Short-term responses to selection for parameters of the allometric-autoregressive model

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1 Short-term responses to seletion for parameters of the allometri-autoregressive model M.M. Sholtz,*.z. Roux and D.S. de Bruin Animal and Dairy Siene Researh nstitute, Private Bag X2, rene 1675, Republi of South Afria S.J. Shoeman Department of Livestok Siene, University of Pretoria, Pretoria 0002, Republi of South Afria The allometri-autoregressive model desribes growth aurately and is useful in the haraterization of growth responses. Hene, the potential of the model for seletion purposes was investigated. Rats were used in a seletion experiment, where seletion was pratised for slope (b) and interept (n a) of the allometri funtion: w = n a + bv [where w = n (body mass) and v = n (umulative feed intake)], and p, the auto slope of n (umulative feed intake). Failities for five seletion groups of 40 rats eah were available. Both upward and downward withinfamily seletions were pratised for n a and b, and only downward seletion for p. n the short term, seletion for n a and b resulted in good diret responses, and it appears that the model an be used to alter the shape of the growth and effiieny urve by seletion. The realized heritabilities orrespond to the heritabilities of previous studies. Although the heritability estimate of p is low, a moderate seletion response was realized in the short term. Only the orrelated responses to seletion for b seem to be of any signifiane during the four generations of seletion. Effiieny during the growth phase in whih seletion was pratised inreased markedly (17%), while total effiieny, whih inludes the estimated effiieny from oneption, also inreased (13%). Furthermore, seletion for b led to an inreased growth rate (15%) and a slight inrease in body mass (8%), whilst intake tended to derease (-5%). Normally intake tends to inrease as growth rate and mass inrease. Die allometriese-outoregressiemodel beskryf groei akkuraat en is bruikbaar vir die karakterisering van groeiresponsies. Gevolglik is die potensiaal van die model vir seleksiedoeleindes ondersoek. Rotte is gebruik in 'n seleksieeksperiment waarin daar geselekteer is vir helling (b) en afsnit (n a) van die allometriese funksie: w = n a + bv [waar w = n (liggaamsmassa) en v = n (kumulatiewe voerinname)], sowel as vir p, wat die outoregressiehelling van n (kumulatiewe voerinname) is. Met die beskikbare fasiliteite kon vyf seleksiegroepe van 40 rotte elk geakkommodeer word. Beide opwaartse en afwaartse binne-familieseleksie is vir n a en b uitgevoer, terwyl daar slegs vir 'n lae p geselekteer is. n die korttermyn het seleksie vir n a en b tot goeie direkte responsies gelei, en dit wil voorkom asof die model gebruik kan word om die vorm van die groei- en doeltreffendheidskurwe deur seleksie te wysig; Die gerealiseerde oorerflikhede stem ooreen met die oorerflikhede van vorige studies. Alhoewel die oorerflikheidsberaming vir p laag is, is 'n matige seleksieresponsie oor die korttermyn gerealiseer. Slegs die gekorreleerde responsie van seleksie vir b was van betekenis gedurende seleksie oor vier generasies. Doeltreffendheid in die groeifase waarin geselekteer is het merkbaar verbeter (17%), terwyl totale doeltreffendheid, wat beraamde doeltreffendheid vanaf konsepsie insluit, ook verbeter het (13%). Verder het seleksie vir b gelei tot 'n verhoging in groeitempo (15%) en 'n geringe verhoging in liggaamsmassa (8%), terwyl inname geneig het om af te neem (-5%). Normaalweg neem inname toe met 'n toename in groeitempo en massa. ntrodution The most important advantage of using growth funtions in the desription of animal growth, is that animal growth an be desribed and evaluated more aurately. Most growth funtions are limited to the desription of growth in terms of output (body mass) only, while input (feed intake) is not taken into aount. The allometriautoregressive model not only takes feed intake into aount but also onsiders the basi allometri nature of growth and desribes growth aurately (Roux, 1974; 1976; Meissner & Roux, 1979; Roux, 1980). The model has proved to be useful in the haraterization of growth responses of breeds and feeds in many nutrition studies (Meissner, Roux & Hofmeyr, 1975; Meissner, 1977; Meissner, Hofmeyr & Roux, 1977; Siebrits, 1979; Roux & Kemm, 1981; Greeff, Meissner, Roux & lanse van Rensburg, 1986a; 1986b). The allometri-autoregressive model also seems to be of value in geneti studies and some of its parameters exhibit signifiant heritabilities (Sholtz & Roux, 1981a; 1981b; Sholtz, Roux, de Bruin & Shoeman, 1990). Sholtz et ai. (1990) found positive orrelations between some of the ommon growth and effiieny traits (effiieny, growth rate, body mass) and b, whereas daily intake appeared to be negatively orrelated with b. Should these orrelations reflet the true situation, it would be advantageous to inrease growth rate via b without an inrease in feed intake. n order to test this hypothesis, a seletion experiment was arried out on some of the parameters of the model to investigate the nature of the diret a!1d orrelated responses, using the rat as model. Material Model and Methods The allometri funtion to desribe growth an be expressed by the equation:

2 y = ax b or w =n a + bv where y = body mass, x = umulative feed intake, w = n y and v = n x (Roux, 1976). Slope (b) and interept (n a) an be estimated by linear least-square proedures. Aording to Roux (1976; 1980), the equation for umulative feed intake (auto) is: x (t) x (0) P E (t) t-l kpie(t-j) j=o n (umulative feed intake) at time t, n (umulative feed intake) at time 0, n (umulative feed intake) with t-700 slope of auto, error term, auto = linear of x(t) as dependent variable on x (t -1) as independent variable. Both upward (H) and downward (L) seletions were applied to the parameters slope (b) and interept (n a) of the allometri funtion, while only downward seletion was pratised for p, the auto slope of n (umulative feed intake). Animals t was deided to use the rat as a model for these seletion experiments, beause of the short generation interval and the general aeptane of the biologial resemblane between laboratory and farm animals. Rat growth may be divided into three growth phases (Sholtz, 1979; Sholtz & Roux, 1981a). Seletion, however, was limited to the seond growth phase, whih is from approximately 37 to 60 days of age. Rats from the outbred Wistar line were used. n an attempt to minimize the influene of maternal effets, the litter sizes were standardized to 12 pups at three days of age. The animals were kept in standard ages under onventional onditions (not pathogen-free), and remained perfetly healthy. Room temperature was kept at 21 ± 2 C, with a relative humidity of 35-50%. Artifiial lighting simulated a diurnal yle of 12 h daylight and 12 h darkness. After weaning at 21 days of age, the rats were kept in individual ages. Body masses and umulative feed intake were measured every seond day without withholding food and water prior to measurement. This protool was followed up to the age of 60 days. Feed was in the form of a ground powder (Epol mixture 4710), and was offqed in speially designed hoppers to minimize waste. Seletion The need to keep inbreeding to a mlmmum, made it neessary to keep all families represented in subsequent generations. Neither individual (mass) seletion nor family seletion satisfy this prerequisite. All the families an only be represented if within-family seletion is pratised (Sholtz, 1987). Within-family seletion has the further advantage that environmental effets ommon to litter-mates and maternal effets are taken into aount (Faloner & Latyszewski, 1952). Matings of least relationships were made aording to the system suggested by Alan Robertson (Faloner, 1973), as shown below: Family no. in urrent generation 9 o 1 x 2 3 x 4 2 x 1 4 x 3 Family no. in next generation Whereas this system does not redue the average rate of inbreeding, it has three advantages over the onventional ylial system. The pratial advantage lies in the mating shedule, whih is the same in every generation, while the theoretial advantages derive from the fat that inbreeding oeffiients are the same for all families in a generation, and that the rate of inbreeding is the same for all generations (Faloner, 1973). The number of animals used in the experiment was limited by restrited failities and labour to 200 rats. t was, therefore, deided to use 4 families with 10 individuals (5 f, 59) eah for eah of the five seletion groups (bh, bl, n ah, n al, p, L). Seletion of an equal number from all families resulted in an effetive population size (Ne) of 16, and a theoretial rate of inbreeding of 132 (L,. F = 12Ne) or 3,125% per generation (Faloner, 1981). Other researhers (MaArthur, 1949; Faloner, 1953; Faloner & King, 1953; Faloner, 1960) have also used seletion groups of this magnitude (Ne = 16, with upward and downward seletion). Eisen (1974) onluded that an effetive population size of 20 is suffiient for most seletion experiments. The two best (highest values for H and lowest values for L) males and females from eah family were seleted. The best male was first mated to both seleted females. After eight days, the seond-best male was mated to the same females in order to maintain the essential family struture. At the same time, the problem of insuffiient litter size was overome. Where the litter size of the best female was insuffiient (not 5 f and 59), it was supplemented with progeny from the seond-best female. t was further deided to use the third-best male and female from eah family for additional matings to foster the exess pups, or to provide additional pups to standardize litter size. n a few ases where both the best and seond-best female did not produe any pups, the pups of the third-best parents were used to maintain the family and seletion struture. n the seletion groups n a and b, the seletion responses were expressed as the differene between H and L. The perentage differene was alulated as follows:

3 n the ase of seletion group p L, no diret ontrol was available. A ontrol value was thus established by adding the values of the n ah, n al, bh and bl groups and dividing the sum by four. Common growth and effiieny traits Effiieny of feed utilization may be alulated as feed onsumed divided by gain produed, or as its inverse. The two ratios differ only in sign, but not in magnitude of their relationships to other traits, and would rank a group of animals in the same way (Lasley, Sellers & Anderson, 1979; Nielsen, 1979). Consequently, the ratio gain per unit of feed was preferred, sine a large value indiated a good performane and a small value a poor performane. The orrelated response (differene between Hand L) in three types of effiienies were investigated. They are: (1) effiieny between two ages, e.g. in the seond growth phase of the rat (± days); (2) effiieny at a speifi point, e.g. at 60 days of age. Aording to Sholtz (1979), effiieny at a speifi point (loal effiieny) is desribed by dy dx = y x(b), where y = body mass and x = umulative feed intake; (3) total effiieny from oneption to 60 days of age. The method of estimating preweaning intake has previously been desribed (Sholtz & Roux, 1980). To estimate the effiieny between two ages, initial and final mass are needed. n ases where animals were not fasted prior to measurement, as in this experiment, umulative feed intake an usually be measured with greater auray than atual body mass (Roux, 1980), due to a variable ontent of the digestive trat. This effet on body mass may be smoothed out by using umulative feed intake to estimate the initial and final mass, with the aid of the allometri funtion. Growth rate, expressed as average daily gain (ADG), was alulated in the same manner. Correlated responses Correlated responses obtained for the different traits tend to vary over generations. t was, therefore, deided to fit a linear to these responses to predit the attained response in a ertain generation, using the following equation: y = + dx where y = response; x = generation number; d = slope; = interept. The response estimated from the linear, is referred to as the realized orrelated response. n linear, the r 2 value gives an indiation of the auray of fit. Hill (1976) indiated that tests of signifiane on these r 2 values were not valid, sine the values of the different generations were not independent. Suh tests of signifiane may be too lenient. However, sine no other suitable proedure exists, it was deided to use r 2 merely as an index of whih orrelated responses deserve attention. n ases of seletion for n a and p, the data of the parental generation and three generations of seletion were onsidered, where an r 2 of 0,81 was needed for signifiane at the 10 % level. n the ase of seletion for b, the data of the parental generation and four generations of seletion were onsidered, in whih ase an r 2 of 0,65 was needed for signifiane at the 10 % level. Results Diret responses Atual responses to seletion for n a, band pare presented graphially in Figure 1. The observed perentage differene between Hand L in the ase of n a and b, and the perentage deviation from the ontrol in the ase of p, are presented in Figure 2. The expeted responses to within-family seletion were alulated using the following equation: R = iawh;, (Faloner, 1981). 2,1 Observed Q) :::l (1) <ii 1,9 > Cl.!: -- 1,7 0,60 0,58 0,56 (2) <ii >.. (3) Q) 0,54 0,52 0,97 0,93... :::l <ii > 0-0,89 '" Expeted response Figure 1 Observed and expeted diret responses in (1) n a, (2) b, and (3) p.

4 (1) "0 : (\J : $.0 U : ::t: (5 0 (Faloner, 1981). Beause within-family seletion was applied in this experiment, the within-family heritability (h;,) was estimated using the following equation (Faloner, 1981): h = RS where R = total response (differene between Hand lines) and S = umulative seletion differential. To onvert the h;, to ordinary heritability (h 2), the following equation was used (adapted from Faloner, 1981): hz=h () -r L (2) "0 : (\J :.0 U : & (5 0 g : 0 u E (3) : 0.s; Cl 0 2 wherer = orrelation of breeding values (0,5 for full sibs), t = intra-lass orrelation for the trait onerned. When seleting for n a, the realized heritability was estimated at generation three of seletion. The realized values for h;, and h 2 were found to be 0,20 and 0,34, respetively. When seleting for b the realized heritabilities at generation four of seletion were found to be 0,16 (h;,) and 0,27 (h 2 ), respetively. Correlated responses with seletion for b The orrelated response in: (1) effiieny in the seond phase, (2) loal effiieny at 60 days of age and (3) total effiieny up to 60 days of age is given in Figures 3, 4 and 5, respetively. Linear was fitted to these Figure 2 Observed and expeted diret responses in (1) n a, (2) bz, and (3) p, expressed as % differene or deviation. +20 Estimates of (J";' (within-family variane) and h;, (within-family heritability) were alulated from the parental generation, while the speifi effetive intensity of seletion (i) was used for eah generation and seletion group. The expeted responses are shown in Figures 1 and 2. From Figure 2, it an be seen that the expeted and observed responses in n a were in good agreement during the first three generations, whereafter the realized response disappeared. During the first four generations, the expeted and observed responses in b were in agreement. Although the heritability estimate for p was so small (0,13) that pratially no response was expeted, Figure 2 shows that a mild seletion response was realized during the first three generations of seletion. "0 ffi +15 : icl Realized heritabilities Response to seletion may be used to estimate the heritabilities in the parental population. Heritabilities estimated in this way are known as realized heritabilities Figure 3 Correlated response in effiieny in phase 2 with seletion for b.

5 Unear Table 1 Correlated responses (%) in effiieny with seletion for b (1) a (2) (3) 23,3 26,6 14,2 17,4 21,3 12,9 0,68 * 0,59 0,94* a See text for explanation. * Signifiant at the 10 % level. b, with the highest response in loal effiieny at 60 days of age. The relatively lower response of total effiieny up to 60 days of age is understandable, sine this parameter inludes effiieny from oneption to 60 days of age. These orrelated responses are in agreement with the orrelations presented by Sholtz et at. (1990). t is also important to report on the orrelated effets on body mass, growth rate (ADG) and intake (AD) with hanges in b and effiieny. From Figure 6 it an be seen that ADG responded relatively strongly and positively to seletion for b. Body mass at 60 days of age also showed a positive response to seletion for b, but this was less marked than for ADG (Figure 7). AD was not 2 3 Linear Figure 4 Correlated response in loal effiieny at 60 days with seletion for b.. '0 ffi +10 j Cl Linear. '0 ffi +15 Q) u Cl " " "" " " 2 3 Figure 5 Correlated response in total effiieny at 60 days with seletion for b. orrelated responses to estimate the realized orrelated responses and the derived data are presented, together with the orrelated responses at generation four and the auray of fit of the linear (r 2 ), in Table 1. From Figures 3, 4 and 5 and Table 1 it is lear that effiieny responded exeptionally well to seletion for. '0 ffi +10, +5 icl eft. Figure 7 for b. Linear Correlated response in 60-day mass with seletion

6 signifiantly altered, although it tended to deline with seletion for a high value of b (Figure 8), whih may be expeted from the results of Sholtz et at. (1990). Normally, intake tends to inrease as ADG inreases. The value of the observed orrelated responses and realized orrelated responses in generation four, as well as the auray of fit (r 2 ) of linear, are given in Table 2. The age at the start of the seond growth phase of the rat (onset of puberty) did not hange with seletion for b (Figure 9). This age seems to be very stable, with hanges varying between + 0,30% and -1,14%. No noteworthy orrelated responses in ommon growth and effiieny traits of the first growth phase of the rat were found with seletion for b of the seond phase. Linear Correlated responses to seletion for n a Seletion for n a did not seem to have any effet on effiieny, although n a is mathematially diretly proportional to effiieny and moderate geneti orrelations between effiieny and n a exists (Sholtz et at., 1990). From Table 3, it an be seen that seletion for n a had no lear ut effet on: (1) effiieny during phase 2, (2) loal effiieny at 60 days of age, or (3) total effiieny at 60 days of age. The same appeared to be true for ADG during phase 2 and body mass at 60 days (Table 3); The orrelated response in AD with seletion for n a was more variable, but no definite trend in response was observed. Furthermore, there was no effet on traits of phase 1. Table 3 Correlated responses (%) in ommon growth and effiieny traits to seletion for n a ""0 C ell!..q Effiieny (1)" Effiieny (2) Effiieny (3) ADG Body mass ntake -1,2-2,3 0,3-1,9-1,8-1,0-3,3-5,3 41,1-1,8-1,9 1,0 0,19 0,22 0,00 0,00 0,12 0,05 Q) U C -5 & (5 f. Figure 8 Correlated response in AD with seletion for b. Table 2 Correlated responses (%) in ADG, body mass and AD with seletion for b Trait Observed response Linear r 2 ADG 19,4 14,8 0,82' Body mass 9,3 7,7 0,81 ' ntake -7,1-4,5 0,26 ""0 +5 ell 0 Q) u i -5 (5 f. 2 Figure 9 Correlated response in age at first break point with seletion for b. Correlated responses to seletion for p The orrelated responses in ommon growth and effiieny traits are given in Table 4. Most of the traits in Table 4 showed no noteworthy trends of orrelated response to seletion for p. Note espeially that ADG in phase 2 showed no definite trend. Total effiieny at 60 days of age showed a very small but steady and signifiant inrease (2 %). There was no effet on traits of phase 1. Table 4 Correlated responses (%) in ommon growth and effiieny traits to seletion for p 2 3 r 2 Effiieny (1)" -4,1 3,9 2,9-7,4 0,07 Effiieny (2) -2,1 4,6 2,9-5,2 0,10 Effiieny (3) 41,8 41,3 41,2 1,5 0,82' ADG in phase 2 5,2 7,5 4,0-2,1 0,64 60-day mass -4,3 5,6 2,2-2,1 O,D ntake in phase 2 41,6 3,0 2,2 2,3 0,43 " See text for explanation., Signifiant at the 10% level. Disussion n the ase of n a and b, the expeted and observed responses (Figure 2) ompared well during the initial stages of seletion (three and four generations respetively). n the short term, the diret responses to

7 seletion for n a and b aorded with geneti theory. The value of these parameters may be hanged by seletion. Thus, it seems that the model may be used to alter the shape of the growth and effiieny urve by seletion during the initial stages of seletion. This is in ontrast to Eisen's (1976) view that, sine heritabilities of the growth funtions of body mass vs. time were low, hanges in growth urves may be more readily ahieved by the appliation of seletion indies to atual body mass rather than to parameters of a growth urve. The realized heritabilities orrespond well with the heritability estimates of Sholtz et at. (1990) of 0,31 and 0,29 for n a and b, respetively. The differene between the realized heritabilities and these estimates was less than 10 %. These small differenes were antiipated from Figure 2, where expeted and observed responses were in good agreement. Thus, this seletion experiment onfirmed that the heritability estimates of Sholtz et at. (1990) appear to be fair estimates of the heritabilities of n a and b. Seletion for p resulted in a moderate response during the first three generations of seletion. This response was muh larger than the expeted response onsidering the magnitude of the heritability estimates. Thus, the heritability estimates for p may not be very reliable as they predit very little response. Furthermore, it may appear that p is not analized to the extent previously thought (Sholtz & Roux, 1981b). Seletion for b resulted in strikingly large, orrelated responses in the three types of effiieny, with the highest response being more than 20 % in loal effiieny at 60 days of age in four generations of seletion. The relatively lower response in total effiieny at 60 days of age may be explained by the fat that this parameter inludes estimated effiieny from oneption to 60 days of age. Effiieny in the first phase was not altered by seletion, thus there was a dilution effet on this type of effiieny. Therefore, it seems possible to hange effiieny in the short term by seleting for the exponent of the allometri equation. Seletion for n a on the other hand, did not signifiantly affet effiieny. This is quite surprising, sine n a and b are highly orrelated (Sholtz & Roux, 1981b). Growth rate and body mass inreased by approximately 15 % and 8 %, respetively, with seletion for b. Responses of this kind are normally expeted to be assoiated with an inrease in effiieny. ntake tended to derease, whih is in ontrast to results from the literature whih suggests that intake tends to inrease as growth rate and body mass inrease (Fowler, 1962; Stanier & Mount, 1972; Hayes & MCarthy, 1976; Hetzel & Niholas, 1978; Eisen & Durrant, 1980; Kownaki & Jezierski, 1980; Wang & Dikerson, 1980). t appears to be advantageous to inrease effiieny, growth rate and body mass, while intake is dereased or kept onstant. Seletion for n a had no effet on any of these traits. Although some of these orrelated responses are so strikingly large (the effiienies), or in ontrast to those reported in the literature (daily intake), they losely orrespond to the diretion and ranking of the ordinary orrelations between b and the ommon growth and effiieny traits estimated by Sholtz et at. (1990). This is illustrated in Table 5 where there is a very good relationship between the realized orrelated responses and the ordinary orrelation of b with the different growth and effiieny traits estimated by Sholtz et at. (1990). A orrelation of 0,98 was found between the two olumns of Table 5. Table 5 Realized orrelated responses and orrelation with b of the different growth and effiieny traits Effiieny (1) b Effiieny (2) Effiieny (3) ADG Body mass ntake a Sholtz et ai., b See text for explanation. Realized orrelated response Correlation with b a 17,4% 0,71 21,3% 0,82 12,9% 0,37 14,8% 0,31 7,7% 0,15-4,5% -0,38 Ordinary orrelation between X and Y = 0,98 Another interesting feature of this seletion experiment is the stability of age at the start of the seond growth phase. This point is assoiated with the onset of puberty and its physiologial proesses in the rat (Sholtz & Roux, 1981a). Seletion for parameters of the allometri-autoregressive model, therefore, does not seem to hange the physiologial proesses of the rat assoiated with the onset of puberty during the early stages of seletion. Referenes ESEN, E.J., The laboratory mouse as a mammalian model for the genetis of growth. Pro. 1st Wrld. Congr. Genet. Appl. Livestok Prod. (Madrid, Spain) 1,467. ESEN, E.J., Results of growth urve analysis in mie and rats. J. Anim. Si. 42, ESEN, E.J. & DURRANT, B.S., Effets of maternal environment and seletion for litter size and body weight on biomass and feed effiieny in mie. J. Anim. Si. 50,664. FALCONER, D.S., Seletion for large and small size in mie. J. Genet. 51, 470. FALCONER, D.S., Seletion of mie for growth on high and low planes of nutrition. Genet. Res. 1, 91. FALCONER, D.S., Repliated seletion for body weight in mie. Genet. Res. Camb. 22, 291. FALCONER, D.S., ntrodution to quantitative genetis. Longman n., New York, Essex. FALCONER, D.S. & KNG, J.W.B., A study of seletion limits in the mouse. J. Genet. 51, 561. FALCONER, D.S. & LATYSZEWSK, M., The environment in relation to seletion for size in mie. J. Genet. 51, 67.

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