Resilience Indicator Traits in three Dairy Cattle breeds in Baden-Württemberg

In recent years, research in animal breeding has increasingly focused on the topic of resilience, which is expected to continue in the future due to the need for high-yielding, healthy, and robust animals. In this context, an established approach is the calculation of resilience indicator traits with time series analyses. Examples are the variance and autocorrelation of daily milk yield in dairy cows. We applied this methodology to the German dairy cow population. Data from the 3 breeds German Holstein, German Fleckvieh and German Brown Swiss were obtained, which included 13949 lactations from 36 farms from the state Baden-Würt-temberg in Germany working with automatic milking systems. Using the milk yield data, the daily absolute milk yields, deviations between observed and expected daily milk yields, and relative proportions of daily milk yields in relation to lactation performance were calculated. We used the variance and autocorrelation of these data as phenotypes in our statistical analyses. We estimated a heritability of 0.047 for autocorrelation and heritabilities between 0.026 and 0.183 for variance-based indicator traits. Furthermore, significant breed differences could be observed, with a tendency of better resilience in Brown Swiss. The breed differences can be due to both, genetic and environmental factors. A high value of a variance-based indicator trait indicates a low resilience. Performance traits were positively correlated with variance-based indicator traits calculated from absolute daily milk yields, but they were negatively correlated with variance-based indicators calculated from relative daily milk yields. Thus, they can be considered as different traits. While variance-based indicators based on absolute daily milk yields were affected by the performance level, variance-based indicators based on relative daily milk yields were corrected for the performance level and also showed higher heritabilities. Thus, they seem to be more suitable for practical use. Further studies need to be conducted to calculate the correlations between resilience indicator traits, functional traits and health traits


INTRODUCTION
Modern livestock production faces the challenge of supplying the world's population with high-quality food and at the same time protecting the environment by maximizing resource efficiency (Madhusoodan et al., 2019).This requires our livestock to maintain a high, stable level of performance while staying healthy.Various environmental factors have an impact on the organism, and their effects are intensified by progressive developments such as climate change, new and evolving pathogens or changing social demands (Dominik, Swan;Hansen et al., 2012;Schader et al., 2015).To breed livestock that meet these challenges, the sole consideration of health traits and heat tolerance may not be sufficient.Overarching traits like resilience -the ability to respond to and recover from short-term disturbances of any kind to return to original performance levels (Colditz and Hine 2016;Poppe et al., 2021) -are becoming increasingly important (Friggens et al., 2022).
In recent years, various ideas have been proposed for defining and measuring an individual's resilience.Because the disturbance events are usually unknown, one of the most promising approaches are resilience indicators based solely on statistical time series analysis (Berghof et al., 2018).First attempts to capture disturbance effects by evaluating the changes trait expressions over time were based on test day data (Codrea et al., 2011), but the regular use of time series analysis only occurred with the further development of precision livestock farming and the availability of longitudinal data (Berghof et al., 2018).Elgersma et al. (2018) and Putz et al. (2018) were one of the firsts to introduce the methodology into livestock research, studying daily milk yields of dairy cattle and daily feed intake in pigs, respectively.However, their methodology did not take into account the individual performance level.Subsequent studies analyzed the deviation of the observed Resilience Indicator Traits in three Dairy Cattle breeds in Baden-Württemberg F. Keßler, 1 * R. Wellmann, 1 M. G. G. Chagunda, 2 and J. Bennewitz 1 performance from a predicted performance.Predicted performance was calculated either for an individual or for the entire sample, with higher accuracy for the former (Bedere et al., 2022).
The deviations from either the mean performance or the predicted performance can be used to calculate resilience indicators, for example the natural logarithm of the variance (lnvar d ) or the lag-1-autocorrelation (r Auto ).The variance quantifies the upward -downward fluctuation in performance, whereby resilient animals are expected to show less intense responses to disturbances, meaning that the variance indicators are small.In contrast, r Auto is expected to provide information about the time until recovery from disturbances (Wang et al., 2022;Poppe et al., 2020;Berghof et al., 2018) and a value close to zero indicates higher resilience, because the deviations of the observed from the expected milk yield after a disturbance were reduced more rapidly.Less resilient animals, on the other hand, take longer to recover the initial performance level, so the deviations between observed and expected daily milk yield persist over a longer period (Dai et al., 2012;Scheffer et al., 2012).Since several studies assessed the heritability and the correlations with different functional and health traits as moderate (Wang et al., 2022;Poppe et al., 2020), the variance turned out to be the more suitable parameter to represent general resilience.However, the number and density of data points needs to be high enough to capture effects of disturbances (Mehrabbeik et al., 2021).Examples for the application of time series analysis include step counts of dairy cows (Poppe et al. 2022a), eggs laid per week in laying hens (Bedere et al., 2022), activity data and feed intake in pigs (van der Zande et al., 2020;Homma et al., 2021), and growth rates in fish (Mengistu et al., 2022).
Different breeds have individual characteristics and differ, for example, in their performance or adaptability.Therefore, it could be hypothesized that different breeds cope differently with external influences.For example, low-yielding breeds often have longer life spans, reduced length of calving intervals, smaller insemination indices, and in some cases lower milk somatic cell counts (Bieber et al., 2019).But also high-yielding breeds differ among each other.Mylostyvyi et al. (2021) found that Brown Swiss showed a lower physiological response and lower drop in milk performance under heat stress than Holstein Friesian, indicating better heat tolerance, while Toledo-Alvarado et al. (2017) reported that Fleckvieh had in general a better fertility than Brown Swiss or Holstein Friesian.For resilience, to the best of our knowledge, only few studies have been conducted that examined resilience indicator breed differences (Adriaens et al., 2023;Bonekamp et al., 2022).We applied the above-mentioned resilience indicators and additional variance indicators to the 3 breeds German Holstein (HF), German Brown Swiss (BS) and German Fleckvieh (FV).Next to absolute daily milk yields, we also consider variance indicators based on relative daily milk yields to correct for individual performance levels.Thus, our objectives were (I) to define and calculate various resilience indicators based on absolute and relative milk yields, (II) to estimate heritabilites and genetic correlations of these resilience indicators for the German dairy cattle population, (III) to estimate genetic correlations between resilience indicators and 305-d performance for milk (MY 305 ), protein (PY 305 ), fat (FPY 305 ), and average daily milk yield (AMPY 305 ), and (IV) to compare the 3 breeds HF, BS and FV with respect to the resilience indicator traits.

MATERIALS AND METHODS
Data processing and evaluation as well as statistical analyses were performed in software R (R Core Team 2022) by using ASReml-R 4 for the genetic analyses.

Materials
The data were collected from 30.09.2017 to 28.03.2023 on 36 farms in Baden-Württemberg that participated in the projects KlimaFit and/or KuhVision.In total 13949 lactations from 6731 cows were considered.The data included 6352 lactations from 3075 HF cows, 6694 lactations from 3150 FV cows, and 903 lactations from 506 BS cows.Data collection and processing was carried out by the Landeskontrollverband Baden-Württemberg.All farms worked with an automatic milking system, which recorded the amount of milk per milking.Aborted milkings were removed from the data set.The milking quantities were summarized to daily milk quantities.That is, the first milking of a day was prorated to the time up to midnight of the previous day and since midnight of the current day.Days when the number of animals milked on the farm differed from the average by 3 standard deviations, were removed, as well as the day before and after.In addition, the first day after and the last day before a gap in an individual's records were excluded.

Modeling Lactation Curve.
A lactation curve was predicted for each lactation of each animal.Because the predicted lactation curve should ideally reflect the expected performance in the absence of disturbances, a spline interpolation with weighting of the data points Keßler et al.: Running Head: Resilience Traits in German Dairy Cattle was performed.Data points corresponding to days in which the cow had a temporary reduction of the milk yield were given lower weights.The spline interpolation was obtained using the package pspline in R (Ramsey and Ripley 2022).
The weights were calculated as follows.For each day d, all intervals shorter than 60 d were considered that include day d.Intervals whose boundaries were less than 5 d away from day d were excluded.For each interval, it was determined whether the milk yield at day d is above or below the straight line that connects the 2 milk yields at the interval boundaries.The number D of times in which the milk yield was above the line was counted, and the weighting factor w d used in the spline interpolation was calculated as w D N d = , where N is the total number of intervals.Figure 1 illustrates this.The algorithm for computing the weights is given in the appendix.
Different order of interpolation from 3 to 9 were tested and compared.Five degrees of freedom were chosen by visual assessment of the lactation curves (not shown elsewhere).For standardizing the observation period, only the period between the 10th and 305th lactation day of each lactation was considered.
Calculation of Resilience Indicators.We denote with y il the n-vector with milk-yields of cow i in lactation l.The variance of the vector is calculated as With t a day and n the number of days, for which daily milk yield were available for this cow.The covariance between 2 succeeding components is calculated as The variance (var) of the daily milk yields satisfies Where 1 is the vector with ones.That is, the variance quantifies the deviation of the actual milk-yields from the mean milk yield.In contrast, the variance indicator (var d ), defined as Taking the natural logarithms of the parameters provides the parameters ln var(y il ), ln var d (y il ), ln var r (y il ), and ln var rd (y il ), respectively.Finally, the lag-1-autocorrelation (r Auto ) between 2 lactation days t was calculated as  ˆ.
An overview of all resilience indicators and their definition can be found in Table 1.

Genetic Analysis -Univariate Analysis
Genetic analyses were performed for both, the entire data set, and for each breed separately.The analysis of the entire data set is called the across breed (AB) evaluation.Only lactations for which at least 50% of the data were available between lactation d 10 and lactation d 305 were considered in the analysis.Univariate analysis was performed for all data sets with the animal model: where y is the vector of observations, b is the vector of fixed effects described in detail later, u is the random vector of additive genetic effects, pe is the random vector of permanent environmental effects, and e is the vector of residuals.The matrices W, X, and Z are the corresponding incidence matrices.The vector of fixed effects b comprised age at first calving in month (20 levels), lactation divided in first or higher lactation (2 levels) and herd-year-season (hys, 585 levels) for all univariate analyses.The seasons were divided into spring: March to May, summer: June to August, autumn: September to November, and winter: December to February.For AB evaluations, a breed effect was included in b.For resilience indicator traits, the completeness of lactation data (divided in ≥90%, 80% -≤ 90%, 70% -≤ 80%, 60% -≤ 70%, 50% -≤ 60%) was included.Levels of fixed effects with less than 5 individuals were excluded.The vectors of additive genetic effects u, permanent environment effects pe, and residuals e were normally distributed with pe ∼ For bivariate analyses, the same model extended to 2 traits was used.The only difference was that hys was included as a random effect to facilitate convergence of the model.It was assumed to be normally distributed with hys N I hys hys ) whereby I hys is an identity ma- trix and σ hys 2 is the variance of hys.Correlations were computed between resilience indicators as well as between resilience indicators and the performance traits MY 305 , PMY 305 , FY 305 , and AMY 305 .

Description of Resilience Indicators
Table 2 shows the descriptive statistics of the resilience indicators across and within breeds.BS had the lowest mean values for all variance-based indicators var, ln var, var d , ln var d , var r and var rd , except ln var r and ln var rd .FV had the lowest mean r Auto .HF showed the highest values for variances-based indicators calculated from absolute milk yields compared with BS and FV, but variance-based indicators based on relative milk yields were between the mean values of these traits in BS and FV.
The results from the univariate analysis using the whole data set are presented in Table 3, whereby most of the variance components were significant different from zero.The highest heritability was estimated for ln var r (h2 = 0.18) and lowest for var rd (h 2 = 0.03), whereby the estimation for the additive genetic effect for r Auto and var rd was close to 0. Except for ln var r , the heritabilities of the variance-based indicators were higher when calculated from absolute rather than relative milk yields.Variances of the animal effects and the permanent environmental effects were similar in magni- Variance of deviation between observed relative and predicted daily milk yield ln var rd Log variance of deviation between observed relative and predicted daily milk yield tude, with the permanent environmental effect tending to be stronger, except for var and ln var.Results of the analyses within breeds are available in the appendix, with highest heritabilities for BS and lowest for FV (Table 7).
Fehler! Verweisquelle konnte nicht gefunden werden.shows the results of the Tuckey's HSD-Test with one plot for each trait, with significant differences marked using different letters.Indicator r Auto was significantly smaller for FV than for HF, BS did not differ significantly from either FV or HF.Variance-based indicators calculated from absolute daily milk yields were lowest for BS, but only significant different from FV for ln var.HF showed significant higher variance-based indicators based on absolute daily milk yields than BS and for var d and ln var d in FV.Variance-based indicators calculated from relative daily milk yields were similar in all breeds, except ln var r with a significant difference between BS and FV.In general, BS showed the smallest values for variance-based indicators, but the largest range.

Correlations between Resilience Indicators
Correlations between resilience indicator traits estimated from the whole data set are represented in Table 4 with genetic correlations below and phenotypic above the diagonal.In general, phenotypic correlations were all positive and genetic correlations between r Auto and any version of variance-based indicator were negative, but mostly with large standard errors.Variance-based indicators based on relative daily milk yields had relative smaller standard errors than variance-based indicators based on absolute milk yields.
Both, genetic and phenotypic correlations between different variance-based indicators were, as expected, positive and often significant.The strongest genetic correlation was found between ln var rd and var rd (r = 0.95).The genetic correlations between ln var and ln var d (r = 0.43) and between ln var r and ln var rd (r = 0.53) were moderate, indicating that variance-based indicators calculated from observed daily milk yield can be considered as different traits compared with variance-based indicators calculated from deviations of daily milk yield.Comparing the same resilience indicators calculated from absolute and relative milk yields, the genetic correlations ranged between r = 0.75 and r = 0.84.The logarithmized traits were highly genetically correlated with their non-logarithmized counterparts (r = 0.91 -0.95).The results from the intrabreed analysis are shown in the appendix (Table 8).Only little deviations from the across breed analysis occurred, although the standard errors were higher.FV and HF were in line with the estimations in the whole data set, and stronger genetic correlations were observed for BS.

Correlations between Resilience Indicators and 305d yields
Means and standard deviations of performance traits MY 305 , FMY 305 , PMY 305 , and AMY 305 , are summarized in Table 5 with highest yields in HF and lowest in FV for all traits.BS and the records of all breeds evaluated jointly ranked in between.
Correlations between performance traits and resilience indicators estimated in the whole data set are presented in Table 6.Phenotypic correlations between r Auto and performance traits were close to zero, while genetic correlations were all positive, but only partly significant.

Modeling of the Lactation Curve
There are different existing and newly developed approaches to modeling lactation curves, which have been tested in the context of resilience research in dairy cattle.The choice of the modeling has only a minor influence on the estimated values of resilience indicators in variance component and correlation analyses, as shown in a previous study, which compared resilience indicators calculated on the basis of different lactation curves (Poppe et al., 2020;Chen et al., 2023).Basically, it has been argued that a separate curve should be predicted for each lactation of each individual for a more accurate estimation (Elgersma et al., 2018), and it should smooth out atypical lactation patterns as good as possible (Wang et al., 2022).We decided for a spline interpolation similar as in Codrea et al. (2011), but used penalized splines instead of B-splines to best represent the data while preserving the variability of the function (Ramsay et al., 1997).Spline interpolation has the advantage over polynomial regression functions that it creates individual polynomial functions for different sections and finally merges them, instead of one function over the entire time (Codrea et al., 2011).
If all dairy milk yields were considered equally for modeling, this would result in an incorrect expected lactation curve because milk yields under the influence of a disturbance would also be included in the estimation.Therefore, very low milk yields should not be weighted at all or should be weighted weaker to obtain good predictions of the lactation curves that would be expected in the absence of disturbances.Known approaches are the removal of daily values that reflect large deviations between observed and expected values on the basis of absolute values (Wang et al., 2022) or the residuals (Adriaens et al., 2020).The weighting we use preserves more data points and captures performance declines more sensitively.

Interpretation of Resilience Indicators
Using time series analysis of daily milk yields for mapping resilience simplifies genetic analyses compared with traditional health and well-being traits (Elgersma et al., 2018) because the raw data are in continuous rather than binary form, data collection is less subject to error and accuracy of statistical analyses is higher (Pitkänen et al., 2012;Sitkowska et al., 2020).
Heritability for ln ln var was slightly higher than in Elgersma et al. (2018) and lower than in Poppe et al. (2020), as well as for ln ln var d , except for BS.Our results were in line with estimated genetic parameters in studies of African (Oloo et al., 2023) and North American dairy cattle (Chen et al., 2023).Across all species and traits examined in recent studies, the heritability of the logarithmized variance of the deviation of an observed to an expected trait expression ranges from 0.1 to 0.4 (Homma et al., 2021;Mengistu et al., 2022;Bedere et al., 2022), and thus our results fall right in between.Under the assumption that a resilient individual shows low fluctuations in performance, low variance means higher resilience (Berghof et al., 2018;Poppe et al., 2020).
Considering r Auto , our results of the variance component analysis were similar to previous studies (Poppe et al., 2020;Wang et al., 2022;Chen et al., 2023).Only the heritability of BS was significantly higher than in the literature, whereby we are the first to study this trait in another breed than Holstein Friesian.As described above, a value of r Auto close to zero indicates a shorter recovery time after a disturbance and a higher resilience.
Variance and autocorrelation of longitudinal measured traits are used to predict system collapses in various scientific fields (Scheffer et al., 2012), where an increase in the indicator value is associated with an increasing probability of a collapse (Wichers and Groot 2016).Both parameters are used simultaneously, as they are similarly robust (Dakos et al. 2012a;Dakos et al. 2012b;Mehrabbeik et al., 2021).In livestock research, variance was found to be more appropriate, because it was higher heritable and stronger correlated with health traits (Bedere et al., 2022;Poppe et al. 2022b).This is consistent with our results, which also showed higher heritabilities.
Negative correlations between r Auto and the variancebased indicators denote that with an increasing variance of the performance, the duration of the recovery phase after a disturbance decreases (Bedere et al., 2022;Poppe et al., 2020).Another explanation could be that a larger baseline fluctuation of the milk yield tends to reduce the autocorrelation, but increases the variance of the performance.
To our knowledge, there are few studies on the correlation between resilience indicators and performance traits.Correlations between resilience indicators and average daily milk yield were in line with literature reports (Poppe et al., 2020), whereas the correlations with lactation milk yield were lower than in previous studies (Chen et al., 2023;Wang et al., 2022).As the resilience indicators and milk performance traits MY 305 and AMY 305 are based on the same raw data, it could be that they are partly influenced by the same genes.Our results only partially support this hypothesis, as only some of the resilience indicators showed highly significant correlations with MY 305 and AMY 305 .In addition, genetic correlation between milk yield and milk protein yield is stronger than between milk yield and milk fat yield, as shown in previous studies, e.g., Soyeurt et al. (2007).This could explain why milk protein yield correlates more strongly with resilience indicators than milk fat yield.

Comparison of variance-based indicators
We considered 8 different variance-based indicators.Logarithmization provides a better normal distribution of the data and genetic as well as phenotypic correlations with performance traits were slightly stronger and standard errors were smaller than for non-logarithmized indicators.Since a normal distribution of a resilience indicator trait is desirable for the computation of breeding values, the use of logarithmized variancebased indicators can be recommended.
The variance-based indicator of absolute daily milk yield var and lnvar, respectively, was calculated as in Elgersma et al. (2018).It is influenced by the milk performance and the persistence over the lactation of an individual.This would result in different variances of different individuals even under the assumption of disturbance-free lactations (Elgersma et al., 2018;Wang et al., 2022).To exclude persistence, we considered the variation of daily milk yield around the predicted lactation curve with var d and lnvar d , respectively, as described in previous studies as LnVar (Berghof et al., 2018;Bedere et al., 2022;Poppe et al., 2020).
Additionally, the effect of the performance level on the magnitude of performance decrease under disturbance in absolute and relative terms should be noted (Berghof et al., 2018;Poppe et al., 2020;Oloo et al., 2023), because when comparing a high-and a low-performing individual with the same absolute decrease in milk yield, the relative decrease is lower for the high-performing cow.This scaling effect already occurred in analyses of environmental sensitivity in livestock (Rönnegård et al., 2013) and in general time series analysis (Dai et al., 2012).Variance-based indica- tors derived from absolute and relative milk yields are different traits, with correlations ranging from 0.75 to 0.84 and opposite correlations with performance traits.Variance-based indicators of absolute daily milk yield gave similar results as shown in previous studies, i.e., the higher the performance, the higher the value of the variance-based indicator, which indicates a lower resilience of the animal (Poppe et al., 2020).Variance-based indicators based on relative milk yields indicate the opposite, i.e., the higher the yield, the lower the value of the variance-based indicator, which indicates a greater resilience.This can be explained mainly by 4 reasons.
First, in favor of a sufficiently large data set, all individuals were included in analyses with the distinction between primiparous and multiparous as a fixed effect, because Poppe et al. (2021) and Chen et al. (2023) found that resilience indicators are highly correlated across lactations from the second lactation upwards.However, milk yield increases with number of lactations (Ray et al., 1992), and cows in a high lactation are inherently more resilient, as they have not already left the farm due to disease or underperforming.
Second, resilient individuals can keep their milk yield stable, which in turn favors high milk yield, and, third, the physiological response to a disturbance differs among individuals.According to the resource allocation theory (Rauw 2009), an individual does not have to re-spond to disturbances with a decrease in performance, but may have impaired health or fertility (Llonch et al., 2020).However, our resilience indicators based on daily milk yields can only reflect performance resilience (Poppe et al. 2022a;Ben Abdelkrim et al., 2021;Bedere et al., 2022).
Fourth, there is a background fluctuation of the daily milk yield that occurs even in the absence of disturbances.The magnitude of the fluctuation could be higher in high performing cows, indicating that variance-based indicators based on absolute milk yields tend to be larger in high performing cows even if their larger values are not reflected by a lower resilience.

Evaluation of resilience across and within different breeds
In addition to the consideration of the whole data set including 3 breeds, all analyses were also performed within breeds, with approximately equal data sets for HF and FV, but smaller for BS.The level of performance traits was, as expected, significantly higher for HF than for the other 2 breeds, which differed significantly only in milk fat yield and milk protein yield with an absolutely higher level for BS.This difference in performance from HF to BS and FV is well known (LKV 2022).The variance-based indicators showed breed differences, with BS being the most resilient across all.However, differences between breeds were small and care must be taken that different breeds tend to be kept in different environments, and thus significant breed differences do not necessarily reflect heritable differences in the resilience of the breeds.FV showed the lowest autocorrelation and thus shortest recovery period, although this may be due to a higher baseline fluctuation of daily milk yields due to environment-specific peculiarities.This higher baseline-fluctuation increased the values of the variance-based indicators but decreased the autocorrelation.

CONCLUSION
Livestock resilience can be represented using the indicator traits variance and autocorrelation of daily milk yield, with the former resulting in higher hertiabilities in our study.To address the problem of scaling effects during performance declines, it is recommended to calculate variance-based indicators using relative rather than absolute daily milk yields.In this regard, ln var r -the log variance of relative milk yields -showed the highest heritabilities and strongest favorable correlations with performance traits.
In addition to the across-breed analysis, we performed uni-and bivariate analyses for HF, FV, and BS.The lower autocorrelation of FV indicates a shorter recovery time after disturbances compared with HF and BS, while lower variance-based indicators of HF and BS indicate that the latter are less susceptible to disturbances.An alternative explanation could be that FV has a higher baseline fluctuation of daily milk yields.Further studies are needed to analyze the interrelationship with health and fertility traits, to assess the suitability of the indicator traits to be included in the breeding goal.Description of resilience indicators can be taken from Table 1.

Figure 1 .
Figure 1.Modeled lactation curve with (red line) and without (green line) weighting of the daily milk yields (gray area) for a German Holstein cow and in the first lactation.
Figure 2. Tuckey's HSD-Test of the resilience indicators for differences between the breeds Brown Swiss (BS), Fleckvieh (FV) and German Holstein (HF). 1 Description of resilience indicators can be taken from Table pe and I e are identity matrices, A is the additive genetic relationship matrix, and σ pe u, respectively.Inter-breed comparison of the average value of resilience indicators was performed as a Tuckey's HSD test using the package biometryassist in R(Nielsen et al., 2022).
traits were genetically and phenotypically positively correlated with variance-based indicators based on absolute daily milk yields, but negatively correlated with variance-based indicators based on relative daily milk yields.More specifically, the variancebased indicators of absolute daily milk yields (var, ln var) tended to show a positive correlation with performance traits, the variance-based indicators of deviations from predicted daily milk yields (var d , ln var d ) had a moderate positive correlation with performance traits, whereas variance-based indicators based on relative milk yields and variance-based indicators based on deviations of relative milk yields were negatively correlated.The resilience indicators tended to show the strongest genetic correlations with MY 305 , PY 305 , and AMY 305 , while the genetic correlations with FY 305 were weaker.For the first 3, the strongest positive genetic correlation was observed with ln var d , while FY 305 had the strongest positive genetic correlation with var d (r = 0.25).The strongest negative genetic correlations for MY 305 , PY 305 , and AMY 305 were obtained for ln var r , and the strongest negative genetic correlation for FY 305 was obtained for var r .Hence, as performance increased, the variance-based indicators of relative daily milk yields decreased.Results for each breed are presented in appendix (Table Keßler et al.: Running Head: Resilience Traits in German Dairy Cattle Keßler et al.: Running Head: Resilience Traits in German Dairy Cattle Table 5. Number of lactations (N), mean (μ) and standard deviation (σ) of the performance traits 305-d-milk yield (MY 305 ), 305-d-protein yield (PY 305 ), 305-d-fat yield (FY 305 ), 305-d-average daily milk yield (AMY 305 ) across breeds (AB) and subdivided by breeds (BS = Brown Swiss, FV = Fleckvieh, HF = German Holstein) Keßler et al.: Running Head:  Resilience Traits in German Dairy Cattle Table7.Estimation of heritability (h 2 ) and variance components of the additive genetic effect σ u 2 ( ) , the permanent environmental effect σ pe 2 ( )and the residuum σ e 2 ( ) (SE given) for resilience indicators calculated from daily milk yields subdivided by breeds (AB = all breeds, HF = German Holstein, BS = German Brown Swiss, FV = German Fleckvieh) -average daily milk yield (AMY 305 ) and resilience indicators calculated from daily milk yields subdivided by breeds (HF = German Holstein, BS = German Brown Swiss, FV = German Fleckvieh) with standard errors in brackets

Table 1 .
Keßler et al.: Running Head:Resilience Traits in German Dairy Cattle Overview and description of the resilience indicator traits d Log variance of deviation between observed absolute and predicted daily milk yield r Auto Autocorrelation of deviation between observed absolute and predicted daily milk yield var r Variance of relative daily milk yield ln var r Log variance of relative daily milk yield var rd

Table 2 .
Keßler et al.: Running Head: Resilience Traits in German Dairy Cattle Number of lactations (N), mean (μ) and standard deviation (σ) for resilience indicators calculated from daily milk yields across breeds (AB) and subdivided by breeds (BS = Brown Swiss, FV = Fleckvieh, HF = German Holstein)

Table 3 .
Estimation of heritability (h 2 ) and variance components of additive genetic σ u 1 Description of resilience indicators can be taken from Table1.

Table 4 .
Keßler et al.: Running Head:Resilience Traits in German Dairy Cattle Correlations (genetically below the diagonal, phenotypically above the diagonal) between the resilience indicators calculated from daily milk yields across breeds with standard errors in brackets 1 Description of resilience indicators can be taken from Table1.

Table 6 .
Phenotypic (corr phenotypic ) and genetic (corr genetic ) correlations between the 305-d-performances for milk (MY 305 ), protein (PY 305 ), fat (FY 305 ), average daily milk yield (AMY 305 ) and resilience indicators calculated from daily milk yields across breeds with standard errors in brackets (n = 8846 lactations) 1 Description of resilience indicators can be taken from Table1.

Table 8 .
Correlations (genetically below the diagonal, phenotypically above the diagonal) between resilience indicators calculated from daily milk yields for breeds BS (German Brown Swiss), FV (German Fleckvieh) and HF (German Holstein) with standard errors in brackets Breed Trait 1 1 Description of resilience indicators can be taken from Table1.