The effect of population structure on the rate and extent of diversity loss in a crossbred sheep flock

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Chapter II.The effect of population structure on the rate and degree of diversity loss in a crossbred sheep flock

K. M. MacKinnon, L. A. Kuehn, and D. R. Notter Department of Animal and Poultry Science, Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0306

ABSTRACT:

This study analyzed changes in genetic diversity in small, closed selection and control lines of sheep established in 1983 from 50% Dorset, 25% Rambouillet, and 25% Finnsheep breeding. Founder animals of the three breeds were mated to create three- way crosses. In 1987, descendents of the 161 founders were divided into a fall-lambing selection line (S) of 125 ewes and 10 rams, a fall-lambing environmental control line (E) of 55 ewes and 5 rams, and a spring-lambing genetic control line (G) of 45 ewes and 5 rams. In each line, measures of genetic diversity were calculated for all rams and ewes available at the time of line formation (REL) and at the end of the study for three sets of animals: all lambs born including dead lambs (L), a single offspring of all matings including potential offspring of ewes that did not lamb (M), and all rams and ewes available (RE). The average generation interval was 2.65 yr in S and 4.28 yr in G. Values used to quantify diversity were the change in inbreeding per generation (∆F), effective number of breeding animals (Ne), effective number of founders (fe), effective number of ancestors (fa), founder genome equivalents (fg), and two additional measures of heterozygosity (GD1, GD2), calculated using the additive relationship matrix and(or) 100 gene drop simulations. The averages of Ne for S and G lines were 33.78 and 29.07; values of Ne were most similar between S and G for RE. The values for fe, fa, and fg, calculated from the additive relationship matrix for REL were 40.25, 38.42, and 24.03, respectively for S and 39.59, 33.95, and 20.50, respectively for G. At the end of the study values for fe, fa, and fg for RE were 31.46, 20.85, and 7.65, respectively for S and 30.80, 19.57, and 10.04, respectively for G. The differences between the actual number of founders and fe shows the loss of diversity due to unequal founder representation, differences between fe and fa are due to bottlenecks, and differences between fa and fg are due to additional drift. Larger decreases in diversity were seen in M and L in both S and G, but particularly in G, where all available breeding rams were not used in all years. For most calculations, values obtained from gene drop and the relationship matrix were very close. The exception was fg in M of G, apparently due to non-random sampling of sires in previous generations that resulted in increased diversity. Gene drop analysis allowed allelic diversity and survival to be estimated. Of the 322 unique alleles assumed present in the founders, 71% in S and 58% in G survived at line formation; all appeared in over 50% of the runs. Of the alleles possible in RE of S and G, only 65% of 254 alleles and 70% of 192 alleles, respectively, survived in any single run, and only 6% and 8% of the possible alleles were present in more than 50 of 100 runs. The number of alleles and heterozygosity lost demonstrates the impact of a closed, small population on diversity. The values obtained also show that RE of S and G were relatively similar in diversity, as desired to determine genetic change in a selection study relative to an appropriate baseline.
Key Words: Allelic diversity, Bottlenecks, Heterozygosity, Inbreeding, Selection, Sheep.

Introduction

Small, closed, selected populations can rapidly lose heterozygosity and allelic diversity. Most breeding programs and studies involving domestic animals acknowledge that inbreeding occurs, and may try to minimize inbreeding or to quantify the increase by calculating the change in inbreeding per generation (∆F) (Boichard et al., 1997). However, calculation of ∆F may not reflect the cumulative effects of inbreeding and random genetic drift on allelic diversity or specify when or how such diversity was lost. Methods more commonly used by conservation geneticists may provide more informative measures of changes in genetic diversity. Procedures derived by Lacy (1989, 1995) and Boichard et al. (1997) allow analysis of founder effects, bottlenecks, and genetic drift. The calculation derived by Boichard et al. (1997) also can be used to identify the most influential ancestors in a pedigree. If populations are evaluated at a single point or in each generation by these methods, the causes of losses in diversity can be identified and potentially corrected, and important ancestors may be evaluated for the trait(s) under selection.
It is also important in a selection experiment to be able to compare genetic change relative to an unselected control line otherwise similar in population structure and original composition. After a breeding structure has been created and implemented, retrospective analysis of rates of inbreeding and of remaining diversity in the selection and control lines can asses the adequacy of the breeding design. The experiment described in this paper was designed to quantify diversity present in a population of sheep and identify which subset of animals provides a better estimate of that diversity. We also compared the genetic control line to the selection line to discuss the impacts of selection and restricted population size, and to determine if the two lines were adequate for comparison in the selection study.

Materials and Methods

An experimental sheep flock was established in 1983 from 50% Dorset, 25% Rambouillet, and 25% Finnsheep breeding. By 1987, all lambs were progeny of three-way crosses, after which the population remained closed. After the 1987 lambing, 45 of 225 ewes were randomly chosen to form a genetic control line (G) that remained on a spring-lambing system. The remaining ewes were randomly divided into a selection line (S) with 125 ewes and an environmental control line (E) with 55 ewes. Both the S and E ewes then were selectively bred to lamb in the fall. Ten rams were used in each year in S, and each ram was exposed to about 13 ewes. The E and G lines used about five rams each, which were bred to approximately 11 and 9 ewes each, respectively (Al-Shorepy and Notter, 1997).
S line. Selection in the S line for fertility in spring (May and June) began in 1988 (Al-Shorepy and Notter, 1997). Up to one-third of the ewes in S were replaced annually as older ewes were culled for declining fertility and unsoundness. All healthy ewe lambs were exposed in the spring at 7 mo of age to selected rams. Pregnant ewe lambs were retained, and additional ewe lambs were selected, as needed, based on their estimated breeding value for fertility. Ewe lambs that had been selected but did not lamb in the first year were given a second chance to lamb before being culled. Four to seven rams were replaced each year. No more than two rams per sire were chosen in any given year. Most rams were used for only 1 or 2 yr; only two of 37 rams were used in a third year (Al-Shorepy and Notter, 1997). The entire S line, from 1987 until the end of the study in 1998, consisted of 1190 lambs (including dead lambs), 297 dams, and 67 sires.
E line. The E line was maintained with approximately the same ewe age distribution as S. Replacement rams and ewes were randomly chosen from the G line, to avoid inadvertent selection for fall- lambing due to a fall-birth. Because of the movement of G animals to E, the breeding stock in E was a sub-sample of the G line. Again, approximately one-third of ewes and one-half of rams were replaced each year. No more than one ram per sire/yr was randomly chosen for use in E. Ewes were culled at random within year of birth. Ewe lambs were randomly chosen, but only one ewe lamb/ewe could be chosen each year. For the purpose of the population analysis, the E line was not used because E rams and ewes did not produce replacement breeding stock. The entire E line consisted of 492 lambs (including dead lambs), 129 dams, and 54 sires.
G Line. Animals in the G line were used as a source of replacements for E in the fall lambing study. In order to minimize genetic drift, ewes in G were only culled for unsoundness or if they failed to produce in two consecutive years. Ewe lambs were randomly chosen with the restriction of one ewe lamb per ewe/yr. An average of 7.5 replacement ewe lambs were used in G each year. Almost all of the G line ewe lambs were retained for use in either E or G. The G line included 922 lambs (including dead lambs), 115 ewes, and 32 sires.
Sire families were identified for G in 1987. Whenever possible, two sons were maintained from each sire family, even if they were not used. When a sire died, a son of the sire was kept, when possible. The maintenance of sire families was used to limit inbreeding and drift in the small G line. Of the 14 sire families present in 1987, 12 were still available in 1993 (Al-Shorepy and Notter, 1997), and 11 were available in 1998. Usually, five sires representing different sire families were used each year. Three new sires were used the following year in order to eventually sample all sire families and maintain genetic connections between years. In the last year of the study, only three rams were used. Rams were culled only for physical unsoundness.

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Pedigree Analysis

Founders were defined as the 161 animals that created the flock, starting in 1983, whose parents were assumed to be unknown. Crossbred animals used in 1983 that were from Virginia Tech flocks had their parents included in the pedigree; all other animals were assumed to have unknown parents. A few animals with one or two unknown parents that were not founders were removed from the pedigree. The entire pedigree consisted of 5041 animals, but animals produced in other studies peripheral to the main selection were removed from the study, resulting in a pedigree that contained 4257 animals.
Generation codes (g) were calculated for all animals as, g = ½ (gs + gd) +1, where gs is the generation code of the sire, gd is the generation code of the dam, and line founder animals were given a generation code of zero. Generation intervals were determined by regressing generation number on year of birth. Inbreeding coefficients and additive relationships were calculated using the pedigree to form the additive relationship matrix. Changes in ∆F in each line were obtained by regressing individual inbreeding coefficients on generation number. The effective number of breeding animals (Ne) calculated as:
Ne = 1 / (2∆F)
Indicates the number of breeding animals that would have produced the observed rate of inbreeding if bred under ideal conditions in one generation.
Genetic diversity was analyzed using the additive relationship matrix, gene drop methods (MacCluer et al., 1986), and an iterative procedure to estimate the effective number of ancestors (Boichard et al., 1997). Gene drop is a computer simulation procedure that is performed by giving each founder a pair of unique alleles and randomly transmitting the alleles through the pedigree (MacCluer et al., 1986). In order to obtain the probability that founder alleles would survive and estimate standard deviations on measures of genetic diversity, the gene drop procedure was repeated 100 times.
Additional measures of genetic diversity. The effective number of founders (fe) indicates the number of equally contributing founders that would have been expected to result in the same level of genetic diversity as that observed in the current population (Lacy, 1989). The fe is calculated as:
n
fe = 1 / ∑pi2
i  1
where pi is the expected proportional genetic contribution of founder i, obtained from the average relationship of the founder to each animal in the current population, and n is the total number of founders (Lacy, 1989). A complimentary measure, genetic diversity (GD1), approximates the amount of heterozygosity still available in the population after reductions due to unequal founder contributions and can be calculated from the additive relationship matrix as:
GD1 = 1 − 12fe
or from gene drop simulations as:
2 n
GD 1 = 1 − ∑ qk 2
k 1
where q k is the frequency of founder gene k averaged over all individuals in the current
generation and all replicates in a gene drop simulation, and n is the number of founder animals (Rodrigañez et al., 1998).
A method created by Boichard et al. (1997) was used to estimate the effective number of ancestors (fa) and to identify animals that have the highest relationship to the current population:
m
fa = 1 / ∑ a i 2
i 1
where a i is the marginal contribution of each ancestor to the current generation, and m is the total number of contributing ancestors. The calculation can be used to identify the most influential ancestors, which may or may not be founders.
The number of founder genome equivalents (fg) was used to estimate the joint effects of unequal founder contributions, bottlenecks, and genetic drift:
c
fg  1 / ∑ (p i 2
i 1
t 2n
/ ri) ≈ t / (2 ∑ ( ∑ q kj2 ))
j 1 k 1
where pi is the expected proportional genetic contribution of founder i, ri takes values of 0.5 or 1 and is the expected proportion of founder i’s alleles that remain in the current population, and c
is the total number of contributing founders (Lacy, 1989), qkj is the frequency of founder gene k
for replicate j, t is the number of gene drop replicates, and n is the total number of founders (Rodrigañez et al., 1998). The effective number of genomes also can be calculated using the additive relationship matrix as:
fg  1/ 2r
where r is half the average relationship (mean coancestry) between all individuals in the current population, including the relationship of each individual to itself (Lacy, 1995). To equate the increase in homozygosity to a loss in heterozygosity due to unequal founder contribution and genetic drift, the following measure of genetic diversity (GD2) was calculated from gene drop:
t 2n
GD2 1- ∑[∑ q kj2 ]/ t
j  1 k  1
where qkj is the frequency of founder gene k for replicate j, t is the number of replicates, and n is
the number of founders (Rodrigañez et al., 1998). The second term of the equation is simply the mean coancestry of the current population, giving an alternative calculation for GD2.
Determination of informative population statistics is complicated by overlapping generations, selection, and the maintenance of sire families that are not sampled in all years. In order to analyze the diversity available in S and G, one set of animals at line formation and three sets of animals from the end of the study were considered in each line: all rams and ewes available at the time of line formation, all lambs born (including dead lambs), one offspring of all matings (including potential offspring of ewes that did not lamb), and all rams and ewes available at the end of the study. The final population of available breeding animals is particularly important in G, where rams were retained but not used in all years and also in S where all ewes may not reproduce in a given year. It is also important to note that the measures in this study were calculated with a complete pedigree, and that missing information may result in a substantial apparent increase in fe, fa, fg, GD1, and GD2.

Results and Discussion

Measures of inbreeding and heterozygosity
The rate of inbreeding in the current rams and ewes of S and G were comparable (Table 2.1). Even though G had fewer breeding animals in each year, the longer generation interval, decreased culling, and maintenance of sire lines limited rates of inbreeding relative to those observed in the larger S line. Differences in ∆F and N e among the last three groups in line S are small. One problem with the Ne metric is that the value indicates the number of breeding animals needed to produce the average ∆F and does not quantify the cumulative decrease in allelic diversity or changes in breeding structure from year to year. Hence, the value obtained for Ne is not comparable to measures of fe, fa, and fg. The change in inbreeding per generation in the current available breeding animals of G is similar to ∆F for the S line due to the increased generation interval and retention of sire lines. Lambs and matings had a slightly higher ∆F in G than in S. The differences observed in both lines between lambs and matings are not large, and are probably not biologically significant.
It is apparent from Figures 2.1 and 2.2 that more matings with inbreeding coefficients greater than or equal to 0.25 resulted in lambs in G than in S. This result may reflect the higher mean fertility in fall-matings compared to spring-matings (88.2% vs. 47.5%). Lambs with inbreeding coefficients greater than or equal to 0.25 generally did not become parents in either line (Figure 2.3) . The lack of rams and ewes with inbreeding coefficients greater than or equal to 0.25 in S could be attributed to decreased survival and selection against decreased fertility in spring. In G, the lack of animals with higher inbreeding coefficients could only be due to decreased survival or to animals that were too sickly or small to be bred.
The difference between the actual number of founders (161) and fe shows that unequal founder representation has a large impact on genetic diversity (Tables 2.2, 2.3, and 2.4), but most of the loss in diversity had occurred by 1987, when the lines were formed (Table 2.2). There was a smaller loss in diversity from line formation to the end of the study, showing that there was either a thorough mixing of founders, which was the goal, and(or) that all line founder genomes were adequately maintained. Similar values for fe were found in the current lambs, matings, and available breeding animals for S (Table 2.3), showing that fe has become relatively constant. In a closed ideal population, fe is expected to plateau when founders are no longer present, because founder representation will eventually be relatively stable among all animals (Caballero and Toro, 2000). The fe is still decreasing in G from available breeding animals to lambs because of the longer average generation interval of 4.6 yr/generation in G, as compared to 2.6 yr/generation in S (Table 2.4) . Although fe in the current animals is less than the actual number of founders by at least 129, the amount of heterozygosity, calculated by GD1, was still relatively high at the start of the lines and in the final animals (Table 2.2, 2.3, and 2.4). There was only a negligible loss in heterozygosity due to founder representation from the beginning of the lines until 1998. It is important to note that the measures of GD are relative to the founding population, which is only a sample of the diversity present in the breed or species. The values obtained for GD1, calculated using the relationship of founders to the current population and gene drop, are comparable showing that founder representation is adequately captured using the relationship matrix.
When compared to fe, fa shows the impact of bottlenecks on the population (Table 2.2, 2.3, and 2.4). It is apparent from the small decrease in rams and ewes present at the formation of the respective line that there were very few bottleneck events that had occurred up to that point, but the G line rams and ewes showed a larger decrease than S due to fewer animals being used at line formation causing a greater potential for bottleneck events (Table 2.2) . Since there was no selection occurring in the matings made to create three-way crosses, it was expected that limited drift due to bottlenecks would occur by the time of line formation.
The difference in fa between the final lambs and matings of S indicates that matings that had resulted in lambs had a more equal distribution of ancestors. It may be that lambs with low contributing ancestors had a better chance of surviving, because they were less likely to be inbred than lambs with prominent ancestors. The slightly larger fa noted in the final available breeding animals of S is due to older animals being present with more diverse relationships to older ancestors. Bottlenecks had some effect in S, but had an even greater effect in the final lambs and matings of G due to the small population size and only one discrete year being represented. The value for fa obtained from the final available breeding animals of G, when compared to lambs and matings of G, shows the beneficial impact of overlapping generations on maintaining diversity by limiting bottlenecks and increasing the possible number of offspring per parent.
Marginal contributions of all prominent ancestors were obtained by calculation of fa, identifying the most influential ancestors in each population (Figure 2.4 and 2.5). The three most influential ancestors, making over 50% of the genetic contribution, in the final lambs and matings of G were the three sires used in the last breeding (data not shown). If G had discrete generations, then these would be bottleneck sires, but the retention and use of additional sires spread the diversity of the population over multiple years. Sixteen animals made up about 80% of the contribution to the current available breeding animals of G (Figure 2.5). Of these animals, only one was born after formation of the G line, six were older sires, two were older dams, six were foundation sires, and one was a foundation dam. Since the most important animals occur before or shortly after formation of G, the currently available breeding animals in G have not experienced narrow bottlenecks, which is also apparent from the change in fe to fa in currently available breeding animals as compared to lambs or matings of G (Table 2.4).
The most important ancestor in all three sets of animals in S was a sire born in 1990 (Figure 2.4). This sire may have contributed genes with a particularly significant positive effect on out-of-season lambing. Seven, six, and nine animals in S made up about 50% of the contributions in final lambs, matings, and available breeding animals, respectively. Only one of the seven most important ancestors of the current lamb crop was born before the formation of S. Of the remaining six animals, three were sires of the last lamb crop, one was an older bottleneck sires, and the remaining two were bottleneck dams. Since the only lamb crop analyzed was the current one and there were overlapping generations, there is the potential for the animals that contributed most to the current lamb crop change each year. There was only one animal in common between the significant ancestors of lambs and of final available breeding animals of S (i.e., in ancestors making up the top 50% of contributions). The 20 influential animals making up the top 80% of the contribution to the currently available breeding animals in S consisted of five sires born in S, four dams and four sires born before line formation and one dam and six sires that were foundation animals. Since most of the high contributors to final available breeding animals of S were older animals, the reason for the differences between lambs and available breeding animals of S is that the parents would be bottleneck animals with discrete generations, but this bottleneck was circumvented by retention of breeding animals from multiple generations. Hence, the influential animals born and used in S may have had a considerable impact on the trait being selected.
When all losses of diversity were accounted for in fg, the impact of a closed population becomes apparent. The numbers obtained from calculation of fg show how many animals would be needed to produce the same genetic diversity if all founders contributed equally and no founder alleles were lost through drift under random mating (Lacy, 1989). The values for fg were estimated through gene drop and the additive relationship matrix (Table 2.2, 2.3, and 2.4). It is apparent from the rams and ewes present at the formation of the lines (Table 2.2) that there was not much diversity loss due to drift and that most of the loss in diversity up to this point was due to unequal founder representation. The G line founder rams and ewes had a slightly smaller number of founder genomes than the S line due to the smaller size of G. The founder genome equivalents estimated through gene drop and the relationship matrix are equivalent as are the measures for GD2 (Table 2.2).
The final populations of lambs and final available breeding animals have similar values for fg in both lines using gene drop or the relationship matrix, but in matings of S and particularly of G, the fg was higher when calculated using gene drop simulation analysis (Table 2.3 and 2.4). It is the difference between values for fg in lambs and matings of G that is of concern. The average difference in fg between lambs and matings in G for all simulations of gene drop was 0.28 with a standard deviation of 0.23. A difference of 0.75 genomes or more between fg in lambs and matings in G had a probability of occurrence of 0.03 in the 100 gene drop simulations. The highest difference observed between fg in lambs versus matings in the gene drop simulations was 1.13 genomes; the second highest difference was 0.80. The discrepancy between lambs and matings in the gene drop and relationship matrix calculations is not out of the range of probability, but the difference in the relationship matrix calculation seems high and may indicate that our pedigree resulted in a higher amount of diversity than other pedigrees with the same relationships.
The fg calculated using the relationship matrix in S and G for lambs is larger than that for matings, because more than one animal was produced in some matings, resulting in less genetic drift. The almost two-fold difference of lambs and(or) matings to final available breeding animals of G is due to the maintenance of sire lines and reduced culling. When all four values of fg in lambs and matings of S and G from gene drop analysis are compared, they are all similar, which is the goal for a genetic control line.
The amount of heterozygosity calculated by GD2, as a function of fg, quantifies the decrease from the founding population (Table 2.3 and 2.4). In S and G, lambs are predicted to retain 92.19% and 90.34% of the original heterozygosity in the founders, respectively. The difference in GD2 between final available breeding animals and lambs of S shows that there has been an estimated reduction of 1.3% heterozygosity from parents to offspring. The difference in the loss of heterozygosity between lambs and available breeding animals of G is larger (4.68%) than S, due to a smaller population.

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Table of Contents
Introduction
Chapter I. Literature Review
Defining Inbreeding
Methods of measuring inbreeding
Application of alternative measurements of inbreeding and relationship
Inbreeding effects in sheep
Growth traits
Birth weight
Weaning weight
Fitness traits
Fertility
Prolificacy
Lamb Survival
Wool traits
Twelve-month fleece weight
Other wool traits
Managing inbreeding
Maintaining genetic gains
Founder contributions
Purging and mixing of founder genomes
Summary
Chapter II. The effect of population structure on the rate and extent of diversity loss in a crossbred sheep flock
Abstract
Introduction
Material and Methods
S line
E line
G line
Pedigree analysis
Additional measures of genetic diversity
Results and Discussion
Measures of inbreeding and heterozygosity
Allelic diversity
Implications
Chapter III. Effects of inbreeding on performance
Abstract
Introduction
Materials and Methods
Animals, management, and experimental design
Statistical analysis
Results and Discussion
Birth weight
Weaning weight
120 d weight
Fall fertility
Lambing date
Survival
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