Journal of Heredity 2009:100(2):197–205
Advance Access publication November 4, 2008
Assessing Parent Numbers from
Offspring Genotypes: The Importance of
? The American Genetic Association. 2008. All rights reserved.
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KRISTINA M. SEFC AND STEPHAN KOBLMU¨LLER
From the Department of Zoology, University of Graz, Universita ¨tsplatz 2, 8010 Graz, Austria (Sefc); the Department of
Evolutionary Biology, Evolutionary Biology Centre, Uppsala University, Norbyva ¨gen 18D, SE-752 36 Uppsala, Sweden
Address correspondence to K. M. Sefc at the address above, or e-mail: firstname.lastname@example.org.
Methods to infer parent numbers from offspring genotypes either determine the minimum number of parents required to
explain alleles and multilocus genotypes detected in the offspring or use models to incorporate information on population
allele frequencies and allele segregation. Disparate results by different approaches suggest that one or perhaps all methods
are subject to bias. Here, we investigate the performance of minimum parent number estimates, maximum likelihood, and
Bayesian analyses (programs COLONY and PARENTAGE) with respect to marker information content in simulated data
sets without knowledge of parental genotypes. Offspring families of different sizes were assumed to share one parent and to
be sired by 1 or 5 additional parents. All methods committed large errors in terms of underestimation (minimum value) and
overestimation (COLONY), or both (PARENTAGE) of parent numbers, unless the data were highly informative, and their
relative performances depended on full-sib group sizes and sire numbers. Increasing the number of markers with low gene
diversity (He? 0.68) yielded only slow improvement of the results, but all 3 methods performed well with 5–7 markers of
He5 0.84. We emphasize the importance of high marker polymorphism for inferring parent numbers and individual parent
contributions, as well as for the detection of monogamous reproduction.
GERUD, monogamy, multiple mating, parentage, paternity
Studies of animal and plant mating systems, sperm and
pollen competition, parental investment in relation to ge-
netic parentage, pre- and postzygotic selection, the distri-
bution of reproductive success, and several other issues of
evolutionary and ethological interest depend on the de-
termination of the number and identity of reproducing
individuals (e.g., Bernasconi 2003; Uller and Olsson 2008).
Molecular methods contributed significantly to the field and
increased our knowledge far beyond the amount of infor-
mation that can, for example, be obtained from behavioral
observation of breeding animals and plant pollinators (e.g.,
Avise et al. 2002; Griffiths et al. 2002; Llaurens et al. 2008).
Accordingly, methods for the analysis of genetic data with
respect to relatedness and parentage inference have been de-
veloped and refined in recent years (e.g., Marshall et al.
1998; Neff et al. 2002; Wang 2004; Jones 2005; Jones et al.
2007). One of the many applications of genetic and allozyme
data to parentage studies is the reconstruction of the
number of parents from the genotypes of animal offspring
or plant seeds and seedlings. Assuming that all offspring in
a group have one of their parents in common, which is the
case for seeds collected from inflorescences and fruits as
well as for broods of animals in which one sex mates with
several individuals of the other sex, the data analysis consists
in first deducing the genotype of the shared parent (if it has
not been sampled) and then determining the number of
additional parents contributing alleles to the offspring
group. The power to exclude unrelated individuals from par-
entage and to discriminate different parents increases with
increasing levels of polymorphism of the genetic markers, as
it becomes more likely that different parents transmit dif-
ferent alleles to their respective offspring (Neff and Pitcher
2002). Such highly polymorphic markers are not always
readily available, and likelihood methods have been de-
veloped to account for the possibility of allele sharing be-
tween different parents using population allele frequencies
and Mendelian expectations for the ratios of alleles in full-
sib groups. With these algorithms, 2 offspring sharing fre-
quent alleles are not necessarily inferred to also share the
same parent (e.g., Meagher 1986; Emery et al. 2001; Smith
et al. 2001; Wang 2004; Hain and Neff 2007). Hence, the
minimum number of parents required to explain the geno-
types detected in the offspring is often smaller than the
maximum likelihood estimate of parent numbers (Campbell
1998; Ma ¨kinen et al. 2007; Portnoy et al. 2007; Sefc et al.
Highly disparate results obtained from the estimation of
parent numbers by parsimonious minimum sire number re-
constructions and maximum likelihood analyses of empirical
data (Sefc et al. 2008; Hermann C, Koblmu ¨ller S, Sefc KM,
unpublished data) and furthermore the failure to retrieve the
correct answers from simulated data with both methods,
when the markers were not sufficiently informative (Sefc
et al. 2008), prompted us to examine the performance of
different methods for paternity reconstruction in more
detail. In the present study, we investigate the effect of
marker information content (number of markers and their
diversity) on reconstructions of minimum parent number,
maximum likelihood, and Bayesian estimates (programs
COLONY and PARENTAGE) in simulated data sets
without knowledge of parental genotypes. We refer to the
simulated data as the genotypes of broods, in which off-
spring share a common mother and were sired by one or
several males, but the same type of data is encountered
when broods are sired by a single father and several mothers
or when plant inflorescences or fruits are tested for
pollination by multiple donors.
Materials and Methods
Parentage was reconstructed from 13 data sets consisting of
different numbers of loci (n 5 3, 5, 7, 9, and 11 loci) and
with 3 different levels of polymorphism per marker
(gene diversity He5 0.57, 0.68, and 0.84). The exclusion
probabilities achieved with each marker set (P1, when one
parent is known, and P0, when neither parent is known)
were calculated in GERUD vs 2.0 (Jones 2005) and are
given in Table 1. The number of alleles and allele
frequencies, which were used for the simulation of brood
genotypes and to represent the population from which
broods were sampled, were as follows: for He5 0.57, 5
alleles at frequencies of 0.54098, 0.36067, 0.06557, 0.02732,
and 0.00546; for He 5 0.68, 8 alleles at frequencies of
0.41919, 0.32576, 0.14393, 0.09091, 0.0101, 0.00505,
0.00253, and 0.00253; and for He 5 0.84, 12 alleles at
frequencies of 0.26053, 0.17105, 0.15789, 0.12368, 0.10526,
0.09737, 0.02895, 0.01842, 0.01316, 0.01053, 0.01053, and
0.00263; these are values that were observed at 3 micro-
satellite loci in a large natural population sample.
The simulation of broods assumed that all offspring
shared one parent and that 5 different individuals acted as
the second parent, for example, such as when a female
mated with 5 males, each of whom sired a proportion of the
clutch. Two brood sizes, n 5 80 and n 5 25, were simulated.
Paternity contributions were either evenly distributed among
the 5 sires, with each male siring 16 or 5 offspring in the
large and small broods, respectively, or had a skewed
distribution with the primary sire accounting for 40 (large
broods) or 13 (small broods) of the offspring and the
remaining 4 males each siring 10 (large broods) or 3 (small
broods) young. ‘‘Large’’ and ‘‘small’’ broods therefore con-
tain full-sib groups of different sizes, whereby larger full-sib
groups provide more information to reconstruct the geno-
types of their parents. Furthermore, monogamous broods
(1 mother and 1 father) with 25 and 80 offspring were
To generate brood genotypes, parental genotypes were
first assembled according to the population allele frequen-
cies. For example, for data consisting of 5 markers, each
with He5 0.68, 10 alleles (2 per locus) were randomly
drawn for each assumed parent from the above allele dis-
tribution of the marker with Heof 0.68. An offspring’s
genotype was then created by randomly drawing 1 allele per
locus from each of its parents. For each of the investigated
combinations of brood type and data set composition, 100
replicate broods were generated and analyzed.
Because all offspring in a brood shared their mother, the
reconstructed number of full-sib groups in a brood was
taken as estimate of the number of different sires con-
tributing to the brood. For each of the multiply sired
broods, we calculated maximum likelihood estimates of sire
(PARENTAGE estimates), and reconstructions of the
minimum number of sires required to explain offspring
genotypes (MIN estimates). For monogamous broods, only
COLONY and PARENTAGE estimates were calculated
than 1 anyway. As neither mutations nor typing errors were
included in the genotype simulations, sibship reconstruction
neither parent is known (P0)
Exclusion probabilities achieved by the marker sets used in brood simulations when one parent is known (P1) and when
# Loci He
3 Loci5 Loci7 Loci 9 Loci11 Loci
He, expected heterozygosity per locus; # loci, number of loci, each with the indicated He, making up the data set. n/a, not applicable.
Journal of Heredity 2009:100(2)
in the program COLONY vs 1.0 (Wang 2004) was carried out
with error rates set to zero.For maximum likelihood estimates
run as described in the manual, using the population allele
frequencies given above. To obtain MIN estimates, the
population allele frequencies were set to 0.001 for all alleles
the offspring) was given a high frequency in order to make
allele frequencies add up to 1. When alleles found in offspring
are assigned low population frequencies, it is more likely that
a shared allele represents shared paternity, and the maximum
likelihood estimate returns the minimally required number of
sire genotypes (Sefc et al. 2008). To confirm convergence
of the MIN method on the minimum sire number,
7 monogamous data sets were analyzed. The necessity to
employ this modification of COLONY, which has the
disadvantage that it may occasionally overestimate the
minimum value (see Results), was given by the need to
automate the large number of analyses. When analyses can be
run individually and no more than 6 sires contributed to the
brood, minimum sire numbers are better calculated by
the program GERUD (Jones 2005), which tests increasing
numbers of sires for compliance with the offspring genotypes
and is therefore guaranteed to arrive at the true minimum.
The Bayesian parentage reconstruction implemented in
PARENTAGE (Emery et al. 2001) evaluates probability
distributions of parent numbers and their relative contribu-
tions conditional on observed offspring genotypes and
population allele frequencies and prior assumptions. Be-
cause of long computation times (exceeding 2 h per run with
the more informative data sets), not all the generated data
sets, and only 50 replicates of each, were analyzed with
PARENTAGE. The analyzed data sets were as follows:
both large and small multiply sired broods with skewed
paternity distributions, as well as large monogamous broods,
with data for 3, 5, and 7 loci at Heof 0.57, 0.68, and 0.84
and small monogamous broods with data for 3 and 5 loci at
Heof 0.57, 0.68, and 0.84. To improve the mixing properties
of the Markov Chain, a low probability of more than 1
mother was set by using a prior distribution with a mean of
1 and a standard deviation of 0.1 (Emery et al. 2001;
PARENTAGE manual). The prior range of possible fathers
was set to 1–15. In previous studies, results were shown to
be robust to changes in priors for father number and
paternity share (Bretman and Tregenza 2005; Beveridge
et al. 2006). The simulated data contain no genotyping
errors and mutations, but because the program does not
allow a mutation rate of zero, the prior for the mutation rate
was set to the low value of 10?10. The here chosen Markov
Chain settings of 5000 iterations with a burn-in of 5000
iterations and a thinning interval of 400 are commonly
employed by users of the program (e.g., Bretman and
Tregenza 2005; Beveridge et al. 2006; Simmons et al. 2007;
Frentiu and Chenoweth 2008).
Scripts to generate brood genotypes and COLONY and
PARENTAGE input files, run the programs, and parse the
output files were written in PERL programming language.
Errors in sire number estimates by the MIN and COLONY
analyses were in most cases due to under- and over-
PARENTAGE estimates deviated from the true value in
both directions (Figures 1 and 3; Supplementary Figure).
The allocation of the correct number of offspring to each
contributing sire is even more difficult than the estimation
of the number of sires involved in a brood. The percentage
of analyses, in which the proportions of paternal contribu-
tions to the broods were correctly reconstructed, was con-
siderably lower than the percentage of analyses with accurate
estimates of sire number, except with the most powerful
marker set (Figure 1; Supplementary Figure).
In a small number of analyses (0.8%), the MIN estimator
overestimated the true value by 1 (and once by 2) sire.
Apparently, the frequency of 0.001 assigned to each ob-
served allele, albeit very low, did not force the likelihood
algorithm to minimize the sire number estimate in all cases.
Hence, even when our MIN estimate was equal to or smaller
than the true sire number, the minimally necessary number
of sires to explain all offspring genotypes may be still
smaller, such that our analyses may underrate the degree to
which the ‘‘accurate’’ minimum numbers would underesti-
mate the true number of sires. However, 2 lines of evidence
indicate that the MIN analyses in COLONY will in most
cases arrive at the accurate minimum sire numbers. In a
previous study, the MIN estimates obtained from the modi-
fied COLONY input were identical to minimum sire
number reconstructions in GERUD (Sefc et al. 2008).
Moreover, in the present study, several data sets of
monogamous broods were analyzed with the MIN method
in COLONY in order to confirm that the method indeed
returned the minimally possible sire number (known to be 1
in monogamous broods). Seven data sets, in which the
maximum likelihood estimate of COLONY overestimated
sire number, were chosen for this check, and the MIN
method correctly estimated a single sire in all replicates
(large broods with data from 3 and 5 loci and Heof 0.57 and
0.68, and 3 loci with Heof 0.84). Although we do not
advocate our modification of the COLONY program to
obtain MIN estimates in cases, where it is possible to use the
program GERUD, one potential advantage of the MIN sire
number reconstruction in COLONY compared with
GERUD lies in the ability of the COLONY model to
account for genotyping errors and mutations in empirical
data sets, which could cause spurious assumptions of
additional sires by GERUD analyses.
thetrue value, whereas
Paternity Reconstruction from Large Full-Sib Groups
In large broods, the distribution of paternity among sires
had little effect on the outcome of paternity reconstruction
with the MIN and COLONY methods, and success rates
were similar in broods with a primary sire and in broods with
equally contributing sires (Figure 1A–C and Supplementary
Sefc and Koblmu ¨ller?Assessing Parent Numbers from Offspring Genotypes
Figure). Apparently, there was little difference in the amount
of information available for paternity reconstruction
between 16 offspring per sire in the even broods and 10
offspring per secondary sire in the skewed broods.
PARENTAGE analyses were conducted on skewed broods
Markers with low polymorphism (He5 0.57) performed
poorly in paternity reconstruction with all 3 methods even
when a high number (n 5 7–11) of such markers was used
(Figures 1A–C and 2A). Unexpectedly, the rate of correct
paternity inference by COLONY decreased, when the
number of markers was increased from 3 to 5 and 7. Only
sets of 9 and 11 markers yielded better COLONY results
than a set of 3 markers, but the proportion of analyses with
correctly inferred paternity remained low, and deviations of
sire number estimates from true values remained high
(Figures 1B and 2A). The proportion of correct sire number
estimates was higher in the PARENTAGE program but still
remained below 50% with up to 7 markers (Figure 1C). Due
to the long computation times, data sets with more than
7 loci were not analyzed with PARENTAGE. The average
deviations between PARENTAGE estimates and true
sire numbers were lower than with the other 2 methods
With moderately polymorphic markers (He5 0.68), at
least 9 markers were required for the MIN method and 11
for the COLONY method to identify the true sire number
in .80% of replicates and minimize the deviation of the
areas represent the percentage of replicate broods, for which minimum (MIN), maximum likelihood (COLONY), and Bayesian
(PARENTAGE) analyses returned the sire numbers given on the y axis. The horizontal line marks the correct estimate of 5 sires,
and bubbles representing the proportions of correct estimates are shaded gray and black. Gray areas indicate the portion of
analyses yielding correct sire numbers but erring in the number of offspring contributed by each sire; black areas correspond to the
proportion of analyses, in which both sire number and contributions were correctly inferred. Marker sets consisted of 3–11 loci
with gene diversities (He) of 0.57 and 0.68 and 3–7 loci with He5 0.84. (A–C) MIN, COLONY, and PARENTAGE analyses of
80 offspring, where the primary father sired 40 young and each of the additional 4 fathers sired 10 young. (D–F) MIN, COLONY,
and PARENTAGE analyses of 25 offspring, where the primary father sired 13 young and each of the additional 4 fathers sired 3
Sire number estimation from simulated brood genotypes with skewed distribution of paternal contributions. Bubble
Journal of Heredity 2009:100(2)
incorrect estimates (Figures 1A–B and 2A). The PARENT-
AGE estimates based on 3, 5, and 7 loci were correct in 40,
28, and 52% of the replicates, respectively, with only modest
improvement of estimates with increasing marker numbers
(Figures 1C and 2A). Although not optimal, the PARENT-
AGE method performed better with small data sets (3–7
markers) than the other 2 methods in terms of the pro-
portion of correct estimates of sire number and paternal con-
tribution and of the average deviation from the true sire
number. Interestingly, fewer markers with Heof 0.57 and
0.68 caused PARENTAGE to underestimate sire numbers,
whereas overestimation was more frequent with data sets
containing more markers.
With highly polymorphic markers (He5 0.84), a set of
3 markers was sufficiently informative to infer sire number
in .80% of the replicates by the MIN method, whereas 5–7
markers were needed to achieve the same success rate with
the COLONY and PARENTAGE methods (Figure 1A–C).
With the most informative marker set (7 loci with He5
0.84), both sire number and individual paternal contribution
were estimated correctly in at least 95% of the replicates by
MIN and COLONY analyses and in .80% of the replicates
Except in the analyses with the most powerful marker
sets, the COLONY method overestimated sire numbers by
up to 100%, whereas the deviations of sire number
estimates from the true value were lower with the MIN
and PARENTAGE methods (Figures 1A–C and 2A). When
interested in mating frequencies (e.g., Song et al. 2007), it
may in fact be more important to minimize the total
deviation across analyses than to maximize the rate at which
the true values are recovered at the cost of large errors for
some broods. In this case, the MIN method and the
PARENTAGE model may be appropriate choices for
analyses of large broods and moderately polymorphic
were averaged across the 100 replicates analyzed for each brood type and marker set with the MIN and the COLONY methods
and the 50 replicates analyzed with PARENTAGE. (A) Broods of 80 offspring sired by a primary father (40 offspring) and 4
additional sires (10 offspring each). (B) Broods of 25 offspring sired by a primary father (13 offspring) and 4 additional sires (3
offspring each). (E) Monogamous broods with 80 offspring. (F) Monogamous broods with 25 offspring.
Average deviations between true sire numbers and numbers estimated from simulated brood genotypes. Deviations
Sefc and Koblmu ¨ller?Assessing Parent Numbers from Offspring Genotypes
Paternity Reconstruction from Small Full-Sib Groups
Given that the amount of information available for paternity
reconstruction increases with increasing numbers of off-
spring per sire, one would expect to obtain better results
from the large broods, where each of the males sired at least
10 offspring, than in the small broods, where some sires are
represented by only 3 offspring. Indeed, the MIN method
produced fewer correct inferences of sire numbers and
contributions and greater deviations of sire number esti-
mates from the true value in the small broods than in the
large broods (Figures 1A,D and 2A,B). MIN analyses with
3–11 markers of He5 0.57 completely failed to reconstruct
the correct sire number, and accurate inference of sire
number in .80% of the replicates required 5–7 markers of
He 5 0.84. Similar results were obtained with the
PARENTAGE program, which produced fewer correct
estimates from small broods except when highly informative
data sets were used (Figure 1F). Although the rates of cor-
rect sire number estimates by PARENTAGE were
comparable to those achieved by the MIN method, none
of the PARENTAGE runs returned correct estimates of
individual paternal contributions (Figure 1F).
The COLONY method generally performed better in
the small broods than it did in the large broods in terms of
the deviations between sire number estimates and true
values (Figure 2B), although not always in terms of the
proportion of correct sire number inferences (Figure 1B,E).
In particular, accurate COLONY sire number estimates
based on the less informative marker sets were obtained
more frequently in the small than in the large broods,
whereas the rates of accurate estimates based on highly
informative marker sets were generally lower in the small
than in the large broods, the latter conforming to expect-
ations on the effect of brood sample size (Wang 2007).
Moreover, the proportions of correct estimates based on the
less informative marker sets were considerably higher, and
deviations from true values were lower, by the COLONY
than by the PARENTAGE and the MIN methods (Figures
1D–F and 2B). Nonetheless, only the most informative
marker set recovered the correct sire number in .80% of
the replicates (Figure 1E).
Both the MIN and the COLONY methods performed
somewhat worse in small broods with skewed sire con-
tributions, in which secondary sires were represented by only
3 offspring each (Figure 1D–E), than in those broods, to
which each of the sires contributed 5 offspring (Supplemen-
tary Figure). A negative effect of reproductive skew on
paternity reconstruction was also observed in other simula-
tion studies (Neff et al. 2002; Myers and Zamudio 2004).
Only skewed broods were analyzed with PARENTAGE.
An accurate reconstruction of the minimum number of sires
required to explain genotypes of ‘‘monogamous broods’’
(i.e., broods sired by a single male and a single female) will
always arrive at the correct sire number of n 5 1, but unless
the exclusion probability of the marker set is very high, this
does not prove monogamy. In fact, in the simulated broods
with 5 sires, a small proportion of the MIN and
PARENTAGE results were consistent with monogamy
(Figure 1A,D,F). The risk of falsely inferring monogamy
from multiply sired broods by the MIN method is closely
related to the exclusion probability of the data and can be
assessed, for example, in the program GERUDSIM (Jones
2005), by simulating and analyzing user-defined broods and
Vice versa, monogamous broods may be erroneously
assigned multiple parents by maximum likelihood and
Bayesian models. Indeed, as in the above COLONY
analyses of multiply sired broods, sire number was greatly
overestimated in monogamous broods unless highly in-
formative marker sets were used, especially when the broods
were large (Figures 3A,C and 2C,D). At least 9 markers of
He5 0.68, or 5 markers of He5 0.84, were required for
COLONY to detect monogamy in .80% of the replicates
in both large and small broods.
In contrast, monogamy of broods was correctly inferred
by PARENTAGE in .80% of replicates with all tested data
sets (Figure 3B,D). Although this result is highly desirable, it
may be linked to the propensity of PARENTAGE to
underestimate sire numbers from small data sets (see above),
which makes results converge on a single sire, rather than
represent superior capability of sire number reconstruction.
Most importantly, our analyses suggest that paternity
inference from brood genotypes requires highly informative
marker sets and that low levels of marker polymorphism
cannot be easily compensated for by increasing the number
of such markers. Moreover, even sophisticated methods
including allele segregation and population allele frequency
information into the estimation of sire number were unable
to arrive at correct solutions when the markers were not
sufficiently informative. Hence, it will in many circum-
stances prove more efficient to invest in the development of
highly polymorphic markers than to sufficiently increase the
number of markers with little or moderate diversity. These
findings may be of particular importance for parentage
studies in plants, where allozyme markers have long
remained the predominant tool (Bernasconi 2003) and have
only recently been superseded by the employment of highly
polymorphic microsatellite markers (Reusch 2000; Teixera
and Bernasconi 2007; Llaurens et al. 2008). However, even
with microsatellites, genetic diversity values above 0.8
(required to obtain correct results in our analyses of 5 and
more loci) may, at least in some species or populations, not
be encountered at many loci. In fact, only few microsatellite-
based paternity studies employ either highly polymorphic
markers (e.g., Adams et al. 2005; Mackiewicz et al. 2005;
Portnoy et al. 2007; Teixera and Bernasconi 2007; Wilson
and Martin-Smith 2007) or more than 7 loci (e.g., Reusch
2000; Myers and Zamudio 2004; Beveridge et al. 2006;
Journal of Heredity 2009:100(2)
Herbinger et al. 2006), whereas the majority of studies are
being conducted with only 3–5 markers of oftentimes
moderate diversity. Investigators should bear in mind that,
without more informative data, estimates of parent numbers
and relative paternal contributions may be approximate
(Sefc et al. 2008).
It is also noteworthy that marker sets with higher
exclusion probabilities did not necessarily produce better
sire number estimates, depending on analysis method and
family structure. For example, although exclusion probabil-
ities increased rapidly between 3 and 7 markers of He5 0.57
(Table 1), COLONY inferences of sire numbers deterio-
rated (Figure 2). Furthermore, a set of 3 markers with He5
0.84 had lower exclusion probabilities than 7 markers with
He 5 0.64 (Table 1) but yielded more accurate MIN
estimates, particularly for small broods (Figures 1 and 2).
The positive correlation between brood size and
corresponding COLONY estimates of sire number is an
artifact of the analysis method but could be mistaken, in
a methodological context, for a failure to detect all
contributing sires in small brood samples (Hain and Neff
2007), or, in a biological context, for an indication of
increasing offspring numbers with increasing numbers of
mates (Bateman 1948; Neff et al. 2008). Generally, both the
overestimation of sire numbers and the failure to detect the
full number of extra sires may compromise conclusions on
the extent of polygamous mating, sneaking rates, and other
alternative reproductive behaviors (e.g., Chapman et al.
2004). In particular, when methods biased toward sire
number underestimation (e.g., the MIN and PARENTAGE
methods) are applied to moderately informative data sets,
inferences of monogamy could also be obtained from
broods with more than a single sire.
Our results prompt no general recommendation of one
of the methods over the others because their performances,
relative to each other, depended on brood size, the true
number of sires, and the distribution of paternal contribu-
tions between sires. Overall, the 3 methods fared poorly
with fewer, and less polymorphic, markers and estimated
sire numbers similarly well when the markers were highly
informative. The COLONY method performed best in
reconstructing the individual contributions of the inferred
sires (Figure 1; Supplementary Figure). Importantly, useful
information can be drawn from comparisons between esti-
mates of the different methods, as disparate results indicate
that there may be insufficient information for accurate
paternity reconstruction. In these cases, the true sire number
will probably lie within the range of the different estimates
(see also Sefc et al. 2008). In contrast, congruency between
estimates from methods biased in opposite directions
provides strong support for the obtained estimate.
Another maximum likelihood parentage reconstruction
(Herbinger 2005), yielded similar results as COLONY from
empirical data (Herbinger et al. 2006; Sefc et al. 2008) and
displayed similar biases in paternity reconstruction from
which maximum likelihood (COLONY) and Bayesian (PARENTAGE) analyses returned the sire numbers given on the y axis.
Black bubbles represent correct estimates, that is, a single sire (also marked by the horizontal line). (A) COLONY and (B)
PARENTAGE analyses of 80 offspring. (C) COLONY and (D) PARENTAGE analyses of 25 offspring.
Sire number estimation from monogamous broods. Bubble areas represent the percentage of replicate broods, for
Sefc and Koblmu ¨ller?Assessing Parent Numbers from Offspring Genotypes
simulated data (Sefc et al. 2008). The tendency of the
PEDIGREE algorithm to split large full-sib groups into
subgroups, which causes a positive correlation between
brood size and inferred sire number, can be compensated by
analysis of parameter settings penalizing group splitting
(Herbinger et al. 2006), such that the minimum number of
sires can be approached with higher penalties, which then
entails the risk of underestimating the true value. The set-
tings required to arrive at the true number of sires vary with
the composition of the broods (Sefc et al. 2008), which
makes the choice of the settings a critical step of the
Jones et al. (2007) compared parentage inference in
COLONY, PARENTAGE, and NEST (their own Bayesian
model, which assigns reproductive success to different
categories of candidate parent individuals based on off-
spring and candidate parent genotypes), and reconstructions
of the minimum numbers of parents per nest, in an
investigation of the reproductive success of different
categories of candidate parents. Their data comprised 23
nests, each represented by 48 offspring genotyped at 5 loci
with Hevalues between 0.57 and 0.88 (mean He5 0.74,
P05 0.92, P15 0.99; Fiumera et al. 2002). On average,
COLONY estimated twice as many mothers per nest as the
other 3 methods. Although the true number of parents per
nest was unknown, it was concluded that COLONY over-
estimated parent numbers. This agrees with our findings for
this level of marker polymorphism. Likewise, the congru-
ency between the minimum parent number and the
PARENTAGE reconstructions (Jones et al. 2007) is con-
sistent with our observation that MIN and PARENTAGE
methods perform similarly well and display a comparable
bias in small broods. Based on NEST analyses of simulated
data and weighing the effort and benefits associated with
increased sampling of loci, different nests, or offspring per
nest, Jones et al. (2007) propose to analyze no more than 3
or 4 loci in order to offset the costs associated with the
genotyping of many broods. Although this number of
markers may indeed be sufficient to reconstruct parentage
when candidate parents are included in the data set, our
analysis indicates that sire number reconstruction without
parental information requires more, or more polymorphic,
loci. Furthermore, although none of the methods tested in
our study was able to reconstruct sire numbers from
moderately and little informative data sets, the employment
of different methods appears to be a useful way to assess the
reliability of the obtained results.
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Received May 20, 2008; Revised September 24, 2008;
Accepted October 2, 2008
Corresponding Editor: Howard Ross
Sefc and Koblmu ¨ller?Assessing Parent Numbers from Offspring Genotypes