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PhenoBR: a model to phenotype body condition dynamics in meat sheep

In situations of negative energy balance (NEB) due to feed scarcity or high physiological demands, body energy reserves (BR), mainly stored in adipose tissues, become the main sources of energy for ruminants. The capacity to mobilize and restore such BRs in response to different challenges is of major concern in the current context of breeding for resilience. Body condition score (BCS) is a common, practical indicator of BR variations throughout successive productive cycles, and quantitative tools for characterizing such dynamics at the individual level are still lacking. The main objective of this work was to characterize body condition dynamics in terms of BR mobilization and accretion capacities of meat sheep during their productive lifespan through a modelling approach. The animal model used in this work was the reproductive meat ewe (n = 1478) reared in extensive rangeland. Regular measurements of BCS for each productive cycle were used as the indicator of BR variations. A hybrid mathematical model and a web interface, called PhenoBR, was developed to characterize ewes’ BCS variations through four synthetic and biologically meaningful parameters for each productive cycle i: BR accretion rate , BR mobilization rate , plus the time of onset and the duration of the BR mobilization, and ΔTi, respectively. The model converged for all the ewes included in the analysis. Estimation of the parameters indicated the inter-individual variability for BR accretion and mobilization rates, and for the length of the mobilization period. Body reserve mobilization rates were closely correlated between productive cycles. Significant correlations between BR mobilization and accretion rates suggest that the two processes are biologically linked. Parameters kp and kb decreased as parity increased. BR mobilization rate and duration increased as litter size increased, while BR accretion rate decreased. Individual characterization of animals by these parameters makes it possible to rank them for their efficiency in the use of body reserves when facing NEB challenges. Such parameters could contribute to better management and decision-making by farmers and advisors, e.g. by adapting feeding systems to the individual characteristics of BR dynamics, or by geneticists as criteria to develop future animal breeding programs including BR dynamics for more robust and resilient animals.

1 Introduction 2 Body energy reserves (BR) are the main source of energy in ruminants facing negative energy 3 balance (NEB) challenges such as highly demanding reproductive cycles or feed scarcity 4 periods (1,2). The capacity of ruminants to mobilize and restore such BRs in response to 5 challenges is of major concern in the current context of breeding for robustness and 6 resilience, and for the ultimate sustainability goals of farming systems. Priorities chosen by 7 complex mechanisms related to nutrient allocation and trade-offs become critical at the 8 individual level. BR administration and operational feeding strategies are among the main 9 resources set by the animal and the farmer, respectively, to cope with such challenges. 10 11 In meat sheep, a broad intra-flock variability in the dynamic of BR was shown during their 12 lifespan including several reproductive cycles. The genetic determinism related to the BR 13 changes has been demonstrated by considering successive physiological stages 14 independently (3,4). The BR dynamics could be considered in selection strategies designed to 15 improve the ewes' adaptive capacities while maintaining production and welfare. It is 16 therefore of major interest to phenotype ewes for their capacity of resilience in situations of 17 NEB. 18 19 Despite the importance of BR dynamics for animal robustness, its use in animal husbandry and 20 breeding is still at its very early stages (5,6). There are two main reasons for this. Firstly, there 21 is a lack of dynamic data describing animal response facing different, successive challenges of 22 different magnitude and amplitude. Progress in technology in the last decades has made it 23 possible to measure several indicators of animal performance with relatively high frequency 24 (i.e. dynamic records). Through the development of new monitoring technologies, dynamic 25 measures of indicators such as body weight (BW), milk yield and feed intake are available with 26 higher frequency and at lower cost. Secondly, the absence of synthetic criteria for 27 characterizing and quantifying BR dynamics is still a limiting factor for the use of such a 28 complex phenotype. Body condition score (BCS) is a practical and conventionally used variable 29 for monitoring BR dynamics. Compared to other variables such as BW, BCS is a proven reliable 30 indicator of an animal's fat reserves (7,8). Although some automatic advances are available, 31 BCS continues to be a subjective but effective variable, measured in general through direct 32 observations carried out by a trained observer (9,10). In outdoor farming systems (e.g. grazing, 33 rangelands, etc.) there are still limitations to overcome regarding, for example, the availability 34 of sound tools for implementing automatic measurement of BCS at the individual level. 35 36 Macé and collaborators concluded on the usefulness of BCS and BW data to study the capacity 37 of BR mobilization and accretion in meat ewes (3 Modelling procedure: General model 98 99 To characterize the ewes' response to the increasing energy requirements at each productive 100 cycle in terms of BCS variations, a system of ordinary differential equations was developed. 101 For present purposes, the significant increase in energy requirements during a productive 102 cycle is termed perturbation (physiological challenge due to pregnancy and suckling). The 103 objective of model development is to describe the ewe's response to that perturbation using 104 BCS variation as the indicator of ewe's response. Two interrelated state variables were used 105 to describe the ewe's response at productive cycle : for the decrease in BCS during the 106 mobilization period and for the variations in BCS during the same productive cycle 107 including its decrease by and its recovery ( Figure 1). The driving force of this model is the 108 intrinsic capacity of the ewes to maintain or to restore their BRs to reach the expected BCS, 109 considered as the value of BCS in the absence of perturbations, noted . The concept of 110 the expected trajectory of performance is already described in the literature (13). In the 111 database used, the ewe population attained at most three productive cycles, and the total 112 BCS variations was calculated as the sum of variations, for ∈ {1,2,3}.  For productive cycle , periods of BR mobilization and accretion are both assumed to start 125 from the point when starts to decrease ( ), considered as the starting point of the 126 perturbation being studied. In this study, it is assumed that BCS is a good indicator of the ewes' 127 BR variations, as previously demonstrated. When the animal is no longer able to meet the 128 energy demands induced by pregnancy and lactation using only the energy available from 129 ingested feeds, it will mobilize the energy stored in its adipose tissues (i.e. its energetic BRs). 130 However, during and after this period, the animal uses internal mechanisms to limit or to 131 compensate for the quantity of BRs used during this period. This is illustrated by the effort of 132 the animal to reach . To clearly separate the effects of each productive cycle, the BR 133 recovery capacity associated with productive cycle starts at and lasts until the beginning 134 of the next productive cycle ( +1 ). 135 136 The BR mobilization period is assumed to be over at , which is the end of the BCS decrease 137 period (i.e. end of perturbation ). is associated with the point where the capacity of BR 138 accretion surpasses the ewe's energy requirement. Equations 2.a and 2.b describe the 139 variations in and the simultaneity and continuity of BR mobilization and accretion 140 processes for productive cycle .
Where and are the rates for BR accretion and mobilization during the productive cycle 147 , respectively. The constant stands for the maximal loss of BCS due to the perturbation. Other parameters of the model are time-related and Δ , which are determined using a 171 data analysis procedure for automatic detection of the perturbation within each productive 172 cycle. The dataset involved ewes with 1, 2 or 3 parities, and the data analysis procedure 173 allowed automatic determination of the number of parities to be considered for each ewe, 174 and the beginning and the duration of the associated perturbation. 175 176 Modelling procedure: Automatic detection of perturbation period 177 178 The beginning and end of each productive cycle was taken to be from one mating to the 179 subsequent one. When all data were missing in a given period, it was taken as a missing 180 productive cycle. In this section, a data analysis procedure based on functional data analysis 181 (FDA) was developed to automate detection of perturbations within each productive cycle. In 182 this procedure, the beginning of a perturbation ( ) is where the observed BCS started to 183 deviate from the initial value of ( ). The end of the perturbation ( ) is where it 184 started to recover. 185 186 The expected value of BCS ( ) is determined depending on ewes' maximum value of BCS 187 ( ). If Although the procedure determined the beginning and end of the mobilization period and 210 , respectively, existing information on ewes' physiology were also considered for a more 211 reliable estimation of these values. In this respect, can take a value approximately between 212 mating and lambing days, and can take a value approximately between lambing and post-213 weaning as defined in (3). In the construction of PhenoBR, the recovery period of each 214 productive cycle is over when the next productive period starts ( = +1 ). A major challenge 215 was then to determine the recovery period when second or third productive cycles were 216 missing for individuals from the original database. For this, it was assumed that in the absence 217 of +1 , the recovery from the productive cycle would be over 150 days after the post-218 weaning period (i.e. the period corresponding to the next mating). 219 220 221

226
This procedure allowed the number of productive cycles and the associated and to be 227 determined for each animal. All missing values of BCS were replaced by values of the function 228 ( ). Figure 2 illustrates the perturbation periods as determined by the data analysis 229 procedure against a reproductive cycle as reported in the original dataset.

290
Large positive correlations were found between parameters of BR mobilization ( for = 291 1, 2, 3) (Figure 3). Positive and significant (p < 0.005) correlations between the BR mobilization 292 rate ( ) and BR accretion rate ( ) were observed for parities 1 and 2. Significant negative 293 correlations between BR mobilization length Δ and rate could also be observed for 294 parities 1 and 3, i.e. the longer the BR mobilization period, the smaller the BR mobilization 295 rate. Positive and significant correlations were also obtained between BR mobilization rates 296 ( , = 1, 2, 3). Figure 3 gives results of all ewes with different numbers of parities. 297  (Table 3). Significant effects (p < 0.05) of these 304 factors were observed for and . Values of Δ were significantly affected by the 305 productive cycle and the litter size. A decrease was observed for and , as productive 306 cycle increased. Ewes had the longest period of BR mobilization Δ at productive cycle 1 and 307 the shortest Δ at productive cycle 2. As the litter size increased, and Δ increased and 308 decreased. Ewes that lambed for the first time at age one year showed lower and than 309 ewes lambing at age 2 years. The interaction between productive cycle and age of the ewes 310 at first lambing could not be tested owing to uneven distribution of ewes in the classes of each 311 factor. Investigation of the effect of the productive cycle for each class of the age of ewes at 312 first lambing showed similar effects of productive cycle to those described above except for 313 no significant effect of productive cycle on in ewes lambing at age one year (see 314 Supplementary Tables S1 and S2).

323 324
A previous study (4), using the ewes involved in the present study, showed that ewes' BCS 325 variations could be characterized by three classes of trajectory for each productive cycle. Ewes 326 with similar trajectories belonged to the same cluster. Major characteristics of these BCS 327 trajectories including BCS level, BCS loss and gain are given in Table 4 based on previous results  328 reported by Macé et al. (2019). The first productive cycle was characterized by clusters BC1, 329 BC2 and BC3, the second by clusters BC4, BC5 and BC6 and the third by clusters BC7, BC8 and 330 BC9. The two major clusters at production cycles 1 and 2 included 99% and 85% of the ewes, 331 respectively (clusters BC1, 63%; BC2, 36% and BC4, 55%; BC5, 30% respectively). In production 332 cycle 3, the major cluster (BC7) included 76% of ewes (BC8, 13%; BC9,11%

359
The aim of the present study was to propose a metric of ewes' capacity to adapt to their 360 increasing and fluctuating energy requirements through several productive cycles. We 361 exploited the existing database derived from historical and dynamic measurements of BCS in 362 reproductive approaches mainly based on data (15). The objective of all these models was to detect 396 perturbations that affect animal performance and health, and to characterize the animals' 397 responses during such periods. When data were available with high frequency, the models 398 were able to detect periods of unknown perturbations. The originality of PhenoBR compared 399 to the existing models is its use of a combination of a data-driven model (via FDA) and a 400 dynamic model to detect perturbation periods despite the limited number of available BCS 401 records, and to subsequently characterize ewe's response. Using the data analysis approach 402 by fda helped to decrease the number of variables to be estimated for the dynamic model and 403 thereby increase the robustness of the parameter estimation process (convergence of the 404 process for all animals). 405 Several biological factors had a significant effect on , and Δ and were similar to those 406 affecting BCS when considered at a single time-point (20, [27][28][29]. 407 exhibiting high level of BR mobilization also exhibited high level of BR accretion (Macé et al.,450 2018). 451 The variability in BCS profiles throughout ewes' lifespan had already been investigated by the 452 presence of clusters in each productive cycle (4). Each of these clusters were characterized by 453 BR trajectories differing in the level of BR and/or shape of BR changes through the productive 454 cycle. In the present results, we found consistency between average values of BR mobilization 455 and accretion rates and characteristics of BR profiles in clusters. Differences between clusters 456 found in the present study for BR accretion rate and BR mobilization rate suggest that 457 such parameters could be used for ranking animals according to their BR dynamics. Thus 458 PhenoBR offers an opportunity to investigate ewes' variability of response at the individual 459 level. 460

461
The existing inter-individual variability for the parameters quantified with PhenoBR, BR 462 mobilization and accretion rates and duration of BR mobilization make them potentially useful 463 for classifying individuals according to their BR dynamics. Such parameters could be used by 464 farmers for animal management, for instance by adapting feeding systems according to the 465 individual characteristics of animals in terms of BR dynamics and the seasonality of feed and 466 forage availability. Tthese parameters could also be used by geneticists as criteria to refine 467 and reinforce future animal breeding programs, including selection strategies for more robust 468 and resilient animals. Combining these new traits with other related metabolites and 469 metabolic hormone data, known to be related to BCS and therefore to the BR mobilization 470 and accretion processes, will take us further in our understanding of mechanisms underlying 471 animal response to NEB perturbations. Altogether, in the perspective of working towards 472 resilient farming systems, PhenoBR will support our approach for taking advantage from 473 ruminants