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    Relatedness determination in the absence of pedigree

    information in three cultured strains of rainbow

    trout (Oncorhynchus mykiss)

    Gavin J. McDonald1

    , Roy G. Danzmann, Moira M. Ferguson*Department of Zoology, University of Guelph, Axelrod Building, Guelph, Ontario, Canada N1G 2W1

    Received 15 April 2003; received in revised form 15 April 2003; accepted 6 August 2003

    Abstract

    We evaluate the utility of a relatedness estimator (r) as a tool for inbreeding avoidance in three

    aquaculture strains of rainbow trout (Oncorhynchus mykiss) that show different amounts of genetic

    variation. The predicted distributions ofrvalues for unrelated, half-sib and full-sib individuals basedon population allele frequencies at 1113 microsatellite loci were compared to those obtained from

    the genotypes of known parents. In two of the three strains, the r distributions derived from

    simulated progeny of known parents were significantly lower than those predicted using pairs of

    individuals created from strain-specific allele frequencies. This was most pronounced for the strain

    with the lowest average number of alleles per locus and derived from a very limited number of

    founders. The net result of these left shifts in the distributions is an underestimation of relatedness. In

    contrast, the third strain showed a more modest but significant right shift for the curves derived from

    the simulated progeny. The result of the right shift would be a reduction in the amount of related

    pairs assigned as unrelated for a given value ofr. Thus, the probability of assigning related pairs as

    unrelated will increase markedly in aquaculture populations with histories of inbreeding and genetic

    bottlenecks.D 2004 Published by Elsevier B.V.

    Keywords: Oncorhynchus mykiss; Relatedness estimation; Inbreeding; Breeding programmes

    0044-8486/$ - see front matterD 2004 Published by Elsevier B.V.

    doi:10.1016/j.aquaculture.2003.08.003

    * Corresponding author. Tel.: +1-519-824-4120x52726; fax: +1-519-767-1656.

    E-mail address:[email protected] (M.M. Ferguson).1 Present address: Center for Genome Research, Whitehead Institute/MIT, One Kendall Square, Bldg. 300,

    Cambridge, MA 02139, USA.

    www.elsevier.com/locate/aqua-online

    Aquaculture 233 (2004) 6578

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    1. Introduction

    Inbreeding, or mating amongst relatives can result in a reduction in the mean

    phenotypic value of fitness traits such as reproductive capacity and physiologicalefficiency (Falconer and MacKay, 1996). This phenomenon, known as inbreeding

    depression, is a particular concern in captive populations of fishes where reduced rates

    of growth and survival can occur (Su et al., 1996; Pante et al., 2001a). The risk of

    inbreeding is particularly high in aquaculture since, given the high fecundity of most

    cultured species, it is possible that the offspring of a single mating could account for an

    entire generation. However, recent work with rainbow trout (Oncorhynchus mykiss)

    suggests that inbreeding depression can be minimized by maintaining a moderate effective

    population size per generation, and by careful attention to the choice of individuals

    selected as broodstock(Pante et al., 2001a,b).

    In order to minimize the deleterious effects of inbreeding, knowledge of parentage

    might be used to ensure matings among unrelated individuals (Norris et al., 2000).

    Unfortunately, physical tagging is not possible with young fish, and rearing families in

    separate tanks requires a complex infrastructure that may not be available at all facilities.

    Furthermore, if families are reared separately, environmental effects can influence the

    estimation of genetic performance of families, thus reducing the efficiency of selection and

    inflating heritability estimates(Harris et al., 1991).An alternative approach, allowing both

    common rearing and the avoidance of inbreeding, is to pool progeny from multiple

    families at an early age and then subsequently assign parentage by use of molecular

    genetic markers(Herbinger et al., 1995; OReilly et al., 1998).Several studies have demonstrated the ability to determine parentage in pooled lots

    of fish using molecular markers (in particular microsatellites). Many of these have

    been able to assign greater than 90% of progeny to a single parental couple using

    between 4 and 12 microsatellite loci (e.g. Estoup et al., 1998; OReilly et al., 1998).

    The number of marker loci required is dependent on several factors including the

    number of parents, the mating design, and the variability of the markers themselves

    (Bernatchez and Duchesne, 2000). The most straightforward method of pedigree

    analysis requires that all potential parents be identified and genotyped in order to

    assign progeny back to their family groups. However, this may not always be

    possible. For example, during the initial phase of a strain development project theremay be no knowledge of contributing parents. Methodologies for the reconstruction of

    sibships in the absence of parental information could be applied in such situations.

    These include Bayesian approaches (Painter, 1997) and Markov chain Monte Carlo

    algorithms for partitioning individuals into sibling groups (Thomas and Hill, 2000;

    Smith et al., 2001). Alternatively, a log-likelihood procedure to test for a sibling

    relationship between two individuals could be done (Goodnight and Queller, 1999).

    Another and more computationally simple approach is to estimate the coefficient of

    relatedness among pairs of potential breeders. The coefficient of relatedness (r) is the

    fraction of alleles in the genome of two related individuals that are identical by descent.

    Several estimators for relatedness among groups and between pairs of individuals havebeen developed (e.g. Queller and Goodnight, 1989; Lynch and Ritland, 1999; Caballero

    and Toro, 2000). In an aquaculture setting, the potential utility of relatedness estimation

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    has been demonstrated for Atlantic salmon (Salmo salar)(Norris et al., 2000).Norris et al.

    (2000) calculated allele frequencies from 200 fish sampled across multiple year classes,

    and used these to estimate relatedness among pairs of individuals of known relationship

    using the relatedness statistic of Queller and Goodnight (1989). The mean values ofestimated relatedness based on many pairs of fish agreed with expectations (i.e. rof full

    sibs = 0.5). This suggests that unrelated pairs might be identified, based on their lower

    estimated relatedness, and thus inbreeding could be minimized.

    Although the above approach appears promising in the particular strain and situation

    studied byNorris et al. (2000),its applicability on a broader scale is unknown. Different

    histories of selection, population size and inbreeding have led to marked differences in the

    amount of background relatedness and genetic variation within aquaculture strains of

    rainbow trout (O. mykiss) (Ferguson and Danzmann, 1998). High levels of background

    relatedness in a population will introduce considerable bias to the estimation of relatedness

    (e.g.Kays et al., 2000). This problem will be exacerbated by the large sampling variances

    that arise from the properties of the restimators themselves(Van de Casteele et al., 2001)

    making it even more challenging to assign pairs to specific relatedness classes.

    The goal of this study is to evaluate the utility of relatedness analysis as a tool for

    inbreeding avoidance in three aquaculture strains of rainbow trout that show different

    amounts of genetic variation and population history. We compare the predicted distribu-

    tions of relatedness for unrelated, half-sib and full-sib individuals based on population

    allele frequencies to those obtained from the genotypes of known parents. In two of the

    three strains tested, we show that the rvalues in progeny of known parents were lower

    than those predicted using pairs of individuals created from strain allele frequencies. Thiseffect was most pronounced in the strain with the lowest amount of genetic variation and a

    history of inbreeding. Thus, the probability of assigning related pairs as unrelated may

    increase markedly in aquaculture populations with histories of inbreeding and genetic

    bottlenecks.

    2. Materials and methods

    2.1. Aquaculture strains

    Adult rainbow trout from each of three aquaculture strains were sampled between

    August 1995 and March 1996. Twenty-four females and 24 males were sampled from each

    strain. The fish used in the present study were received as embryos in 1991 and grown to

    maturity at the Alma Aquaculture Research Station, Alma, Ontario (McKay and

    McMillan, 1997). Two of the strains were acquired from Ontario farms (Blue Springs,

    Hanover, and Aqua Cage Fisheries, Hillsburgh) while the third was from a farm in

    Washington State (Beiteys Resort). Both Blue Springs (O) and Beiteys Resort (B) fish

    were derived from production lots. Those obtained from Aqua Cage Fisheries (G) were a

    recently domesticated strain from the Ganaraska River that had been donated by the Ontario

    Ministry of Natural Resources and were used by Aqua Cage solely for Research.Strain O has undergone many generations of selection for faster growth and has

    reduced genetic variation at microsatellite loci and in mtDNA haplotype frequencies

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    compared to strains B and G (Ferguson and Danzmann, 1998; presentstudy). Strain G has

    been subjected to selection for only two generations(Quinton, 2001),while the selection

    history for Strain B is unknown.

    2.2. Molecular protocols

    DNA was isolated from liver using a phenol chloroform extraction technique(Bardakci

    and Skibinski, 1994). Genotypes at 10 microsatellite loci were determined with two

    multiplexed PCR reactions (Fishback et al., 1999). PCR products were visualized on a

    Perkin-Elmer/Applied Biosystems (PE/ABI) ABI 377 DNA sequencer. Alleles were

    scored using the GENESCANk 2.0.0 and GENOTYPERk 1.1r8 software packages.

    Two loci (Omy207UoG, Omy301UoG) used by Fishback et al. (1999) were not used

    because of overlapping allele size ranges with other loci or inconsistent amplification.

    Several loci were discarded from the analysis of a particular strain if they had null alleles

    based on a pedigree analysis with the progeny of the fish used here (Table 1). An

    additional four loci (OmyFGT12TUF, OmyRGT41TUF, Ssa85DU and Ssa289DU) were

    analyzed using single locus PCR reactions of 11 Al. The reaction cocktail was composed of

    100 ng DNA, 0.91 (Ssa289DU) or 0.091 (remaining three loci) PCR buffer, 5 nmolof MgCl2, 0.25 U Taq DNA polymerase, 1.5 nmol of each dNTP, 1 Ag BSA and 5 pmol of

    both forward and reverse primers. Six nanomoles of [TAMRA]dCTP was added to the

    reactions ofOmyRGT41TUF,Ssa85DUand Ssa289DU.OmyFGT12TUFwas end-labeled

    with Hex fluorescent dye and therefore did not require the addition of [TAMRA]dCTP.

    The DNA was amplified with the following thermal profiles. The PCR conditions forSsa85DUand Ssa289DUwere an initial denaturation step at 95 jC for 3 min, followed by

    36 cycles of 95 jC for 30 s, annealing at 52 jC (Ssa85DU) or 46 jC (Ssa289DU) for 1

    min and extension at 72 jC for 1 min or 3 min for the final cycle. A touchdown profile of

    95 jC for 3 min, 5 cycles of 95 jC for 30 s, 60 jC ( 1 jC per cycle) for 1 min and 72 jCfor 1 min was used forOmyFGT12TUFPCR. This was followed by 28 cycles of 95 jC for

    30 s, 54 jC for 1 min and 72 jC for 1 min. The program was concluded with a prolonged

    extension at 72 jC for 20 min.OmyRGT41TUFwas amplified using an identical profile to

    that previous except the initial 5 cycles began at an annealing temperature of 64 jC and

    were followed by 28 cycles using an annealing temperature of 58 jC.

    Formamide (without zylene cyanol) was added to each reaction mixture at a volume of5 Al, and 2 Al of this mixture was loaded in a 6% polyacrylamide-7 M urea gel. Following

    1 1/2 h at 1500 V, the gel was scanned using an FMBIORII fluorescent imaging system

    (Hitachi Genetic Systems). The resulting gel image was analyzed using the FMBIOR II

    software. Allele bp size was determined using 350-Tamra lane standard.

    2.3. Data analysis

    Allele frequencies, expected and observed heterozygosities and conformity of

    genotype frequencies to Hardy Weinberg expectations at each locus were calculated

    for each strain using GENEPOP (Version 3.1b) (Raymond and Rousset, 1995). Exactp values were calculated using either complete enumeration (loci with four or fewer

    alleles) or a Markov Chain method. Probability thresholds for the Hardy Weinberg

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    Table 1

    The identity of the microsatellite loci used for allele frequency calculations in three strains of rainbow trout

    Locus Reference Strain

    B G

    # alleles He/Ho P # alleles He/Ho P

    Omy27DU Hologene 6 0.66/0.54 0.263 4 0.65/0.63 0.063

    Omy77DU Morris et al. (1996) 9 0.84/0.81 0.351 9 0.83/0.83 0.663

    Omy325UoG OConnell et al. (1997) N/Aa N/Aa

    OmyFGT5TUF Sakamoto et al. (1994) 5 0.52/0.56 0.713 6 0.71/0.71 0.779

    OmyFGT12TUF Sakamoto (1996) 17 0.91/0.90 0.465 11 0.88/0.85 0.270

    OmyFGT14TUF Sakamoto (1996) 4 0.64/0.44 0.011 4 0.23/0.21 0.358

    OmyFGT15TUF Sakamoto (1996) 5 0.56/0.54 0.856 5 0.33/0.33 0.178OmyFGT23TUF Sakamoto (1996) 10 0.88/0.88 0.831 N/Aa

    OmyRGT41TUF Sakamoto (1996) 8 0.82/0.83 0.551 10 0.81/0.79 0.573

    One18ASC Scribner et al. (1996) 5 0.75/0.75 0.798 6 0.71/0.79 0.528

    Ots1BML Banks et al. (2000) 11 0.87/0.92 0.314 5 0.72/0.81 0.233

    Ssa20.19UCG Sanchez et al. (1996) N/Aa N/Aa

    Ssa85DU OReilly et al. (1996) 12 0.85/0.85 0.320 6 0.72/0.77 0.516

    Ssa289DU McConnell et al. (1995) 7 0.76/0.79 0.299 7 0.84/0.90 0.684

    Mean 8.25 0.75/0.73 6.64 0.67/0.69

    The loci used for the relatedness calculations are indicated in addition to the number of alleles, expected heterozygosity with

    P value. Those loci not used for relatedness calculations in a particular strain are indicated with N/A along with the reasa

    Null alleles detected in this strain during a molecular pedigree analysis(McDonald, 2001).b Only two alleles detected at this locus.

    * Hardy Weinburg testPvalue < 0.05 after sequential Bonferonni correction (# of tests corrected for = 14 loci 3 strai

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    tests were adjusted by Bonferonni correction. Differences between the strains in the

    average number of alleles per locus and mean expected (He) and observed (Ho)

    heterozygosities were tested using ANOVA (loci as blocks). Loci with null alleles

    were not used in these tests.

    2.3.1. Predicted distributions of relatedness (population allele frequencies)

    The observed allele frequencies were used to generate 2500 pairs of individuals for

    each of three relatedness classes (full-sib, half-sib, unrelated) for each strain with a visual

    basic program (Blouin, unpublished). The program calculated relatedness for each of these

    pairs using the following equation of the relatedness coefficient (r) of Queller and

    Goodnight (1989):

    r

    Xx

    Xk

    Xl Py P*X

    x

    X

    k

    X

    l

    Px P*

    where x indexes individuals (two in pairwise comparisons), k indexes loci and l indexes

    allelic position.Pxis the frequency of an allele at allelic position l at locus k in individual

    x. Pyis the frequency of that allele in individual yand P* is the frequency of the allele in

    the population. This calculation is considered symmetric as both individuals are consid-

    ered as x and y (individual allele frequencies, corrected for their occurrence in the

    population, for each allelic position for each locus for each individual are summed in boththe numerator and the denominator prior to division) (Queller and Goodnight, 1989).Di-

    allelic loci cannot be used with this equation as the relatedness between a pair of

    heterozygotes will be undefined. This occurs because the denominator (and the numerator)

    will always sum to zero (Queller and Goodnight, 1989). As mentioned previously, loci

    were not used if they contained null alleles or were di-allelic (Table 1).

    The calculated values of r from the generated pairs were plotted to produce

    expected distributions for each relatedness class within each of the three strains (see

    Blouin et al., 1996 for details of the approach). Expected rates of error were

    determined for specific cut-off values of r as the proportion of related pairs whose

    r-value falls to the left of (less than) the cut-off (probability of assigning a related pairas unrelated). This was repeated for r values ranging from 0 to 0.3 for both thehalf- and full-sib distributions. This was chosen as a useful range for minimizing

    inbreeding because while the probability of inadvertently selecting a related pair will

    continue to decrease with lower values of r, few unrelated pairs will be available for

    selection. Conversely higher cut-off values, while allowing for more unrelated pairs to

    be available, will increase the error rate to unacceptable levels. In practice, this range

    could be adjusted to meet the needs of the breeder in obtaining enough breeding pairs

    while minimizing the inclusion of related pairs.

    2.3.2. Actual distributions of relatedness (progeny of known parents)A second set of distributions for pairs of progeny based on known parental

    genotypes was created for each of the three strains in order to determine how

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    accurate these distributions of r would be for the selection of unrelated couples. While

    actual progeny had been produced from the adult fish used here (McDonald, 2001),

    their numbers were too small to allow for the determination of distributions of r in the

    populations. This limitation was overcome as follows. For each strain, 12 males and12 females were randomly selected from the 48 individuals used to estimate allele

    frequencies. Two simulated progeny genotypes were produced for all possible male by

    female parent combinations within each strain PROBMAXG (Danzmann, 1997). This

    program uses entered parental genotypes to generate possible progeny genotypes

    according to Mendelian expectations. r was then calculated for all pairs of simulated

    progeny within each strain using the software package, RELATEDNESS (version 5.6)

    (Queller and Goodnight, 1989). The allele frequencies used in the calculations were

    the same as those used in the previous analysis and were based on 48 individuals in

    each strain. While the simulated progeny could be used to provide sufficient

    relatedness comparisons to produce r distributions for both unrelated and half-sib

    classes, not enough full-sib comparisons could be made. Thus, 10 additional progeny

    were generated for each full-sib family and r was calculated for all pairs of

    individuals within those families.

    In order to standardize the number of pairwise comparisons per distribution, rvalues

    for 2500 pairs were randomly selected from all those that were available for each

    relatedness class within each strain. The potential error rate of assigning related pairs as

    unrelated was again determined as the proportion of related pairs whose calculated rvalue

    falls to the left ofrvalues ranging from 0 to 0.3.

    3. Results

    The three strains differed significantly in the average number of alleles per locus

    (P= 0.0015) and marginally in average He (P= 0.057) (Table 1). No differences were

    detected for Ho (P>0.05). The degree of conformity of genotype proportions to Hardy

    Weinberg expectations also differed among strains. Strain O showed significant deviations

    from Hardy Weinberg proportions at eight loci while strains G and B showed no

    deviations after Bonferroni correction.

    Table 2

    Mean (standard deviation) forr distributions of different classes of relatedness in three strains of rainbow trout

    Strain Distribution Unrelated Half-sib Full-sib

    B Predicted 0.002 (0.148) 0.248 (0.155) 0.498 (0.148)

    Actual 0.046 (0.180) 0.277 (0.160) 0.526 (0.146)

    G Predicted 0.017 (0.172) 0.255 (0.172) 0.500 (0.170)

    Actual 0.012 (0.185) 0.218 (0.182) 0.451 (0.183)

    O Predicted 0.008 (0.180) 0.255 (0.181) 0.500 (0.167)

    Actual 0.017 (0.189) 0.154 (0.187) 0.347 (0.185)

    Predicted distributions were determined with randomly generated pairs of individuals based on allele frequencies.

    The actual distributions were generated from genotypes of known individuals in the strains. Each distribution is

    comprised of 2500 pairwise comparisons.

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    Fig. 1. (AC) Relatedness coefficient (r) distributions for three aquaculture strains of rainbow trout (B, G, O).

    Each plot shows rvalues for three different relatedness classes (xunrelated, nhalf-sib and .full-sib).

    Solid lines represent distributions obtained from actual population comparisons (between generated progeny of

    known parents) while dashed lines represent predicted distributions based on pairs of individuals randomly

    generated from population allele frequencies.

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    Fig. 2. (AC) The probability of assigning either full- (.) or half- (n) sib pairs as unrelated (type II error under

    null hypothesis that pair is unrelated) at or below differing values ofrfor each of the three strains of rainbow trout

    examined. Dashed lines indicate values based on the predicted distributions while solid lines represent the rates

    from distributions derived from the actual populations.

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    The predicted distributions ofr(those calculated by generating pairs of each relatedness

    class usingempirically determined allele frequencies) had means corresponding to those

    expected (Fig. 1; Table 2). Unrelated, half-sib and full-sib distributions showed mean

    values of approximately 0, 0.25 and 0.5, respectively, in all three strains. However, thestrains differed in the degree of overlap among the distributions of the three relatedness

    classes (i.e. in the standard deviations). For instance, Strain B showed the least degree of

    overlap (Fig. 1) and consequently the standard deviations for the distributions are the

    lowest(Table 2). Strains G and O showed similar standard deviations. Thus, the predicted

    error rate (probability of assigning a half-sibor full-sib pair as unrelated based onrvalues)

    is expected to be lowest in strain B (Fig. 2).

    The distributions of r produced by the simulated progeny from known parents

    within each of the three strains differed from those based on strain allele frequencies

    (predicted distributions). For strains O and G, the mean r values generated from

    known parents were significantly lower (Table 2) than those based on strain allele

    frequencies (Mann Whitney U; P< 0.0001 for both strains at all three levels of

    relatedness). This was characterized by a shifting to the left of all distributions

    compared to those predicted (Fig. 1). The most marked left shift was observed for the

    half- and full-sib distributions of strain O. These left shifts would increase the amount

    of error (assignment of related pairs as unrelated) for a given value of r over that

    predicted above (Fig. 2). Conversely, strain B showed a more modest but highly

    significant (MannWhitney U; P< 0.0001) right shift for the curves derived from the

    simulated progeny (Fig. 1; Table 2). The result of the right shift would be a reduction

    in the amount of related pairs assigned as unrelated for a given value of r.

    4. Discussion

    The application ofQueller and Goodnights (1989) relatedness statistic to the estima-

    tion of relatedness had varied success in the three strains of rainbow trout examined here.

    In two of the three strains (O and G), the rdistributions derived from potential progeny of

    known parents were lower than those predicted using pairs of individuals created from

    strain specific allele frequencies. This was most pronounced for strain O. The net result of

    these left shifts in the distributions is an underestimation of relatedness. An underestima-tion of relatedness for pairs of known pedigree has been observed in several studies using

    this technique (e.g.Altmann et al., 1996; de Ruiter and Geffen, 1998; Hansson et al., 2000;

    Kays et al., 2000) and has been attributed to a high degree of relatedness among the

    individuals used to estimate population allele frequencies.

    The existence of left shifts in the distributions ofrand the consequent underestimation

    of relatedness among pairs has implications to captive breeding programs of fishes. The

    selection of a cut-off value ofrfrom predicted distributions (based on pairs generated with

    allele frequencies) thought to represent an acceptable probability of assignment of related

    pairs as unrelated might result in higher error than anticipated. This can be visualized as a

    greater proportion of the rdistributions, produced from the real populations, falling to theleft of the cut-off than predicted. The inclusion of a greater number of related pairs would

    result in an increase in inbreeding.

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    The results reported here for three rainbow trout strains suggest that the accurate

    estimation of relatedness demonstrated by Norris et al. (2000) is not expected to be

    universal. The approach may be more suitable in strains with certain genetic attributes and

    breeding histories. For example, strains G and B appear to have been derived fromrelatively large numbers of males and females and have not experienced intense selection

    (McKay, personal communication). In contrast, strain O has undergone strong selection

    with associated reductions in genetic effective population size during its culture history.

    This strain has experienced inbreeding due to the use of a limited number of broodstock in

    each generation (e.g. one to four females). Moreover, the individuals used to estimate

    population allele frequencies arose from gametes produced by three females and an

    unknown number of males. The relatedness among individuals in strain O is expected to

    be high and can explain the severe bias and left shift in rdistributions observed here. Thus,

    strain O is not a good candidate for the estimation of relatedness among fish when

    pedigree information is lacking.

    Another factor that may have contributed to the bias observed in these strains is that the

    individuals used to estimate allele frequencies may be the product of spawnings conducted

    over a limited period of time (grandparents of the progeny examined here). Embryos

    produced at the same time tend to hatch within a day or so of each other and within all three

    strains synchronized hatching was observed (McKay, personal communication). It is

    possible that females spawning at a particular time tend to be more related to each other

    (Leary et al., 1989) than those spawning at different times due to the high heritability

    reported for the trait of spawning time(Su et al., 1999).If this is the case, the progeny which

    were used to estimate the allele frequencies would also be more related to each other.Distinct spawning sub-populations have been identified in aquaculture populations of

    rainbow trout using both microsatellites(Fishback et al., 2000)and mtDNA(Ferguson et

    al., 1993; Danzmann et al., 1994) and therefore sampling within a sub-group may not

    provide an accurate estimate of strain allele frequencies.

    Aside from contributing towards bias, the short period of spawning for females could

    further influence the success of this approach in selecting unrelated pairs. At any cut-off

    level of r, only a proportion of the expected distribution of all unrelated pairs in the

    population is available for breeding. Additionally, female rainbow trout have a very

    restricted ovulation period (less than a week) and may not be sexually mature when needed

    (based on their rvalues with available males) and thus the number of available pairs isfurther reduced. Therefore, the chosen cut-off may be dependant more on the provision of

    enough breeding pairs to produce another generation rather than an acceptable error rate,

    unless the population is very large.

    The particular relatedness estimator used in the present analysis has been criticized as

    being biased in that the estimated means of relatedness are not equal to the true value of

    relatedness of the pairs being tested(Van de Casteele et al., 2001).This observation should

    not affect the approach being investigated here. To be successful, the estimated distribu-

    tions based on individuals generated according to allele frequencies should be identical to

    the distributions produced from actual pairs within the population being investigated. As

    long as this is true, even if the distributions do not centre exactly around the true value ofrelatedness (e.g. 0.5 for full-sibs), it should not affect the accuracy of unrelated pair

    selection.

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    A comparison of the results reported here with that ofBlouin et al. (1996)andNorris et

    al. (2000)illustrates the effect of locus number and relative polymorphism on the potential

    success of such an analysis. While Blouin et al. (1996) reported mean heterozygosities

    similar to those of strain B, their reported standard deviations for relatedness distributionswere less (0.1140.122) than those observed for the predicted distributions in this study.

    This is due to their use of a greater number of loci in r calculations (resulting in more

    accurate pairwise values of rand thus a reduction in distribution width for relatedness

    classes). Norris et al. (2000) achieved similar standard deviations (0.130.16) to those

    observed for the predicted distributions of strain B, but only required eight loci to achieve

    this. This was due to a greater mean heterozygosity of those markers (0.85)(Norris et al.,

    1999). These studies coupled with the results reported here suggest that the most efficient

    approach for relatedness estimation is to choose fewer numbers of highly variable loci. It

    may be difficult to identify such loci in aquaculture strains that have experienced severe

    bottlenecks in their genetic histories as they will have substantially lower amounts of

    variation overall. Of course the application of this approach in these strains will be

    precluded anyway due to the high background relatedness that would result in inaccurate

    relatedness estimation.

    Acknowledgements

    This work was supported by funds from the Ontario Ministry of Agriculture, Food and

    Rural Affairs (Program 42-Aquaculture). We thank Alastair Wilson for commenting on the

    manuscript and Dr. Michael Blouin for providing software used in the data analysis.

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