Hybrid vigor between native and introduced
salamanders raises new challenges for conservation
Benjamin M. Fitzpatrick*†and H. Bradley Shaffer‡
*Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996; and‡Evolution and Ecology, University of California, Davis, CA 95616
Edited by John C. Avise, University of California, Irvine, CA, and approved August 10, 2007 (received for review May 22, 2007)
Hybridization between differentiated lineages can have many
different consequences depending on fitness variation among
hybrid offspring. When introduced organisms hybridize with na-
tives, the ensuing evolutionary dynamics may substantially com-
plicate conservation decisions. Understanding the fitness conse-
quences of hybridization is an important first step in predicting its
evolutionary outcome and conservation impact. Here, we mea-
sured natural selection caused by differential viability of hybrid
larvae in wildpopulationswhere
Salamanders (Ambystoma californiense) and introduced Barred
Tiger Salamanders (Ambystoma tigrinum mavortium) have been
hybridizing for 50–60 years. We found strong evidence of hybrid
vigor; mixed-ancestry genotypes had higher survival rates than
genotypes containing mostly native or mostly introduced alleles.
Hybrid vigor may be caused by heterozygote advantage (over-
dominance) or recombinant hybrid vigor (due to epistasis or
complementation). These genetic mechanisms are not mutually
exclusive, and we find statistical support for both overdominant
and recombinant contributions to hybrid vigor in larval tiger
salamanders. Because recombinant homozygous genotypes can
breed true, a single highly fit genotype with a mosaic of native and
introduced alleles may eventually replace the historically pure
California Tiger Salamander (listed as Threatened under the U.S.
Endangered Species Act). The management implications of this
outcome are complex: Genetically pure populations may not per-
sist into the future, but average fitness and population viability of
admixed California Tiger Salamanders may be enhanced. The
ecological consequences for other native species are unknown.
native California Tiger
Ambystoma ? fitness ? hybridization ? invasive species ? genetics
organisms (1–3). Consequences of hybridization include fusion
of previously distinct lineages, extinction or local extirpation of
one or both lineages, evolution of reproductive isolation via
reinforcement, and production of novel, highly fit hybrid phe-
notypes. These outcomes depend on the distribution and inher-
itance of fitness among hybrids and often have important
implications for both evolutionary and conservation biology.
In evolutionary biology, hybrid fitness and its genetic basis are
important for understanding the evolution of reproductive iso-
lation and the consequences of horizontal gene flow on the
diversity and complexity of life (4–7). In conservation biology,
hybrid fitness is a key to the mechanistic basis of inbreeding and
outbreeding depression, the potential loss of biodiversity due to
genetic swamping, and the evolution of invasiveness (8–11).
These considerations become particularly important when in-
troduced organisms successfully hybridize with natives.
Unlike cases of natural hybridization, some outcomes of
human-mediated hybridization are generally considered less
desirable than others. Low fitness of hybrids can reduce mean
population fitness, rendering populations more vulnerable to
extinction (8, 12). Novel hybrid genotypes may contribute to de
novo evolution of invasiveness (9), and admixed populations may
be considered less valuable than an authentic native gene pool
(10). On the other hand, admixture may rescue declining native
ybridization (interbreeding between differentiated lin-
eages) occurs in almost all sexually reproducing groups of
populations by alleviating inbreeding depression (13, 14) or
facilitating adaptive evolution in modified or degraded habitats
The long-term consequences of hybridization are strongly
influenced by the genetic basis of hybrid fitness. In the case of
hybrid vigor, genetic models fall into two classes: heterozygote
advantage and recombinant hybrid vigor (18–20). Heterozygote
advantage (overdominance) refers to beneficial interactions
between heterospecific alleles of a single locus. Recombinant
by epistasis (beneficial interactions between heterospecific al-
leles from different loci) or by complementary effects of inde-
20). For example, if different loci have fixed deleterious alleles
in each parental population, hybrids bearing the superior allele
at each locus will have higher fitness than either parent.
Unlike heterozygote advantage, where the most fit genotype
cannot breed true, recombinant hybrid vigor favors the fixation
of a single recombinant genotype bringing together beneficial
alleles from each parent. This new, true breeding genotype may
be considered a modified version of one of the parental lineages
or a new hybrid species. In conservation terms, fixation of a
recombinant genotype may represent a minor evolutionary
modification or total genetic ‘‘extinction’’ of a native form (this
may depend more on one’s perspective than on the genetic
details). Perhaps more important, the new form may have
undesirable ecological effects on native communities (9).
Recent, human-mediated hybridization between native Cali-
fornia Tiger Salamanders (Ambystoma californiense) and intro-
duced Barred Tiger Salamanders, (Ambystoma tigrinum mavor-
conservation consequences of hybridization (21–23). Before the
salamander larvae to bass fishermen), the two lineages had been
geographically separated for ?5 my (24, 25). Despite such a long
period of divergence, they hybridize readily and have formed a
hybrid swarm in the Salinas Valley of California (21–23). Mul-
tiple introduction points, combined with subsequent dispersal
and movements of salamanders across the landscape (23) have
led to broad-scale admixture across 15–20% of the natural range
of the native California Tiger Salamander. The recent listing of
Act (26) recognized hybridization as a major conservation
In this study, we estimated viability of hybrid tiger salamander
larvae over the first few weeks after hatching. This period of high
mortality represents an enormous opportunity for natural se-
Author contributions: B.M.F. and H.B.S. designed research; B.M.F. and H.B.S. performed
research; B.M.F. analyzed data; and B.M.F. and H.B.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
†To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2007 by The National Academy of Sciences of the USA
www.pnas.org?cgi?doi?10.1073?pnas.0704791104 PNAS ?
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lection to operate on the diverse genotypes of a hybrid popula-
tion (27). Observations were made in five wild breeding popu-
lations including the three major types of breeding habitats
found in the Salinas Valley: natural vernal pools, seasonal cattle
ponds, and perennial ponds (22). We categorized individual
hybrids using multilocus genotypes based on nine physically
unlinked molecular markers. Each individual was characterized
native, heterozygous, or homozygous introduced at each nuclear
marker (22). Thus, our approach has the advantages of consid-
ering the fitness of genotypes defined more finely than simple
pedigree categories (F1, backcross, etc.) and of estimating fitness
in the wild across the range of larval habitats found within the
hybrid swarm (28, 29). We focused on how early larval survival
varies among hybrid genotypes in the wild. Specifically, is the
pattern of survival consistent with hybrid dysfunction or hybrid
vigor, and does fitness variation depend more on additive,
dominant (heterozygous), or recombinant genetic effects?
Generalized linear models relating survival probability to mo-
lecular marker-based hybrid indices clearly support hybrid vigor
heterozygosity, ?H, and intermediate ancestry, ?S(see Methods).
Negative coefficients for ?S2indicate that surviving larvae
tended to be of less pure and more mixed ancestry. A more
complex model (with ?H2and ?S? ?Hterms) did not fit the data
better than the reduced model shown in Table 1 [supporting
information (SI) Table 2]. The significant effect of mixed
recombinant genotypes have enhanced survival that is not
predicted by heterozygote advantage alone.
Details of the multivariate outcome differed among ponds
(Table 1), but this is attributable to differences in initial geno-
type frequencies. Ponds that started highly introduced became
more native and ponds that started highly native became more
introduced (Fig. 1). This is consistent with selection favoring
mixed ancestry over either pure native or pure introduced
genotypes. Fig. 1 shows triangular regions of genotype space
defined by the interdependence of ancestry and heterozygosity.
Pure native or introduced genotypes, by definition, have no
heterozygous loci. Individuals with all heterozygous loci must
have evenly mixed ancestry, but mixed ancestry can also be
achieved when some loci are homozygous for native alleles and
others are homozygous for introduced alleles. Fig. 1 shows the
density of individuals across this triangular genotype space
before (hatchlings) and after (larvae) natural selection. In every
pond, there is a clear shift toward a higher frequency of
mixed-ancestry salamanders. That is, in all five ponds, the
multilocus ancestry index shifts toward a more intermediate
value and away from initially more extreme values. This was true
regardless of whether the before-selection ancestry indices were
fairly evenly distributed (Pond F) or skewed toward native (Pond
G) or nonnative (BW1, CVP, JCL 2) ancestry values (Fig. 1).
Changes in single-locus allele frequencies were idiosyncratic
frequencies (28/40 marker-pond combinations) showed a trend
in the direction of increased frequency of heterozygotes after
Table 1. Multivariate analyses of the difference between hatchlings and survivors
BW1 CVP Pond F Pond G JCL2
A positive coefficient for ?Sindicates selection favoring nonnative alleles, a positive coefficient for ?Hindicates selection favoring heterozygous hybrid
genotypes, and negative coefficients for ?S2indicate selection favoring mixed genotypes regardless of heterozygosity. These heuristic interpretations of the
coefficients are correct when all else is equal; refer to Fig. 1 to see actual changes in genotype distributions.
selection) and larvae (after selection) in five populations of hybrid tiger
salamanders were estimated by using a two-dimensional density-estimation
procedure with a bivariate normal kernel [function kde2d in R (30, 31)]. Gray
triangles represent potential genotype space described by ancestry (the frac-
tion of introduced alleles in an individual’s marker genotype) and heterozy-
gosity (fraction of markers heterozygous for native and introduced alleles).
Darker areas are those with larger numbers of observed individuals.
Approximate densities of multilocus genotypes in hatchlings (before
www.pnas.org?cgi?doi?10.1073?pnas.0704791104Fitzpatrick and Shaffer
selection, supporting the interpretation of hybrid vigor (SI Table
3). One possible exception is the GNAT1 marker, for which the
dominance coefficient was negative (albeit not statistically sig-
nificant) in all five ponds, suggesting low fitness of heterozygotes
(SI Table 3).
Our study of early-larval survival in hybrid tiger salamanders
reveals higher fitness of hybrid genotypes with evenly mixed
ancestry than genotypes composed predominantly of alleles
from one parental lineage. Such strong evidence of hybrid vigor
was unexpected based on previous studies suggesting constraints
on admixture, inferred from high levels of linkage disequilibrium
and habitat-dependent invasion success (21, 22). Our statistical
analyses suggest that hybrid survival is influenced by both
heterozygote advantage and recombinant hybrid vigor. Correct
interpretation of the underlying genetics is crucial to predicting
the evolutionary outcome of admixture between native Califor-
nia Tiger Salamanders and introduced Barred Tiger
Salamanders. From a conservation perspective, hybrid vigor may
be viewed as good or bad for the California Tiger Salamander,
populations or genetic purity as a primary conservation goal.
The Genetic Basis of Hybrid Vigor. When considering the genetic
basis of hybrid vigor, it is important to recall that our markers
represent a very sparse sample of the genome. Our ability to
derive information from this set of markers is enhanced by
extensive linkage disequilibrium due to admixture in hybrid
populations (22). Admixture linkage disequilibrium decreases
the likelihood that a particular marker–trait association repre-
sents close physical linkage between the marker and a quanti-
tative trait locus (32). By the same token, admixture linkage
disequilibrium increases the accuracy of our marker-based esti-
mates of genomic ancestry (?S) and heterozygosity (?H) because
the sampled loci are correlated with many other regions of the
genome (33, 34).
Our analyses show a strong positive relationship between
heterozygosity and probability of survival (Table 1 and Fig. 1).
This result is consistent with heterozygote advantage (overdomi-
nance for fitness) contributing to the genetic basis of hybrid
vigor. The coefficient on the ‘‘admixture’’ term (?S2) is consis-
tently negative, implying that recombinant hybrid vigor also
plays a role. Recombinant hybrid vigor may be caused by
synergistic interactions between heterospecific alleles at differ-
ent loci (epistasis) or complementary effects of superior intro-
duced alleles at some loci and superior native alleles at other loci
(19, 20). That is, ?S2is better viewed as an indicator of overall
genomic admixture rather than additive ? additive interaction
Hybrid vigor in other systems has often been attributed to
heterozygote advantage (35–39). However, heterozygote advan-
tage is lost each generation because of segregation among
gametes. If the most-fit genotype is heterozygous at many loci,
it cannot breed true and will rarely, if ever, reappear in gener-
ations beyond the F1(40). In contrast, if hybrid vigor is caused
by complementary or epistatic genes, the most-fit genotype is
homozygous for alleles derived from each lineage at different
loci (19). Such recombinant homozygotes appear only in later
generations, and they can breed true. True breeding recombi-
nant genotypes can therefore establish new lineages with ge-
nomes that are mosaics of the two ancestral genomes (41–44).
If both heterozygote advantage and recombinant hybrid vigor
are operating in the Ambystoma hybrid zone, then one likely
outcome is a population of tiger salamanders that is fixed for
native alleles at some loci, advantageous introduced alleles at
other loci, and segregating native and introduced alleles as
balanced polymorphisms at still other loci. However, the statis-
tical pattern of high mean fitness of highly heterozygous geno-
types may be transient, a temporary consequence of the current
levels of admixture and linkage disequilibrium that may abate as
the population genetic background changes from a highly vari-
able hybrid swarm to a more stable mosaic of native and
introduced alleles in different parts of the genome. As the
population becomes fixed for a single admixed genetic back-
ground, the heterozygote advantage at a given locus may disap-
pear (SI Text).
Variation, linkage disequilibrium, and divergent allele fre-
quencies between habitats have been maintained over 12–24
generations of admixture between A. californiense and A. t.
mavortium in the Salinas Valley (22, 23). However, hybrid vigor
tends to maintain genetic variation, decrease linkage disequi-
librium between conspecific alleles, and homogenize allele fre-
quencies across habitats. All of these processes are illustrated in
Fig. 1. Three processes are likely working against the tendency
of hybrid vigor to bring about a stable distribution of mixed-
ancestry genotypes. First, genetic drift contributes to variance
among breeding ponds (45). Second, higher frequencies of
introduced alleles are maintained in perennial than in seasonal
breeding ponds (22). Finally, immigration from pure native
populations outside of the hybrid swarm tends to increase native
allele frequencies and contribute to a broad-scale geographic
gradient in allele frequencies (23).
The high frequencies of introduced alleles in perennial ponds
remains one of the strongest genetic patterns in the tiger
salamander hybrid system; it may be maintained by habitat
choice or selection in later life history stages. Fitzpatrick and
Shaffer (22) hypothesized that introduced genotypes gain an
advantage in perennial water bodies by extending their larval
period or even breeding in the larval (paedomorphic) condition.
Pure native California Tiger Salamanders must metamorphose
to reproduce (46), but Barred Tiger Salamanders regularly forgo
metamorphosis in perennial ponds and breed as paedomorphs
(47, 48). Paedomorphs often reach sexual maturity earlier than
metamorphs, produce larger clutches, and may breed earlier in
a given season; any of these life-history factors may provide
introduced genotypes with an advantage in perennial ponds (49,
50). The perennial pond populations studied here (BW1 and
JCL2) show strong viability selection favoring hybrids during the
early part of the larval period (Table 1 and Fig. 1). Antagonism
between hybrid vigor for larval survival in all ponds and later
selection favoring introduced genotypes in perennial ponds may
explain the persistent pattern of high introduced allele frequen-
cies in perennial ponds and relatively even native and introduced
allele frequencies in seasonal ponds throughout the range of the
hybrid swarm (23).
Conservation Consequences of Hybrid Vigor. Hybridization between
an introduced form (A. t. mavortium) and a declining native
(i) what are the consequences of hybridization for population
viability? (ii) what are the consequences for other native species
and the communities in which they occur? (iii) which individuals
or populations of salamanders should be protected? and (iv)
should any individuals or populations be eradicated? The an-
swers to iii and iv depend, in part, on the answers to i and ii but
may also depend on practical considerations and perspectives on
the merit of genetic purity as a conservation goal. Our results
have important implications for population viability and genetic
purity of California Tiger Salamanders and for potential impacts
on other organisms native to California ponds and grasslands.
Hybrid vigor is probably not detrimental to population via-
bility. However, some authors have raised the concern that
negative effects of introgressive hybridization on fitness may not
Fitzpatrick and Shaffer PNAS ?
October 2, 2007 ?
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be evident except during infrequent ‘‘ecological crunches’’ (10,
52). Such episodic changes in selection do occur (53–55), and
may be widespread on the California landscape, given its tre-
mendous among-year variance in rainfall and pond hydroperiod.
Introgression could potentially contribute to loss of a crucial
adaptation during an interlude between episodes of selection,
leaving the population more vulnerable to extinction when the
next crunch arrives. In addition, our characterization of hybrid
fitness is incomplete, focusing only on early larval mortality.
However, native and introduced tiger salamanders have been
mixing in California for ?50 years, and the hybrid swarm has
survived and expanded (23) through droughts, El Nin ˜os, and
substantial anthropogenic environmental change. The effect of
admixture on population viability in California Tiger
appear to us, at this time, to be a major threat.
Hybrid vigor implies that the native gene pool is not resistant
to invasion of introduced alleles. Thus, a mixture of gene pools
is expected, with fixation of advantageous introduced alleles and
preservation of advantageous native alleles. This constitutes a
loss of biodiversity, because alleles and genotypes unique to A.
californiense are being lost. However undesirable it may be, this
evolutionary transformation should not engender the same
ethical concerns raised by true demographic extinction. In fact,
the aesthetic appeal of a genetically authentic native gene pool
may be in conflict with the best interests of the animals if hybrid
vigor enhances population viability. Whether or not population
viability is enhanced in this case depends on the relationship
between average fitness and density regulation (56).
If hybrid vigor results in higher densities, larger body sizes, or
more rapid growth of larvae in hybrid populations, the impacts
of hybridization will almost certainly extend to other members of
the ecological community. Tiger salamander larvae are vora-
cious consumers of anuran tadpoles and aquatic invertebrates.
Endangered, threatened, and sensitive prey that share habitats
with tiger salamanders in the hybrid zone include California
Red-Legged Frogs (Rana draytonii), Western Spadefoots (Spea
hammondii), and Vernal Pool Fairy Shrimp (Branchinecta lyn-
chi). Thus, hybrid vigor in tiger salamander larvae presents a
credible but unproven threat to other pond-breeding organisms.
Our results support the view that hybridization can alter the
evolutionary process by contributing novel genetic advantages to
admixed populations (1, 15, 41). This view also suggests that
hybridization between native and introduced lineages could
accelerate the evolution of invasiveness and intensify the eco-
logical impact of a biological invasion (9). Understanding the
effect of hybridization on the ecological interactions of tiger
salamander populations is a priority for future work in this
Natural selection among hybrid genotypes was estimated by
using a cohort analysis in which we compared the distributions
of genotypes in a single group of offspring at two different points
in time. This provides a direct measure of the response to natural
selection within a single generation (57). Furthermore, by fo-
cusing on diagnostic codominant molecular markers, we mea-
sured genetic changes that can be readily explained in terms of
additive, dominant, and epistatic or complementary effects of
differences between the native and introduced salamanders.
Sampling. We studied a subset of the breeding sites described in
ref. 22. Pond F and CVP are natural vernal pools that fill during
winter rains and dry by early to midsummer. They represent the
natural, unmodified breeding habitat for native California Tiger
Salamanders (46). Pond G is a man-made seasonal cattle pond
with a hydroperiod similar to vernal pools. JCL2 and BW1 are
perennial ponds that normally hold water through the summer,
although both had dried completely during the summer before
We quantified multilocus genotypes during two early life-
history stages. Our before-selection samples consisted of eggs
collected during the laying season, whereas our after-selection
samples were drawn early in the larval stage. Each pond was
outfitted with artificial oviposition sites consisting of 25 bamboo
stakes (1 m long and 0.5 cm in diameter) planted into the pond
bottom in water 30 cm deep and four 1.2-m-long coils of
12-gauge galvanized steel wire in water 40–50 cm deep. Ponds
were visited weekly from December 2002 through February
2003. On each visit, all salamander eggs (if present) were
removed from all stakes and wires to guarantee that all eggs
collected were laid during the preceding week. Eggs were
counted and placed in a bucket, from which a random sample of
50 eggs was collected. Remaining eggs were scattered in shallow
water where they could readily adhere to submerged vegetation
and rocks (natural oviposition sites). Collected eggs were held in
cups containing 20% Holtfretter’s solution (58) and allowed to
hatch. Hatchlings were killed and stored at ?80C.
Young larvae were captured by haphazardly seining ponds.
Collections were made on February 6 and March 26, 2003.
28, when there was a single bout of egg laying. The artificial
oviposition sites in Pond G were destroyed in early February by
cattle. Therefore, these two ponds are represented by single
samples of larvae. In the other three ponds, we found no
statistically significant (? ? 0.05) differences between the two
samples of larvae (data not shown) and therefore pooled them
for all hatchling vs. larvae comparisons below.
Molecular Methods. Each individual was assayed for the nine
molecular markers used by Fitzpatrick and Shaffer (22). These
are single nucleotide differences that distinguish native A.
californiense from introduced A. t. mavortium alleles at mtDNA
and eight mapped nuclear genes. Each individual was charac-
terized as having native or introduced mtDNA and as being
homozygous native, heterozygous, or homozygous introduced at
each nuclear marker. Primer sequences and PCR conditions can
be found in ref. 22 (also see refs. 21 and 59). Diagnostic alleles
were identified by restriction enzyme digestion and agarose
electrophoresis of PCR products, as described by Fitzpatrick and
Data Analyses. We used both single-marker and multilocus sta-
tistical analyses to evaluate variation in survival among geno-
types. For single locus selection analyses, we used standard
marker–trait regressions (60, 61);
1 ? P? ? intercept ? bAXA? bHXH? error,
where P is the probability that a data point is a surviving larva,
XA ? ?1, 0, or 1 for homozygous native, heterozygous, and
homozygous introduced genotypes, respectively, and XH? 0 or
1 for homozygous and heterozygous genotypes, respectively. The
fitted coefficients bAand bHrepresent additive and dominance
effects. Regressions were fitted in the program R 2.4.1 (31) by
using the glm() function with a binomial error distribution and
observations weighted by stratum (see below). We assume fitted
models represent indirect responses to selection on loci with
unknown linkage relationships to our markers. The residual
error includes variance due to incomplete linkage between
For multilocus selection analyses, we used the quantitative
genetics approach described by Lynch (18). This model identifies
www.pnas.org?cgi?doi?10.1073?pnas.0704791104 Fitzpatrick and Shaffer
additive, dominance, and epistatic effects on hybrid fitness as
terms in a linear statistical model. In our case,
1 ? P? ? intercept ? ?1?S? ?1?H? ?2?S2? ?2?H2
? ????1?S?H? error,
where individual genotypes are described by ?S, a linear ancestry
index ranging from ?1 (all native alleles) to ?1 (all introduced
alleles) and ?H, a heterozygosity index ranging from ?1 (all
markers homozygous) to ?1 (all markers heterozygous). The
fitted coefficients ?1and ?1describe simple additive and dom-
inance effects, whereas ?2, ?2, and (??)1 describe additive ?
additive, dominance ? dominance, and additive ? dominance
epistasis, respectively (18). This model was fitted to the data
from each pond by using the glm() function with a binomial error
distribution and observations weighted by stratum, as for the
single-locus case (see below).
Two additional issues needed to be addressed in our statistical
analyses. First, an interesting problem was created by the tem-
porally extended breeding season in three of our study ponds
(BW1, G, and JCL2). In these ponds, breeding consisted of three
to five major episodes corresponding to significant rain storms;
each episode potentially involved a different set of adults with
different genotype frequencies. Thus, our before-selection sam-
ples were stratified simple random samples. Each weekly sample
(stratum sample) was weighted by stratum size when estimating
before-selection genotype frequencies and their moments (62).
We used the total number of eggs laid on our artificial ovipo-
sition sites each week as that week’s stratum size (we assume this
number is proportional to the total number of eggs produced in
the pond that week). Each before-selection observation (hatch-
ling) was weighted according to stratum size [(stratum size ?
stratum sample size) ? (total sample size ? sum of stratum
weighting scheme, the after-selection individuals each get a
weight of 1.0 because they come from a single stratum, and the
averages of the individual weights before and after selection are
Second, traditional estimates of confidence intervals for re-
gression coefficients do not account for error in the independent
variables. However, ?Sand ?Hwere estimated with error because
our markers are samples of the genome (?S? 2PT? 1, and ?H?
2PCT? 1, where PTis the fraction of an individual’s marker
alleles derived from A. t. mavortium, and PCTis the fraction of
markers heterozygous for native and introduced alleles). There-
fore, we used a bootstrap and randomization procedure to
incorporate this sampling variance into hypothesis tests regard-
ing the fitted coefficients described in Eq. 2. For each of 10,000
replicates, we performed a two-step Monte Carlo procedure.
First, we bootstrapped across nuclear markers. Bootstrapping
across markers addresses error in individual estimates of ?Sand
?Hdue to sampling only a fraction of each salamander’s genome.
This is in the same spirit as bootstrapping across characters in
phylogenetic analysis (63) and results in each individual having
associated with it a distribution rather than a single point
estimate of each ?. MtDNA was treated as a fixed effect; it was
included once and only once in every replicate, because there is
only a single mitochondrial allele to sample. Excluding mtDNA
slightly affected parameter estimates but not their signs or P
values. Including mtDNA in the pool of markers to resample is
inappropriate because it does not contribute to ?H. The second
step in each replicate was to randomize observations to simulate
the null hypothesis that hatchlings and surviving larvae were
random samples from a single distribution of genotypes. We
recorded the fraction of replicates giving coefficients larger
(fLarger) and smaller (fSmaller) than the estimate from the original
data and estimated two-tailed P values as 2 ? minimum(fLarger,
fSmaller). The procedure was applied separately to each of our five
The full Lynch (18) model (Eq. 2) may overfit some data sets
(particularly those with highly skewed allele frequencies), lead-
ing to problems with colinearity of variables and high variances
around coefficient estimates. Therefore, we also fitted a reduced
1 ? P? ? intercept ? ?1?S? ?1?H? ?2?S2? error.
This model focuses on fitness variation as a function of
individual ancestry (?S), individual heterozygosity (?H), and as a
function of individual admixture (?S2) decoupled from ancestry
and heterozygosity (?S2equals 1 in both pure native and pure
introduced genotypes, and it equals 0 in individuals with evenly
mixed ancestry, i.e., half native and half introduced alleles
regardless of heterozygosity). The coefficient ?2 represents
effects of mixed ancestry not depending on heterozygosity but
does not distinguish true epistasis from complementary effects.
We compared the likelihoods of the full and reduced models by
means of Akaike’s Information Criterion (AIC) (64).
We thank A. Chang, M. Fujita, O. J. Abramyan, P. C. Trenham, and
W. K. Savage for assistance in the field and laboratory; the H.B.S.
laboratory for discussion; and many ranchers for access to their prop-
erties. Our work was funded by Environmental Protection Agency
Grants U 91572401 and R 828896, the U.S. Department of Agriculture
(Exotic/Invasive Pests and Diseases Research Program Grant 04XN022
and National Science Foundation Grants DEB 0516475 and DEB
0213155), CAL FED Grant 01-N43, and the University of California,
Davis, CA, Agricultural Experiment Station.
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