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Predicting the consequences of social stressors on pig food intake and performance¹

Animal Nutrition and Health Department, Scottish Agricultural College, West Mains Road, Edinburgh, EH9 3JG Scotland

	Abstract

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The influence of social stressors on pig performance, although undeniable, is frequently underestimated, and in pig growth modeling is generally ignored. The aims here were to quantify the effects of the main social stressors (i.e., group size, space allowance, feeder space allowance, and mixing) on the performance of growing pigs and to incorporate these relationships into a general growth simulation model. Effects of the individual stressors were described by conceptual equations derived on biological grounds. Parameter values were estimated from experimental data, while taking steps to avoid the problems of using a strictly empirical approach. It was assumed that social stress decreases the capacity of the animal to attain its potential. This is equivalent to lowering the maximum rate of daily gain (ADG_p, kg/d). Because it is generally assumed that animals eat to attain their potential, a decrease in ADG_p necessarily leads to a decrease in intake. Genetic variation among genotypes in their ability to cope with social stressors was accounted for by introducing an extra genetic parameter (EX) into the model. The value of EX adjusts both the intensity of stressor at which the animal becomes effectively stressed and the extent to which stress decreases performance and increases energy expenditure at a given stressor intensity. Rather than using an empirical adjustment to predict values for the model output variables, such as intake and gain, the chosen functional forms were integrated into a general growth model as mechanistic equations. This allowed the effects of interactions that exist between social stressors and the other variables, such as the genotype, feed composition, and environment on pig intake and growth, to be explored and, at least in principle, predicted. The adapted model is able to predict the performance of pigs differing in both the potential and ability to cope with environmental stressors when raised under given dietary, physical, and social environmental conditions. The social stressor equations developed here can be incorporated into other pig growth simulation models.

Key Words: Behavior • Growth • Intake • Pigs • Simulation Model • Social Stress

	Introduction

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The performance of commercial pigs is often below that seen under good experimental conditions. Campbell and Taverner (1985) found growth rate to be 28% lower in commercial units than in experimental conditions. At least some of this decrease in performance can be attributed to environmental stressors. We use the word stressor with no implication about any specific physiological mechanism. Quantifying stressor effects may allow the removal of constraints that prevent pigs from achieving their potential and substantially increase the profitability of pig enterprises.

Stressors in the physical environment have been comprehensively modeled (e.g., Black et al., 1986), allowing predictions of performance under varying conditions to be made. However, social stressors—including group size (N), space allowance (SPA, m²/BW^0.67), feeder space allowance (FSA, feeders per pig), and mixing—have been largely ignored, mainly due to a lack of quantitative data on which to build models and a lack of understanding of how such stressors affect performance. The effects of N and SPA have been considered for their effects on heat exchange (e.g., Black et al., 1986), and the model of NRC (1998) includes a social stressor effect on performance, with SPA directly affecting dietary energy intake. However, this is considered to be "a crude estimate [that] should be used with caution" (NRC, 1998). Kornegay and Notter (1984) developed regressions relating performance to SPA and N for pigs in three weight ranges, but these equations are difficult to interpret and implement (Chapple, 1993), and they fail to predict interactions between the type of pig and the environment in which it is kept.

The aims of this paper were to quantify the effects of social stressors on the performance of growing pigs, including variation in their ability to cope, and to incorporate these relationships into a more general growth model (Wellock et al., 2003a) to allow the prediction of more complex interactions.

	Materials and Methods

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Representing the Effects of Social Stressors on Performance

It is assumed that social stress decreases the animal’s capacity to attain its potential, an "upper-limit" defined by the animal’s genotype. This is equivalent to lowering the maximum rate of daily gain (ADG_p, kg/d) that the pig is able to achieve. The food intake needed for ADG_p is the desired feed intake (FI_d, kg/d; Kyriazakis and Emmans, 1999). A decrease in ADG_p is assumed to necessarily lead to a decrease in FI_d. In the model, food intake is directly affected only when FSA is limiting and constrains intake.

Choice of Functional Form and Parameter Estimation

Rather than predicting values for the model output variables, such as daily intake and gain, by an empirical adjustment, the approach used herein integrates the chosen functional forms into a general growth model as mechanistic equations. This method allows any interactions that exist between the type of pig (i.e., its potential) and its environment to be explored and, at least in principle, predicted.

Experimental data were used to test the chosen functional forms for their relevance and to enable realistic quantitative values to be assigned to the parameters (Table 1). To avoid the various problems of using a strictly empirical approach, the following measures were taken.

1. By only using either experiments in which all variables other than the one of interest were controlled or experiments designed using a factorial method in the analysis. This method was chosen to avoid the confounding effect of variables, especially N and SPA.
   
2. By using more biologically sound methods when possible. For example, the method proposed by Petherick (1983) was used for calculating the effect of SPA on performance. This method relates SPA to the spatial requirements of pigs according to body weight (BW, kg) rather than simply area per pig.
   
3. By taking differences in BW into account. Relative daily gain (R) is used as the measure of performance rather than daily gain, thus eliminating the need for separate equations according to BW. This also allows a greater amount of information to be used in the analysis.
   
4. By calculating R relative to the performance seen at the lowest degree of stressor in each experiment. This accounts for differences in the potential of pigs used in the different experiments.
   
5. By using a statistical model within GenStat (GenStat 5th ed., NAG Ltd., Oxford, U.K.) to account for differences between the experiments and to give appropriate weighting for the number of replications in each experiment. A necessary assumption of using a naive empirical approach is that all experiments summarized were carried out under the same conditions (i.e., they are all replicates of the same experiment).
   
6. By checking that the equations used are sensible when extrapolated over the full range of interest.
   

Space Allowance

The approach devised by Petherick (1983) was used to achieve a biological description of space requirements rather than simply using area per pig. It is based on the spatial requirement of pigs, dependent upon their BW, and has physiological significance because pigs use postural changes to broaden their zone of thermal comfort. The effective space allowance per pig is calculated as

[1]

where Area is in square meters per pig and q is the body weight scalar calculated to be 0.67 (Petherick, 1983).

Decreasing SPA decreases intake and growth (Edwards et al., 1988; Gonyou and Stricklin, 1998). The extent may depend on the type of pig. It is assumed that there is a critical value for SPA (SPA_crit m²/BW^0.67), below which performance becomes depressed. Solid floors have a greater SPA_crit than partially or totally slatted floors (Turner et al., 2000) mainly due to pigs’ avoiding lying in dung (Spoolder et al., 2000). It is assumed that, above SPA_crit, SPA has no effect on performance. Growth rate goes to zero when SPA reaches SPA_min (m²/BW^0.67). The value assigned to SPA_min is the area required for a pig to lie on its sternum, 0.019 m²/BW^0.67 (Petherick, 1983). When SPA_min < SPA < SPA_crit, relative daily gain, R_SPA, in relation to that recorded at a SPA > SPA_crit, is calculated as

[2]

The values of b₁ and g₁ are affected by genotype. The shape of the relationship between SPA_crit and SPA_min was chosen after inspection of experimental data.

All experiments used in the analysis varied pen area with a fixed group size and were carried out on floors that were either partially or fully slatted. The few studies that used solid floors were omitted (Table 2). The value assigned to SPA_crit was 0.039 m²/BW^0.67. This is the value proposed by Gelbach et al. (1966) and is consistent with the values proposed by Edwards et al. (1988) and Gonyou and Stricklin (1998) of 0.034 and 0.039, respectively. It is also within the range proposed by Black et al. (1995) of 0.035 to 0.039 m²/BW^0.67. A log regression equation gave the best fit and was chosen as the most suitable for the prediction of performance below SPA_crit (see Table 1). To take account of the greater space requirements of pigs housed on solid floors, SPA in Eq. [2] is decreased by 25%, in agreement with Whittemore (1998), when pigs are housed on solid floors.

Most experiments report a decrease in performance as group size (N) increases (e.g., Wolter et al., 2000; Hyun and Ellis, 2001). Others show little or no effect (Randolph et al., 1981). However, in many experiments, the effects of N, SPA, and FSA are confounded (e.g., Walker, 1991; Ferguson et al., 2001).

There seems to be an effect of grouping per se because individually housed pigs have been widely shown to outperform their group-housed counterparts (e.g., Gonyou et al., 1992). The effect of increasing N on performance is therefore compared with that of individually housed pigs, assumed to be achieving their potential. Increasing N by a fixed quantity has a greater influence on smaller groups than larger ones because the social hierarchy of small groups is disrupted to a greater degree than that of large groups, which appear to lack social structure (Arey and Edwards, 1998; Turner et al., 2001). A logarithmic form is used to represent this observation:

[3]

In this equation, R_N is the relative daily gain as a percentage of that of a singly housed counterpart, the constant b₂ is equal to 100, and g₂ is a scalar assumed to differ among breeds (see below). Calculated parameter values are given in Table 1. As group sizes greater than 10 have almost always been mixed, only experiments that allowed reasonable time periods after mixing before taking measurements were included in the analysis (Table 3).

[4]

The value of x₁ will differ among genotypes and is discussed later. When N N_m, N_m replaces N in Eq. [4].

Heat production (HP, MJ/d) due to activity was reported to be between 8 and 13% of metabolizable energy intake in growing pigs (van Milgen et al., 1998), equivalent to about 30% of E_maint. Similar values of 7 to 13% of total HP and 30% of fasting heat production were reported by Quiniou et al. (2001) for group-housed growing pigs. To account for a 50% increase in activity (an increase in E_maint of approximately 15%), as N increases to N_m, a value of 0.0075 was assigned to x₁ (Table 1). A value of 20 was assigned to N_m to represent the group size beyond which E_N no longer increases.

Feeder Space Allowance

Intake is decreased when the number of feeder spaces available to a group of pigs falls below a critical value (FSA_crit, feeders per pig) and continues to decrease as FSA decreases further (Nielsen et al., 1995; Turner et al., 2002). It is assumed that only a single pig can occupy a single feeder space at a given time. Critical FSA is reached when all of the pigs in the group can no longer satisfy their FI_d due to increased pig competition at the feeders. To try to maintain intake as FSA decreases, pigs extend their temporal pattern of feeding often into the night (Morrow and Walker, 1994) and both visit duration and feeding rate (FR, kg/min) (Nielsen et al., 1995) are increased as the number of visits decreases. Therefore, FSA_crit is dependent upon N, FI_d, and maximum feeding rate (FR_max, kg/min). The number of minutes in the day, 1,440, is needed for consistency of units.

[5]

The parameter FR_max depends on aspects of mouth capacity (Illius and Gordon, 1987), which increases as the animal grows (Nienaber et al., 1990; Nielsen, 1999), with feed composition (Brouns et al., 1997; Whittemore et al., 2003a), and with method of feed presentation. In addition, the physical form in which a feed is given will be of considerable importance. It needs to be noted that the data used come only from instances in which pelleted feeds were offered. The form relating FR_max to BW is assumed to be

[6]

The parameter m states how FR_max changes with BW. A value of 1.0 is assigned to m rather than 0.33 used by Illius and Gordon (1987) for ruminants because it is mouth volume rather than incisor breadth that is relevant here. The parameter g₃ appropriately scales FR_max to BW. It is assumed that neither m nor g₃ is affected by genotype.

To test that m = 1.0 is a reasonable assumption, and to estimate g₃ for a particular feed, the results of the experiment of Walker (1991) were used. He investigated the effects on performance and feeding behavior of pigs (37 to 90 kg) in group sizes of 10, 20, or 30 with a single-spaced feeder supplying high-quality feed and constant space allowance per pig. No differences in average daily feed intake (kg/d) and gain (kg/d) were reported, but, as expected, the FR of individual pigs and the total occupancy time of the feeder increased with decreasing FSA. It was assumed that the FR reported for the largest group size of 30 was at a maximum because FR did not increase by much when N increased from 20 to 30. The values of the parameter, g₃, did not change systematically as BW increased from 43 to 57 to 74 kg with a mean value of 0.788 x 10^-3 kg of feed•min^-1•kg BW^-1. The lack of change indicates that the assumption that m = 1.0 is a safe one.

It is expected that FR_max will vary with feed composition, and this will be reflected in the value of g₃. In the absence of anything better, the water-holding capacity of the feed (WHC, kg/kg), which has been shown to be a relevant descriptor for the purposes of feed intake (Kyriazakis and Emmans, 1995; Whittemore et al., 2001) is used. This is supported by the data set of Whittemore et al. (2003a). They measured the FR of growing pigs on diets differing in WHC and found that the scaled rate of feeding was directly proportional to the reciprocal of WHC, such that

[7]

Combining Equations 6 and 7 gives

[8]

The WHC value for the feed used by Walker (1991) is not known. For the value of g₃ of 0.788 x 10^-3 kg•min^-1•kg BW^-1 estimated from his data to be consistent with Eq. [7], the food would need to have a WHC value of 3.6 kg/kg. This would seem to be a reasonable estimate based on the feed composition used by Walker (1991) and values for other feeds given in the literature (Tsaras et al., 1998; Whittemore et al., 2001).

When FSA is limiting (i.e., FSA < FSA_crit), then the constrained feed intake, FI_c (kg/pig), is calculated as

[9]

It is assumed here that pigs do not avoid feeding immediately adjacent to one another, and, where troughs are used rather than individual feeders, FSA is calculated as the total number of pigs able to feed simultaneously. This is calculated from total trough width (m) and the width of the pig at the shoulders as estimated by Petherick (1983).

[10]

where the scalar j and exponent k are equal to 0.064 and 0.33, respectively (Petherick, 1983).

Mixing

Mixing is a transient stressor. Given sufficient time, there may be no noticeable effects of mixing on performance (Spoolder et al., 2000, Heetkamp et al., 2002) as losses in gain due to mixing become hidden by variation. There is an initial decrease in performance immediately after mixing (Tan et al., 1991; Stookey and Gonyou 1994). Over time, levels of performance return to normal (e.g., Tan et al., 1991). Performance following mixing is depressed to a greater extent in larger animals (Stookey and Gonyou, 1994; Spoolder et al., 2000) and the influence of mixing is described by

[11]

The term R_mix is the performance (%) relative to that of a nonmixed pig, the constant b₃ is equal to 100, g₄ and g₅ are scalars likely to change with genotype (see below), and t is the time in days where mixing occurs on d 1. At some value of t, R_mix will be estimated to be 100. From then on, performance is normal and no longer affected by the past mixing.

In most experiments, pigs are mixed to create pens of equal-weight animals. In others, they are mixed to create groups of diverging weights (e.g., Heetkamp et al., 1995). Others again have produced mixed groups on the basis of behavioral traits (e.g., Hessing et al., 1994). A further complication is that the type of building used has been shown to affect the impact of mixing on performance (Spoolder et al., 2000). The apparent inconsistency in the experimental results, and the lack of data particularly for the important first few days after mixing, meant that values for the parameters in Eq. [11] could only be approximated (Table 1). Values were chosen so that mixing decreased performance by an average of approximately 25% in a 70-kg pig in the first week after mixing (Tan et al., 1991) and had an effect that lasted for 2 to 3 wk (Tan et al., 1991; Stookey and Gonyou, 1994).

Heetkamp et al. (1995) found that mixing increased the energy expenditure of pigs especially in the first few days after mixing. The increase in energy expenditure due to mixing (E_mix, MJ/d), which decreases over time as activity levels return to normal, is added to the daily energy requirements.

[12]

The values of the parameters x₂ and x₃ change with genotype and were chosen to represent an increase in E_maint by a maximum of 15%, following E_N, and to have an effect that lasts for 2 to 3 wk (see Table 1).

Incorporating Effects of Social Stressors into a More General Model

Information Required. The initial model used is that of Wellock et al. (2003a). Information about the pig, its diet, and the social and physical environments in which it is kept is needed. No additional inputs are required to describe either the thermal environment or the dietary composition. In addition to the three growth and body composition parameters, an extra one is required. The inputs needed to describe the social environment are pen area (m²), the number of pigs in the group, the number of feeders or trough length (m), and the occurrence or not of mixing. Up to two mixing events are allowed during a run; the weight(s) at which mixing occurs are required.

Genetic Differences. It is envisaged that there is genetic variation between pigs in their ability to cope with social stressors (Beilharz and Cox, 1967; Grandin, 1994). This is accounted for by introducing a parameter (EX) to describe the ability of the pig to cope when exposed to social stressors. The EX adjusts both the intensity of a stressor at which the animal becomes stressed (e.g., SPA_crit) and the extent to which stress decreases performance and increases energy expenditure (activity) at a given stressor intensity. It is assumed in the model that these two factors are correlated, with pigs that show signs of stress earlier also being stressed to a greater degree by the same intensity of stressor. Increasing EX from 0 to 10 represents a decreasing ability to cope and modifies the effect of each stressor on R by multiplying the parameters by appropriate scaling factors (shown in Table 4). An EX value of 5 represents the mean. Because the genetic variation in abilities of pigs to cope with stressors has not been formally quantified, values for the scaling factors were estimated to represent deviations of approximately 1% from the mean performance per unit change in EX. For example, EX values of 0 and 10 predict an approximate increase and decrease respectively in R of 5% from the mean at a given stressor intensity. The value of SPA_crit decreases from 0.042 to 0.031 m²/BW^0.67 as EX increases from 0 to 10.

[13]

where R_p is the pig’s potential relative daily gain calculated from the pig’s ADG_p. ADG_p is dependent upon the genotype and the current state of the pig.

[14]

The value of R_s is calculated on a daily basis and is used to calculate the new lower stressed maximum daily gain, ADG_s, which replaces ADG_p in the model.

[15]

Predictions of the feed intake required to attain ADG_s, (FI_ds, kg/d) and actual intake and gain are then made taking account of any changes in energy requirements due to increases in activity, E_N and E_mix, and possible constraints on intake due to limiting FSA, feed composition, and the climatic environment.

	Results

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The model was used to simulate some relevant experiments with social stressors and other factors as the variables. Where model inputs are not stated, the default values of the input variables are shown in Table 5. Other than where described below, SPA and FSA and feed bulk were always nonlimiting and temperature remained thermoneutral throughout.

Figure 1 shows the predicted time taken to grow from 20 to 50 kg when pigs are kept in varying group sizes and SPA. Group size varied between 1 and 100, and pen area was set at values of 0.3, 0.4, 0.5, and 0.6 m²/pig. As N increased and SPA decreased, the predicted time to reach 50 kg increased. An increase in N from 1 to 100 increased the time taken to reach 50 kg by 9 d from 40 to 49 at a SPA of 0.5 m²/pig, whereas at 0.3 m2/pig the time taken was increased by 10 d from 43 to 53 d. The interaction arises because SPA_crit is reached at 21 kg in pigs given 0.3 m²/pig, as opposed to 45 kg in pigs allowed 0.5 m²/pig. Growth rate in the former is then limited earlier and for a longer period of time.

View larger version (36K): [in this window] [in a new window]   Figure 1. Effect of pen area and group size (N) on the time taken for pigs to grow from 20 to 50 kg.

The model was set up to predict the effect of mixing in "cold" and "hot" environments on the ADG and time taken to reach 90 kg from an initial weight of 50 kg. Temperatures were set at 5 and 28°C for the cold and hot environments, respectively, and remained outside the thermoneutral zone throughout. Groups of 10 pigs were either mixed or not at 60 kg. The time courses of treatment effects on ADG are shown in Figure 2. In both hot and cold conditions, mixing decreased performance. In cold conditions, ADG was decreased to a greater extent immediately after mixing, -40% (0.359 kg/d) compared with hot conditions, -29% (0.202 kg/d). Also, ADG was depressed below that of nonmixed counterparts for an additional 7 d in the cold. The ADG of pigs mixed in cold conditions returned to levels achieved by nonmixed pigs, whereas in hot conditions the ADG of mixed pigs returned to levels exceeding that of their nonmixed counterparts. This is because mixed pigs were smaller for a given age than nonmixed pigs due to their depressed ADG and as a consequence had increased upper critical (UCT, °C) and lower critical temperatures. Consequently, mixed pigs in the hot treatment were less affected by heat stress than their larger nonmixed counterparts and thus able to achieve a higher ADG. Mixed pigs in the cold treatment were able to overcome the increased extra thermal demand and maintain gain by increasing intake. As a result, mixing pigs in the hot environment increased the time taken to reach 90 kg by only 1 d as opposed to 3 d for those kept in the cold environment.

View larger version (16K): [in this window] [in a new window]   Figure 2. The effect of mixing at cold and hot temperatures on the ADG of pigs grown from 50 to 90 kg.

Figure 3 shows the effects of ability to cope when exposed to social stressors (EX = 0, 5, or 10) on the ADG of pigs with two levels of potential performance, "intermediate" and "good," from 20 to 80 kg when kept in groups of between 1 and 100. The ADG_p of the intermediate and good genotypes were 0.85 and 1.07 kg/d, respectively, and achieved by increasing the growth rate parameter, B, from the default value (intermediate) to 0.016 (good). As N increased, ADG was predicted to decrease for both genotypes, with pigs with the poorest ability to cope (EX = 10) showing the largest decrease in ADG. Pigs with EX values of 10 in groups of 100 were predicted to show 8 and 16% decreases in ADG and 4 and 7% decreases in ADFI compared to their counterparts with EX values of 5 and 0, respectively. When N > 25, the intermediate pigs with low values of EX (EX = 0) were predicted to outperform the good pigs with high values for EX (EX = 10), having greater daily gains and intakes and reaching 80 kg 2 d earlier.

View larger version (21K): [in this window] [in a new window]   Figure 3. The effect of group size (N), pig potential (intermediate and good), and ability to cope when exposed to stressors (EX = 0, 5, or 10) on the ADG of pigs grown from 20 to 80 kg.

The model was run to predict the effect of changing dietary digestible energy content (DEC, MJ/kg) on the FSA_crit of pigs differing in potential at a BW of 80 kg. Five pig genotypes were simulated to have ADG_p values ranging from 0.85 to 1.53 kg/d at 80 kg. This was achieved by increasing B in the model. The model was run using five feeds decreasing in 1-MJ intervals from 15 to 10 MJ DEC/kg. In reality, this can be achieved by diluting the feed with a low-energy material, such as wheat bran (WB) (from 0 to 86%). This would increase the WHC from 3.5 to 4.6 kg/kg following the equation used by Whittemore et al. (2003b), WHC = 3.5 + (0.013WB). The remaining feed descriptors were kept constant. Results from the simulations are shown in Figure 4. The maximum number of pigs able to satisfy their FI_d per feeder space, N/FSA_crit, is predicted to increase as ADG_p decreases and DEC increases. Values predicted for N/FSA_crit ranged from 23.6 for pigs with the highest potential on the lowest DEC feed to 37.9 for pigs with the lowest potential on the highest DEC feed. This is because FI_d decreases as ADG_p decreases and DEC increases. Values for N/FSA_crit are predicted to remain constant for the higher potential pigs on the lower DEC, higher WHC feeds because of a feed bulk constraint on intake. Pigs with the lowest potential were able to satisfy their FI_d on all five feeds, whereas pigs with the highest potential were only able to fulfill FI_d on the highest energy feed.

View larger version (45K): [in this window] [in a new window]   Figure 4. The effect of potential daily gain (ADGp) and dietary digestible energy (DE) content on the maximum number of pigs able to satisfy their desired feed intake per feeder space (N/FSAcrit).

The effect of temperature and SPA on the ADG of three genetic lines of pigs was predicted. The three genetic lines were "poor" (B = 0.01, P_m = 33, L_m/P_m = 3, EX = 2), "intermediate" (default values), and "good" (B = 0.014, P_m = 38, L_m/P_m = 2, EX = 8) and had ADG_p values of 0.77, 0.98, and 1.11 kg/d, respectively. The pigs weighed 60 kg at the start and the simulation was for 1 d. Pen area was increased in increments of 0.1 m²/pig from 0.3 to 0.8 m²/pig, giving SPA values between 0.019 to 0.047 m²/BW^0.67, and temperature was increased in 5°C intervals from 0 to 30°C. The ADG was predicted to decrease as temperature increased above the UCT and as SPA fell below SPA_crit. Decreases in ADFI and ADG of 61 and 48%, respectively, were predicted for the good genotype pig kept at 0.3 m²/pig and 30°C compared with one at 0.8 m² and 0°C. The equivalent predicted decreases in ADFI and ADG for the poor genotype were 56 and 40%, respectively. The reason for the greater decrease in ADFI and ADG in the good genotype is because the upper critical temperature, UCT, is predicted to be lower, and SPA_crit is predicted to be higher, due to an enhanced growth rate and poorer ability to cope when exposed to social stressors, respectively. The UCT was predicted to be 22, 25, and 26°C and SPA_crit, 0.64, 0.61, and 0.56 m²/pig for the good, intermediate, and poor genotypes, respectively.

	Discussion

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The influence of social stress on pig performance, although undeniable, is frequently underestimated and in pig growth modeling, generally ignored. Black (2002) noted that "current pig models do not predict well the effects of stress encountered by pigs reared in commercial environments." The aims here were to describe and quantify the effects of the major social stressors on the performance of growing pigs and to incorporate these relationships into an existing pig growth simulation model (Wellock et al., 2003a). The adapted model described here is an initial attempt at quantifying and predicting the effects of the major social stressors on the intake and gain of various genotypes of pigs.

The conceptual equations between the social stressors and pig performance described here were derived, where possible, on biological grounds rather than by using some polynomial regression technique to fit data (e.g., Kornegay and Notter, 1984, and Turner et al., 2003). To some extent, this allows the problems of using a strictly empirical approach to be avoided, and effects may be able to be interpreted biologically. For example, the equations of Kornegay and Notter (1984) and Turner et al. (2003) predict an ADG of zero when group size reaches 338 and 1,363, respectively in growing pigs. This cannot be the case as pigs in groups of up to 2,000 are now kept in profitable pig production enterprises; it is rather a consequence of the range of data used in the empirical analysis. Incorporating equations such as those developed here into a more general model allows any interactions that exist between the type of pig and its environment to be predicted, and is an improvement over simply altering output parameters by an empirical adjustment.

Integrating the derived equations into a growth model poses the problem of describing how social stressors affect pig performance. Detailed experiments in which not only intake and gain are measured, but also body composition and physiological parameters relating to stress and the control of growth are required to quantify the underlying biological mechanism responsible for stressor effects (Morgan et al., 1999). Until evidence is available to elucidate the exact mechanism(s), a decrease in the animal’s capacity to attain its potential is used here to represent the mechanism responsible for the decreased performance of socially stressed animals. This is in preference to other potential mechanisms, such as increased metabolic demands diverting resources from the growth process (Elsasser et al., 2000) or a direct reduction in appetite (Matteri et al., 2000).

A decrease in the capacity of an animal to attain its potential is the mechanism that is chosen because it allows the desired intake of the stressed animals, FI_ds, to be predicted in a simple way. This, in turn, makes the task of incorporating the mechanism into the growth model easier and is consistent with the experimental evidence, including that of Chapple (1993). The value of FI_ds is predicted directly from the depressed potential of the animal as opposed to first determining the nonstressed appetite (intake), FI_d, from which FI_ds is calculated. This latter method is used when a direct reduction in appetite is employed as the mechanism, such as in the enriched theory of food intake regulation by Kyriazakis (2003). Chapple (1993) used the AUSPIG simulation model of Black et al. (1986) to investigate how changes induced by social stressors observed in experiments, including increases in body lipid percentage, may come about. He found that the experimental observations could not be explained by a reduction in intake alone, that is, a direct reduction in appetite, but required instead a reduction in the pig’s ability to "deposit body tissue." Experiments in which an increased protein supply given to crowded pigs did not overcome their decreased performance relative to noncrowded pigs ( NCR-89, 1993; Edmonds et al., 1998; Ferguson et al., 2001) also support the chosen mechanism.

Although there is some circumstantial evidence that a decrease in the ability of the animal to attain its potential is the responsible mechanism, the underlying cause at the physiological level is not clear. It has been suggested that physiological factors, such as growth hormone (MacRae and Lobley, 1991), plasma cortisol (Von Borell et al., 1992), insulin-like growth factor, and cytokines (Chapple, 1993), may be responsible for directly down-regulating tissue growth. Further work to quantify how the mechanism may operate is required.

For the model to be used to make predictions, accurate descriptions of the social and physical environment, feed composition, and pig genotype are needed. Some of the inputs (e.g., group size, feeder space, floor type, and dietary energy and protein contents) are relatively easy to obtain. Accurate descriptions of the genotype of pig, including a description of the potential of the pigs (Knap et al., 2002) and ability to cope when exposed to stressors, EX, are more difficult to obtain. As the parameter EX reflects a newly introduced concept, there is currently no means of assigning an accurate estimation of its value to a particular genotype. However, assuming that there is a measurable phenotypic difference between types of pigs, it is thought that genetic characterization is possible. The work of de Greef et al. (2003) and Kanis et al. (2003) supports this. They described and evaluated a conceptual framework for breeding for improved welfare in pigs and showed that it is possible to select for abilities to cope with stressors, such as environmental temperature. To fully describe a particular pig’s genetic potential, a concise set of model parameters are required (Knap et al., 2002). In the model used here, they are the mature protein mass, P_m, the ratio of lipid to protein at maturity, L_m/P_m, and a growth rate parameter, B (Wellock et al., 2003a). Although these parameters are not universally regarded as the most suitable descriptors of potential growth (e.g., Schinckel and de Lange, 1996), they have much support (Ferguson et al., 1997; Whittemore and Green 2002; Pomar et al., 2003). Methods to characterize them have been suggested by Ferguson and Gous (1993) and Knap et al. (2002).

Validating models is a difficult process (Black, 1995; Wellock et al., 2003b). No model can be validated in any general way and any apparent invalidation will always be subjective (Black, 1995). Furthermore, suitable experimental data to enable sensible comparisons with model predictions of multiple interactions are almost nonexistent. An exception is Hyun et al. (1998a,b), who investigated the effects of combinations of SPA, temperature, and mixing on pig performance, but because the resulting data were used in the estimation of parameter values, they cannot be used for model testing.

Although the model here cannot be validated, its performance can be evaluated. Quantitatively, predictions made by the functional forms are in good agreement with previous attempts to quantify social stressor effects. The model predicts a decrease in performance of approximately 7.5% over a change in SPA from 0.039 to 0.030 m²/BW^0.67. This compares with a 10% decrease in performance predicted by Black et al. (1995) over the same range. It is expected that there is no effect of SPA when SPA > 0.039, and therefore the 10% decrease in performance over the range of 0.048 to 0.031 m²/BW^0.67 suggested by Whittemore (1998) also compares favorably. Although the empirical equations of Kornegay and Notter (1984) and Turner et al. (2003) have their limitations as discussed above, they are the only sources available for comparing the effects of group size on performance. As N increased from three, the minimum range for the equations of Kornegay and Notter (1984) and Turner et al. (2003), to their maximum ranges of 33 and 120, respectively, a decrease in ADG of 9 and 8.6% are predicted for growers. This compares to the model predictions of 9.2 and 14.1% over the same ranges. The effects of FSA and mixing have not been considered in equations elsewhere and so no comparison is possible. However, FR_max predicted by the model compares well with experimental data of Nielsen et al. (1995). They measured FR_max for 42-kg pigs, kept in groups of 20, to be 31.6 g/min, which compares to the value of 34.2 g/min predicted by the model when a realistic value for WHC of 3.5 is used.

When estimating the values of the parameters in the conceptual equations, many assumptions had necessarily to be made. For example, when predicting the effect of FSA on intake, it was assumed that there was a 24-h feeding period, no feed wastage, a nonlimiting rate of feed supply, and that all pigs were constrained equally when FSA became limiting. It was also assumed that one pig immediately succeeded another at the feeder. The assumption that all pigs were equally constrained highlights one of the problems, and perhaps the main limitation of using a model that represents the single, average pig. In reality, not all of the individual animals will be affected equally when exposed to the same stressors. For example, in established groups, dominant pen mates may chronically stress others, while remaining relatively unaffected, causing some animals to decrease their intake long before others (Nielsen, 1999).

To account for individual differences within a group, a population model is required and this is a sensible next stage of model development. In addition to accounting for differences in individual ADG_p, as is the case in the models of Knap (2000) and Pomar et al. (2003), differences in ability to cope when exposed to stressors is also required. Although these individual differences may be difficult to quantify and genetic characterization is an area where much work is still needed, the model described here provides a framework that is capable of dealing with these differences. The parameter EX, used to account for differences in responses to social stressors, can be used as the starting point for modeling individual pig differences, with individual animals of a group being assigned varying values around the group mean. There is evidence that selecting for increased lean in pigs has indirectly selected for aggression (van Erp-van der Kooij et al., 2000), and this may be one way of assigning EX parameter values to individuals, with leaner pigs assumed to be affected to a greater degree by stressors. This would assume that ability to cope and aggressiveness are correlated, which may not be the case. It should be noted that not only will individuals react differently to the environment, but also they will be influenced by others, and in turn influence them (Muir and Schinckel, 2002). One of the advantages of extending a model of an individual to a population, as discussed above, is that such effects can be accounted for.

	Implications

Top Abstract Introduction Materials and Methods Results Discussion Implications Literature Cited

 
Current models account only in part for factors affecting pig performance in commercial enterprises. Among the real effects operating in practice that are usually omitted are those due to social stresses, such as group size, space allowance, feeder space allowance, and mixing. The conceptual equations developed here are able to predict the intake and performance of growing pigs differing in both growth potential and the ability to cope with social stress when raised under given dietary, physical, and social environmental conditions by incorporating them into a more general pig growth model. One of the main advantages of simulation models is that they are able to make quick, inexpensive predictions about the effects of multiple factors simultaneously and to demonstrate any interactions that exist. These interactions may be crucial in decision-making processes because different types and maturities of pigs may react differently in the same environment and have important financial implications.

	Footnotes

 
¹ This work was supported by the Biotechnology and Biological Sciences Research Council of the United Kingdom and the Scottish Executive, Environment, and Rural Affairs Department. Thanks also to D. Green for helpful programming advice and S. Turner for useful comments on the manuscript.

² Correspondence: Bush Estate, Penicuik, EH26 0PH (phone: +44 131 5353212; fax: +44 131 5353121; E-mail: I.Wellock{at}ed.sac.ac.uk).

Received for publication April 4, 2003. Accepted for publication July 25, 2003.

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