct additive genetic variance; σ 2 m is the maternal additive genetic variance; σ 2 c is the maternal environmental variance; σ 2 e is the error variance; A is the numerator relationship matrix; and I c and I n are identity matrices of order c and n, respectively.Covariance between direct and maternal genetic variances is assumed to be zero for this study.The phenotypic variance of the observations is estimated as Table 2. Descriptive statistics of simulated data, with ranges given in parentheses  The model is now extended to incorporate milk source information, because model [1] assumes that all milk and nurturing are provided by the genetic dam and no cross-suckling occurs.Let Z i represent the design matrix associating calves with the ith dam and note there are 2 forms, one for genetic and one for nongenetic dam effects, the former having extra columns of zero pertaining to the other animals in the pedigree.The maternal contribution of the 6 cows to the jth calf can be written as where u m(dij) is the maternal genetic effect and c (dij) is the maternal environment effect for the cow that is the ith (foster) dam of calf j.The design matrices for u m (dij) and c (dij) can be written as ∑ 5 i=0 t i Z i (2 forms being Z * m and Z * c ), where t i Z i is a special product, in which the rows of Z i are scaled by the corresponding value of t i .Thus, we have fitted 5 models (models 2 to 6) derived from various stages of inclusion of t i in the models: where Z * c represents a combined design matrix relating observations to maternal permanent environment effects, where the rows are scaled by the proportional time spent by the calf with all dams (i.e., t 0 to t 5 ); Z * m represents a combined design matrix relating observations to maternal genetic effects, where the rows are scaled by the proportional time spent by the calf with all dams (i.e., t 0 to t 5 ); c 0 and c* represent vectors of maternal permanent environment effects, reflecting only the genetic dam in the case of c 0 , and including foster dams in the case of c*; and u m0 and u * m represent vectors of maternal additive genetic effects for only the genetic dam in the case of u m0 and including foster dams in the case of u * m .It should be noted that although the 6 values of t i sum to one for each calf, no attempt was made to make the contributions of a cow to all calves that suckle her sum to 1, although, on average, that was the case.The proportional time spent by all calves (own and foster) with a cow ranged from 0.47 to 1.64, with a mean of 1.00 and a variance of 0.03.Thus, the individual cow effects represent the relative differences in the generosity and the milking ability of the cows, but are also affected by the shyness of the calves.Consequently, the variance components no longer represent components in the traditional sense, because the t values are squared in the variance matrix and the sum of squares is less than 1.We overcame this problem by weighting the variance components affected by the inclusion of information on t i by the appropriate average sum of squared t i values, as discussed later.

Maternal Ability of the Cow. The proportional time
spent by the calf with its own mother (t 0 ) was also analyzed both as a trait of the calf and as a trait of the cow.When t 0 was treated as a trait of the calf, it was analyzed by using a model similar to model [1] (model [7]).Considered as a trait of the cow, t 0 possibly represents the mothering ability of the cow.Because this trait is essentially a maternal trait, data were rearranged to treat t 0 as a trait of the cow and the analysis was carried out by using model [8].Note that the permanent environmental effects in this model are due to animal, and animal in this model is the dam of the original data, which has repeated measurements of mothering ability depending on the number of its own calves: where w is an n × 1 vector of n observations on t 0 (as a trait of the dam); b is a p × 1 vector of fixed effect with p levels; u a is a q × 1 vector of direct additive genetic effects, where q is the number of animals in the pedigree; c is a c × 1 vector of permanent environment effects of the animal, where c is the number of dams; X is a design matrix of order n × p relating the observations in w to t 0 = proportional time spent by the calf with its own mother; t i = proportional time spent by the calf with (non)dam i , where 1 ≤ i ≤ 5 (dam1 to dam5 are the non-dams with which the calf had contacts); σ 2 a = additive genetic variance; σ 2 m = maternal additive genetic variance; σ 2 c = variance due to permanent environmental of the dam; σ 2 e = error variance; variances averaged over 100 replications. 2 The negative terms simply define interactions for subsequent inclusion in the and() terms; the and() model function as the design for its argument to the design matrix of the preceding model term; ide(dam) represents the permanent maternal environment.
the fixed effects in b; Z a is the design matrix of the order n × q relating observations in w to the random effects in u a ; Z c is a design matrix of the order n × c relating observations to the permanent environmental effects; and e is a vector of random residual effects.
To further understand the variation in generosity of the cows, the proportional time spent by the calves with various nondams (t non ; i.e., t 1 to t 5 for each cow) was analyzed as a repeated measure of the dam by using a model similar to model [8] (model [9]).
Stage 1 simulation was replicated 20 times to generate phenotype files with milk supply traits, and for each of these sets, 5 replications of stage 2 were generated to test for the stochastic nature of contact information of the simulation.The 9 models mentioned above were used to analyze the data from these 100 replications.

RESULTS AND DISCUSSION
The influence of a dam on her young, through nutrients provided by the uterus and the mammary gland, is recognized as a special case of joint action of genotype and environment (Robison, 1981).Calf weaning weight is strongly influenced by the growth environment provided by the cow and is partly genetic in nature.This maternal environmental effect can be accounted for in full by the traditional maternal model if the calf is obtaining almost all the maternal environmental effect from its own dam.However, this cannot be guaranteed in an extensive pastoral system in which calves may spend time with and get milk from other cows.Therefore, the maternal genetic and maternal environmental effects need to be apportioned by the proportion of time the calf spends with each cow.
In the present study, the proportion of time spent by the calf with its own mother varied between 35% of the total time (based on contact information) to 100%, with a mean of 72% (Table 2).This estimate derived from the simulated data was slightly greater than the targeted t 0 of 60%.The simulated t 1, t 2 , t 3 , t 4 , and t 5 averaged 15, 7, 3, 2, and 1%, respectively.It is apparent in the simulated data that some calves spent almost half the time with nondams and some calves spent time with fewer than the 5 nondams permitted in the simulation, as can be seen from the number of records for t 1 to t 5 (Table 3).High negative correlations between t 0 and t 1 to t 5 are observed in the simulated data, reflecting the fact that as the calf spends more time with its own mother, it spends relatively less time with other dams.This negative relationship is expected given that as t 0 increases, a calf may not need to visit as many nondams, and even if visited, will spend less time with them.
On the basis of several experiments in pigs (Robison, 1981), it was hypothesized that piglets suckling sows that are producing little milk turn to supplementary feed sooner than piglets suckling heavy-milking sows.Similarly, in the cattle context, lack of milk from the mother may drive the calf to look for milk from other cows in the herd or to start grazing earlier.The success of the calf depends on the interaction between the availability of milk from the nondam approached by the calf, the generosity of that cow, and the shyness or lack thereof of the calf itself.This complex phenomenon is reflected by the time a particular calf spends with its own dam as opposed to other dams (nondams).This can be a breed-specific trait and may be more important in breeds with low milk yields (Le Neindre, 1989).A low positive relationship between t 0 and weaning weight is observed in the simulated data, and low negative correlations are observed between t 1 to t 5 and weaning weight, indicating that a calf's weaning weight is greater when it is reared by its own dam than when it is reared by t 0 = proportional time spent by the calf with its own mother; t i = proportional time spent by the calf with a (non)dami, where 1 ≤ i ≤ 5 (dam1 to dam5 are the non-dams with which the calf had contacts); σ 2 a = additive genetic variance; σ 2 m = maternal genetic variance (scaled); σ 2 c = variance due to permanent environmental effect of the dam (scaled); σ 2 e = error variance; σ 2 p = phenotypic variance (using scaled components); h 2 = heritability; m 2 = maternal heritability (σ 2 m /σ 2 p ); c 2 = σ 2 c /σ 2 p ; variances averaged over 100 replications and where appropriate (in bold) scaled by the average sum of squared t i (0.5274 for t 0 alone and 0.557 for all t i ); SD over 100 replications are given in parentheses for model [1].

2
The negative terms simply define interactions for subsequent inclusion in the and() terms; the and() model functions as the design for its argument to the design matrix of the preceding model term; ide(dam) represents the permanent maternal environment.
foster dams.The correlations among t 1 , t 2 , t 3 , t 4 , and t 5 are positive and range between 0.12 and 0.66, with greater magnitudes for adjacent proportions.This is also influenced by the fact that they are arranged in descending order for each calf.These relationships in the simulated data are consistent with our expectations of real data.
The average estimated variance components over 100 replications for weaning weight for models [1] to [6] are presented in Table 4.The log-likelihood (LogL) was significantly greater in models [2] to [6] compared with model [1], with model [5] recording the greatest LogL.However, the variance components cannot be compared directly because of the differences in the design matrices.For example, the difference between model terms ide(dam) (the permanent maternal environment) and ide(dam).t0 is simply that the values of 1 in the former are replaced with t 0 values in the latter, ranging from 0.35 to 1.00, with an average of 0.72.Hence, the respective variance components were derived by scaling them with appropriate average sum of squared t i values (Table 5).Given the range of t 0 values, the average of the squared t 0 values was 0.5274.Thus, for model [2], the derived maternal environment variance component is 326 (619 × 0.5274).We observed, however, that the maternal genetic component dropped sharply (222 to 68) and the maternal environment increased (219 to 326).Thus, t 0 is a good predictor of the dam effect in a random regression sense, and this effect is strong relative to the genetic covariance attributable to relatives.With respect to model [3], which is a better model with a greater LogL, the Z * c Z * c ′ matrix has off-diagonal values relating to calves that suckle multiple cows.The maternal environment variance is estimated to be 302 (543 × 0.5570), using the sum of the 6 average squared t i values (0.5570) as the scaling coefficient.The σ 2 c is still high in relation to model [1], but the σ 2 m (90) is slightly less depressed.Given the impact of using ide(dam).t0 in model [2], further improvement in the LogL of model [4] is not surprising.Interestingly,in model [4], σ 2 a and σ 2 c (147 = 278 × 0.5274) have dropped and the σ 2 m has increased (316 = 599 × 0.5274) relative to model [1].However, model [5] is the best model, with the full suckling covariance structure at the maternal environment level, but only the direct (weighted by t 0 ) maternal genetic effect with a σ 2 m of 266 (504 × 0.5274) and σ 2 c of 190 (341 × 0.5570).Including the covariance structure of multiple cows in the maternal genetic structure (model [6]) is only slightly better (−4,187 vs. −4,198) than ignoring the proportional time structure completely at the genetic level (model [3]).The fact that model [6] is not better than model [5] indicated the nongenetic nature of cross-suckling events, as discussed later.
The traditional model without taking into account the proportional time spent by the calves with various dams (model [1]) resulted in h 2 of 0.21, m 2 of 0.17, and c 2 of 0.17 in comparison with the targeted parameters of h 2 of 0.23, m 2 of 0.12, and c 2 of 0.19.This similarity in the t 0 (as a trait of the calf) = proportional time spent by the calf with its own mother; t 0 (as a trait of the dam) = repeated measures of the proportional time spent by various calves with their own mother; t non (as a trait of the dam) = repeated measures of proportional time spent by calves with nondams (i.e., essentially t 1 to t 5 measured as a trait of the dam); σ 2 a = additive genetic variance; σ 2 m = maternal additive genetic variance; σ 2 c = variance due to permanent environmental effect of the dam for t 0 (as a trait of the calf) and variance due to permanent environment of the animal for t 0 (as a trait of the dam) and t non (as a trait of the dam); σ 2 e = error variance; σ 2 p = phenotypic variance; h 2 = heritability; m 2 = maternal heritability (σ 2 m /σ 2 p ); c 2 = σ 2 c /σ 2 p ; variances and their ratios averaged over 100 replications and the SD over 100 replications are given in parentheses for the parameters.
variance components from the traditional model suggests that the simulated growth based on the contacts is plausible.It can also be concluded that the inclusion of cow-calf contact information in the design matrices for maternal genetic and environmental effects has greatly improved the model fit compared with the traditional model [1] in this simulated data.The genetic parameters of 0.18 (h 2 ), 0.21 (m 2 ), and 0.15 (c 2 ) from the best model (model [5]) are comparable to the traditional model (model [1]), although with slightly lower h 2 and greater m 2 .
We have therefore shown how such information can be incorporated into an analysis and that it is potentially advantageous to do so.The next step is to attempt these analyses on real data.The current simulation was based on the observations from a small-scale study undertaken by using Belmont Red cattle at the Belmont Research Station.However, the maternal behavior of certain other breeds, such as Brahmans, is supposedly different from that of the Belmont Red.Brahmans have better milking capability, which in turn has been attributed to their maternal ability and greater weaning BW of calves under tropical conditions (Prayaga, 2003).Anecdotal evidence suggests that Brahmans are more generous mothers with respect to allowing cross-suckling.Some of these behavioral observations can be quantified and used in improving breed-specific genetic parameters based on contact logging information.However, use of cow BLUP from these analyses will be complicated because of the need to incorporate the t-values in the prediction, and t itself is likely to be under genetic control.
The results of the genetic analyses of t 0 , both as a trait of the calf and as a trait of the dam, and t non are presented in Table 6.These results clearly demonstrate that t 0 as a trait of the calf and trait of the dam is under moderate genetic influence, with heritabilities of 0.29 and 0.14, respectively.The repeated measures of proportional time spent by calves with nondams (t non ), analyzed as a trait of the dam, is not under genetic influence in the simulated data, with an h 2 estimate of only 0.02.This is reflected in the analyses of weaning weight data, in which model [6] is worse than model [5] (Table 4).There also does not seem to be any influence of a permanent environment effect of the animal for t non .In future studies, t 0 can be further studied as a trait of interest for selection, because it may be positively related to maternal abilities of the cow, which are quite important in extensive production systems of beef cattle.
There has been increased interest in individual animal identification with the intention of increasing the traceability of animal products.This has been driven mostly by recent disease outbreaks and their impact on the international meat trade (Bailey and Britt, 2001).The use of electronics, for example, the National Livestock Identification System in Australia, has been the major driver of such a capability.Quantification of cow-calf interactions has implications for animal breeding, with the potential to better define the traits of economic importance such as maternal ability and to better model maternal traits.With advances in the miniaturization of electronic technology, the goal should be to embed contact logging devices in the electronic ear tags, making them part of the normal husbandry practices.In such a situation, volumes of data generated on animal-to-animal interactions can be used to redefine and improve accuracy in evaluating some of the existing economic traits.In the short term, efforts need to be made to collect these data on pedigreed resource populations and to validate the accuracy of information generated.
This current study is intended as an initial step in highlighting the possibilities for such data in genetic analyses.Research is needed to evaluate the correlation between the number of contacts and the suckling events of the calves.It is also important to note that the duration of contacts and number of contacts together may provide a better estimate of cow-calf affiliation than only the number of contacts.In light of these developments, it is not difficult to foresee the inclusion of quantified components of animal behavior in economic trait definitions and genetic evaluations in the near future.

Table 1 .
Portion of a sample data set after combining the information from BW and contacts

Table 3 .
Product moment correlations between proportional time spent by the calves with various cows and their weaning weight1,2,3Average number of records for each of the proportions is given in parentheses.Within each calf, t 1 to t 5 are arranged in descending order based on number of contacts.

Table 4 .
Variance components estimated for weaning weight under various models considering the proportional time spent by the calves with various dams1

Table 6 .
Variance components and genetic parameters estimated for proportional time spent by the calf with its own mother (t 0 ) and the proportional time spent with other dams 1 (t non ) Atkins, K. D., J. S. Richards, and S. J. Semple.2006.The application of genetic principles to precision production systems in sheep.