Molecular Ecology (2011) 20, 67–79
doi: 10.1111/j.1365-294X.2010.04930.x
The imprecision of heterozygosity-fitness correlations
hinders the detection of inbreeding and inbreeding
depression in a threatened species
C A T H E R I N E E . G R U E B E R , J O N A T H A N M . W A T E R S and I A N G . J A M I E S O N
Department of Zoology, University of Otago, Dunedin 9054, New Zealand
Abstract
In nonpedigreed wild populations, inbreeding depression is often quantified through
the use of heterozygosity-fitness correlations (HFCs), based on molecular estimates of
relatedness. Although such correlations are typically interpreted as evidence of
inbreeding depression, by assuming that the marker heterozygosity is a proxy for
genome-wide heterozygosity, theory predicts that these relationships should be difficult
to detect. Until now, the vast majority of empirical research in this area has been
performed on generally outbred, nonbottlenecked populations, but differences in
population genetic processes may limit extrapolation of results to threatened populations. Here, we present an analysis of HFCs, and their implications for the interpretation
of inbreeding, in a free-ranging pedigreed population of a bottlenecked species: the
endangered takahe (Porphyrio hochstetteri). Pedigree-based inbreeding depression has
already been detected in this species. Using 23 microsatellite loci, we observed only weak
evidence of the expected relationship between multilocus heterozygosity and fitness at
individual life-history stages (such as survival to hatching and fledging), and parameter
estimates were imprecise (had high error). Furthermore, our molecular data set could not
accurately predict the inbreeding status of individuals (as ‘inbred’ or ‘outbred’,
determined from pedigrees), nor could we show that the observed HFCs were the result
of genome-wide identity disequilibrium. These results may be attributed to high
variance in heterozygosity within inbreeding classes. This study is an empirical example
from a free-ranging endangered species, suggesting that even relatively large numbers
(>20) of microsatellites may give poor precision for estimating individual genome-wide
heterozygosity. We argue that pedigree methods remain the most effective method of
quantifying inbreeding in wild populations, particularly those that have gone through
severe bottlenecks.
Keywords: bottlenecked populations, conservation, identity disequilibrium, microsatellites,
pedigree, Porphyrio hochstetteri
Received 15 July 2010; revision received 28 September 2010; accepted 7 October 2010
Introduction
The management of inbreeding has represented an
important component of captive breeding programmes
for many years, but presents a challenge for threatened
wild populations for which pedigree data remain difficult, if not impossible, to collect (Pemberton 2004; GrueCorrespondence: Ian G. Jamieson, Fax: 64 3 479 7584;
E-mail: [email protected]
! 2010 Blackwell Publishing Ltd
ber & Jamieson 2008). When robust pedigree data are
unavailable, the primary option for determining pairwise relatedness and individual inbreeding levels typically involves the use of molecular methods, with two
frequently used approaches. First, as related individuals
share alleles by definition, shared neutral marker alleles
identified in the laboratory are presumed to indicate
shared ancestry, and various metrics are available that
allow the interpretation of shared alleles as a scale for
the degree of relatedness (Blouin 2003). Second, as
68 C . E . G R U E B E R , J . M . W A T E R S and I . G . J A M I E S O N
inbreeding increases identity disequilibrium of loci
across the genome, it is expected that inbred individuals will be more homozygous overall than their outbred
counterparts, by a degree proportional to the severity of
the inbreeding (Frankham et al. 2002). Again, numerous
metrics have been proposed for quantifying multilocus
heterozygosity (MLH) (Aparicio et al. 2006; Coulon
2010).
In practice, however, the relationship between marker
homozygosity and the pedigree metric of individual
inbreeding coefficient (f) is often weak, especially in
large populations where inbreeding is generally rare
(Balloux et al. 2004; Pemberton 2004; Slate et al. 2004;
Szulkin et al. 2010). Nevertheless, the scientific literature
contains many examples of studies that have attempted
to quantify inbreeding depression in nonpedigreed populations by examining the relationship between MLH
and various measures of evolutionary fitness (reviewed
in Grueber et al. 2008b; Chapman et al. 2009). Such analyses are generally termed ‘heterozygosity-fitness correlations’ (HFCs). In reality, though, even when statistically
significant, the vast majority of reported HFCs are weak
(Chapman et al. 2009), and whether HFCs truly reflect
underlying patterns of inbreeding depression has been a
subject of much debate in recent years (David 1998;
Hansson & Westerberg 2002; Pemberton 2004; Slate
et al. 2004; DeWoody & DeWoody 2005; Aparicio et al.
2007; Hansson & Westerberg 2008; Chapman et al. 2009;
Ljungqvist et al. 2010; and others). It is clear that recent
pedigree inbreeding cannot necessarily be implicated as
the cause of all HFCs (Hansson & Westerberg 2002).
Hansson & Westerberg (2002) detailed the three main
hypotheses or mechanisms giving rise to HFCs: (i)
under the direct effects hypothesis, the markers used are
themselves responsible for observed heterozygote
advantage [suggested to be particularly important in
some studies using allozymes, major histocompatibility
complex (MHC) loci, or single-nucleotide polymorphisms (SNPs)]; (ii) under the local effects hypothesis,
some of the markers under study are in linkage disequilibrium with non-neutral loci, creating apparent heterosis at the typed loci; and (iii) under the general effects
hypothesis, marker heterozygosity is representative of
heterozygosity across the genome as a whole due to
general identity disequilibrium due to inbreeding.
Although these hypotheses are not necessarily mutually exclusive, determining whether any or all of these
mechanisms contribute to HFCs in a given population
remains a stumbling block in many studies (Szulkin
et al. 2010). Furthermore, different populations can display characteristics that make distinguishing among the
aforementioned hypotheses even more challenging
(Grueber et al. 2008b). For example, bottlenecked populations may exhibit increased incidence of inbreeding,
as well as a long history of inbreeding if the bottleneck
was prolonged, both of which can reduce the variance
in fitness with respect to recent pedigree inbreeding
(i.e. cause reduced variance in inbreeding depression),
relative to nonbottlenecked populations. In addition,
the difficulty in determining whether general effects
because of ‘inbreeding’ are the result of recent consanguineous matings, or other population genetic processes
such as genetic drift, further impairs the interpretation
of HFCs in wild populations (Szulkin et al. 2010). Thus,
the extensive literature of HFC studies on large outbred
populations may not be relevant to conservation management of threatened populations (Grueber et al.
2008b). Previous reviews and simulation studies have
shown that in order for HFCs to provide a good representation of underlying inbreeding coefficients and thus
inbreeding depression, the data set must fulfil two main
criteria: the population must have a high variance in f
and large numbers of highly polymorphic molecular
markers must be assessed (Slate and Pemberton 2002;
Balloux et al. 2004; Slate et al. 2004). These requirements make analysis of HFCs in threatened species
difficult, because of the small sample sizes and low
genetic diversity that typify such populations. Regardless, the ability to evaluate inbreeding depression and
relatedness without the need for detailed labour-intensive pedigrees would be extremely useful in conservation research (Grueber et al. 2008b).
This study investigates HFCs in a threatened species,
the New Zealand takahe (Porphyrio hochstetteri). This
free-ranging, insular study population presents an ideal
opportunity to study such processes as it has detailed
pedigree data and high variance in inbreeding coefficient (Jamieson et al. 2003; Grueber & Jamieson 2008).
Using this pedigree, it has already been shown that
subtle inbreeding depression in the takahe population
accumulates across life-history traits (Jamieson et al.
2003; Grueber et al. 2010). In addition, 24 polymorphic
microsatellite markers have been optimised for takahe
(Grueber et al. 2008a) to enable characterization of individual heterozygosity. Given the species’ bottlenecked
population history (Lee & Jamieson 2001), it is predicted that any HFCs observed in takahe are likely to
be the result of inbreeding (general effects), which can
be tested using heterozygosity–heterozygosity correlations (Balloux et al. 2004; Pemberton 2004).
Methods
Study species background
The takahe (Porphyrio hochstetteri), once widespread
throughout New Zealand, was thought to be extinct by
the end of the 1800s until a remnant population was
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H F C S I N A N I N B R E D P O P U L A T I O N 69
discovered in 1948 in the remote Fiordland region of
the South Island (Lee & Jamieson 2001). During the
1980s and 1990s, as part of the recovery programme,
the New Zealand Department of Conservation (DOC)
translocated 25 takahe (mostly juveniles), sourced from
widely dispersed breeding pairs in the Fiordland population, to four offshore islands (for location maps and
details of translocations see Jamieson et al. 2003; Grueber & Jamieson 2008). Eighteen of the 25 founders bred
successfully, although founder genome representation
among the descendent population is highly skewed
(Grueber & Jamieson 2008). The number of adult takahe
now totals 72 on the four islands (15 on Kapiti Island,
35 on Mana Island, 12 on Maud Island and 10 on Tiritiri Matangi Island) (Wickes et al. 2009), and these birds
are managed as a single meta-population, thought to be
at carrying capacity (CEG and IGJ unpubl. data). Importantly, island takahe are free-ranging and select their
own territories and mates. They are all uniquely colourbanded to allow close annual monitoring and collection
of breeding data by DOC staff.
Pedigree and fitness data
Methods of pedigree development and analysis of pedigree structuring for the island takahe population have
been described previously (Jamieson et al. 2003; Grueber & Jamieson 2008; Grueber et al. 2010). Takahe are
observed to be socially and genetically monogamous
(Lettink et al. 2002; CEG & IGJ unpubl. data), and so
pedigree data were derived from annual breeding
records. Individual inbreeding coefficients and pairwise
kinship coefficients were calculated using PM2000
(Pollak et al. 2002). As the accuracy of inbreeding coefficients depends on pedigree depth (Keller 1998), we
calculated values for only those individuals for whom
all four grandparents were known. The current analysis
encompasses 21 years (1986–2006) of annual takahe
breeding data collated from DOC records from the four
islands of Kapiti, Mana, Maud and Tiritiri Matangi
(hereafter referred to as the ‘island population’). Additional data routinely collected by DOC, and assessed
here, included egg fertility (fertility rate of known
eggs), hatching rate, fledging rate (defined as survival
to independence, approximately 100 days), survival to
2 years (breeding age) and recruitment (defined as successful pairing and laying at least one egg) (see also Jamieson et al. 2003). Analysis of the latter two
parameters was restricted to only those individuals
with at least 2 years of survival data. The current analysis was performed in a similar manner to that of
Grueber et al. (2010), in that we assessed the fitness of
a breeding pair in response to their relatedness over
two stages. First, survival probability of offspring was
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assessed during the growth and recruitment stages
(hereafter referred to as the ‘vital stage’). Second, the
survival probability of the offspring’s offspring was
examined during the ‘reproductive stage’. This
approach allowed us to investigate the effects of MLH)
through all life-history stages up to and including
grand-offspring recruitment (see Results).
DNA samples
This analysis used DNA samples that had been
extracted from blood samples collected for a previous
study (samples of birds hatched prior to 1999) (Lettink
et al. 2002) in addition to samples routinely collected
by DOC for genetic sexing (birds hatched from 2000
to 2003) (I. Anderson, Equine Blood Typing Unit, Massey University). All samples had been extracted using
a standard Chelex" method (Walsh et al. 1991), and
the DNA in solution was stored at )20 #C for up to
8 years prior to amplification. Of the sampled island
birds, 71 had all four grandparents identified. To maximize statistical power, however, analyses that did not
require inbreeding coefficients were extended to all
island birds for which DNA samples were available,
regardless of pedigree depth (n = 87). Pairwise estimates of genetic diversity required DNA samples from
both partners, allowing us to include data from 34 of
a possible 89 pairs for which breeding data were
available.
The data set also included 88 birds of Fiordland origin as a comparison for levels of genetic diversity. Care
should be taken not to assume panmixia as such
assumptions, if incorrect, can confound population
genetic and demographic inferences (Slate & Pemberton
2006; Amos & Acevedo-Whitehouse 2009). Thus,
although the island and Fiordland birds share a recent
common ancestry, we consider them separately here.
However, we consider takahe from the four island sites
as a single population, because of the high level of
translocation among sites and the policy of managing
the four subpopulations collectively (Wickes et al.
2009).
Molecular data
All takahe samples were genotyped at 24 microsatellite
loci. One locus was a cross-species amplification of Crex7
(Gautschi et al. 2002), while the remaining loci were
developed specifically for takahe (19 as described in
Grueber et al. 2008a; plus an additional four developed
using the same method, see Supporting information
Table S1). PCR and polyacrylamide gel electrophoresis
were performed following the methods used in Grueber
et al. (2008a). Although not all individuals were
70 C . E . G R U E B E R , J . M . W A T E R S and I . G . J A M I E S O N
genotyped at all loci, 97.3% of samples were genotyped
at more than 20 loci and all samples were genotyped at a
minimum of 17 loci.
One locus (Pho44) was monomorphic among island
samples and so was excluded from subsequent estimates of heterozygosity for island birds. One locus
(Pho47) was monomorphic among Fiordland samples.
As two markers (Pho06 and Pho38) appeared to be
Z-linked, only software that could accommodate the
presence of female hemizygous data was used in this
analysis. Where such analysis was not possible, heterozygosity data were calculated for males only at these
loci. Locus-specific statistics were calculated using
GENEPOP (Rousset 2008). GENEPOP was also used to
calculate locus-specific observed and expected heterozygosities (HO and HE, respectively), using the following Markov chain parameters: dememorization: 1000;
100 batches; 5000 iterations per batch.
To estimate genetic relatedness values for breeding
pairs, we used a method-of-moments estimator of relatedness (^r, Ritland 1996) calculated using GENALEX 6.2
(Peakall & Smouse 2006) (Fig. 1a). This estimator is an
efficient metric for pairwise relatedness as it considers
the number of shared alleles relative to population
allele frequencies so that ^r is positively correlated with
pedigree-based relatedness (Ritland 1996). Negative values are only observed when very few alleles are shared
between individuals (Ritland 1996).
To calculate MLH for individuals (i.e. the pair’s offspring), we used standardized heterozygosity (SH, Coltman et al. 1999) and internal relatedness (IR, Amos et al.
2001) using IRMACRON4 (Amos et al. 2001) (Fig. 1b). IR
is particularly suitable for analysis of inbreeding because
it estimates the probability of parental relatedness by
weighting the homozygosity of rare alleles higher than
common alleles, where animals born to unrelated parents have an expected IR = 0, but negative values are
possible (Amos et al. 2001; Acevedo-Whitehouse et al.
2005). It is also an appropriate measure of heterozygosity for populations that exhibit high inbreeding (Aparicio et al. 2006; Coulon 2010). We chose not to use the
mean-d2 estimator of heterozygosity (Coulson et al.
1998) because of theoretical difficulties with its interpretation (Hansson 2010). IR is expected to be negatively
correlated with MLH, while SH should be positively correlated with it. IR and SH were highly correlated to each
other (Pearson correlation, q = )0.962), so IR values
were used for the main analysis, with comparisons made
to SH where appropriate.
Statistical procedure
We modelled the effect of a molecular estimate of
breeding pair relatedness, ^r, and a molecular estimate
of inbreeding, IR, (both of which are forms of MLH) on
survival with generalized linear mixed effects models
fitted using the R library lme4 (Bates & Maechler 2009).
Survival at each life-history stage was modelled as a
binomial response variable where the binomial numerator (event) was the number of successes (e.g., number
of offspring that fledged) and the denominator (trials)
was the number of successes in the previous stage (e.g.,
number of offspring that hatched). Both molecular measures were entered into the models as continuous input
variables. Final models were derived by model averaging the top 2AICC (Akaike information criterion, small
sample size correction, Hurvich & Tsai 1989) of models
(i.e. models where DAICC < 2) (Burnham & Anderson
2002). Model averaging was performed using the functions available in the R package MuMIn (Bartoń 2009).
To directly compare sizes of fixed effects across different scales, as well as enable the comparison of main
effects where interactions are present (see Gelman 2008;
Schielzeth 2010), input variables were standardized
Fig. 1 Schematic representation of the metrics that are used to evaluate multilocus heterozygosity of island takahe (at 23 microsatellite markers) for the two levels of this analysis: ^r was calculated for pairs (to assess vital rates, a) and IR (or SH) was calculated for
individuals (to assess reproductive rates, b).
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H F C S I N A N I N B R E D P O P U L A T I O N 71
using the function available in the R library arm
(Gelman et al. 2009). We undertook this information
theoretical approach to modelling as it enabled us to
estimate the effect sizes of fixed factors even where
their effects are weak and have large error. Such effects
would have probably been excluded from the model
had we relied on arbitrary significance thresholds, and
no parameter estimates obtained.
Additional fixed effects included in all models were
island site, and time period (‘early’, ‘mid’ or ‘late’),
which was included to control for the increasing population size since founding. Maternal age was controlled
in the vital analysis, and individual age and sex were
controlled in the reproductive analysis. As the breeding
data set for individuals included up to 18 breeding seasons for each individual (mean 5.9 seasons, Fig. 2), we
were able to evaluate the effect of age on annual hatching success, as well as interactions between age and IR.
All models included the random factors PairID (in the
vital analysis) or IndID (in the reproductive analysis) to
control for multiple breeding attempts.
Although the effects of MLH (^r or IR) on each fitness
response were examined using the full, continuous
range of observed MLH values, we also used our models to evaluate the biological impact of heterozygosity
by comparing the predicted fitness of individuals at
either end of the observed range of MLH. We dichotomized the effect of MLH on fitness by comparing point
estimates at the extremes of observed MLH values. In
addition, to avoid any potential bias from outliers (individuals with extremely high or low MLH), we recalculated this comparison taking point estimates at the 5%
Fig. 2 Distribution of sample size relative to the number of
breeding seasons for which individuals laid at least one egg
(n = 53).
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and 95% quantiles of the range of MLH. The fitted proportion of successes for each life-history stage was calculated as the proportion of successes from the
previous stage multiplied by the probability of successful transition. By multiplying success probabilities
across the full life-history continuum, we can calculate
the lifetime impact of high vs. low heterozygosity in
takahe.
Unless specified otherwise, all statistical analyses
were performed in R (R Core Development Team 2009).
Following the recommendations of Stephens et al.
(2005), conclusions were based on null hypothesis testing for analyses where straightforward univariate relationships were expected, but the importance of effect
sizes and standard errors (or confidence intervals,
where possible) remained a major focus (Nakagawa &
Cuthill 2007).
Correlation between inbreeding coefficient and MLH
Equations 1 and 4 of Slate et al. (2004) were used to
calculate the predicted magnitude of the correlation
between inbreeding coefficient and MLH. The observed
relationship between inbreeding coefficient and MLH
was estimated by linear regression, with a confidence
interval evaluated by bootstrap resampling microsatellite loci with replacement (10 000 iterations) in VISUAL
BASIC (MS EXCEL 2003). After observing a significant relationship between pedigree-based inbreeding coefficient
and MLH (see Results), we tested whether the
observed HFCs could be attributed to general effects
by testing for heterozygosity–heterozygosity correlations, RH,H, using the method proposed by Balloux
et al. (2004) (and subsequently also used by Gage et al.
2006; Da Silva et al. 2009). It is predicted that if the
genotyped markers are representative of underlying
inbreeding coefficients, heterozygosities among loci
should be positively correlated (Balloux et al. 2004).
We wrote a resampling macro in Visual Basic to randomly assign the 23 loci to each of two groups (of
sizes 12 and 11 loci) and measure whether IR calculated for all individuals using loci in the first group
was correlated with IR using loci from the second
group. Then, by randomizing the 23 loci at each iteration, and repeating 10 000 times, we obtained a mean
and 95% confidence interval (CI95%) for the correlation. In addition to testing for positive RH,H correlations, our molecular data were also used to calculate
the parameter g2 and its standard error using the software RMES (David et al. 2007). This statistic is a molecular indicator of identity disequilibrium and is thus an
additional method of determining whether the markers
under study reflect patterns of underlying inbreeding
(David et al. 2007; Szulkin et al. 2010).
72 C . E . G R U E B E R , J . M . W A T E R S and I . G . J A M I E S O N
Results
Microsatellite diversity of island takahe was very low,
consistent with the magnitude of genetic diversity initially observed during primer development (Grueber
et al. 2008a). The mean number of alleles per locus
across all sampled island birds was 2.30 [23 polymorphic
loci, number of alleles (NA) range 2–4, n = 87], similar to
the Fiordland birds (2.26, 23 loci, NA range 2–4, n = 88),
but expected heterozygosity was lower among the island
birds (HE = 0.387, SD = 0.173) than the Fiordland birds
(HE = 0.537, SD = 0.735). The mean ^r of island breeding
pairs was 0.015 (SD = 0.116, range = )0.149 to 0.376).
The mean IR of island birds was )0.021 (SD = 0.220,
range = )0.486 to 0.525). Mean pedigree inbreeding
and its variance are both high among takahe (mean
f = 0.0473, variance = 0.0054) (Grueber et al. 2010).
Relationship between heterozygosity and fitness
After model averaging, MLH (as measured by pair relatedness, ^r or internal relatedness, IR) was an important,
although not statistically significant, predictor of survival probability at every life-history stage except survival to hatching and survival to recruitment (Table 1).
This result indicates that MLH featured in either the top
model or at least one model within 2AICC of the top
model, for most life-history stages. The importance of ^r
or IR relative to other model parameters varied widely
depending on the stage, from being unimportant in predicting the probability of both survival to hatching and
recruitment [see relative importance (RI) column,
Table 1A] to being one of the most important parameters for predicting the ability of individuals to raise offspring that survive to 2 years (Table 1B).
For all response variables, the unconditional standard
errors of the parameter estimates for each model are very
large relative to the effect sizes, and this is probably a
result of relatively small sample sizes, particularly in the
vital stages where DNA samples were required for both
parents to estimate their relatedness (Table 1). Indeed,
the 95% confidence intervals (CI95%; b ± 1.96 · SE; Sokal
& Rohlf 1997; Nakagawa & Cuthill 2007) for ^r and IR
include zero in all cases, indicating that these effects
Table 1 Standardized predictors found to have important effects on vital (A) and reproductive (B) life-history stages (see Methods)
after model averaging submodels with DAICC < 2. All models in A include the random factor ‘PairID’; models in B include the random factor ‘IndID’. See Supporting information Tables S2–S9 for details of the submodels that were used to generate these averages
Hatching rate
Predictor*
A: Vital stage
(Intercept)
Pair relatedness (^r)
Time period (maternal age)2
Maternal age
^r · Maternal Age
Island§
B: Reproductive stage
(Intercept)
Internal relatedness (IR)
Time period
Sex
(Age)2
Sex · (Age)2
Sex · Age
Age
IR · Age
IR · Sex
Island§
b (SE)†
Fledging rate
RI‡
1.11 (0.587)
—
1.62 (0.691)
)1.50 (0.759)
)1.72 (0.741)
)
)0.274 (0.672)
0.839 (0.241)
)0.003 (0.306)
0.693 (0.278)
0.279 (0.350)
)1.22 (0.476)
)1.88 (0.957)
)0.701 (0.478)
)0.688 (0.274)
)0.983 (0.479)
)0.538 (0.560)
)0.104 (0.313)
0.58
1.00
0.78
1.00
0.64
0.43
1.00
0.57
0.14
0.51
b (SE)
RI
b (SE)
0.290 (0.309)
)0.671 (0.425)
)0.535 (0.408)
)0.656 (0.886)
)0.184 (0.449)
2.01 (1.05)
)0.222 (0.436)
0.77
0.29
0.12
0.34
0.29
0.31
1.62 (0.335)
)0.138 (0.306)
—
—
)0.092 (0.251)
—
—
0.555
)0.304
)0.510
0.210
0.477
—
—
0.400
—
—
)0.388
Offspring
recruitment
2-year survival
(0.254)
(0.295)
(0.262)
(0.227)
(0.501)
0.25
0.84
0.17
0.18
(0.281)
0.42
(0.275)
1.00
1.70 (0.233)
)0.980 (0.539)
)0.194 (0.491)
0.393 (0.470)
—
—
—
)0.609 (0.574)
—
—
—
RI
0.25
0.22
0.83
0.13
0.17
0.21
b (SE)
RI
3.22 (0.710)
—
—
—
—
—
—
2.12 (0.456)
)0.869 (0.722)
)1.08 (0.635)
—
0.449 (1.360)
—
—
0.688 (0.722)
—
—
)0.619 (0.772)
0.35
0.56
0.08
0.12
0.19
*Predictors were standardized to a mean of zero and 0.5 standard deviations.
†b, coefficient; SE, unconditional standard error.
‡RI, relative importance of each fixed effect, when compared to the others in the final model. Blanks indicate only one ‘top’ model
(averaging not required, see Methods).
§Kapiti was the reference category. The effect size presented is a weighted mean based on the number of pairs (in A) or individuals
(in B) from each island.
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H F C S I N A N I N B R E D P O P U L A T I O N 73
Table 2 Standardized predictors found to have important
effects on male fertility after model averaging the top 2AICC of
submodels from a global model, all models include the random factor ‘IndID’. See Supporting information Table S10 for
details of the submodels that were used to generate this average
Male fertility
Predictor*
b (SE)†
RI‡
(Intercept)
IR
(Age)2
Island§
1.05 (0.306)
0.691 (0.626)
)0.244 (0.405)
)0.001 (0.132)
0.70
0.36
0.14
*Predictors were standardized to a mean of zero and 0.5
standard deviations.
†b, coefficient; SE, unconditional standard error
‡RI, relative importance of each parameter, when compared to
the other parameters in the final model.
§Kapiti was the reference category. The effect size presented is
a weighted mean based on the number of pairs (in A) or males
(in B) from each island.
would not be considered significant at a = 0.05. The
exception to this is the IR · Age interaction at the reproductive hatching success stage (where CI95% = )1.462,
)0.044, from Table 1), indicating that the effect of IR on
fitness varies across ages.
Despite the lack of precision of the estimates, a consistent trend emerges across all life-history stages: in all
cases where ^r or IR appeared in the final model, the
coefficients are in the expected, negative, direction
(Table 1). Using point estimates taken from the
extremes of the distributions of ^r and IR, we see that
pairs with the lowest observed MLH exhibited a 93.3%
reduction in completed fitness over all life-history
stages relative to pairs with maximal heterozygosity. If
we take a conservative approach and model fitness at
the 5% and 95% quantiles rather than extremes of ^r
and IR, this reduction is 72.4% over all life-history
stages. The exception to this pattern is male fertility,
where increased fertility was observed with increasing
IR, but the standard error of this estimate is high
(Table 2). For female fertility, or clutch size, the numbers of eggs laid by individuals with IR above the median were similar to the number laid by individuals with
IR below the median [mean 2.42 (SD = 1.39) and 2.60
(SD = 1.17) eggs per season, respectively].
Do the markers reflect underlying identity
disequilibrium and inbreeding?
To investigate whether the overall trend for low heterozygosity to be associated with decreased fitness could
! 2010 Blackwell Publishing Ltd
be attributed to underlying identity disequilibrium
(inbreeding effects), we first tested for heterozygosity–
heterozygosity correlations, RH,H, under the prediction
that if the genotyped markers are representative of
underlying inbreeding coefficients, heterozygosities
among loci should be positively correlated (Balloux
et al. 2004). The relationship was slightly negative and
close to zero (RH,H = )0.029; CI95% )0.178 to 0.120),
interpreted as an indication that heterozygosities within
the sampled birds were not correlated and therefore not
representative of identity by descent. However, heterozygosities were highly variable among loci [mean
HE = 0.387, r2 = 0.030 (Grueber et al. 2008a)]. In addition, g2 did not differ from zero (g2 = )0.012,
SE = 0.008, p = 0.905), further indicating that the molecular markers used here are not informative of underlying identity by descent.
The predicted correlation between pedigree inbreeding coefficient f and standardized heterozygosity (SH),
based on the equations of Slate et al. (2004), was
)0.288, which was similar to the observed correlation
(Rf,SH = )0.327; Fig. 3a). These values also fell within
the bootstrap confidence interval for the observed value
(CI95% )0.527 to )0.127), which excludes zero, indicating that the relationship is statistically significant at
a = 0.05. Using the equations of Slate et al. (2004), we
inferred that very large numbers of loci would be
required to detect a substantially stronger correlation.
For example, 100 loci of the same mean heterozygosity
as those used here would have given a moderate correlation of )0.508, whereas 275 loci would be required to
give a ‘strong’ correlation of )0.70. The observed correlation between f and IR was Rf,IR = 0.336 (CI95% 0.121–
0.551, Fig. 3b), which was in the expected direction and
of a similar magnitude to the correlation with SH. There
was nevertheless a high variance in both SH and IR at
any given level of inbreeding (Fig. 3).
To determine the biological importance of the
observed relationship between f and IR we investigated
whether molecular methods could be used to evaluate
inbreeding coefficients for nonpedigreed individuals. To
examine the predictive power of MLH with respect to
inbreeding status, we categorized birds of known
inbreeding coefficient into a binomial response variable
(‘inbred’: f > 0, or ‘outbred’: f = 0) and used discriminant analysis to evaluate the predictability of inbreeding status from IR. In this analysis, 50% correct
assignments would be expected by chance alone.
Although IR is thought to be the most effective heterozygosity metric for inbred populations (Aparicio et al.
2006), it was a poor predictor of whether individual
takahe were inbred or outbred (discriminant analysis:
56.3% of cases correctly assigned). Given the relationships in Fig. 3, we tested whether IR could be used to
74 C . E . G R U E B E R , J . M . W A T E R S and I . G . J A M I E S O N
(a)
(b)
distinguish close inbreeding (f ‡ 0.125), and discriminatory ability was only marginally improved (67.6% of
cases correctly assigned to ‘inbred: f ‡ 0.125’ or ‘outbred: f < 0.125’).
Discussion
This genetic study of threatened takahe shows that
MLH—determined from 23 microsatellite markers—is a
poor predictor of an individual’s pedigree inbreeding
status, even in a bottlenecked species with high variance in pedigree inbreeding coefficient. Specifically,
although the relationship between estimates of heterozygosity and inbreeding coefficient was statistically significant, it was weak (Rf,IR = 0.336, Fig. 3). Our data
further suggest that MLH may be a weak predictor of
variation in fitness of takahe. Despite an overall trend
of decreasing fitness with decreasing heterozygosity at
most life-history stages, resulting in a large reduction in
fitness of maximally homozygous individuals relative to
those that are maximally heterozygous, these effects
carried considerable uncertainty (because of the large
standard errors observed at each life-history stage,
Table 1). This pattern is similar to an earlier finding
that inbreeding depression based on pedigrees was not
detectable at single life-history stages but did have an
important cumulative effect across the full life-history
continuum (Grueber et al. 2010).
Despite evidence of a relationship between MLH and
f, the 23 loci used here failed to predict inbreeding
coefficients at the individual level, as shown by the
high variance in heterozygosity within inbreeding classes (Fig. 3). It is also interesting that both the heterozygosity–heterozygosity correlations (RH,H = )0.029;
CI95% )0.178 to 0.120) and the estimate of g2 (g2 =
)0.012, SE = 0.008, p = 0.905) indicate that the markers
used here are not representative of individual inbreeding coefficients (identity disequilibrium). Nevertheless,
it has been previously shown that inbreeding depres-
Fig. 3 The relationship between inbreeding coefficient (f, based on pedigrees) and standardized heterozygosity
(a) or internal relatedness (b) based on
23 microsatellite loci in 71 island takahe
for which four grandparents are known.
Note that the scales of the y-axes differ
between A and B.
sion does appear to negatively impact the fitness of
takahe (Grueber et al. 2010), and we thus suggest that,
in the absence of pedigree data, the poor precision of
MLH estimates could lead to the erroneous conclusion
that inbreeding is not the cause of fitness reduction, if
heterozygosity–heterozygosity correlations and g2 estimates are used as the test. As indicated by others (Pemberton 2004, 2008), our results suggest that without
improvement in the methods of estimating genomewide heterozygosity and identity disequilibrium, MLH
estimates based on small numbers of loci cannot substitute for pedigree and demographic data as a tool for
individual-based management activities such as selecting individuals for translocation.
Failure to detect a general effect does not imply lack
of inbreeding depression. Indeed, even in our previous
analysis of inbreeding using a relatively deep pedigree
of the study population, inbreeding depression was difficult to detect (Grueber et al. 2010). This may be, at
least in part, because of the limited sample size available
(samples from both members of 34 of a possible 89 pairs
were genotyped in the current study). However, the
sample size is not unreasonable given the highly endangered status of the study population. Given the high
variance in inbreeding coefficients and biological evidence of inbreeding depression in the study population
(Grueber et al. 2010), it is intriguing that identity disequilibrium (general effects) could not be shown to be
the cause of the weak heterozygosity-fitness correlations
(HFCs) detected in this study. It is possible that the
inability to implicate the general effect in this study is a
consequence of the long-term bottleneck experienced by
this species (Lee & Jamieson 2001). Although the bottleneck will have increased population-wide mean kinship,
and thus decreased the true variance in inbreeding coefficients (as the founders are unlikely to be unrelated, as
is assumed), previous simulations have shown that pedigrees with as few as three generations are nearly as
informative as pedigree relationships based on up to 50
! 2010 Blackwell Publishing Ltd
H F C S I N A N I N B R E D P O P U L A T I O N 75
extreme level of monomorphism (Grueber et al. 2008a),
with very low heterozygosity detected in the current
study (HE = 0.39). Despite this low diversity, we were
able to obtain a similar number of microsatellite markers as those used in other studies of HFCs (only three
recently published studies of the Rf,H relationship used
more, Table 3). Correspondingly, the observed and predicted relationships between MLH and pedigree-based
inbreeding coefficient ()0.327 and )0.288, respectively)
were similar to most other published values (Table 3).
This statistic indicates that results for takahe presented
here appear to be robust and not a specific consequence
of the historic bottleneck (Lee & Jamieson 2001) nor low
levels of genetic diversity (Grueber et al. 2008a).
generations of data (Balloux et al. 2004). Thus, recent
inbreeding may still negatively affect takahe. Furthermore, it is certainly possible that the weak relationship
between MLH and fitness that we observed here,
although not significant, is because of fitness effects at a
small number of loci (local effects). However, there are
statistical and analytical complications with disentangling these relationships (such as distinguishing among
demographic causes of inbreeding, as detailed in Szulkin et al. 2010), which we will consider elsewhere (the
authors, ms in prep).
A further consequence of the long-term bottleneck
experienced by takahe is the low level of population
genetic diversity. Takahe microsatellites show an
Table 3 Observed correlations (ranked from highest to lowest) between molecular heterozygosity and individual inbreeding coefficient (Rf,H Obs) in a number of species, comprising studies listed in Slate et al.’s (2004) review and those published since. Provided
are the mean and variance (r2) of inbreeding coefficient (f), sample size (N) and mean expected heterozygosity (HE) of microsatellite
loci
r2 (f)
N
Mean HE
Rf,H
Species
Mean (f)
Wolf (Canis lupus)*
0.103
0.0192
30
0.66
29
)0.72
Large ground finch (Geospiza
magrinostris)*
Saharawi dorcas gazelle (Gazella dorcas
neglecta)
Domestic dog (Canis familiaris)—24
breeds
House sparrow (Passer domesticus)
Siberian jay (Perisoreus infaustus)
Takahe (Porphyrio hochstetteri)
Red deer (Cervus elaphus)*
Song sparrow (Melospiza melodia)*
0.070
0.0143
76
0.66
14
)0.54
Hedrick et al. (2001) and Vila
et al. (2003)
Grant et al. (2001)
0.053
0.0011
89
0.72
19
)0.50
Ruiz-Lopez et al. (2009)
1514
0.62
21
)0.43
Leroy et al. (2009)
0.05
0.026
0.047
0.019
0.051
0.0084
0.0040
0.0054
0.0025
0.0041
169
200
71
553
285
0.94
—
0.39
0.76
0.63
7
21
23
9
6
)0.38
)0.33
)0.33
)0.25†
)0.22†
Cuvier’s gazelle (Gazella cuvieri)
Soay sheep (Ovis aries)*
0.178
0.017
0.0011
0.0020
91
1429
0.55
0.64
19
18
)0.22
)0.21
Medium ground finch (Geospiza fortis)*
0.010
0.0004
212
0.64
13
)0.20
Arabian oryx (Oryx leucoryx)*
0.041
0.0066
122
0.42
6
)0.18†
Coopworth sheep (Ovis aries)*
Bighorn sheep (Ovis canadensis)*
Mhorr gazelle (Gazella dama mhorr)
Collared flycatcher (Ficedula albicollis)*
0.052
0.015
0.101
0.002
0.0008
0.0020
0.0036
0.0005
590
107
112
2107
0.72
0.66
0.48
0.82
101‡
20
17
3
)0.17
)0.15
)0.12
)0.08†
Cactus finch (Geospiza scandens)*
0.042
0.0044
75
0.61
13
)0.04
Lipizzan horse (Equus caballus)*
0.101
0.0007
360
0.67
17
)0.03
Jensen et al. (2007)
Alho et al. (2009)
Current study
Marshall et al. (1998, 2002)
Keller (1998) and Jeffery et al.
(2001)
Ruiz-Lopez et al. (2009)
Coltman et al. (1999), Marshall
et al. (2002) and Overall et al.
(2005)
Petren (1998) and Keller et al.
(2002)‡
Marshall & Spalton (2000) and
Marshall et al. (2002)
Slate et al. (2004)
Slate et al. (2004)
Ruiz-Lopez et al. (2009)
Sheldon & Ellegren (1999) and
Kruuk et al. (2002)
Petren (1998), Keller et al. (2002)
and Slate et al. (2004)
Curik et al. (2003)
Mean
Median
0.053
0.047
0.0044
0.0031
403
169
0.65
0.66
20
17
)0.26
)0.26
0.034
—
No. loci
*Studies cited in Table 1 of Slate et al. (2004).
†Expected values as calculated by Slate et al. (2004) using the formulas they derive.
‡An approximated value, see Slate et al. (2004).
! 2010 Blackwell Publishing Ltd
Obs
References
76 C . E . G R U E B E R , J . M . W A T E R S and I . G . J A M I E S O N
This analysis adds empirical data from a threatened
species to a growing body of evidence suggesting that
heterozygosity evaluated from a moderate number of
molecular markers cannot adequately estimate genomewide heterozygosity and inbreeding (Balloux et al. 2004;
Slate et al. 2004; DeWoody & DeWoody 2005; Ljungqvist et al. 2010). For example, to detect a ‘strong’ correlation of )0.7 in takahe, 275 polymorphic loci would be
required to reduce the variance in MLH (Fig. 3) both
overall and within inbreeding classes. However, in this
genetically depauperate threatened species, 2380 loci
would need to be developed and screened to be 90%
certain of attaining 275 that were polymorphic (based
on the binomial distribution and a polymorphism rate
of 0.124, Grueber et al. 2008a). Developing and screening this many markers would be unfeasible in this species with current methods and may be difficult in many
endangered species, which tend to exhibit low levels of
genetic diversity (Lacy 1987). Creative solutions to this
dilemma—that the species with the highest levels of
inbreeding often exhibit the lowest genetic diversity—are required. In the future, given the advent of
high-throughput automated genotyping and next-generation sequencing, other molecular estimates of heterozygosity (such as single-nucleotide polymorphisms, SNPs)
may allow greater numbers of loci to be genotyped
more quickly and efficiently (Avise 2010; Slate et al.
2010).
While molecular estimates of relatedness are generally limited in their ability to directly infer levels of true
pedigree relatedness and inbreeding, the use of molecular data to recover pedigree relationships (which are
then used to calculate inbreeding coefficients, Santure
et al. 2010) is a rapidly developing field in cases where
some demographic data are available (such as the ability to assign individuals to cohorts). In recent years,
vast improvements have been made to molecular methods for reconstructing pedigrees, including algorithms
that now incorporate polygamous mating systems,
mutations and genotyping errors (Wang 2004; Hadfield
et al. 2006; Wang 2007; Wang & Santure 2009; Jones &
Wang 2010). In the current study, these methods could
not be tested because not all of the birds in the takahe
pedigree have been DNA sampled, leading to increased
uncertainty in molecular pedigree reconstruction (Pemberton 2008; Jones & Wang 2010). We anticipate forthcoming research in this area as an alternative approach
for evaluating pedigree relationships and inbreeding
depression in wild populations.
Acknowledgements
We thank G. Wallis, J. Slate, F. Allendorf, H. Spencer and
three anonymous reviewers for constructive comments on an
earlier draft, S. Nakagawa and R. Laws for statistical assistance, and T. King for assistance in the laboratory. We are
grateful to the Takahe Recovery Group, especially L. Kilduff,
G. Greaves, and the island managers for providing pedigree
and fitness data. This research was funded by the Department
of Conservation (Contract no. 3576), Landcare Research (Contract no. C09X0503), Takahe Rescue partnership with Mitre
10$, and University of Otago. CEG acknowledges the
support of a Tertiary Education Commission Top Achiever’s
Doctoral Scholarship.
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Supporting information
Additional supporting information may be found in the online
version of this article.
Table S1 Microsatellite loci isolated from takahe (Porphyrio
hochstetteri) using the methodology of Grueber et al. (2008a);
repeat motif and product length (allele size range) are those of
the amplified product
Table S2 Top model set (top 2AICC) of generalised linear
mixed models for the survival response hatching probability.
All models were fitted with a random factor ‘PairID’. The final
model is provided in Table 1
Table S3 Top model set (top 2AICC) of generalised linear
mixed models for the survival response fledging probability.
All models were fitted with a random factor ‘PairID’. The final
model is provided in Table 1
Table S4 Top model set (top 2AICC) of generalised linear
mixed models for the probability of survival to 2 years. All
models were fitted with a random factor ‘PairID’. The final
model is provided in Table 1
Table S5 Top model set (top 2AICC) of generalised linear
mixed models for the probability of recruitment. The model
was fitted with a random factor ‘PairID’. The final model is
provided in Table 1
Table S6 Top model set (top 2AICC) of generalised linear
mixed models for the probability of successfully hatching
! 2010 Blackwell Publishing Ltd
H F C S I N A N I N B R E D P O P U L A T I O N 79
offspring. All models were fitted with a random factor ‘IndID’.
The final model is provided in Table 1
ment. All models were fitted with a random factor ‘IndID’.
The final model is provided in Table 1
Table S7 Top model set (top 2AICC) of generalised linear
mixed models for the probability of successfully fledging offspring. All models were fitted with a random factor ‘IndID’.
The final model is provided in Table 1
Table S10 Top model set (top 2AICC) of generalised linear
mixed models for male fertility. All models were fitted with a
random factor ‘IndID’. The final model is provided in Table 2
Table S8 Top model set (top 2AICC) of generalised linear
mixed models for the probability of successfully raising offspring to 2 years. All models were fitted with a random factor
‘IndID’. The final model is provided in Table 1
Table S9 Top model set (top 2AICC) of generalised linear
mixed models for the probability of grand-offspring recruit-
! 2010 Blackwell Publishing Ltd
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