Long-term responses, changes in genetic variances and inbreeding depression from 122 generations of selection on increased litter size in mice

J. Anim. Breed. Genet. ISSN 0931-2668 ORIGINAL ARTICLE Long-term responses, changes in genetic variances and inbreeding depression from 122 generations of selection on increased litter size in mice M. Holt*, T. Meuwissen & O. Vangen Department of Animal and Aquacultural Sciences, Agricultural University of Norway, Norway Correspondence Marte Holt, Department of Animal and Aquacultural Sciences, Agricultural University of Norway, PO Box 5025, 1432 Ås, Norway. Tel: + 47 62 51 01 43; Fax: +47 62 51 01 01; E-mail: marte.holt@aquagen.no *Present address: Marte Holt, PO Box 504, N-2304 Hamar, Norway. Received: 2 July 2004; accepted: 28 February 2005 Summary Data on mice selected for litter size over 122 generations have been analysed in order to reveal the effect of long-term selection on responses and changes in variances over a long selection period. Originally, three lines were established from the same base population, namely an H line selected for large litter size, an L line selected for small litter size and a K line without selection. In generation 122, the mean number of pups born alive (NBA) was 22 for the H line and 11 for the K line. Phenotypic response to selection is reduced over generations, but crossing of plateaued lines increased responses and realized heritabilities. Both realized heritabilities and heritabilities from residual maximal likelihood (REML) analyses were, in general, calculated from generation ()1) 44 (period 1), 45 70 (period 2) and 71 122 (period 3) separately. Realized heritabilities were in general smaller than heritabilities estimated from mixed model analysis. An overall estimate of heritability for NBA was found to be 0.19 (±0.01) by REML analysis. Additive variance is constant over all periods in the high line and the control line, but is reduced over periods in the low line. The reduction of additive variance in the low line could probably be explained by changes in gene frequencies. In all lines, environmental variances increased over periods. Inbreeding reduced the mean litter size by 0.72 (±0.10) pups per 10% increase in inbreeding, with substantial variance between periods and lines. Introduction Some of the improvements in quantitative genetics theory have been based on results from selection experiments. Long-term selection experiments are useful to measure changes in variances and changes in the rate of responses caused by the selection itself. These changes depend on the number of genes, their effect and their frequencies. Sorensen & Kennedy (1984) demonstrated that using an animal model with a complete pedigree would correct for inbreeding and selection and provide estimates of the additive genetic variance in the base population when selection has operated over several generations. Long-term selection studies would then provide the animal breeding industry with valuable information about changes in additive genetic variance caused by selection, in addition to knowledge about selection limits and correlated traits. As long-term selection experiments with a limited population size are affected by genetic drift and inbreeding, such experiments are important resources to estimate the effect of inbreeding on the trait under selection. The analyses in the present study are based on data from 122 generations of selection on litter size in mice. The aim was to evaluate response to selection and changes in genetic levels and variances caused by long-term selection. In the present study, J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin 199

Data on mice selected for litter size over 122 generations M. Holt et al. heritabilities are evaluated by estimates from realized heritabilities and from residual maximal likelihood (REML). Estimates of additive genetic variance and changes in the genetic level for the trait number of pups born alive (NBA) in addition to the effect of inbreeding on this trait are evaluated by REML analyses. Materials and methods Animals The present selection study on increased litter size in mice was initiated in 1972. The base population was a cross of two outbred strains (L. A. C. Grey and C. F. W), imported to Norway from Great Britain in 1968 (Joakimsen & Baker 1977). Three lines were established from the base population: a high line selected on high litter size (H), a low line selected on low litter size (L) and a control line without selection (K). An overview of the selection history is given in Figure 1. The selection was based on the phenotypic litter size performance of the female, with two sons and two daughters selected from the 50% best first parity litters in the selected lines and a corresponding random selection in the K line in order to have a similar rate of inbreeding. Within litter selection was made at random. The population size varied between 40 and 90 breeding females in each generation. Each male was in general mated to one female. Mating of selected animals was random, but mating of full-sibs and cousins were avoided. The lines have undergone different selection strategies and merging with other lines, as described earlier by Joakimsen & Baker (1977) and Vangen (1993, 1999). This includes the introduction of a Dutch line (B) to the H line in generation 20, and the creation of a new synthetic line (X) from the cross of H and B in generation 22 (Figure 1). Line B had been selected 33 generations for large litter size before it was imported to our mouse-laboratory, with a realized heritability in the first 29 generations of 0.11 (Bakker et al. 1978). The selection history of this line is described by Bakker et al. (1978). After generation 30, little response was achieved in line B B X H Selection on large litter size H4 H8 H12 HK HI HK2 H2 Base population No selection K Selection on small litter size Selection on large litter size L Gen 0 10 20 30 40 50 60 70 80 90 100 110 120 Period 1 Period 2 Period 3 Establishment of the high line (H), the low line (L) and the control line (K). Introduction of an imported Dutch line (B) in generation 20, line X is made of a cross of the H and B line in generation 22 Selection on low litter size in the low line (L) Different maternal environments in the high lines Reversed selection for large litter size in the low line (L) Establishment of a new high line (H2) and a new high-control line (HK2) Continued selection on large litter size in the L line Figure 1 The different periods and selection objectives of the selection study. Period 1: generations ()1) 44, period 2: generations 45 70 and period 3: generations 71 122. 200 J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin

M. Holt et al. Data on mice selected for litter size over 122 generations (Buis 1988). In the low line (L), the selection criterion was reversed from generation 45 on, with selection for high litter size. In generation 45 46 the H, B and X lines were crossed and bred for two generations with random selection. Each line contributed equally to this randomization period. After this randomization, four new high lines with different standardization levels in addition to a high control (HK) were established (Figure 1). The H4, H8 and H12 lines had litter size standardized with 4, 8 and 12 pups at birth, respectively, while HI had no standardization of litter size. Generation 68 was the last in a period that involved studies of maternal traits and longevity. In this generation parents for the next generation were recruited from parity number four instead of parity number one. Additionally, the females were mated to a new male in parity three and four. In generation 71, the high lines were crossed for a second time, and a new high line (H2) and a new HK2 were established (Figure 1). The H4, H8, H12 and HK had all equal contribution to the two new lines, and all matings in the first generation (generation 71) were made of a cross between two different lines. Litter size has been standardized to eight, when larger than eight, on the day of birth in all lines and generations, except for generations 47 70 where standardization levels varied between lines. All animals were at least 8 weeks when mated. The mice had free access to pellet concentrate and water. The lights were on for 16 h and off for 8 h. The average temperature was set at 23 C. From generation 109 on, only the K line and the H2 line were maintained. The selection in the L line was ended after generation 105, while the maintenance of HK2 was ended in generation 108. Statistical analysis The analyses were based on data from 122 generations of selection. The dataset was divided in three periods based on the selection history presented in Figure 1. Period 1 is used to find estimates of the variance components in the base population. All 46 generations in this period were used in order to include the genetic variance introduced with line B in generation 20. All lines are linked through a common base population (except line B), which includes all animals in generation )1, the generation before the selection starts. No data from the 40 previous generations in the B line before the line was imported to the mouse laboratory were available for the analyses. In total, the dataset covered 29 393 female mice with observations on litter size, while the pedigree file contained 74 473 animals. The number of animals in the different periods and lines are given in Table 1. To estimate realized heritabilities, the response per generation was estimated as the deviation between the means of the selected lines and the original control line (K). The total cumulative selection differential was estimated as the difference between the mean of the selected animals and the mean of all animals, taking into account a delay in the expression of the selection differentials for the males, as explained by Joakimsen & Baker (1977). Realized heritabilities (h 2 realizedþ were estimated as the regression of selection response on total cumulative realized selection differential. The regression coefficients were multiplied by two as selection was based on the phenotype of the mother. Standard errors of the realized heritabilities were estimated by the formula given by Hill (1972). Estimates for realized heritabilities were calculated separately for the three periods, Table 1 Number of females with records per generation and in total, and number of animals in the pedigree in the selection study Period Line Number of females with observations per generation Total number of females with observations Animals in pedigree file High line Period 1 H 66.7 3067 B 59.1 1300 X 61.3 1227 Period 2 H4 43.9 1055 H8 46 1104 H12 46.5 1116 HK 42.3 1015 HI 43.8 1051 Period 3 H2 62.2 3232 HK2 70.3 2671 Periods 1 3 All 16 838 44 417 K line Period 1 K 67.5 3107 Period 2 K 59.2 1421 Period 3 K 43.4 2256 Periods 1 3 K 6784 17 237 L line Period 1 L 63.2 2906 Period 2 L 50.3 1209 Period 3 L 47.3 1656 Periods 1 3 L 5771 13 945 All lines Period 1 All 11 607 Periods 1 3 All 29 393 74 473 J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin 201

Data on mice selected for litter size over 122 generations M. Holt et al. to see if the realized heritabilities were different between periods. To study changes in variances over time, variance components in different periods of the selection study were estimated using ASReml (Gilmour et al. 1999). These variance components were also used to calculate heritabilities for the selection criterion, NBA. The model used was a univariate animal model (Ollivier 1999). A complete pedigree file was available, and the data file contained observations on the NBA back to the base population. The base population includes all animals with unknown parents and consist of all animals in generation )1 and the animals in generation 20 in line B. All lines have been included in the relevant mixed model analyses, even though HI, HK and HK2 are not focused in the results. The following model was used to find the estimated breeding values (EBVs) for the NBA: NBA ¼ mean þ generation þ parity þ inbreeding dam þ animal þ error generation and parity were treated as class effects while inbreeding was a regression variable. As the inbreeding of the mother is expected to affect NBA most (Falconer & Mackay 1996), a model including inbreeding of the dam was chosen. Inbreeding coefficients of the dams were estimated from the complete pedigree using a programme written by John James (J. James, unpublished observation). The EBVs were plotted against generation number to find the genetic trends for the trait NBA. As the model adjusts for inbreeding, the EBVs show additive responses to selection free of inbreeding depression. The model also provides estimates of inbreeding depression for the trait NBA. As the variance in each generation seemed to increase with increasing mean, a log transformation of the data was performed. However, the variance was still dependent of the mean after log transformation, but in the opposite direction. All analyses were therefore based on non-transformed data. Estimates of the variance components in the base population were based on data from period 1 for reasons explained earlier. Generation ()1) is considered as the base population in all analysis, except when line B is analysed separately. For this analysis, data only on line B (generations 21 44) is included, and the animals imported to the mouse laboratory were considered as the base population for this line. When each line was analysed separately in period 1, the data from the base population were included in each dataset. When periods 2 and 3 were analysed separately within each line, a pedigree file including all generations up to that time in the pedigree was used, while only data from the relevant period was used. Analysis of periods 2 and 3 across the lines was not reasonable as the environmental variance was highly different between lines. Results Phenotypic trends Figure 2 shows the mean NBA in each generation of the selection study. The mean NBA in generation 122 was 11.3 (phenotypic standard deviations (SD p ) ¼ 2.3) in the K line and 21.8 (SD p ¼ 5.7) in 25 20 15 NBA 10 5 0 0 20 40 60 Generation number 80 100 120 K HK2 L H maternal HK H B X Figure 2 Mean number of pups born alive in the selected lines and the control line. H is the average of line H, B and X. H maternal is the average of the lines H4, H8 and H12. 202 J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin

M. Holt et al. Data on mice selected for litter size over 122 generations the H2 line. This is an increase in the mean NBA of 3.6 SD p (in base population). In Figure 2, the H, B and X lines were averaged in period 1, as all three lines had approximately the same mean and standard deviations (numbers not presented). H4, H8 and H12 are averaged in period 2 for the same reason. As observed from Figure 2, the mean NBA decreased in generations 20 42 despite continuous selection on increased litter size. The crossing of the H, B and X line in generations 44 45 resulted in an increased mean NBA. Even though the high line had been a closed population with selection for 26 generations when the H2 line was created in generation 71, H2 still showed response to selection in the following 50 generations. In period 3, the regression of response on generation number was 0.02 (±0.01) pups per generation. Selection on low litter size in the L line gave little response after generation 20 (Figure 2). The selection criterion was reversed in generation 44, and after this a considerable response was achieved. When the L line was terminated in generation 105, the mean NBA was 14.1 (SD p ¼ 2.6). In the K line, the mean NBA decreased slightly over the first 65 generations (Figure 2). After this generation, the mean NBA increased again, and in generation 122 the mean NBA was 11.3 (SD p ¼ 2.3). In the new control line (HK2), established in generation 71 from the randomized high lines, the mean NBA dropped significantly. At the same time, the mean NBA in the original K line seemed to increase slightly (Figure 2). Realized heritabilities Estimated realized heritabilities in the selected lines are given in Table 2. As can be seen from the table, the realized heritabilities varied from line to line and Table 2 Realized heritabilities with standard errors (SE) h 2 realized High lines Period 1 (H) 0.062 0.001 Period 1 (B) )0.030 )0.0004 Period 1 (X) )0.010 )0.001 Period 2 0.246 0.042 Period 3 (H2) 0.020 0.010 L line Period 1 0.150 )0.018 Period 2 0.288 0.022 Period 3 0.046 0.004 p 0.05. SE from period to period. For the high lines, the realized heritabilities were low in period 1. As can be seen from Figure 2, the responses were low in generations 22 44 in all high lines in this period. This caused low, and even negative, realized heritabilities for period 1 for these lines. It must be specified that the estimates of realized heritabilities in line B and line X were based on 20 generations of selection. In period 2, the lines H4, H8 and H12 were analysed together. Response to selection was high in this period, and the realized heritability for this period was also high (Table 2). In period 3, response to selection was small, which was reflected in a low heritability estimate for this period. For the L line an estimate of realized heritability for period 1 was found to be 15%, which is higher than the estimates in the high lines. After the selection was reversed in this line (beginning of period 2), the response to selection was high. Like for the high lines, this high response was reflected in a high heritability estimate for this period. As for the high lines, response to selection in period 3 was low, which resulted in a small estimate of realized heritability in this period. REML analysis The heritabilities and variance components estimated by REML in different lines and periods of the selection study are given in Table 3. The estimates of the Table 3 Residual maximal likelihood estimates of heritabilities with standard errors (SE) and variance components for litter size in mice h 2 SE r 2 A r 2 e r 2 P High lines Period 1 (H) 0.06 0.03 0.50 8.42 8.92 Period 1 (B) 0.13 0.05 1.37 9.07 10.44 Period 1, all lines 0.11 0.02 1.10 8.92 10.02 Period 2 0.16 0.02 1.82 9.72 11.54 Period 3 0.15 0.02 2.58 14.64 17.22 All high lines and all periods 0.13 0.01 1.70 11.24 12.94 K line Period 1 0.25 0.04 1.58 4.66 6.25 Period 2 0.16 0.06 0.97 4.90 5.86 Period 3 0.27 0.06 2.11 5.77 7.89 All periods 0.20 0.03 1.28 5.26 6.54 L line Period 1 0.37 0.05 2.51 4.23 6.75 Period 2 0.07 0.05 0.43 5.72 6.16 Period 3 0.17 0.08 1.75 8.63 10.38 All periods 0.13 0.03 0.98 6.41 7.39 All lines Period 1 0.18 0.02 1.52 6.75 8.27 All periods 0.19 0.01 2.00 8.78 10.77 J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin 203

Data on mice selected for litter size over 122 generations M. Holt et al. heritability in the base population are significantly different and highly variable when estimates from each line analysed separately are compared. In general, the REML estimates of heritabilities were higher than the estimates of realized heritabilities in Table 2. As mentioned in Materials and methods, all lines except B and X were founded from the same base population. For the high lines, the estimates of the additive variance seem to increase over periods, but this increase is not significant. In the L line a significant decrease in the additive variance was found over periods (Table 3). For all lines, the environmental variance increased over periods. This resulted in a higher phenotypic variance when all three periods were included compared with only data from period 1 in all lines. In the high lines, the heritabilities increased over periods, while again the opposite was found in the L line. When analyses were performed across all lines (Table 3), heritabilities were constant over periods when only period 1 was analysed versus when all three periods were analysed together. Genetic trends Mean EBVs per generation for the trait NBA in the different lines in the selection study are plotted in Figure 3. The EBVs are from the analysis across all lines and with all generations included in the dataset. As the model adjusts for inbreeding, the graph shows the actual response to selection. As can be seen from Figure 3, the mean EBV has increased by almost 12 pups in the high line. The figure also reveals that there has been a certain non-intended selection response or genetic drift in the K line. The success of the reversed selection criterion in the L line is very clear. In general, the estimated genetic trend is very much confirmed by the phenotypic trends in Figure 2. Inbreeding depression Figure 4 provides the average inbreeding coefficient for dams over generations for each line in the selection study. In generation 122, the average inbreeding level in the K line was 0.64. Because of the cross with line B (generation 22) and the crossing of several sub lines in generation 70, the average inbreeding coefficient in H2 was smaller (0.36) than in the control (K). This number was however highly underestimated, because the kinship within the Dutch (B) line and between the B and the H line was set to zero, while it was actually around 40% (Bakker et al. 1978). The increase in inbreeding per generation varied because of a variation in population size within each line and ranged from 0.33 (±0.00) to 1.19% (±0.01) increases in the mean inbreeding coefficient per generation. In general, the increase in inbreeding per generation was highest in periods 1 and 2 of the study (data not shown). The REML estimates of the effect of inbreeding on NBA in the selected lines and the K line are given in Table 4. The numbers show the average performance decrease per 10% increase in the inbreeding level of the dam. Estimates of inbreeding depression were not significant when each line and period were analysed separately. Averaged over all lines and periods, the inbreeding depression was 0.39 pups. For 15.00 10.00 Average EBV 5.00 0.00 5.00 10.00 0 20 40 60 Generation 80 100 120 HK2 K L H and H2 H maternal HK Figure 3 Estimated breeding values for the trait number of pups born alive in the selected lines and the control line of mice. H is the average of lines H, B and X. H maternal is the average of the lines H4, H8 and H12. 204 J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin

M. Holt et al. Data on mice selected for litter size over 122 generations 0.7 Average inbreeding coefficient 0.6 0.5 0.4 0.3 0.2 0.1 Figure 4 Development in inbreeding coefficients of the dams in the selected lines and the control line. H maternal is the average of the lines H4, H8 and H12. 0 0 20 40 60 Generation number 80 100 120 K H and H2 HK2 B L X H maternal HK Table 4 Inbreeding depression for the different lines in different periods of the experiment with standard errors (SE) shown as the decrease in the mean phenotypic performance per 10% increase in the inbreeding level of the dam analysis across lines inbreeding depression was higher when period 1 was analysed separately versus when data from all periods were included (Table 4). Discussion Regression coefficient High lines Period 1 (H) )0.66 0.66 Period 1 (B) )1.15 0.91 Period 2 )0.18 0.34 Period 3 )1.02 0.61 Over all lines and periods 1 3 )0.86 0.19 K line Period 1 )0.28 0.53 Period 2 )2.14 0.87 Period 3 )0.13 1.03 Periods 1 3 )0.67 0.42 L line Period 1 0.80 0.57 Period 2 0.65 0.79 Period 3 )1.25 1.48 Periods 1 3 0.35 0.46 All lines Period 1 )1.68 0.17 Periods 1 3 )0.72 0.10 Phenotypic trends In this long-term selection study, response to selection has been high, and has resulted in a mean litter size in the high line twice that in the original control line. In the high line, two periods of randomization SE have been successful in order to increase the response to selection. The low line was initially selected for low litter size, and for this line the selection criterion was effectively reversed to selection for large litter size from generation 45 onwards. This result shows that the plateau in the previous generations was not caused by a total loss of the genetic variance. Results from selection for increased litter size in mice have been reported in several other studies Falconer 1971; Eklund & Bradford 1977; Bakker et al. 1978; Eisen 1978; Kirby & Nielsen 1993). Lines selected on large litter size were reported to plateau on generation 31 36 (Falconer 1971; Eklund & Bradford 1977), while a line selected on small litter size was reported to plateau in generation 20 (Eklund & Bradford 1977). These results are comparable with results found in period 1 in the present study. Despite continued selection on increased litter size in the high lines in the present study, the average litter size declined after the selection plateau in period 1. This decrease in NBA is also clear in the control line. As discussed earlier by Vangen (1993), this decline cannot be explained by inbreeding depression alone, and is possibly also caused by changes in the environment. The decline in litter size at the end of period 1 results in a low relative response over all generations (0.1 pups/generation) and also to reduced realized heritabilities in period 1. In the present study, the high lines were crossed for the first time at the beginning of period 2 and for the second time at the beginning of period 3 to examine if crossing could increase response to selection. According to Eisen (1980), crossing is expected to have a positive effect because of increased genetic variance, reduction of linkage disequilibrium and a J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin 205

Data on mice selected for litter size over 122 generations M. Holt et al. possible neutralizing of the effect of undesirable recessive genes at low frequencies. In the present study crossing increased the phenotypic response to selection, but was disrupted by two large drops in average litter size in generation 49 and 62 in period 1. No certain explanation for these drops can be given, but the drop in generation 62 is also clear in the K line, so this drop could be caused by a change in the environment. After the second crossing of the sublines in the high line (beginning of period 3), the same improvement was not achieved, but this might be because no new lines were introduced to the population. The reversed selection criterion (large litter size) in the L line from generation 45 onwards was very successful. This result shows that the plateau in the previous generations was not caused by a total loss of the genetic variance. Realized heritabilities In general the realized heritabilities reflect the response to selection, and are, because of a negative selection response in generations 30 44 of period 1, generally smaller than what have been reported in other studies. Falconer (1971) and Kirby & Nielsen (1993) reported realized heritabilities of 0.076 and 0.10 from upward selection, and 0.25 in downward selection (Falconer 1971). Eklund & Bradford (1977) found realized heritabilities of 0.16 for the first 15 generations and of 0.00 for generations 30 45 from upward selection on litter size, while Eisen (1978) reported a realized heritability of 0.19 for litter size over 12 generations of selection. Realized heritabilities for period 1 of the present study were estimated previously by Vangen (1993). For those analyses, period 1 was divided into two parts, one including generations 0 21 and another including generations 22 41. For generations 0 21, realized heritabilities ranged from 0.15 to 0.17 in the selected lines, but in generations 22 41 realized heritabilities were negative or non-significant (caused by the negative selection response in these generations) (Vangen 1993). These results are comparable with the other results presented above. The realized heritabilities estimated in the present study are based on the performance in the original K line, but could also possibly be estimated from the new control lines (HK and HK2) established in periods 2 and 3, in order to compare lines with a more similar level of inbreeding. However, this was not carried out, mainly because HK2 was ended in generation 109, and therefore it would not be possible to utilize information from the H2 line after this generation on. REML analysis The animal model provides a way of accounting for the effects of selection and limited population sizes in long-term selection experiments, and it also allows for evaluating the validity of the underlying assumptions (Ollivier 1999). Based on the infinitesimal model, the genetic variance is expected to remain constant over short periods except as a result of inbreeding and selection causing linkage disequilibrium. The REML analyses presented in Table 3 reveal a non-constant additive variance over periods in the L line, and an increased environmental variance over periods in all lines. The additive variances seem to vary from period to period in the high lines and the control line, but these differences were not found to be significant. Significant changes in patterns of response and the additive variance have been estimated in other long-term selection populations (Meyer & Hill 1991; Beniwal et al. 1992; Heath et al. 1995). However, Martinez et al. (2000) reported consistent results in the estimation of additive variance from a series of analyses from 20 generations of selection. Heritability estimates from the same study were also very close among analysis. Meyer & Hill (1991) concluded that the decrease in heritabilities were larger than expected from selection and inbreeding in the infinitesimal model, and suggested that changes in additive variance were because of changes in gene frequency. This could be a possible explanation for the decreased additive variance found over periods in the low line in the present study as well. In all lines the environmental variance increases from period to period. This resulted in an increased phenotypic variance in all lines. An increased environmental variance does not necessarily mean that the increase is mainly non-genetic, but it could also be caused by an increase in the non-additive genetic variance. Also, genetic variance that does not fit the model of a linearly increasing variance may erroneously be partitioned into the environmental or litter components (Heath et al. 1995). Differences in environmental variance between lines may be because of the different selection criteria in the lines. In the present study, realized heritabilities were in general smaller than heritabilities estimated by REML. The same result was reported by Heath et al. (1995) and Juga & Thompson (1989). Meyer & Hill (1991) found on average realized heritabilities to be 206 J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin

M. Holt et al. Data on mice selected for litter size over 122 generations slightly higher than REML values; however, this result was expected as they did not utilize all data from the selected lines. With selection over several generations, estimates of realized heritabilities are biased downwards, because of linkage disequilibrium generated by selection and genetic random drift [summarized by Juga & Thompson (1989)]. Also, estimates of realized heritabilities are highly dependent on the performance in the control line, and may especially be biased when the control line is not replicated. The use of a complete relationship matrix that takes account of selection would therefore make REML the best method to estimate heritabilities. Genetic trends The genetic trends in Figure 4 give the changes of the genetic levels in the different lines. The figure reveals some unintended selection or genetic drift in the K line. According to the figure, the genetic level in the high line has increased by approximately 12 pups from generations 0 122. This is almost the same as the increase in phenotypic values. The drop in the genetic level in the H line in generation 20 is caused by the introduction of the Dutch line (B). As the animals in generation 20 in the B line are the base animals for this line, they have low EBVs compared with the animals in line H from the corresponding generation. The decrease in average litter size in HK2 (period 3) is less evident in the genetic trends than in the phenotypic trends. Again, the successful reversed selection in line L is very clear. According to Ollivier (1999), animal model estimates are highly dependent on the model assumed, and may not provide adequate measures of the actual responses. In particular, to ignore dominance variance will give an overestimation of the response. Also, the infinitesimal model does not account for new genetic variance as a result of new mutations. Even though the estimates of additive variance in different periods of the study are variable, the changes in genetic levels of the animals presented in Figure 4 are very much confirmed by the phenotypic trends in Figure 2. Inbreeding depression Long-term selection studies with limited population sizes are affected by genetic drift and inbreeding. Inbreeding was also one of the reasons why new control lines were established in periods 2 and 3 of this study. The inbreeding level is calculated to be much higher in the K line compared with the high lines. The underestimated level of inbreeding in the high lines caused by the line cross with line B does not affect the rate of inbreeding (increase in percentage points per generation), but the absolute level. The rate of inbreeding is assumed to affect inbreeding depression most. In the present study, the inbreeding increased by 0.33 1.19% per generation. The two periods of randomization in the high lines affect the inbreeding level, but do not affect the rate of inbreeding much. Inbreeding has been found to have a negative effect on reproduction in several other studies (Chai 1966; McCarthy 1967; Ehiobu et al. 1989; Lacy et al. 1996; Bünger & Hill 1999), but on the contrary, Beilharz (1982) did not find any significant effect of inbreeding on litter size. The estimates of inbreeding depression in the present study are comparable with a decline of 0.6 pups (Bowman & Falconer 1960) and 0.5 pups (McCarthy 1967) per 10% increase in inbreeding respectively. In pigs, two different studies reported that a 10% increase in the inbreeding coefficient of the dam reduced the mean litter size by 0.23 (Hill & Webb 1982) and 0.24 (Bereskin 1968) piglets. The reason why the estimates of inbreeding depression have large standard errors when each line and period is analysed separately might be that the inbreeding coefficients within each generation are very similar, and the effect of generation and the level of inbreeding might be difficult to separate. The positive inbreeding depression in the low line periods 1 and 2 may be explained by an overprediction of the selection response in the low line by the animal model, i.e. genetic gain is less than predicted, and the model tries to explain the discrepancy between observed response and expected response by increasing the inbreeding depression estimate. Hence, the inbreeding depression estimate in the low line would be overestimated. A similar overprediction of selection response in the high line would lead to an underestimation of the inbreeding depression. In the control line no such bias is expected, and also across all lines the under- and overestimations might, at least to some extend, cancel each other out. In addition to studying how the rate of response found in earlier generations continues, some of the key objectives with long-term selection studies are to estimate long-term correlated responses. Other studies also based on this long-term experiment have shown that both 3 and 6-weeks body weights are significantly increased as a result of selection for litter size (Holt 2001). A study on generation J. Anim. Breed. Genet. 122 (2005) 199 209 ª 2005 Blackwell Verlag, Berlin 207

Data on mice selected for litter size over 122 generations M. Holt et al. 101 of the same lines states that the high line females produce more offspring relative to their own body weight (Rauw et al. 2003). The same study also revealed that high line females produce more offspring to a greater cost to their own metabolism, which leads to a reduced pup development and increased preweaning mortality rates. Holt et al. (2004) studied losses through pregnancy in the H2 line and the K line, and found that selection mainly caused a higher ovulation rate, but probably also an increased embryonic mortality in late pregnancy. The long-term selection experiments presented in this paper have been useful to evaluate long-term responses and changes in genetic levels over time in addition to measure and evaluate correlated traits. Selection on increased litter size has been very successful in the present study, and part of this success is because of two periods of randomization in the high lines. It seems reasonable to assume that the selection response in farm animals (e.g. pigs) would probably be smaller than in this model experiment. There are many causes for a reduced response when selecting for fertility: natural selection working against artificial selection, small additive genetic variance, genotype by environment interactions and genetic and environmental maternal effects. It is also more difficult to standardize the environmental factors in larger farm animals. For selection in production animals, production traits are often more important than fertility traits, and may have unfavourable genetic correlations with fertility traits. The crossing of different high lines may also be very difficult because it requires several lines with a high genetic level for the trait litter size. However, this selection experiment, one of the longest lasting in the world, reveals the large potential for genetic variation in a reproductive trait. 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